genesys v8 synthesis i: classic filter...

GENESYS V8

Synthesis I:Classic Filter Synthesis

Copyright 1986-2001

Eagleware Corporation635 Pinnacle CourtNorcross, GA 30071

Phone: (678) 291-0995FAX: (678) 291-0971E-Mail: [email protected]://www.eagleware.com

Printed in the USA

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TABLE OF CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . xiGENESYS and Synthesis Programs . . . . . . . . . . . xiFILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiA/FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiM/FILTER . . . . . . . . . . . . . . . . . . . . . . . . . xiv

Chapter 1: FILTER Operation . . . . . . . . . . . 1First Example . . . . . . . . . . . . . . . . . . . . . . . . 2Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Modifying a Design . . . . . . . . . . . . . . . . . . . . . 5Noise-BW . . . . . . . . . . . . . . . . . . . . . . . . . . . 5N-help . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Output Defaults . . . . . . . . . . . . . . . . . . . . . . . 5Writing Superstar Files . . . . . . . . . . . . . . . . . . . 6Q Defaults . . . . . . . . . . . . . . . . . . . . . . . . . . 6Exiting FILTER To Windows . . . . . . . . . . . . . . . . 7Using SuperStar and Filter Together . . . . . . . . . . . . 7Using Other GENESYS Supported Tools . . . . . . . . . . 8

Chapter 2: FILTER Types . . . . . . . . . . . . . 9Monotonic or Elliptic . . . . . . . . . . . . . . . . . . . . 10Minimum Inductor All-pole Lowpass . . . . . . . . . . . 11Minimum Capacitor All-pole Lowpass . . . . . . . . . . 11Minimum Inductor All-pole Highpass . . . . . . . . . . 12Minimum Capacitor All-pole Highpass . . . . . . . . . . 12Minimum Inductor All-pole Bandpass . . . . . . . . . . 13Minimum Capacitor All-pole Bandpass . . . . . . . . . . 14Coupled All-pole Bandpass Filter Types . . . . . . . . . 15Mixed Coupling Reactors . . . . . . . . . . . . . . . . . 16Top C Coupled All-pole Bandpass . . . . . . . . . . . . . 17Top L Coupled All-pole Bandpass . . . . . . . . . . . . . 18Shunt C Coupled All-pole Bandpass . . . . . . . . . . . 19Tubular All-pole Bandpass . . . . . . . . . . . . . . . . 20Blinchikoff 4th Order Flat Delay All-pole Bandpass . . . 21Symmetry Preserving All-pole Bandpass . . . . . . . . . 22Symmetric Transform . . . . . . . . . . . . . . . . . . . 23Symmetric Transform Limitations . . . . . . . . . . . . 25Full Transform All-pole Bandstop . . . . . . . . . . . . 27Minimum Inductor Elliptic Lowpass . . . . . . . . . . . 28Minimum Capacitor Elliptic Lowpass . . . . . . . . . . 28Minimum Inductor Elliptic Highpass . . . . . . . . . . . 29Minimum Capacitor Elliptic Highpass . . . . . . . . . . 29

Full Transform Elliptic Bandpass . . . . . . . . . . . . . 30Minimum Inductor (“Zig Zag”) Elliptic Bandpass . . . . 31Elliptic Bandstop . . . . . . . . . . . . . . . . . . . . . . 32

Chapter 3: FILTER Examples . . . . . . . . . . 33Example 1 - Transmission Line resonators . . . . . . . 33Example 2 - Bessel Crystal Filter . . . . . . . . . . . . . 37Example 3 - Filter Symmetry . . . . . . . . . . . . . . . 38Example 4 - Creating a Unique Lowpass Prototype . . . 41Example 5 - Designing a Bandpass Filter

From the New Prototype . . . . . . . . . . . . . . 43

Chapter 4 : A/FILTER Operation . . . . . . . . . 45First Example . . . . . . . . . . . . . . . . . . . . . . . 45Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Modifying a Design . . . . . . . . . . . . . . . . . . . . . 49Noise-BW & N-Help . . . . . . . . . . . . . . . . . . . . 49Output Defaults . . . . . . . . . . . . . . . . . . . . . . 49Component Defaults . . . . . . . . . . . . . . . . . . . . 50Preferences . . . . . . . . . . . . . . . . . . . . . . . . . 51

Chapter 5: A/FILTER Types . . . . . . . . . . . 55Lowpass All Pole Minimum Inductor . . . . . . . . . . . 56Lowpass All Pole Minimum Capacitor . . . . . . . . . . 57Lowpass All Pole Single Feedback . . . . . . . . . . . . . 58Lowpass All Pole Multiple Feedback . . . . . . . . . . . 59Lowpass All Pole Low Sensitivity . . . . . . . . . . . . . 60Lowpass All Pole VCVS . . . . . . . . . . . . . . . . . . 61Lowpass All Pole State Variable (biquad) . . . . . . . . . 62Lowpass Elliptic Minimum Capacitor . . . . . . . . . . . 63Lowpass Elliptic VCVS . . . . . . . . . . . . . . . . . . . 64Lowpass Elliptic State Variable . . . . . . . . . . . . . . 65Highpass All Pole Minimum Inductor . . . . . . . . . . . 66Highpass All Pole Minimum Capacitor . . . . . . . . . . 67Highpass All Pole Single Feedback . . . . . . . . . . . . 68Highpass All Pole Multiple Feedback . . . . . . . . . . . 69Highpass All Pole Low Sensitivity . . . . . . . . . . . . . 70Highpass All Pole VCVS . . . . . . . . . . . . . . . . . . 71Highpass All Pole State Variable . . . . . . . . . . . . . 72Highpass Elliptic Minimum Inductor . . . . . . . . . . . 73Highpass Elliptic VCVS . . . . . . . . . . . . . . . . . . 74Highpass Elliptic State Variable . . . . . . . . . . . . . 75Bandpass All Pole Top C . . . . . . . . . . . . . . . . . . 76Bandpass All Pole Top L . . . . . . . . . . . . . . . . . . 77

iv Table of Contents

Bandpass All Pole Multiple Feedback . . . . . . . . . . 78Bandpass All Pole Multiple Feedback Max Gain . . . . . 79Bandpass All Pole Dual Amplifier . . . . . . . . . . . . 80Bandpass All Pole Dual Amplifier Max Gain . . . . . . . 81Bandpass All Pole Low Sensitivity . . . . . . . . . . . . 82Bandpass All Pole State Variable . . . . . . . . . . . . . 83Bandpass Elliptic VCVS . . . . . . . . . . . . . . . . . . 84Bandpass Elliptic State Variable . . . . . . . . . . . . . 85Bandstop All Pole VCVS . . . . . . . . . . . . . . . . . . 86Bandstop All Pole State Variable . . . . . . . . . . . . . 87Comparison Table . . . . . . . . . . . . . . . . . . . . . 88

Chapter 6: A/FILTER Examples . . . . . . . . . 89Example 1 - Lowpass Minimum Inductor . . . . . . . . 89Example 2 - Lowpass Minimum Capacitor . . . . . . . . 92Example 3 - Lowpass Single Feedback . . . . . . . . . . 94Example 4 - Lowpass Multiple Feedback . . . . . . . . . 98Example 5 - Bandpass Maximum Gain Dual Amplifier 100

Chapter 7: M/FILTER Menus . . . . . . . . . . 103Overview of rhe M/FILTER Screen . . . . . . . . . . . 103Using the Procedure Flowchart . . . . . . . . . . . . . 103File Menu . . . . . . . . . . . . . . . . . . . . . . . . . 105Type Menu . . . . . . . . . . . . . . . . . . . . . . . . 107Schematic Menu . . . . . . . . . . . . . . . . . . . . . 107Layout Menu . . . . . . . . . . . . . . . . . . . . . . . 107Utilities Menu . . . . . . . . . . . . . . . . . . . . . . 108Setup Menu . . . . . . . . . . . . . . . . . . . . . . . 109Layout Window . . . . . . . . . . . . . . . . . . . . . . 111Tuning Parameters . . . . . . . . . . . . . . . . . . . 111

Chapter 8: M/FILTER Operation . . . . . . . . 113Entering Parameters . . . . . . . . . . . . . . . . . . 113Using SuperStar with M/FILTER . . . . . . . . . . . . 115Electrical or Physical? . . . . . . . . . . . . . . . . . . 116Writing DXF/Gerber Files . . . . . . . . . . . . . . . . 119Selecting Output Options . . . . . . . . . . . . . . . . 120

Chapter 9: M/FILTER Types . . . . . . . . . . 123Filter Shapes And Processes . . . . . . . . . . . . . . 124Filter Physical Size . . . . . . . . . . . . . . . . . . . 125Filter Examples . . . . . . . . . . . . . . . . . . . . . 126Edge Coupled Bandpass . . . . . . . . . . . . . . . . . 127Hairpin Bandpass . . . . . . . . . . . . . . . . . . . . 129

Table of Contents v

Stepped-Z Lowpass . . . . . . . . . . . . . . . . . . . . 130Stepped-Z Bandpass . . . . . . . . . . . . . . . . . . . 131Combline Bandpass . . . . . . . . . . . . . . . . . . . 132Interdigital Bandpass . . . . . . . . . . . . . . . . . . 133Elliptic Lowpass . . . . . . . . . . . . . . . . . . . . . 134Elliptic Bandpass . . . . . . . . . . . . . . . . . . . . . 135End Coupled Bandpass . . . . . . . . . . . . . . . . . 136Stub Lowpass . . . . . . . . . . . . . . . . . . . . . . . 137Stub Highpass . . . . . . . . . . . . . . . . . . . . . . 138Edge Coupled Bandstop . . . . . . . . . . . . . . . . . 139

Chapter 10: M/FILTER Error Messages . . . . 141

Appendix A: Filter Shapes . . . . . . . . . . . 145Butterworth . . . . . . . . . . . . . . . . . . . . . . . . 146Chebyshev . . . . . . . . . . . . . . . . . . . . . . . . 147Bessel . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Blinchikoff Flat Delay Bandpass . . . . . . . . . . . . 149Singly-Equalized Delay . . . . . . . . . . . . . . . . . 150Singly-Terminated . . . . . . . . . . . . . . . . . . . . 151Cauer-Chebyshev . . . . . . . . . . . . . . . . . . . . . 152User Filters . . . . . . . . . . . . . . . . . . . . . . . . 153Observing G Values . . . . . . . . . . . . . . . . . . . 154Prototype Files . . . . . . . . . . . . . . . . . . . . . . 154Included Prototype Files . . . . . . . . . . . . . . . . . 155Linear Phase Equiripple Error . . . . . . . . . . . . . 156Transitional Gaussian . . . . . . . . . . . . . . . . . . 156Singly-terminated Cauer-chebyshev . . . . . . . . . . 157Bessel Passband Elliptic Stopband . . . . . . . . . . . 157Prototype File Selection Assistance . . . . . . . . . . . 157N-Help . . . . . . . . . . . . . . . . . . . . . . . . . . 158

Appendix B: Noise Bandwidth . . . . . . . . . 161General Case . . . . . . . . . . . . . . . . . . . . . . . 162Noise Bandwidth Example . . . . . . . . . . . . . . . . 163Frequency Range And Step Size . . . . . . . . . . . . . 164

Appendix C : File Formats . . . . . . . . . . . 167

Appendix D: GIC Transform Fundamentals . . 169

Appendix E: Training . . . . . . . . . . . . . . 173

Appendix F: References . . . . . . . . . . . . . 175

vi Table of Contents

Introduction

GENERAL INFORMATION

For system requirements, installation, and setup informa-tion, refer to the GENESYS SIMULATION manual. ThisSYNTHESIS manual describes Eagleware’s classic filtersynthesis programs, FILTER, A/FILTER, and M/FILTER.(S/FILTER is in a separate manual).

GENESYS AND SYNTHESIS PROGRAMS

The synthesis programs are launched from the SuperStarProfessional simulator. This enhances the integration ofthe synthesis and simulation process.

GENESYS synthesis programs also support the simulatorTouchstone from HP/EEsof, generic Berkeley SPICE 2 andSPICE 3 formats and specific SPICE based simulators.Although very slow, SPICE based simulation provides arich set of output data unavailable in linear and harmonicbalance simulators such as bias simulation, oscillatorstarting time analysis and filter transient analysis.

The synthesis programs write text and SCHEMAX filesfor SuperStar and text files for Touchstone and SPICE.Thus a schematic environment for both Touchstone andSPICE simulation is provided by writing SCHEMAX filesfrom the synthesis programs. The use of GENESYS pro-grams with Touchstone and SPICE simulators is de-scribed in more detail in the Reference manual.

A/FILTER and FILTER have a “Place in EQUATE block”checkbox in the Component Setup dialog. If this box ischecked, the component quality factors and op-amp pa-rameters are placed in the SuperStar EQUATE block.This allows easy group (gang) tuning of components, andallows easy sensitivity analysis with respect to part qual-ity.

FILTER

FILTER makes designing L-C filters a snap. WithGENESYS you can simulate the filter performance, cus-tomize or optimize the filter and check the effects ofparasitics.

The following chapters are devoted to FILTER:

FILTER Operation Chapter 1

FILTER Types Chapter 2

FILTER Examples Chapter 3

Filter Shapes Appendix A

Noise Bandwidth Appendix B

Chapter 1 provides the basic information required todesign all the filters built into FILTER. Chapter 2 andAppendix A are designed for further clarification andreference. They discuss the filter topologies and responseshapes. They may be read rather quickly and referred tolater when designing certain filters.

Chapter 3 provides additional ideas and tips on filterdesign and the use of FILTER and SuperStar Professionalto modify, optimize and customize filter designs.

Appendix B (Noise Bandwidth) discusses the effectivenoise bandwidth of filters. FILTER automatically inte-grates the S-parameter data file of any filter analyzed by

xii Introduction

SuperStar to determine the effective noise bandwidth ofthe filter.

FEATURE OVERVIEW

FILTER synthesizes many L-C filter types suitable for awide range of applications. Principle features include:

• 20 filter topologies. Topology choices provide for practicalrealizations and specific application needs

• A wide range of transfer approximations (amplitude anddelay response shapes)

• Effective noise bandwidth calculation

• Writing SuperStar circuit or schematic files.

A/FILTER

A/FILTER makes designing active filters fast and easy.A/FILTER also includes EQUALIZE for active equalizersynthesis. With a GENESYS simulator, you can simulatethe filter performance, customize or optimize the filter,and check the effects of parasitic reactances or finiteop-amp parameters, such as unity gain bandwidth.

The following chapters are devoted to A/FILTER:

A/FILTER Operation Chapter 4

A/FILTER Types Chapter 5

A/FILTER Examples Chapter 6

GIC Transform FundamentalsAppendix D

Chapter 4 introduces program operation with a quickexample and describes unique A/FILTER features.

For information on filter shape approximations or noisebandwidth calculations are given in Appendix A and B.

Chapter 5 discusses the filter types designed by A/FIL-TER. The topologies are discussed, and the benefits of

Introduction xiii

each is given. This chapter can be read rather quickly, andused as a reference when selecting a filter type.

In Chapter 6, additional ideas and tips on filter design andthe use of A/FILTER and SuperStar to modify optimizeand customize filter designs are given.

FEATURE OVERVIEW

A/FILTER synthesizes many filter types suitable for awide range of applications. Principle features include:

• Over 30 filter topologies. Choices provide for practicalrealization of specific application needs. Many types allowspecification of passband gain.

• A wide range of transfer approximations (amplitude, phaseand delay response shapes).

• Effective noise bandwidth calculation

• Writing SuperStar circuit or schematic files.

M/FILTER

M/FILTER is the GENESYS synthesis program whichdesigns microwave distributed filters. SPICE simulationpoorly supports distributed circuits and Touchstone doesnot include the models required for certain popular micro-wave filters, so the preferred GENESYS simulator for usewith M/FILTER is SuperStar Professional.

A feature of M/FILTER is the ability to absorb discontinu-ties during synthesis. Independent SuperStar responsecalculation verifies the synthesis process.

The following chapters are devoted to M/FILTER:

M/FILTER Menus Chapter 7

M/FILTER Operation Chapter 8

M/FILTER Types Chapter 9

M/FILTER Error Messages Chapter 10

xiv Introduction

The book HF Filter Design and Computer Simulation alsoincludes additional information on filter theory, elementsand a variety of practical microwave filter structures.

FEATURE OVERVIEW

The principal features of M/FILTER include:

• Lowpass, highpass, bandstop and a wide range ofbandpass filter types

• Five different implementation processes including simpleelectrical, microstrip, stripline, slabline and coaxial.

• Automatically writes SuperStar .SCH and .CKT files

• Automatically displays layout or schematic on screen

• Allows specification of units, size and cross hairs for finalboard layout

Introduction xv

Chapter 1

FILTER Operation

FILTER is launched by starting GENESYS and thenselecting FILTER from the Synthesis menu (top of thescreen). The FILTER main window and menu ap-

pear. The screen should look like the sample screenfigure.

Input “fields” appear on the bottom section of the screen.The top part contains the schematic and values of the filter

Figure 1-1 Sample FILTER screen.

being designed. At any time you may press F1 for help onthe input at the cursor location,or press Alt-F1 (hold downthe Alt key and press F1) for general help.

The cursor is initially located on the order input field. Youmay press the arrow keys to move between and edit inputfields. To automatically continue to the next input field,press the Tab or Enter key. To go to the previous inputfield, press Shift-Tab. Optionally, the left mouse buttonmay be used to select a radio button or to move the cursor.When the cursor is on an input field you may type in a newvalue for that field. As you change an input, the outputwill automatically update.

FIRST EXAMPLE

Try an example. The design will be a 7th order lowpassfilter with a .25 dB passband ripple Chebyshev response.The cutoff frequency is 70 MHz and the characteristicimpedance is 50 ohms.

First, press Alt-T to access the topology menu. Select thechange type item. A new subwindow will appear. Thiswindow will contain three sets of radio buttons. Use theup and down arrow keys or the left mouse button to changethe highlighted radio button in each section, and use theTab or Enter key to move between sections. Make theseselections: Lowpass, All-pole, and Minimum Capacitor.Select the Close button to continue (press Enter when itis highlighted.

Next, the shape subwindow appears. Select the Cheby-shev button. Choose the Close button to continue. Addi-tional help about shapes can be obtained before closing thewindow by pressing F1 (help). You may then use PgUpand PgDn or the scroll bar to move between help pages.Press Escape to exit the help window. The additionalinformation in this section pertains to filters which haveunequal input and output impedances, such as even order

2 FILTER Operation

Chebyshev and singly-terminated filters. More about thisis given in Appendix A.

The cursor will now be located on the main window at theorder prompt. Enter 7. (Filters up to 21st order may bedesigned for most types.) The suggested range area of thescreen gives you a reminder of the range for an input.

Next enter the passband ripple: 0.25. FILTER directlycomputes the lowpass prototype G values for popularresponse shapes and does not use tables for these shapes,so any passband ripple greater than zero and less than 3dB may be chosen. This is true even for elliptic Cauer-Che-byshev filters.

The cutoff frequency of all-pole filters, such as Butter-worth, is normally defined as the 3 dB attenuation fre-quency. The cutoff of filters with ripple in the passband,such as Chebyshev, is often defined as the ripple value.FILTER allows the user to specify the attenuation, Aa, ofthe cutoff frequency for Butterworth and Chebyshev fil-ters. For these filters, Aa is prompted. For normallydefined cutoff attenuation, enter Aa equal to the ripple forChebyshev filters, and Aa equal to 3.0103 dB for Butter-worth filters.

For this example, enter 0.25 at the Aa prompt.

Next, for Butterworth and Chebyshev filters, FILTERprompts for Fca, the desired cutoff frequency. FILTERthen computes and displays the cutoff frequency at thenormally defined cutoff attenuation. This value is used bythe FILTER program during the design process. For filterresponse shapes other than Butterworth and Chebyshev,the prompts for Aa and Fca are skipped, and the programprompts for Fc.

Enter 70 at the Fca prompt in this example.

FILTER Operation 3

Finally the input impedance Rin is requested. Enter 50.After entering the input impedance, FILTER will computeand display the output impedance. In the case of odd orderChebyshev filters, the output impedance is equal to theinput impedance. For even order Chebyshev filters, theoutput impedance will be greater or less than the inputimpedance, depending on the subtype selected. FILTERautomatically calculates and displays the correct imped-ance.

Certain filter types allow specifying the output impedanceindependent of the input impedance. For these filters,FILTER requests the desired output impedance.

The results on the screen should be similar to the screenshown earlier in this chapter.

OTHER DATA

Also displayed on the lower right portion of the screen isthe summation of the lowpass prototype “g” values of thefilter just designed. This quantity may be used to estimatethe insertion loss, Lo, and group delay, Do, of the filter atfrequencies well removed from the cutoff. These esti-mated parameters are also displayed.

UNITS

The units used in FILTER are the same units used inSuperStar. They are:

Resistance.....ohms

Inductance.....nanohenries

Capacitance.....picofarads

Frequency.....Megahertz

4 FILTER Operation

MODIFYING A DESIGN

FILTER remembers the selections previously made, somodifying a design is easy. This is true even if FILTER isexited. For a permanent record, the filter design may besaved to a *.fi$ file (a setup file, not a circuit file) using thefile menu options save, save as, and open.

NOISE-BW

FILTER can be used to calculate the effective noise band-width of lowpass and bandpass filters. This is done byintegrating the amplitude response of any filter analyzedby the SuperStar Professional program. This offers theadvantage of being unrestricted to theoretical “ideal” re-sponse types. Even the effects of finite component Q orapproximate bandpass transforms are taken into account.Using FILTER to calculate filter effective noise bandwidthis discussed in Appendix B.

N-HELP

See Appendix A for information on N-Help.

OUTPUT DEFAULTS

When FILTER writes a SuperStar Professional text orschematic file, FILTER specifies in the OUTPUT block ofthe SuperStar Professional file what output data is to bedisplayed. The data specified by FILTER may be changedby the user by pressing Alt-S to choose the Setup menu.Select the circuit file default item. Up to four lines ofgraphical data (GPH and SMH) or one line of tabular data(DSP or PRI) may be specified. The rules for use of thesecodes is identical to their use in SuperStar Professional.Please refer to the description of these codes in the Ele-ment Reference chapter of the SIMULATION manual.Select Close to return to the main FILTER window.

The normal form of an OUTPUT block line is

FILTER Operation 5

GPH S21 -100 0.

Once changed in FILTER, these output options are usedto write a text or shematic file until new output data isspecified. The output data format may also be manuallyedited in SuperStar but this does not effect the output dataformat written the next time by FILTER.

WRITING SuperStar FILES

FILTER automatically writes SuperStar Professional cir-cuit text files (.CKT) or schematic files (.SCH) for SCHE-MAX. SuperStar Professional then computes anddisplays the frequency responses of that filter. SuperStarProfessional is used to tune or optimize the filter, test theeffect of component Q, test the results with standardvalues, compute and display the group delay or investigateeffects of component tolerances.

To write a SuperStar circuit file, press F8, or select “Write.CKT file” from the file menu. Then enter the desiredfilename using the file dialog box. FILTER automaticallyuses the extension “.CKT” unless a different extension isentered. To write a schematic file for SCHEMAX, select“Write .SCH file” from the file menu. After writing the.CKT or .SCH file you may select to launch SuperStarProfessional or return to FILTER.

The .CKT files written by FILTER are ASCII files. SCHE-MAX .SCH files are binary and should not be opened orviewed in a text editor.

Q DEFAULTS

When FILTER designs filters it assumes infinite compo-nent Q unless otherwise specified. The effects of finitecomponent Q are readily observed by analyzing filterswith SuperStar Professional. When FILTER writes a file,the default component Q is one million.

6 FILTER Operation

The component Q used for writing files may be changedby selecting the Components option from the Setup menu.The effective Q of resonators (inductor and capacitor com-binations) is given by:

For example, an inductor Q of 120 and capacitor Q of 600results in a resonator Q of 100.

FILTER writes all capacitors with equal Q and all induc-tors with equal Q. They may be independently specifiedonce in SuperStar Professional. Once the default Qs arechanged, they remain in effect until they are changedagain, or a new filter setup file (*.FI$) is loaded.

EXITING FILTER TO WINDOWS

FILTER can be exited by selecting the Exit option fromthe File menu. Alternatively, programs may be closed bypressing Alt-F4.

USING SuperStar AND FILTER TOGETHER

After FILTER has written the SuperStar Professionalcircuit file it prompts for the next desired action:

• Return to FILTER

• Automatically run SuperStar

If Run SuperStar Professional is chosen, FILTER causesthe following to occur: FILTER terminates, SuperStarProfessional runs, the last circuit file written by FILTERis loaded, SuperStar Professional analyzes that circuitand you are given control of SuperStar. This provides afast and convenient environment for designing, simulat-ing and customizing filters.

Q

Q Q

r

l c

=+

11 1

FILTER Operation 7

USING OTHER GENESYS SUPPORTED TOOLS

SPICE is useful for determining the time-domain re-sponse of filters. Using FILTER with other GENESYSsupported simulators is described in the GENESYSSIMULATION manual. This description includes an ex-ample time-domain response.

8 FILTER Operation

Chapter 2

FILTER Types

Filter type specifies whether the filter is lowpass, high-pass, bandpass or bandstop. Type also specifies ellip-tic or all-pole. Each of these generic types may have

alternate forms. For example, the lowpass type, can havea series inductor first (minimum capacitor) or a shuntcapacitor first (minimum inductor).

Schematics of the 20 filter topologies designed by FILTERare given on the following pages. The values of the ele-ments in these filters determine the response shape. Re-sponse shapes, such as Butterworth andCauer-Chebyshev are discussed in Appendix A.

All-pole filters have monotonically increasing attenuationin the stopbands with increasing frequency from the pass-band. All zeros of transmission occur at DC or infinitefrequencies. The elliptic transfer function has one or morezeros at finite frequencies. For a given number of induc-tors, this type of filter has superior performance in somerespects to all-pole filters. Selectivity is improved at theexpense of ultimate attenuation and complexity.

The elliptic functions used in FILTER are of the Cauer-Chebyshev type. This is further discussed in AppendixA. The minimum order for Cauer-Chebyshev filters isthree.

MONOTONIC OR ELLIPTIC

When do you choose a monotonic stopband filter and whenan elliptic filter? For a given number of inductors, theelliptic filter will give better selectivity. For a givennumber of components, the monotonic filter will generallygive better selectivity. The elliptic filter is less advanta-geous when high stopband attenuation is required.

The elliptic filter frequency response sensitivity to compo-nent tolerances may be greater, and tuning may be moredifficult.

Table 2-1 gives some examples of selectivity of 0.25 dBpassband ripple Chebyshev and Cauer-Chebyshev low-pass filters. Each filter has a cutoff frequency of 1 MHz.The dB column numbers in the table are the frequenciesin MHz where the stopband attenuation has reached thespecified level of 40 or 70 dB. Also given in the table arethe number of inductors and the number of total compo-nents in each order filter.

Order Components Inductors 40 dB 70 dB

All-Pole Chebyshev

6th 6 3 1.69 MHz 2.82 MHz

7th 7 3 1.50 MHz 2.25 MHz

Elliptic Cauer-Chebyshev

4th 5 2 1.76 MHz 3.88 MHz

5th 7 2 1.34 MHz 2.32 MHz

6th 8 3 1.16 MHz 1.70 MHz

7th 10 3 1.08 MHz 1.40 MHz

Table 2-1 Selectivity in 0.25dB Ripple 1 MHz lowpass filters

10 FILTER Types

MINIMUM INDUCTOR ALL-POLE LOWPASSMINIMUM CAPACITOR ALL-POLE LOWPASS

Minimum inductor and minimum capacitor subtypes arethe lowpass options. Because inductors are usually larger,more expensive and have lower Q, minimum inductancefilters are normally the first choice. For even order, bothtypes have an equal number of inductors and capacitors,so subtype choice is less significant.

Both types are open to ground and pass DC. However, atfrequencies well into cutoff, a series inductor becomes ahigh impedance and a shunt capacitor becomes a lowimpedance. This may affect the selection in some applica-tions, such as diplexers or in active interstage couplingnetworks where stability may be a factor.

C1

3529 pF

L1

10394 nH

C2

5635 pF

4th Order

C1

3284 pF

L1

9131 nH

C2

3284 pF

3rd Order

L2

6510 nH

4th Order3rd Order

L1

8209 nH

C1

3652 pF

L2

8209 nH

L1

8824 nH

C1

4158 pF

L2

14088 nH

C2

2604 pF

All-pole lowpass minimum inductor (top) and minimum capacitor(bottom) filters.

FILTER Types 11

MINIMUM INDUCTOR ALL-POLE HIGHPASSMINIMUM CAPACITOR ALL-POLE HIGHPASS

Minimum inductor and minimum capacitor refer to therelative number of inductors or capacitors in the odd orderhighpass filter, and not the lowpass prototype. Many ofthe same factors affect the selection of Highpass subtypeas in the lowpass filter case.

However, unlike the lowpass case, DC coupling to groundis effected by the selection.

C1

2871 pF

L1

6092 nH

C2

1798 pF

L2

9727 nH

4th Order3rd Order

C1

3086 pF

L1

6935 nH

C2

3086 pF

3rd Order 4th Order

L1

7714 nH

C1

2774 pF

L2

7714 nH

L1

7177 nH

C1

2437 pF

L2

4495 nH

C2

3891 pF

All-pole highpass minimum inductor (top) and minimumcapacitor (bottom) filters.

12 FILTER Types

MINIMUM INDUCTOR ALL-POLE BANDPASS

Minimum inductor is a full transform to bandpass of theminimum inductor lowpass filter. Each series L in thelowpass prototype becomes a series L-C network, and eachshunt C in the lowpass prototype becomes a parallel L-Cnetwork. Therefore the minimum inductor and minimumcapacitor bandpass filters have an equal number of induc-tors and capacitors for even and odd order.

This filter type is most useful for wide bandwidth (>30%)filters. For narrower bandwidths, consider using a cou-pled filter type.

L1

1.78 nH

C1

10.95 pF

L2

30.44 nH

C2

0.6402 pF

L3

1.78 nH

C3

10.95 pF

L1

1.656 nH

C1

11.76 pF

L2

34.65 nH

C2

0.5624 pF

L3

1.037 nH

C3

18.78 pF

L4

21.7 nH

C4

0.8979 pF

3rd Order

4th Order

FILTER Types 13

MINIMUM CAPACITOR ALL-POLE BANDPASS

The all-pole bandpass minimum capacitor type is a directtransform of the all-pole lowpass minimum capacitor type.Each series L in the lowpass prototype becomes a seriesL-C network, and each shunt C in the lowpass prototypebecomes a parallel L-C network. This filter type is similarto the minimum inductor type but has a series resonatorfirst.

This filter type is most useful for wide bandwidth (>30%)filters. For narrower bandwidths, consider using a cou-pled filter type.

L1

1765 nH

C1

95.69 pF

L2

203.1 nH

C2

831.5 pF

L3

2818 nH

C3

59.93 pF

L4

324.2 nH

C4

520.8 pF

L1

1642 nH

C1

102.9 pF

L2

231.2 nH

C2

730.5 pF

L3

1642 nH

C3

102.9 pF

4th Order

3rd Order

14 FILTER Types

COUPLED ALL-POLE BANDPASS FILTER TYPES

The minimum inductor and minimum capacitor bandpasssubtypes have the disadvantage that for narrow band-widths, or even moderate bandwidths, the values of theelements in the series and shunt branches are very differ-ent from each other. This makes practical construction ofthe inductors very difficult. The shunt inductors tendsmaller and the series inductors tend larger for narrowerbandwidths. For this reason, the minimum inductor andminimum capacitor bandpass subtypes are more usefulfor wider bandwidths, particularly at higher center fre-quencies where parasitics are often a greater problem.

Therefore for narrow bandwidths, the top capacitor (topC), top inductor (top L), shunt capacitor (shunt C) andtubular coupled bandpass subtypes are frequently used.All resonators are of the same type (series or parallel), socomponent values are closer in value to each other. Thesenarrow bandwidth filters also provide for input and out-put matching via the end coupling reactors.

These filters are excellent choices for filters with band-widths less than 20%, and are useful for bandwidths of upto 30%. The passband shape, bandwidth and center fre-quency will increase in error for larger bandwidths. Theroutines in FILTER apply the Cohn lowpass to bandpassaccuracy enhancements for these topologies [2].

Also, for wider bandwidths, the stopband and skirts ofthese topologies become asymmetric. For the top-C band-pass filter, the stopband and skirt above the passbandsuffer. For the shunt-C, top-L and tubular topologies thestopband and skirt below the passband suffer. As thebandwidth is narrowed, the symmetry of these filtersimproves, and as the bandwidth is widened, the symmetryof the response worsens.

FILTER Types 15

For wider bandwidths, the order requirement determinedby the N-Help routine in FILTER is pessimistic on one sideor the other for these subtypes. Often, selectivity is moreimportant on one side than another, and the subtypechoice can be made accordingly. Otherwise, a higher order,a narrower bandwidth or the full transform filters mustbe used. Sample responses are shown on the followingpages to illustrate this issue.

MIXED COUPLING REACTORS

If selectivity is almost adequate, the trick of changing acoupling capacitor to an inductor can improve selectivityon one side at the expensive of the selectivity on the otherside. An example of this transform is given in Chapter 3.This technique may also be used to change the DC cou-pling or stopband impedance characteristics of these fil-ters.

Eagleware sometimes receives requests to include ap-proximate transform bandpass filters with mixed couplingelements, such as alternating capacitors and inductors.These filter types were not included for a specific reason.Approximate transform bandpass filters designed withoutthe Cohn correction mentioned earlier are limited to anupper bandwidth limit of 2-5% percent, otherwise theresulting response has a significant frequency shift.Bandpass filters designed with practical inductor Q’s arelimited to bandwidths greater than 2-5% percent. There-fore, in general, there is no acceptable bandwidth foraccurate design of this type of practical bandpass filterswithout the Cohn correction. Unfortunately the Cohncorrection only applies to like coupling elements.

The problem is not that a solution does not exist. Theproblem is that the closed formulas are not known. Thesefilters can be designed by converting a coupling elementtype and using tuning or optimization techniques.

16 FILTER Types

TOP C COUPLED ALL-POLE BANDPASS

The top-C bandpass filter subtype consists of shunt par-allel resonant L-C circuits coupled via series capacitors.This type of filter is an approximate transform, withdecreasing accuracy for increasing bandwidths. It is mostaccurate (and useful) for bandwidths of less than 30%.

This type is very practical since all inductors are the samevalue, and that value can be specified by the user. Option-ally, by choosing an inductor value just inside the givenlimit, the input and output coupling capacitors will be-come large enough so that they may be eliminated fromthe design.

C1

478.1 pF

L1

220 nH

C2

596.9 pF

C3

248 pF

L2

220 nH

C4

596.9 pF

C5

478.1 pF

2nd order filter schematic and typical (5th order) response.

FILTER Types 17

TOP L COUPLED ALL-POLE BANDPASS

The top-L bandpass filter subtype consists of shunt paral-lel resonant L-C circuits coupled via series inductors. Thistype of filter is an approximate transform, with decreasingaccuracy for increasing bandwidths. It is most accurate(and useful) for bandwidths of less than 30%.

This type is very practical since all capacitors are the samevalue, and that value can be specified by the user. Option-ally, by choosing a capacitor value just inside the givenlimit, the input and output coupling inductors will becomesmall enough so that they may be eliminated from thedesign.

L1

247.7 nH

L2

255.9 nH

C1

1200 pF

L3

692 nH

L4

255.9 nH

C2

1200 pF

L5

247.7 nH


18 FILTER Types

SHUNT C COUPLED ALL-POLE BANDPASS

The shunt-C coupled bandpass filter consists of seriesresonant L-C circuits, coupled via shunt capacitors. Likethe top-C and top-L transforms, the shunt-C transform isalso an approximate bandpass transform. It is most accu-rate (and useful) for bandwidths of less than 30%.

This type is very practical since all inductors are the samevalue, and that value can be specified by the user. Bychoosing an inductor value just inside the given limit, theinput and output coupling capacitors will become smallenough so that they may be eliminated from the design.

C1

15.88 pF

L1

330 nH

C2

11.41 pF

C3

31.96 pF

L2

330 nH

C4

11.41 pF

C5

15.88 pF


FILTER Types 19

TUBULAR ALL-POLE BANDPASS

The tubular bandpass filter is a derivative of the shunt-Ccoupled bandpass created by converting internal capacitor“tee” networks into equivalent “pi” networks. It is anapproximate bandpass transform and is most accurate(and useful) for bandwidths of less than 30%. This type isoften used as a basis for coaxial tubular filters.

By choosing an inductor value just inside the given limit,the input and output coupling capacitors will becomesmall enough so that they may be eliminated from thedesign.

FILTER

C1

20.785 pF

L1

470 nH

C2

5.0695 pF

C3

0.8911 pF

C4

5.0695 pF

L2

470 nH

C5

20.785 pF


20 FILTER Types

BLINCHIKOFF 4TH ORDER FLAT DELAYALL-POLE BANDPASS

The Blinchikoff 4th order wideband bandpass filter isunique in that it has constant delay through the pass-band[1]. It is a special class of filter whose properties weresynthesized directly as a bandpass filter. This avoids thenormal destruction of lowpass prototype phase propertiesduring the transform to bandpass. The Blinchikoff band-pass filters are available for 30 to 70% bandwidth.Blinchikoff filters are further discussed in Appendix A.

L1

454.2 nH

C1

6.481 pF

C2

33.68 pF

L2

192 nH

C3

22.67 pF

L3

59.6 nH

C4

69.85 pF

L4

67.55 nH

C5

21.52 pF

FILTER Types 21

SYMMETRY PRESERVING ALL-POLE BANDPASS

It is well known that the Top-C coupled bandpass filterhas poor symmetry for bandwidths exceeding 5% to 10%.Carassa proved[4] that the ratio of the number of trans-mission zeros in a filter at infinite frequency to the numberat DC must be approximately 3:1 if the filter is to exhibitgood delay and arithmetic amplitude symmetry for widebandwidth.

Unfortunately, none of the published lowpass to bandpasstransforms result in a filter topology needed for symme-try. This is true for even the conventional bandpass trans-form, which has a multiplicity ratio of 1:1, and thereforehas greater low side selectivity.

It is feasible to manually modify the topology of a band-pass filter to achieve a multiplicity of 3:1. However, it isthen necessary to numerically determine the required newcomponent values.

Many workers have contributed much to the art of sym-metric filters. Szentirmai[5][6] developed methods forsynthesizing symmetric bandpass filters. This approachdeveloped a characteristic function which resulted inspecified bandpass filter performance. Hummel[7] devel-oped 2nd and 4th order bandpass filters with desirablephase characteristics. Blinchikoff and Savetman[8] car-ried forward Hummel’s work and developed a class ofwideband flat delay bandpass filters, and this work is thebasis of the Blinchikoff filter designed in FILTER. Eachof these works consider the bandpass directly to avoidundesirable lowpass to bandpass transformation effects.Consequently, network synthesis techniques are requiredto realize the filter. Eagleware has developed a generallowpass to bandpass transform with good symmetry at-tributes, which can be applied to filters of arbitrary degreeand which uses simple closed form formulas to determinecomponent values.

22 FILTER Types

SYMMETRIC TRANSFORM

The all-pole lowpass to bandpass transform which satis-fies these conditions is presented next. We will refer tothis transform as the symmetric transform. On the left ofthe figure above are the topologies of conventional band-pass filters for orders two through five. We use the con-vention that bandpass filter order is equal to the order ofthe lowpass prototype from which it is developed. Whilenot rigorous, the convention is broadly used.

Shown above are the topologies of the symmetric bandpassfilters of corresponding order. The symmetric bandpassfilter topology results when the first and then every othershunt parallel resonator is replaced with a series resona-tor. The parallel to series resonator conversion is based onimpedance inverters as published by Cohn[9]. It can beshown that the multiplicity ratio of these symmetrictransform filters for even order is 3:1 and asymptoticallyapproaches 3:1 with increasing odd order. The remainingtask is therefore to find a process for determining compo-

CONVENTIONAL SYMMETRIC TRANSFORM

N = 2

N = 3

N = 4

N = 5

FILTER Types 23

nent values. An approximate solution is known and is thetechnique utilized in the symmetric transform incorpo-rated in the FILTER program.

Shown on the above figure are the amplitude and delayresponses for a conventional 6th order 0.1 dB ripple Che-byshev bandpass filter with 45% arithmetic bandwidth

24 FILTER Types

centered at 100 MHz, and for 6th order 0.1 dB rippleChebyshev symmetric transform bandpass filters de-signed by FILTER for 15%, 30%, 45%, 60% and 75%bandwidths. (The 75% filter was tuned somewhat inSuperStar). The results illustrate marvelous symmetry.

SYMMETRIC TRANSFORM LIMITATIONS

The approximate method used to compute componentvalues limits the practical bandwidth. Depending on theacceptable levels of center frequency error, ripple or re-sponse error, and return loss, bandwidths to 40% or 50%are generally practical. If some error in the response isacceptable, for certain lowpass prototypes, or if optimiza-tion is employed, greater bandwidths may be specified.

For wider bandwidth the passband is not equi-ripple, butthe response is improved by tuning the resonator induc-tors or capacitors. The 75% bandwidth filter shown aboverequired tuning of the resonators using SuperStar.

For even wider bandwidths, some element values may benegative. The bandwidth at which this occurs is a func-tion of the lowpass prototype selected. Prototypes with alarge variation in G values, such as is the case withcontrolled phase prototypes, may be restricted to 20% orless bandwidth. It may be possible to extend the band-width before negative values result by reversing the orderof the G-values. The delay preserving attributes of thesymmetric transform is not as desirable as the symmetryattributes.

The practical lower BW limit is similar to the conventionalbandpass filter. As the bandwidth decreases, the ratio ofthe inductors in the series and shunt branches becomesextreme. For bandwidths below approximately 5% to10%, the symmetry of the top-C coupled and the shunt-C

FILTER Types 25

coupled bandpass filters is generally acceptable, and thesefilters are preferred.

26 FILTER Types

FULL TRANSFORM ALL-POLE BANDSTOP

The bandstop filter is a full transform from the lowpassprototype. The input section is a shunt series resonantL-C network. The next branch is a series parallel resonantL-C network. This form is automatically chosen for thebandstop filter, so a subtype selection is not necessary.

L1

385.7 nH

C1

6.634 pF

99.5 MHz

C2

138.7 pF

L2

18.45 nH

99.5 MHz

L3

385.7 nH

C3

6.634 pF

99.5 MHz

FILTER Types 27

MINIMUM INDUCTOR ELLIPTIC LOWPASSMINIMUM CAPACITOR ELLIPTIC LOWPASS

There are two elliptic lowpass filter subtypes in FILTER,minimum inductor and minimum capacitor. The mini-mum inductor subtype has a shunt capacitor for the inputbranch. The next branch is a series parallel resonant L-C.For odd order filters, the output branch is a shunt capaci-tor. For even order filters, the output branch is not aresonant network. It is a series inductor.

The minimum capacitor elliptic lowpass has a series in-ductor for the input branch. The second branch is a shuntseries L-C network. For odd order, the output branch is aseries inductor. For even order, the output branch is justa shunt capacitor.

C1

337.7 pF

C2

17.34 pF

L1

986 nH

38.49 MHzC3

551.4 pF

L2

653.9 nH

L1

844.2 nH

38.49 MHz

L3

1378 nH

C2

261.6 pF

L2

43.35 nH

C1394.4 pF

Minimum Inductor

Minimum Capacitor

28 FILTER Types

MINIMUM INDUCTOR ELLIPTIC HIGHPASSMINIMUM CAPACITOR ELLIPTIC HIGHPASS

There are two elliptic lowpass subtypes in FILTER, mini-mum inductor and minimum capacitor. The minimuminductor subtype has a series capacitor in the inputbranch and has the minimum number of inductors. Thenext branch is a series L-C to ground. For odd order, theoutput branch is a series capacitor. For even order, theoutput branch is an inductor to ground.

The minimum capacitor has a shunt inductor in the inputbranch and has the minimum number of capacitors. Thenext branch is a parallel L-C series branch. For odd order,the output branch is an inductor to ground. For even order,the output branch is a series capacitor.

Notice the DC passing and bypassing characteristics ofthe elliptic highpass are different for minimum inductorand minimum capacitor.

C1

300 pF

2.404 MHz

C3

183.8 pF

L2

968.4 nH

L1

750.1 nH

C1

256.9 pF

L2

14608 nH

2.598 MHz

L3

459.4 nH

C2

387.4 pF

C25843 pF

L1

750.1 nH

Minimum Inductor

Minimum Capacitor

FILTER Types 29

FULL TRANSFORM ELLIPTIC BANDPASS

This type is a full bandpass transform of the minimuminductor elliptic lowpass prototype. Each shunt capacitoris transformed into a shunt parallel resonant L-C. Eachseries parallel resonant L-C is transformed into a pair ofseries parallel resonant L-C networks. The output seriesinductor of the even order lowpass prototype is trans-formed into a series branch series resonant L-C network.

This filter has the same disadvantages as the all-pole fulltransform bandpass filter. This filter has the additionalproblem of stray capacity at the common node of the seriesbranch parallel resonant network pair may be a problem.

L1

15.15 nH

C1

168.8 pF

C2

12.74 pF

L2

94.32 nH

145.2 MHz

C3

27.13 pF

L3

200.8 nH

68.19 MHz

L4

9.281 nH

C4

275.7 pF

L5

327 nH

C5

7.826 pF

30 FILTER Types

MINIMUM INDUCTOR (“ZIG ZAG”) ELLIPTICBANDPASS

An elliptic bandpass filter that reduces these problems isthe minimum inductor subtype. It is a marvelous filter inthat no other bandpass filter with the same number orfewer inductors can achieve the selectivity performance ofthis design. It is based on the work of R. Saal and E.Ulbrich[3].

When constructed with precision capacitors, tuning isaccomplished by simply adjusting the zero frequencieswith the inductors. The fact that this filter has not enjoyedwider use is clearly understood by anyone who has manu-ally calculated the values for even one design.

The schematic for a 4th order filter is shown above.

L1

14.43 nH

C1

172.8 pF

C2

9.625 pF

C3

8.794 pF

L2

136.7 nH

145.2 MHz

L3

33.56 nH

68.19 MHz

C5

148.3 pF

L4

317.8 nH

C6

8.259 pF

C4162.3 pF

FILTER Types 31

ELLIPTIC BANDSTOP

The elliptic bandstop filter input branch is a series L-C toground. The next branch is series and consists of a cascadeof parallel L-C networks. For odd order, the output branchis a series L-C to ground. For even order, the output branchis series and consists of one parallel L-C.

L1

375 nH

C1

6.822 pF

99.5 MHz

C2

250.4 pF

L2

9.7 nH

102.1 MHz

C3

263.8 pF

L3

10.22 nH

96.93 MHz

L4

229.7 nH

C4

11.14 pF

99.5 MHz

C5

193.7 pF

L5

13.21 nH

99.5 MHz

32 FILTER Types

Chapter 3

FILTER Examples

I n this chapter, useful tricks and filter customizationusing SuperStar Professional are illustrated with vari-ous examples. These examples demonstrate SuperStar

Professional and FILTER operation and interaction usingtext circuit files.

EXAMPLE 1 - TRANSMISSION LINERESONATORS

A 5th order 0.25 dB Chebyshev 860 to 900 MHz bandpassTC filter is designed and then converted to a top-C coupledtransmission line resonator filter with similar perform-ance characteristics. The original L-C design is done inFILTER and the modification in SuperStar.

First start SuperStar and then launch FILTER from theShell menu. Enter data into the FILTER input cells asillustrated in Figure 3-1. The final values in the schematicshould be readable on your screen. If not, the view zoommay be controlled using the M, +, - and scroll buttons.

Next, select “Write .CKT File” from the FILTER File menu,enter a filename and select Run SuperStar.

FILTER terminates and SuperStar Professional runs anddisplays responses of the L-C filter. Press F8 to examinethe circuit file in the SuperStar editor, as shown in Table3-1. Your component Q and output formats may be differ-ent.

Next, the inductor-capacitor pairs from a node to groundare converted to shorted quarter-wavelength transmis-sion line stubs.

The characteristic impedance of the lines are defined by[14]

where ω is 2 π times the resonant frequency of the substi-tuted L-C pair. The frequency of the first three L-C pairsare 986.682, 906.803 and 903.503 respectively. The ele-ment values are symmetric so the other resonator frequen-cies are the mirror image of these. The electrical lengthof each line is 90 degrees at the resonant frequency. Theinductance in each case in 8.67 nH so the resulting stub-line impedances are 42.215, 38.797 and 38.656 ohms re-spectively.

Z Lo

= π ω4

Figure 3-1 Sample Filter Screen

34 FILTER Examples

This conversion procedure is approximate so the fre-quency at which each line is 90 degrees long is optimizedin SuperStar to equalize the insertion loss ripple and thereturn loss.

Original L-C filter responses are given on the left in theFigure 3-2 and the responses of the converted filter before(solid) and after optimization (dashed) are also given. Thefollowing circuit file after conversion and optimization isgiven in Table 3-2.

CIRCUITCAP 1 2 C=0.6747 Q=1E6 ‘C1IND 2 0 L=8.67 Q=1E6 ‘L1CAP 2 0 C=3.001 Q=1E6 ‘C2CAP 2 3 C=0.1259 Q=1E6 ‘C3IND 3 0 L=8.67 Q=1E6 ‘L2CAP 3 0 C=3.553 Q=1E6 ‘C4CAP 3 4 C=0.1 Q=1E6 ‘C5IND 4 0 L=8.67 Q=1E6 ‘L3CAP 4 0 C=3.579 Q=1E6 ‘C6CAP 4 5 C=0.1 Q=1E6 ‘C7IND 5 0 L=8.67 Q=1E6 ‘L4CAP 5 0 C=3.553 Q=1E6 ‘C8CAP 5 6 C=0.1259 Q=1E6 ‘C9IND 6 0 L=8.67 Q=1E6 ‘L5CAP 6 0 C=3.001 Q=1E6 ‘C10CAP 6 7 C=0.6747 Q=1E6 ‘C11DEF2P 1 7 FILTERWINDOWFILTER(50,50)GPH S21 -60 0GPH S21 -5 5GPH S11 -30 0GPH DLY 0 200FREQSWP 830 930 101

Table 3-1

FILTER Examples 35

Figure 3-2 Original L-C filter responses (left) and responses ofthe converted filter before (solid) and after optimization (dashed)

CIRCUITCAP 1 2 C=0.6747TLE 2 0 Zo=42.215 L=90 F=?992.372CAP 2 3 C=0.1259TLE 3 0 Zo=38.797 L=90 F=?906.996CAP 3 4 C=0.1TLE 4 0 Zo=38.656 L=90 F=?903.723CAP 4 5 C=0.1TLE 5 0 Zo=38.797 L=90 F=?906.996CAP 5 6 C=0.1259TLE 6 0 Zo=42.215 L=90 F=?992.372CAP 6 7 C=0.6747DEF2P 1 7 FILTERWINDOWFILTER(50,50)GPH S21 -60 0GPH S11 -30 0FREQSWP 830 930 101

Table 3-2 Circuit file after conversion and optimization

36 FILTER Examples

EXAMPLE 2 - BESSEL CRYSTAL FILTER

The shunt-C coupled bandpass filter topology is similar toladder crystal bandpass filters. Since the shunt-C filterallows specifying the series inductance, designing laddercrystal filters is straightforward.

A 5th order Bessel filter with a center frequency of 8.999MHz, a bandwidth of 500 Hz and 600 ohms terminatingimpedance is designed using a crystal with the followingparameters:

• Rs= 20 ohms

• Lm= 32 millihenries (32E6 nH)

• Co= 2.4 pF

• Cm resonates with Lm at the crystal series frequency.

Use FILTER to design the shunt-C coupled bandpass,specifying 32E6 nH for the inductor, and then write theSuperStar file. Each series inductor-capacitor pair is con-verted to a crystal XTL model. The circuit file is shown inTable 3-3.

Figure 3-3

FILTER Examples 37

The 2.4 pF crystal parallel capacitance causes the highside selectivity to be greater. This places an upper limiton the bandwidth of this type of ladder crystal filter.Placing an inductor in parallel with the crystal to resonateout Co may allow a wider bandwidth.

EXAMPLE 3 - FILTER SYMMETRY

Some filter applications require amplitude and delay arit-hmetic symmetry about the center frequency. For narrowband filters, this is approximately realized by most trans-forms. However, for wider bandwidths, symmetry fre-quently suffers. This is further discussed in the chapterEQUALIZATION. In this example, the symmetry of anelliptic filter is significantly improved.

First design a 4th order elliptic minimum-inductor (zig-zag) bandpass filter with Fl= 50 MHz, Fu= 90 MHz, 0.177

CIRCUITCAP 1 0 C=5.916XTL 1 2 Rs=20 Lm=3.2E+7 Cm=9.777113E- 3 Co=2.4CAP 2 0 C=52.31XTL 2 3 Rs=20 Lm=3.2E+7 Cm=9.777338E-3 Co=2.4CAP 3 0 C=112.3XTL 3 4 Rs=20 Lm=3.2E+7 Cm=9.776086E-3 Co=2.4CAP 4 0 C=166.3XTL 4 5 Rs=20 Lm=3.2E+7 Cm=9.775578E-3 Co=2.4CAP 5 0 C=278.7XTL 5 6 Rs=20 Lm=3.2E+7 Cm=9.775854E-3 Co=2.4CAP 6 0 C=104.1DEF2P 1 6 FILTERWINDOWFILTER(600,600)GPH S21 - 60 0GPH S21 -5 5GPH S11 -30 0GPH DLY 0 2E6FREQSWP 8.9975 9.0025 101

Table 3-3

38 FILTER Examples

dB passband ripple,Amin= 45 dB, type C equal terminationand 50 ohms terminating impedance. Define the outputblock to display the data shown in Figure 3-4 and changethe frequency sweep to

SWP 0 200 41

Results in Figure 3-4 showgreater low-sideselectivity,andhigher low-side group delay. As it turns out, the reason for

Figure 3-4

FILTER Examples 39

this is too many transmission zeros at DC in relation tothe number of transmission zeros at infinity. The numberof zeros at DC can be reduced by one by converting thefirst shunt inductor (55.46 nH) to a series inductor.

The parallel 67.96 nH inductor and 50 ohm source resis-tance are converted to the series equivalent via the rela-tions:

Rs, 13.1 ohms, is the new input impedance of the filter. Xsis the reactance of the series inductor and is used tocalculate a series inductance of 50.1 nH.

The modified file with ?’s added to optimize componentsand with an OPT block is given in Table 3-4. Notice forthe optimization, the number of frequency points has beenreduced to 41, to decrease optimization time.

RR X

R Xso p

o p

=+

2

2 2

XR X

R Xso p

o p

=+

2

2 2

CIRCUITIND 1 2 L=?50.1CAP 2 0 C=?94.12CAP 2 3 C=?26.94IND 3 4 L=?146.2CAP 3 4 C=?9.36IND 4 7 L=?92.81CAP 7 0 C=?249.5CAP 4 0 C=?86.68IND 4 5 L=?199.7CAP 5 6 C=?30.56DEF2P 1 6 FILTER

WINDOWFILTER(13,50)GPH S21 -100 0GPH S21 -5 5GPH DLY 0 100FREQSWP 0 200 41OPT0 20 S21<-50 W21=150120 200 S21<-50 W21=15050 90 S21>-.177

Table 3-4

40 FILTER Examples

After several rounds, optimization was stopped and theFREQ block was modified for 101 frequencies to obtain asmooth plot.

Notice the greatly improved amplitude and delay symme-try. The input resistance is only 13 ohms. A 1:4 broadbandtransformer could be used at the input, or the inputresistance can be changed to 50 ohms, and the responsere-optimized. The resulting bandwidth is somewhat widerwhen this is done.

EXAMPLE 4 - CREATING A UNIQUE LOWPASSPROTOTYPE

In this example, a class of lowpass prototype G values ismade. It’s desired to have a filter type with Bessel pass-band characteristics (flat delay and improved selectivity).

Use FILTER to design a 6th order lowpass Bessel filterwith 1 ohm input and output impedance and a cutoff of 1MHz. Then modify the file, adding a capacitor in parallelwith the second and fourth elements, both series induc-tors. The intent is to add zeros in the stopband, and modifyall values in an attempt to retain nearly flat delay in thepassband. The form of the prototype is identical to a 6thorder elliptic. Starting capacitor values are small (100 pF)so as not to destroy the Bessel characteristic at the start.

The optimize goals are flat delay (DLY%), at least 50 dBof attenuation from 3 to 3.6 MHz and at least 70 dB ofattenuation above 3.6 MHz. To achieve the stopband re-quirements, the optimizer might make the passband verynarrow; an easy way out. However, decreasing the band-width increases delay, making it more difficult to flattenthe delay. The optimizer is therefore forced to maintainpassband bandwidth.

FILTER Examples 41

The results are very gratifying. The original and 25 roundpattern search response is shown in Figure 3-5. The file,after optimization, is shown in Table 3-5.

Figure 3-5

CIRCUITCAP 1 0 C=?21693.6IND 1 2 L=?70.1333CAP 1 2 C=?12202.58CAP 2 0 C=?104981.7IND 2 3 L=?134.0087CAP 2 3 C=?4623.676CAP 3 0 C=?166671.2IND 3 4 L=?391.341DEF2P 1 4 FILTERWINDOWFILTER(1,1)GPH S21 -100 0GPH S21 -5 5GPH DLY 0 1000FREQSWP 0 6 31OPT0.2 2 DLY% WDL=.0013 3.6 S21<-50 W21=1E33.6 6 S21<-70 W21=1E4

Table 3-5

42 FILTER Examples

EXAMPLE 5 - DESIGNING A BANDPASS FILTERFROM THE NEW PROTOTYPE

There are several advantages to creating a lowpass proto-type when designing a unique filter. The prototype, oncedeveloped, can be used over and over to design lowpass,bandpass, etc., filters with different frequencies and band-widths or terminating impedances. Also, there are farfewer parts in the prototype than a bandpass filter, sooptimization is faster and can be done on higher orders.

The elliptic lowpass prototype developed in Example 5 wasfor 1 ohm and 1 MHz. To be used as a standard prototype,the frequency must be normalized to 1 radian/sec. This isaccomplished by multiplying each inductor and capacitorby 2*3.14159*1E6. The resulting prototype values are:

G(0)=1 G(5)=0.0291G(1)=0.136 G(6)=0.842G(2)=0.0767 G(7)=1.047G(3)=0.441 G(8)=2.459G(4)=0.660 G(9)=1

Figure 3-6

FILTER Examples 43

Run FILTER and design a 68.456 to 71.544 MHz ellipticfull transform bandpass with the “User File” selection inthe Shape option of the Topology menu. Once “User File”is selected, you are asked to specify a filename for holdingthe above data which is entered in the format describedin Appendix A.

Use 50 ohm terminating impedances. The results areshown in Figure 3-6. The file was modified to includedelay output. There is some slope in the delay. This canbe removed by optimization.

44 FILTER Examples

Chapter 4

A/FILTER Operation

A /FILTER is launched by starting GENESYS andthen selecting A/FILTER from the Synthesis menu(top of the screen). The main A/FILTER screen

looks like the sample screen in Figure 4-1.

Input “fields” appear on the bottom section of the screen.The top part contains the schematic and values of the filterbeing designed. At any time, press F1 for help on the inputat the cursor location.

The cursor is initially located on the order input field.Press the arrow keys to move between and edit inputfields. To automatically continue to the next input field,press the Tab or Enter key. To go to the previous field,press Shift-Tab. Optionally, the left mouse button maybe used to select a radio button or to move the cursor.When the cursor is on an input field you may type in a newvalue for that field. After changing an input parameter,the component values on the schematic will automaticallyupdate.

FIRST EXAMPLE

The first design example will be a Single Feedback 7thorder lowpass filter with a 0.25 dB passband ripple Che-byshev response. The cutoff frequency is 10 kHz, and thefilter will have +2dB gain in the passband.

First, select Alt-T, or click on Topology to access thetopology menu. Selecting the Type item causes a newwindow to appear. This window will contain three sets ofradio buttons, labeled Types, Poles, and Topologies. Thetypes box specifies what type of filter you are designing.The poles box contains selections for elliptic and all-poleresponse realizations. The topologies box contains differ-ent filter schematic realizations of the current type, eachwith differing benefits.

Use the up and down arrow keys or the left mouse buttonto change the highlighted radio button in each selection,and use the Tab or Enter key to move between sections.Make these selections: Lowpass, All-Pole, and SingleFeedback. Select the OK button to continue (press Enterwhen it is highlighted).

Next, the Shape subwindow appears. This defines theshape approximation type for the filter. Select the Cheby-shev button. Help on the shapes can be obtained before

Figure 4-1 Sample A/FILTER Screen

46 A/FILTER Operation

closing the window by pressing F1 (HELP). Use PgUpand PgDn or the scroll bar to move between help pages.Press Escape to exit the help window. Choose the OKbutton to continue.

Filters which have unequal input and output imped-ances, such as even order Chebyshev and singly-termi-nated filters, are covered in detail in Appendix A.

The cursor is now located on the main window at the orderprompt. Enter 7. Filters up to 21st order may be designedfor most types. The suggested range at the bottom of thescreen gives a reminder of the valid range for the currentlyselected input.

Next enter the passband ripple: 0.25.

A/FILTER directly computes the lowpass prototype Gvalues for popular response shapes and does not use tablesfor these shapes, so any real value less than 3 dB may bechosen for the passband ripple. This is true even forelliptic Cauer-Chebyshev filters.

The cutoff frequency of all-pole filters, such as Butter-worth, is normally defined as the 3 dB attenuation fre-quency. The cutoff of filters with ripple in the passband,such as Chebyshev, is often defined as the ripple value.A/FILTER allows specification of the attenuation, Aa, atthe cutoff frequency for Butterworth and Chebyshev fil-ters. For normally defined cutoff attenuation, enter Aaequal to the ripple value for Chebyshev filters, and 3.01dB for Butterworth filters.

For this example, enter 0.25 at the Aa prompt.

Next, for Butterworth and Chebyshev filters, A/FILTERprompts for Fca, the desired frequency at which the speci-fied cutoff attenuation Aa will occur. A/FILTER then com-putes and displays the cutoff frequency at the normally

A/FILTER Operation 47

defined cutoff attenuation. This value is used by A/FIL-TER during the design process. For filter response shapesother than Butterworth and Chebyshev, the prompts forAa and Fca are skipped, and the program prompts for Fc.

Enter 0.01 at the Fca prompt for this example, to indicatea cutoff of 0.01 MHz (10 kHz).

The Std R input is the desired value for the selectableresistors in the current filter. Std C is the desired valueof capacitance. Certain filter types allow the user tospecify one or more part values. When this is the case,A/FILTER prompts for the value. This can be any validpart value. Not all of the part values are selectable. Somefilter types allow selection of all resistors, whereas somedo not allow any freedom. This is discussed in furtherdetail in Chapter 5.

For this example, enter 10000 (10 kΩ) for the resistorvalue, and 10000 (10000 pF) for capacitor value.

The schematic of the filter just designed is shown on thescreen.

OTHER DATA

Also displayed on the lower right portion of the screen isthe summation of the lowpass prototype G values of thefilter just designed. This quantity may be used to estimatethe insertion loss, Lo, and group delay, Do, of the filter atfrequencies well within the passband. These estimatedparameters are also displayed.

UNITS

The units used in A/FILTER are the same units used inSuperStar. They are:

Resistance.......ohms

Capacitance.....picofarads


Frequency........megahertz

MODIFYING A DESIGN

A/FILTER remembers the selections made, so modifyinga design is easy. This is true even if A/FILTER is exited.For a permanent record, the design can be saved to a *.AF$file (a setup file, not a circuit file) using the file menuoptions save, and save as.

NOISE-BW & N-HELP

Please refer to Chapter 1 for coverage of these topics.

OUTPUT DEFAULTS

When A/FILTER writes a SuperStar circuit file, it includesoutput data specifications. The data used by A/FILTERcan be specified by selecting the Output Block option fromthe Setup menu.

Up to four different output parameters can be selected.The only restriction is that output options 2 and 4 mustcoincide with the formats of 1 and 3, respectively. That is,if output 1 is a polar plot and output 2 is used, it also mustbe a polar plot.

There are 4 buttons at the top of the screen labeled 1 to 4.Begin by choosing the button whose number correspondsto the plot to be changed. This is done by using the arrowkeys to select the desired option, or by clicking the optionwith the left mouse button.

Next, choose the form in which to display the output data.The options are displayed in the Types box. They are:

NONE Display no output for this option numberGPH Graph of selected data vs. frequencySMH Smith Chart outputPOL Polar chart output


LOG Diplays GPH using log frequency scaleDSP Displays a window with numeric data

The Options box contains circuit parameters available foroutput display. Choose the parameter that should bedisplayed in the selected format.

Finally, if either GPH or POL is chosen as the output type,the display range information at the bottom of the screenmust be filled in. The Minimum and Maximum boxescontain the upper and lower display values for the GPHoption. The POL box is the desired radius for a polar plot.

Another output number can be selected to add more out-put displays, or select Close to accept the settings. SinceA/FILTER saves the settings after each exit, these settingsbecome the default until they are changed again.

Please refer to the FILTER manual for information onwriting SuperStar files.

COMPONENT DEFAULTS

A/FILTER allows specification of capacitor Q and opera-tional amplifier characteristics. SuperStar then usesthese values in the determination of the filter response.To view or change these values, select Components fromthe Setup menu. Several input boxes are displayed. Thefirst is the desired value for capacitor Q. A new value canbe specified, or simply press Enter or one of the verticalarrow keys to move to another field.

The op-amp parameters allow A/FILTER to model virtu-ally any real amplifier by knowing critical operating pa-rameters. The Input Resistance is the series DC inputresistance of the amplifier. The Output Resistance is theapparent DC output resistance. GDC is the DC open-loopgain, and the 0 dB frequency is the frequency in MHz atwhich the amplifier’s characteristic curve yields a maxi-


mum gain of 0 dB. Typical amplifier parameters areavailable from online help in A/FILTER.

PREFERENCES

Most of the filter topologies designed by A/FILTER use aminimum number of components, and do not match to aspecified source or load termination. For this reason, thetransmission and reflection parameters may behave er-ratically unless a matching buffer is added at either end.For instance, the Minimum Inductor and Minimum Ca-pacitor types assume a near zero source termination, andnear infinite load resistance.

Unless low or high values are specified for the source andload terminations (A/FILTER default) the source sees amismatch and voltage follower buffers must be added oneach port. These buffers add a shunt resistance equal tothe source resistance on the source side of the input buffer.A/FILTER does not do this by default, but it can be enabledby selecting the Preferences option from the Setup menu.

Two options are available. They are:

• Zo matching buffer...Matching buffer (follower) withresistance equal to the specified port terminationresistance.

• Voltage follower...Voltage follower with no matchingresistor.

These can be placed on either port, or not used at all.

Some filter types have no gain built inherently into theirstructure. If no gain is allowed in a filter that has beendesigned but voltage followers are used, A/FILTER canadd feedback resistors to these followers in an attempt toprovide the requested gain.

The preferences box contains four other options to custom-ize the way that A/FILTER selects sections during thefilter design process. They are:


• Allow third order sections

• Distribute Gain

• Use simple first order section

• Reverse order of poles

A/FILTER can design a three pole section using a singleop-amp. This is useful since it can eliminate parts from adesign, but it does not allow gain. It can, however, be usedto simplify the overall filter design for orders greater thantwo. The section has a high sensitivity to componenttolerances, since one element can tune three poles simul-taneously. The three pole section allows specification of asingle value for all resistors. This provides a greatercomponent flexibility than the two pole section, but doesnot allow gain. Check the Allow Third Order Sections boxif the three pole section should be used in designs.

When a filter contains more than one section which canprovide gain, A/FILTER can distribute the required gainevenly among them. This can lessen the strain on eachop-amp, and in some cases allow a lower bandwidth am-plifier to be used. Check the Distribute Gain box to havethe overall gain distributed through the allowed sections.

In odd order filters not using the three pole section, asingle inverting amplifier is used to realize the extra pole.This can add an extra gain section, but it adds parts to adesign. However, buffering capability is present in themore complex circuit, so a voltage follower on the outputis not normally required. Check the Use Simple FirstOrder Section box for A/FILTER to use a single RC sectionrather than an additional op-amp pole.

By default, A/FILTER places all pole pairs first in the filtercascade. For the real pole to be placed first, or for the polepairs to be reversed, check the Reverse Order of Poles box.This may be desirable in low-noise design, since most ofthe gain occurs in the first section with the poles reversed.


Even 0dB gain filters will generally amplify the signal insome stages while attenuating it in others, so use thisoption with caution. When this option is on, the amplify-ing sections will be first, so the input level must be muchsmaller to avoid saturating the op-amps in the first stages.For more details on gain levels in individual sections, seeChapter 5.


Chapter 5

A/FILTER Types

Filter type specifies whether the filter is lowpass, high-pass, bandpass, or bandstop. For each type, A/FIL-TER offers several available topologies. Each of these

has different options and benefits, depending on the ap-plication need. Schematics and descriptions of the topolo-gies designed by A/FILTER are given on the followingpages.

Please refer to Appendix A for a discussion of filtertransfer approximations (shapes).

LOWPASS ALL POLE MINIMUM INDUCTOR

The minimum inductor type is a direct element transfor-mation of an LC minimum inductor filter using the 1/stransform. This topology is particularly useful when lowsensitivity is needed. See Appendix E for a completedescription of the transform types.

This filter is insensitive enough to component tolerancesthat tuning is not usually needed. However, the cutofffrequency is tuned by adjusting the grounded resistor (R3)in each D element (see Appendix E).

This filter type allows the user to choose a value for allspecifiable capacitors and resistors. For equal termina-tion filters (e.g. Butterworth and odd-order Chebyshev),all capacitors have the same value.

Gain is not available in this type. In fact, there is aninherent loss of 6dB.

FILTER

C1

4700 pF

C2

4700 pF

R1

1000 ohm

Q2

Q1

C34700 pF

R2

1000 ohm

R3

?1476.6 ohm

C4

4700 pF

R4

100000 ohm

56 A/FILTER Types

LOWPASS ALL POLE MINIMUM CAPACITOR

This type is a direct transform of the LC minimum capaci-tor filter using the 1/s transform. For odd order filters,there are fewer D elements in this type than in a compa-rable minimum inductor filter. However, there are moreresistors in series with the signal path in this type. SeeAppendix E for a complete discussion of GIC transforms.

The minimum capacitor filter is tuned exactly as theminimum inductor type. Resistor R4 in the schematictunes the cutoff frequency of the response.

This filter type allows the user to choose a value for allspecifiable capacitors and resistors. For equal termina-tion filters (e.g. Butterworth and odd-order Chebyshev),all capacitors have the same value.

Gain is not available in this type, and there is an inherentloss of 6dB.

FILTER

C1

4700 pF

R1

478.89 ohm

C2

4700 pF

R2

1000 ohm

Q2

Q1

C34700 pF

R3

1000 ohm

R4

?2088.2 ohm

C4

4700 pF

R5

100000 ohm

A/FILTER Types 57

LOWPASS ALL POLE SINGLE FEEDBACK

The single feedback type has a minimum number of parts,and allows gain. The user may specify one resistor and onecapacitor value per section (C2 and R2 in the schematicabove). This type also allows added feedback resistors forgain (R3 and R4 above), but does not use them if unity gainis requested. This allows even fewer parts if gain is notneeded. R1 tunes the response Q and cutoff frequency.

This type is sensitive to component tolerances, but has ahighly flexible gain allowance.

FILTER

R1

?55.786 ohm

C1

78.074 pF

R2

55.786 ohm

C2

100 pF Q1

R3

1000 ohm

R4

1000 ohm

58 A/FILTER Types

LOWPASS ALL POLE MULTIPLE FEEDBACK

The multiple feedback filter uses few parts, and providesgain without additional components. This type requiresone less component than the single feedback type withgain, but one more than the single feedback type withoutgain.

One capacitor value per section is selected arbitrarily (C2in the schematic above). Resistor R2 in the schematictunes the Q and cutoff frequency of the filter.

This type has a high sensitivity to component tolerances.

FILTER

R1

2300 ohm

C1

520.7 pF

R2

?1372.1 ohm

Q1

C2

100 pF

R3

3400.9 ohm

A/FILTER Types 59

LOWPASS ALL POLE LOW SENSITIVITY

The low sensitivity realization uses two op-amps per polepair,but has a low sensitivity to the op-amp open loop gain.

This topology allows two capacitors per section (C1 and C2in the schematic) to be chosen. Resistor R1 on the sche-matic is used to tune the response. This type has a lowsensitivity to differences in op-amp open loop gain be-tween sections, but requires the two amplifiers withineach section to have similar characteristics. Usually, op-amps on a dual or quad package will have closely matched,if not identical operating parameters.

This topology does not allow gain.

FILTER

R1

?3572.2 ohm

Q1R2

6801.7 ohm

C1

100 pF

Q2

C2

100 pF

60 A/FILTER Types

LOWPASS ALL POLE VCVS(Voltage Controlled Voltage Source)

The VCVS has uniform capacitors throughout the struc-ture, whose values are specifiable. There are also two userselectable resistors per section (R3 and R4 on the sche-matic above).

This filter allows tuning of response Q and frequencyusing resistor R1. There is a high sensitivity to componenttolerances in this structure.

Gain is selectable for odd order filters with this type, buteven orders provide a gain of 2 (6.02 dB) per section.

FILTER

R1

?3572.2 ohm

R2

6801.7 ohm

C1

100 pF

Q1R3

100 ohm

R4

100 ohm

C2

100 pF

A/FILTER Types 61

LOWPASS ALL POLE STATE VARIABLE (Biquad)

The state variable filter is best known for its tunability.This type contains many parts per section, but everyaspect of the filter response is tuned directly. This gives alarge degree of freedom for component tolerances.

This type also exhibits low sensitivity to operational am-plifier characteristics, such as narrow bandwidth andopen-loop gain.

The state variable structure allows user specifiable uni-form capacitors throughout the entire circuit as well astwo resistors per section (R3 and R4 in the above sche-matic).

For tuning, refer to the above schematic:

1) Adjust R5 for correct cutoff frequency2) Adjust R6 for desired Q3) Adjust R1 for overall gain desired

FILTER

R1

?3333.7 ohm

Q1R2

4929.2 ohm

Q2

C1

100 pF

R3

100 ohm

Q3

R4

100 ohm

R5

?4929.2 ohm

R6

?3572.2 ohm

C2

100 pF

62 A/FILTER Types

LOWPASS ELLIPTIC MINIMUM CAPACITOR

The minimum capacitor elliptic type uses a 1/s transfor-mation. See Appendix E for a complete discussion of thetransform types.

This filter is tuned by adjusting the grounded resistor (R5)in each D element (see Appendix E). The zero frequencyis tuned by using R2 in the schematic above.

This topology has a very low sensitivity to componenttolerances, and a loss of 6dB within the filter passband.

Gain is not available with this topology.

FILTER

C1

470 pF

R1

5279.2 ohm

R2

?158.9 ohm

C2

470 pF

R3

1000 ohm

Q2

Q1

C3470 pF

R4

1000 ohm

R5

?279.3 ohm

R6

5279.2 ohm

C4

470 pF

R7

100000 ohm

A/FILTER Types 63

LOWPASS ELLIPTIC VCVS

The VCVS uses user selected capacitors throughout thestructure. There is also one user selectable resistor persection (R5 on the above schematic).

This type has a low sensitivity to component tolerances,and does not usually require tuning, however the filter istuned using the resistors R1 and R4 shown on the sche-matic above.

This filter type produces gain, but does not allow itsspecification by the user.

FILTER

R1

?738.57 ohm

C1

250 pF

R2

369.28 ohm

C2

250 pF

R3

738.57 ohm

C3

3300 pF

R4

?7487.4 ohm

Q1

R5

10000 ohm R6

118436 ohmC4

500 pF

R7

?1332.8 ohm

Q2

R8

1970.7 ohm

C5

500 pF

64 A/FILTER Types

LOWPASS ELLIPTIC STATE VARIABLE

This type contains many parts per order, but every aspectof the filter response is tuned directly. This gives a highdegree of freedom for component tolerances.

This type also exhibits low sensitivity to operational am-plifier characteristics, such as narrow bandwidth andgain.

This structure allows user specifiable uniform capacitorsthroughout the entire circuit as well as two resistors persection.


1) R6 tunes the cutoff frequency, and the zero frequency.2) R2 tunes the quality of the zero.3) R4 tunes the response Q.4) R5 tunes the passband gain.5) R10 tunes the overall gain.

FILTER

R1

2060.8 ohm

Q1

C1

500 pF

R2

?10000 ohm

R3

10000 ohm

R4

?2060.8 ohm

R5

?1766.6 ohm

R6

1766.6 ohm

Q2

C2

500 pFR7

10000 ohm

R8

10000 ohm

Q3

R9

?391.71 ohm

Q4

R10

?436.96 ohm R11

?1970.7 ohm

Q5

R12

1970.7 ohm

C3

500 pF

A/FILTER Types 65

HIGHPASS ALL POLE MINIMUM INDUCTOR

The minimum inductor type is a direct element transfor-mation of an LC minimum inductor filter using the GIC.See Appendix E for a discussion of GIC transforms.

This filter is insensitive enough to component tolerancesthat tuning is not usually needed. However, the cutofffrequency is tuned by adjusting the grounded resistor ineach GIC (R4 in the schematic above).

This filter type allows the user to choose a value forcapacitors and resistors. For equal termination filters (e.g.Butterworth and odd-order Chebyshev) all capacitorshave the same value.

This filter provides power gain, rather than voltage gain.This means that S21 should be displayed, rather thanE21.


FILTER

C1

21220.8 pF

R1

1000 ohm

R2

1000 ohm

Q2

Q1

R3

1000 ohm

C2

470 pF

R4

?126.99 ohm

C3

21220.8 pF

66 A/FILTER Types

HIGHPASS ALL POLE MINIMUM CAPACITOR

This type is a direct LC GIC transform. For odd orderfilters, there are more GIC elements in this type than ina minimum inductor filter of the same order. However,there are fewer capacitors in series with the signal pathin this type. See Appendix E for a complete discussion ofthe transform types.

Resistor R4 in the schematic above tunes the cutoff fre-quency of the response.

The user may choose a value for capacitors and resistors.For equal termination filters (e.g. Butterworth and odd-order Chebyshev) all capacitors have the same value.


Gain is not available in this type, and there there is aninherent loss of 6dB.

FILTER

R1

1000 ohm

R2

1000 ohm

Q2

Q1

R3

1000 ohm

C1

470 pF

R4

?179.59 ohm

C2

15005.4 pF

A/FILTER Types 67

HIGHPASS ALL POLE SINGLE FEEDBACK

This type has a minimum number of parts, and allowsgain. This section also allows added feedback resistors (R3and R4) but does not use them if unity gain is requested.This allows even fewer parts if gain is not needed.

This filter is tuned by adjusting R1 shown in the schematicabove.

The user may specify a single value for uniform capacitorsin this filter; however, if the value specified for the capaci-tors is too small, A/FILTER will be unable to set bothcapacitors to the same value. If this occurs, you maysimply specify a larger value for the capacitance.

FILTER

C1

?47000 pF

R1

680.76 ohm

C2

47000 pF

R2

558.2 ohm Q1

R3

1000 ohm

R4

1000 ohm

68 A/FILTER Types

HIGHPASS ALL POLE MULTIPLE FEEDBACK

The multiple feedback filter uses few parts, and providesgain without additional components. This type requiresone less component than the single feedback type withgain.

Two capacitors per section are selected arbitrarily (C1 andC3 in the schematic above). Resistor R1 is used to tunethis filter.


FILTER

C1

100 pF

R1

?5627 ohm

C2

200 pF

Q1

R2

22508.2 ohm

C3

100 pF

A/FILTER Types 69

HIGHPASS ALL POLE LOW SENSITIVITY

The low sensitivity realization uses two op-amps per polepair,but has a low sensitivity to the op-amp open loop gain.

This topology allows one capacitor per section (C1 in theschematic above) to be chosen. Resistor R2 on the sche-matic is used to tune the response. This type has a lowsensitivity to differences in op-amp open loop gain be-tween sections, but requires the two amplifiers per sectionto have similar characteristics. Usually, op-amps on adual or quad package will have closely matched, if notidentical, operating parameters.

This topology does not allow gain.

FILTER

C1

560 pF

Q1C2

280 pF

R1

4019.3 ohm

Q2

R2

?4019.3 ohm

70 A/FILTER Types

HIGHPASS ALL POLE VCVS

The VCVS has three user specifiable components in eachsection: capacitor C1, and resistors R2 and R3 on theschematic above.

This filter is tuned using resistor R4 shown on the sche-matic above. There is a high sensitivity to componenttolerances in this structure.

Gain is specifiable for odd order filters with this topology.Even order filters have a set gain of 6.02dB per section.

FILTER

C1

560 pF

C2

280 pF

R1

4019.3 ohm

Q1R2

10000 ohm

R3

10000 ohm

R4

?4019.3 ohm

A/FILTER Types 71

HIGHPASS ALL POLE STATE VARIABLE

The state variable filter is best known for its tunability.This type contains many parts per section, but everyaspect of the filter response is tuned directly. This gives alarge degree of freedom for component tolerances.


The state variable structure allows user specifiable uni-form capacitors throughout the entire circuit as well astwo resistors per section (R4 and R5 in the above sche-matic).



FILTER

R1

10000 ohm

R2

5115.5 ohm

Q1R3

7234.4 ohm

Q2

C1

220 pF

R4

10000 ohm

Q3

R5

10000 ohm

R6

?7234.4 ohm

R7

?5115.5 ohm

C2

220 pF

R8

10000 ohm

R9

14142.1 ohm

Q4

R10

?10000 ohm

72 A/FILTER Types

HIGHPASS ELLIPTIC MINIMUM INDUCTOR

This type is a direct LC transform. This topology is par-ticularly useful when low sensitivity is needed. See Ap-pendix E for a complete discussion of GIC transforms.

This filter is insensitive enough to component tolerancesthat tuning is not usually needed. However, the cutofffrequency is tuned by adjusting the grounded resistor ineach GIC (R4). Capacitor C2 is tuned to adjust the zerofrequency.

The user may choose a value for capacitors and resistors.For equal termination filters (e.g. Butterworth and odd-order Chebyshev) all capacitors have the same value.



FILTER

C1

13611.5 pF

C2

?452233 pF

R1

1000 ohm

R2

1000 ohm

Q2

Q1

R3

1000 ohm

C3

1000 pF

R4

?112.89 ohm

C4

13611.5 pF

A/FILTER Types 73

HIGHPASS ELLIPTIC VCVS

The VCVS uses uniform capacitors throughout the struc-ture. There is also one user selectable resistor per section(R5 on the above schematic).

This type has a low sensitivity to component tolerances,and does not usually require tuning. However, the filteris tuned using the resistors R1 and R4 shown on theschematic above.


FILTER

R1

?27437.3 ohm

C1

500 pF

R2

13718.6 ohm

C2

500 pF

R3

27437.3 ohm

R4

?2507.4 ohm

Q1

R5

1000 ohm R6

9892.1 ohmC3

1000 pF

C4

1000 pF

Q2

C5

1000 pF

R7

?2570.7 ohm

74 A/FILTER Types

HIGHPASS ELLIPTIC STATE VARIABLE

This type contains many parts per order, but every aspectof the filter response is tuned directly. This gives a largedegree of freedom for component tolerances.


This structure allows user specifiable uniform capacitorsthroughout the entire circuit as well as five resistors persection (R2, R4, R5, R6 and R10 in the schematic above).


1) R6 tunes the cutoff frequency, and the zero frequency.2) R2 tunes the quality of the zero.3) R4 tunes the response Q.4) R5 tunes the passband gain.5) R10 tunes the overall gain.

FILTER

R1

3345.2 ohm

Q1

C1

1000 pF

R2

?1000 ohm

R3

1000 ohm

R4

?3345.2 ohm

R5

?2867.7 ohm

R6

2867.7 ohm

Q2

C2

1000 pFR7

1000 ohm

R8

1000 ohm

Q3

R9

?896.43 ohm

Q4

R10

?1000 ohm C3

1000 pF

Q5

C4

1000 pF

R11

?2570.7 ohm

A/FILTER Types 75

BANDPASS ALL POLE TOP C

The top C transform type is a direct GIC transformationfrom the top C coupled LC filter. See Appendix E for acomplete discussion of the GIC transform.

There are three resistors and one capacitor per sectionthat are user specifiable: R1, R2, R3 and C2 in the sche-matic above. This type has fewer resistors per sectionthan the Top L bandpass filter.


This structure does not allow gain.

FILTER

C1

87094.4 pF

R1

1000 ohm

R2

1000 ohm

Q2

Q1

R3

1000 ohm

C2

1000 pF

R4

?350 ohm

C3

481040 pF

C4

103533 pF

76 A/FILTER Types

BANDPASS ALL POLE TOP L

The top L transform type is a direct GIC transformationfrom the top L coupled LC filter. See Appendix E for acomplete discussion of the transform types.

There are three specifiable capacitors and two resistorsper section: C1, C2, C3, R3 and R4 in the above schematic.This type has fewer capacitors per section than the Top Cbandpass filter. For equal termination filters (e.g. butter-worth and odd-order chebyshev) all capacitors have thesame value.

This structure does not allow gain, and there is an inher-ent loss of 6dB.

FILTER

C1

1000 pF

R1

79098.8 ohm

R2

41256.9 ohm

C2

1000 pF

R3

1000 ohm

Q2

Q1

C31000 pF

R4

1000 ohm

R5

?88.889 ohm

R6

79098.8 ohm

C4

1000 pF

A/FILTER Types 77

BANDPASS ALL POLE MULTIPLE FEEDBACK

The multiple feedback filter uses few parts, and providesgain without additional components. This type requiresfewer components than the single feedback type with gain,but more than the single feedback type without gain.

One value is user specified for uniform capacitors withinthis filter.

This type has a high sensitivity to component tolerances.For tuning, refer to the above schematic:

1) Adjust R2 and R3 for the correct cutoff frequencies2) Adjust R1 for the desired gain

FILTER

R1

2053.6 ohm

R2

424.18 ohm

C1

100 pF

Q1

R3

5998.1 ohm

C2

100 pF

R4

1233.4 ohm

R5

254.77 ohm

C3

100 pF

Q2

R6

3602.5 ohm

C4

100 pF

78 A/FILTER Types

BANDPASS ALL POLE MULTIPLE FEEDBACKMAX GAIN

The multiple feedback filter uses few parts, and providesgain without additional components. This type requiresone less component per section than the multiple feedbacktype with controllable gain.

One user specified capacitor value is used.



1) Adjust R2 for the correct lower cutoff2) Adjust R4 for the desired Q and overall gain

FILTER

R1

351.56 ohm

C1

100 pF

Q1

R2

?5998.1 ohm

C2

100 pF

R3

211.15 ohm

C3

100 pF

Q2

R4

?3602.5 ohm

C4

100 pF

A/FILTER Types 79

BANDPASS ALL POLE DUAL AMPLIFIER

The dual amplifier topology allows gain, but has a highsensitivity to component tolerances.

This filter is tuned by adjusting R1 and R7 shown in theschematic above. These resistors act together to tune thehigh and low sides of the response.

If R2 is tuned up to a standard value, R6 should be tuneddown by the same percentage. Conversely, if R2 is tuneddown to a standard value, R6 should be tuned up by thesame percentage.

Resistors R4 and R5 must be nearly equal and thereforemay require small tolerance parts. If they differ too much,the response may not be recoverable by the suggestedtuning method. In this case, R6 in the first section is tunedto correct the filter response.

FILTER

R1

3455.6 ohm

R2

1452.1 ohm

R3

22697.3 ohm

C1

100 pF

Q1

R4

10000 ohm

R5

10000 ohm

R6

1452.1 ohm

C2

100 pF

Q2R7

2075.5 ohm

R8

872.17 ohm

R9

13632.2 ohm

C3

100 pF

Q3

R10

10000 ohm

R11

10000 ohm

R12

872.17 ohm

C4

100 pF

Q4

80 A/FILTER Types

BANDPASS ALL POLE DUAL AMPLIFIER MAXGAIN

The dual amplifier maximum gain type requires one lessresistor per section than the standard dual amplifier filter.This topology allows gain, but has a high sensitivity tocomponent tolerances.

This filter is tuned by adjusting R1 and R6 shown in theschematic above. In general, the bandpass types exhibitsymmetry.

Within each stage, if resistors R2 and R5 in the schematicabove are to be set to standard values, one should be tunedup while the other is tuned down. This will correctlyadjust the response.

If R3 and R4 differ in the constructed filter, the responsemay not be recoverable by the suggested tuning method.In this case, R6 in the first section is tuned to correct thefilter response.

FILTER

R1

2999 ohm

R2

1452.1 ohm

C1

100 pF

Q1

R3

10000 ohm

R4

10000 ohm

R5

1452.1 ohm

C2

100 pF

Q2R6

1801.3 ohm

R7

872.17 ohm

C3

100 pF

Q3

R8

10000 ohm

R9

10000 ohm

R10

872.17 ohm

C4

100 pF

Q4

A/FILTER Types 81

BANDPASS ALL POLE LOW SENSITIVITY

This type has a low sensitivity to op-amp characteristics.It uses generalized impedance converters, and exhibitsbetter behavior at high frequencies than the dual ampli-fier type. However, it requires one more op-amp per sec-tion. This type has a low sensitivity to differences inop-amp open loop gain between GIC sections, but requiresthe two amplifiers per section to have similar charac-teristics. Usually, op-amps on a dual or quad package willhave closely matched operating parameters.

This filter is tuned by adjusting the grounded resistor ineach section (R5 in the above schematic).

Gain is allowed in this filter.

FILTER

R1

2999 ohm

R2

1452.1 ohm

R3

1452.1 ohm

Q2

Q1

R4

1452.1 ohm

C1

100 pF

R5

?1452.1 ohm

C2

100 pF Q4

R6

10000 ohm

R7

5848.9 ohm

R8

1801.3 ohm

82 A/FILTER Types

BANDPASS ALL POLE STATE VARIABLE

The state variable filter is best known for its tunability.This type contains many parts per section, but everyaspect of the filter response is tuned directly. This gives ahigh degree of freedom for component tolerances.


The state variable structure allows user specifiable uni-form capacitors throughout the circuit as well as tworesistors per section (R3 and R4 in the above schematic).



FILTER

R1

?1295.7 ohm

Q1R2

1452.1 ohm

Q2

C1

100 pF

R3

10000 ohm

Q3

R4

10000 ohm

R5

?1452.1 ohm

R6

?2999 ohm

C2

100 pF

A/FILTER Types 83

BANDPASS ELLIPTIC VCVS

This type has one user selectable resistor per section (R5on the above schematic).

R1 is used to adjust the cutoff frequency, whereas R4 isused to tune the response Q.


FILTER

R1

?33170.6 ohm

C1

2350 pF

R2

16585.3 ohm

C2

2350 pF

R3

33170.6 ohm

R4

?13612.9 ohm

Q1

R5

10000 ohm R6

31931.9 ohmC3

4700 pF

84 A/FILTER Types

BANDPASS ELLIPTIC STATE VARIABLE

This type contains many parts per order, but every aspectof the filter response is tuned directly. This gives a highdegree of freedom for component tolerances.


This structure allows user specifiable uniform capacitorsthroughout the entire circuit as well as four resistors persection (R2, R3, R7 and R8 in the schematic above).


1) Adjust R2 to tune the quality of the zero2) Adjust R15 to tune the response Q.3) Adjust R10 to tune the overall gain.

FILTER

R1

4201.4 ohm

Q1

C1

100 pF

R2

?10000 ohm

R3

10000 ohm

R4

?4201.4 ohm

R5

?1974.3 ohm

R6

1974.3 ohm

Q2

C2

100 pFR7

10000 ohm

R8

10000 ohm

Q3

R9

?5100.4 ohm

Q4

R10

?5013.5 ohm

A/FILTER Types 85

BANDSTOP ALL POLE VCVS

This type has one user selectable resistor per section andone capacitor per section (R5 and C4 on the schematic).

This filter is tuned by adjusting resistor R1 shown on theschematic above. There is a high sensitivity to componenttolerances in this structure.

Gain is available for odd order filters with this topology.

FILTER

C1

40.042 pF

R1

?2417.6 ohm

C2

20.021 pF

C3

22.222 pF

R2

?2178.2 ohm

R3

4356.3 ohm

R4

?10879.4 ohm

Q2R5

10000 ohm

R6

11510.7 ohm

C4

100 pF

86 A/FILTER Types

BANDSTOP ALL POLE STATE VARIABLE

The state variable filter is best known for its tunability.This type contains many parts per section, but everyaspect of the filter response is tuned directly. This gives ahigh degree of freedom for component tolerances.


The state variable structure allows user specifiable uni-form capacitors throughout the entire circuit as well asfour resistors per section (R2, R3, R7 and R8 in the aboveschematic).


1) Adjust R5 and R9 for the correct zero frequency2) Adjust R4 for desired Q3) Adjust R10 for desired overall gain

FILTER

R1

2999.2 ohm

Q1

C1

100 pF

R2

?10000 ohm

R3

10000 ohm

R4

?2999.2 ohm

R5

?1452.1 ohm

R6

1452.1 ohm

Q2

C2

100 pFR7

10000 ohm

R8

10000 ohm

Q3

R9

?7281.7 ohm

Q4

R10

?15848.9 ohm

A/FILTER Types 87

Filter Type Tunability Simplicity Insensitivity

LOWPASS

ALL

POLE

Minimum Inductor 3 3 10

Minimum Capacitor 3 4 10

Single Feedback 5 6 2

Multiple Feedback 5 5 2

Low Sensitivity 7 3 5

VCVS 5 3 5

State Variable 10 1 8

EL

Minimum Capacitor 3 4 10

VCVS 5 4 5


HI

GHPASS

ALL

POLE

Minimum Inductor* 3 4 10

Minimum Capacitor* 3 3 10

Single Feedback 5 6 2



VCVS 5 4 5


EL

Minimum Inductor* 3 4 10

VCVS 5 3 5


BANDPASS

ALL

POLE

Top C* 3 3 10

Top L 3 1 10


Multiple Fb, Max Gain 5 4 2

Dual Amplifier 5 1 2

Dual Amplified, Max Gain 5 1 2



EL

VCVS 5 4 5


BS

AP

VCVS 5 4 5


*Starred filters provide power gain (S21) and use finite termination impedances.All other filters provide voltage gain (E21) unless Zo matching buffers are added.The circuit file defaults should be changed accordingly.

88 A/FILTER Types

Chapter 6

A/FILTER Examples

I n this chapter, some helpful tips are presented withpractical examples using filters designed by A/FILTER.All were built and the results of the actual measure-

ments are presented along with the SuperStar simulation.

EXAMPLE 1 - LOWPASS MINIMUM INDUCTOR

The following files are used in this example:

AFEX1.AF$ Initial design

AFEX1.SCH/CKT Circuit file written out by A/FILTER

A third order lowpass minimum inductor Chebyshev filterwith 0.1 dB ripple and a 10 kHz cutoff is designed andsimulated with µA741 op-amps. Measured results areincluded. The A/FILTER design screen is shown in Figure6-1.

This filter is designed using LC/GIC transforms. For moreinformation on LC/GIC transforms, see Appendix E. Inthis particular filter, the transform yields a circuit thatdoes not have a DC path to ground. This results in possiblerailing of bias voltages. To compensate, A/FILTER auto-matically includes a 100kΩ resistor to ground at theoutput. This will work fine, as long as 100kΩ is largecompared to the impedance of the output capacitor withinthe filter passband. If it is not, the parallel combinationof the shunt resistor and capacitor may cause a mismatch

at the load. Therefore, if small valued capacitors must beused, the output resistor may need to be increased torestore the filter response.

There is an inherent loss of 6dB in this filter type. If yourapplication requires no loss or requires gain, this can beachieved by the use of an output buffer. Output bufferingis setup from the Setup menu, Preferences Window. Onceenabled, the main A/FILTER window will have an inputcell for gain to control the gain of the output buffer.

Tuning the grounded resistor in each “D element” (R3 andR7 in the schematic above) directly affects the cutofffrequency. The “D elements” are independent enough thatusually only one resistor needs to be adjusted unless awide tuning range is needed.

This type is very sensitive to op-amp bandwidth. With a1 MHz bandwidth amplifier, a 10 kHz filter may start to

Figure 6-1 A/FILTER Screen For Example 1 ( AFEX1.AF$)

90 A/FILTER Examples

experience rolloff prematurely. This can usually be fixedby optimization within SuperStar.

A/FILTER automatically writes an optimization block intothe circuit or schematic file. Several components withineach filter type are marked for tuning and/or optimization.These parts can be used to tune the filter response back ifother components are set to standard values, or varyslightly due to tolerances. (This will be illustrated inExample 4.)

Figure 6-2 shows the predicted and measured responses.The circles show the response when using 347 op-amps (3MHz bandwidth), while the triangles show the responsewhen using µA741 op-amps (1 MHz bandwidth).

Figure 6-2 Predicted and measured responses for Example 1.The solid, predicted response is contained in AFEX1.CKT/SCH.The circles show the constructed filter using LF347 op-amps. Thetriangles show the constructed filter using µA741 op-amps.

A/FILTER Examples 91

A final note on this filter type is that, even though it is alowpass type, it will not actually pass DC due to the seriescapacitor at the input. If your application needs to passDC, then a large resistor can be added in parallel to theinput capacitor. The proper resistor value must be deter-mined experimentally in SuperStar, but is generally in theneighborhood of a 100kΩ. If the value is too large, it willhave no effect; if it is too small, the filter will have gain atDC.

EXAMPLE 2 - LOWPASS MINIMUM CAPACITOR



AFEX2.SCH/CKT Circuit file written out by A/FILTER

A fifth order lowpass minimum capacitor Chebyshev filter

Figure 6-3 A/FILTER Screen For Example 2 (AFEX2.AF$)


with 0.1dB ripple, 0.1dB Aa, and a 5 kHz cutoff frequencyis designed and tested with µA741 op-amps. The A/FIL-TER design screen is shown in Figure 6-3.

Resistors R4 and R8 can be used to completely tune theresponse to a different cutoff frequency. This filter is veryinsensitive to component tolerances, but fairly sensitive toop-amp bandwidth.

This type of filter has an inherent loss of 6dB within thepassband. The circuit in Figure 6-3 was initially con-structed with 5% parts, and the response was 6.5dB downin the passband. All resistors and capacitors were re-placed with 1% parts, and the new attenuation was 5.9dB.

Figure 6-4 shows the predicted and measured responsesfor example 2.

Figure 6-4 Predicted and Measured Responses For Example 2.The solid, predicted response is contained inAFEX1.CKT/SCH.The circle trace shows the measured response.


EXAMPLE 3 - LOWPASS SINGLE FEEDBACK


AFEX3.AF$ Initial design (see Figure 6-5)

AFEX3A.SCH/CKT Circuit file as written out by A/FILTER

AFEX3B.SCH/CKT Circuit file after putting parts onstandard values and optimizing

the filter response using SuperStar

AFEX3T1.SCH/CKT Output of probe from first sectiondemonstrate the tuning process)

AFEX3T2,AFEX3T3.SCH/CKT Output of probe from second andthird sections.

An eighth order single feedback lowpass Chebyshev filterwith 0.1dB ripple, 0.1dB Aa and 10 kHz cutoff with 0dBgain is designed, simulated, and measured. The A/FIL-TER screen is shown in Figure 6-5.



This filter was designed with non-ideal op-amp parame-ters. In SCHEMAX, all non-tuned parts were placed onavailable values, and SuperStar then optimized the re-sponse to compensate. Figure 6-6 shows a plot of thepredicted response of this filter. The solid trace shows theoptimized response using LF347 op-amp parameters. Thedotted trace shows the same circuit response, except thatnear-ideal op-amp parameters were added. The “ideal”response starts to roll-off prematurely, while the “non-ideal” response behaves as expected. This illustrates thenecessity to correct for non-ideal elements.

AFEX3A.SCH was written from A/FILTER. All non-tunedcomponents were set to standard values and the file wasoptimized in SuperStar to correct for the non-ideal com-ponents and for the standard values. The final responseas shown in Figure 6-6 is contained in AFEX3B.SCH.

This filter was tuned in stages. After optimizing the

LF347 Op-AmpsLF347 Op-Amps

Ideal Op-AmpsIdeal Op-Amps

Figure 6-6 Example 3 Response Using Real And IdealOp-Amps


overall response, the output node was moved from theoutput of the filter to points between each stage to allowSuperStar to show the calculated response for that stage.When the filter was constructed, each stage was tuned byreferring to these cumulative responses.

Figure 6-7 shows the filter schematic modified to give thefirst stage response. The output of each successive stagewas probed in the same way to obtain the individualresponses. Note that when the second and third stageswere probed that the responses are actually the cumula-tive response from all previous stages. The output of thefourth stage is, of course, the complete output of the filter.The responses from probing the output of each of the foursections are shown in figures 6-8, 6-9, 6-10 and 6-11,respectively.

FILTER

R1

?926.55 ohm

C1

247000 pF

R2

1000 ohm

C2

1000 pF Q1

R3

?6470.27 ohm

C3

47000 pF

R4

1000 ohm

C4

1000 pF Q2

R5

?19675.9 ohm

C5

30000 pF

R6

1000 ohm

C6

1000 pF Q3

R7

?70896.4 ohm

C7

23500 pF

R8

1000 ohm

C8

1000 pF Q4

FIRST SECTION OUTPUT

CONTRACT NO.

DWN

ENGR

CHK

PROD

APVD

APVD

Eagleware Corporation(404) 939-0156=A/FILTER= Example 3

AP Lowpass Single Feedback

10kHz,AMin=50

A 3 T1SIZE DWG NO. REV

SHEET 1 OF 1

Figure 6-7 First Section Output For Example 3(AFEX3T1.SCH/CKT)


Figure 6-8 Section 1 Response (AFEX3T1.SCH/CKT)



Figure 6-11 Overall Response for Example 3


The input level should be kept low, since the first sectionprovides almost 20dB of gain near the cutoff (see Figure6-8). If the input level gets too large, the second and thirdsections can saturate, destroying the response. If the filtermust handle larger signal levels, then the “Reverse orderof poles" option in the Setup Menu, Preferences windowshould be toggled. In this example, the Reverse orderoption was set.

EXAMPLE 4 - LOWPASS MULTIPLE FEEDBACK



AFEX4B.SCH/CKT Circuit file after putting parts onstandard values and optimizing the

filter response using SuperStar

A fifth order lowpass multiple feedback Chebyshev filterwith a 10kHz cutoff, 0.1dB ripple and 0.1 Aa is designed



and simulated with µA741 op-amp parameters. Figure6-12 shows the A/FILTER design screen. This filter shouldbe tuned as in Example 3 by placing the output betweensections and tuning them separately.

In this example, all the capacitors were set to standardvalues, and the response was tuned using the resistors.

Element Tuning Effects:R1 - adjusts gain with minimal perturbation of the responseR4 & R5 - flattens gain, but cannot fix cutoff frequencyR3 - adjusts gain of filter but distorts responseR6 - redundant adjustment of R4 & R5. Only adjust if cap val-ues are changed drastically.

R2, R4, R5 and R6 were optimized since the capacitorswere changed drastically. Once optimized, only R2,R4 andR5 were adjusted on the bench.

FILTER

R1

4700 ohm

C1

47000 pF

R2

?1897.88 ohm

Q1

C2

470 pF

R3

4700 ohm

R4

820 ohm

C3

47000 pF

R5

?1089.24 ohm

R6

?1663.66 ohm

C4

4700 pF

C5

47000 pFQ2

CONTRACT NO.

DWN

ENGR

CHK

PROD

APVD

APVD

Eagleware Corporation(404) 939-0156=A/FILTER= Example 4

AP Lowpass Multiple Feedback

Chybyshev, 10kHz

A 4 BSIZE DWG NO. REV

SHEET 1 OF 1

Figure 6-13 Schematic for Example 4 After Optimization(AFEX4.SCH)


Figure 6-13 shows the final schematic with standard valuecaps and optimized resistor values.

EXAMPLE 5 - BANDPASS MAXIMUM GAIN DUALAMPLIFIER

The following files are used in this example:AFEX5.AF$ Initial design


AFEX5B.SCH/CKT Circuit file after putting parts on standard values andoptimizing the filter response using SuperStar

A fourth order bandpass dual amplifier Chebyshev filterwith 0.1dB ripple and 0.1 Aa is designed, simulated, andmeasured with µΑ741op-amps. Figure 6-14 shows theA/FILTER design screen.

This filter should be tuned by probing between sectionsand tuning the sections individually. The filter responsecan be completely tuned by adjusting the series resistorsbetween sections.

Figure 6-14 A/FILTER Screen for Example 5 (AFEX5.AF$)


The predicted and actual (measured) responses for thisexample are shown in Figure 6-15.

Figure 6-15 Predicted and Measured Responses For Example5 (AFEX5B.SCH/CKT)


Chapter 7

M/FILTER Menus

M /FILTER is launched by starting GENESYS andthen selecting M/FILTER from the Synthesis menu(top of the screen). Other GENESYS supported

simulators such as Touchstone and Spice simulators areless well suited for distributed filters than they are forother circuits. These simulators do not have certain mod-els required for many distributed filters and reducedfunctionality may result if SuperStar is not used.

OVERVIEW OF THE M/FILTER SCREEN

A sample M/FILTER screen is shown in Figure 7-1. Thisis a typical M/FILTER display with the Menu bar, currentfilter layout, procedure flowchart with selectable options,and user-specified filter parameters.

USING THE PROCEDURE FLOWCHART

In Figure 7-1, nine buttons are shown on the left side ofthe screen. These buttons are arranged in a flowchartpattern, with arrows to suggest the next step.

M/FILTER and SuperStar manage the entire design pro-cedure from “Start-to-Art.” Procedures are launched andthe current status is indicated by this flowchart whichcontains selectable buttons. The basic design flow is asfollows:

• Start by selecting a filter type

• Choose filter parameters in an interactive session whileobserving the on-screen layout

• Write a circuit file and run SuperStar

• Analyze, tune and optimize the responses in SuperStar

• Return to M/FILTER from the Shell menu in SuperStar

• Load modified values from SuperStar into M/FILTER

• Finalize layout information in a limited interactive mode

• Plot the layout to printer or disk file.

Two procedure buttons automatically illuminate duringM/FILTER execution. If Auto Recalc is set, when a filterparameter is modified the Calc button illuminates redwhile the new design and layout are recalculated, andthen grays at completion. If Auto Recalc is not set, whena filter parameter is entered the Calc button stays illumi-nated and synthesis algorithms are not invoked until you

Figure 7-1 Sample main M/FILTER screen

104 M/FILTER Menus

press F6 or press the Calc button. The Absorb buttonilluminates when parasitics are being absorbed by thesynthesis algorithms.

These procedures are highly automated by the M/FILTERprogram environment and the procedure flowchart. Sim-ply follow the arrows until the design is complete.

MENU BAR

To activate the menu bar, hold the Alt key while pressingthe underlined letter of the menu item that you desire.Once the menu is selected, the arrow keys highlight theavailable menu items. Press Enter to select the desireditem once it has been highlighted. With a mouse, simplyclick on the target menu item. The menu bar has six mainmenus: File, Type, Schematic, Layout,Utilities,and Setup.

FILE MENU

Press Alt-F to select the File menu. The options listed are

NewOpen FileSaveSave AsWrite CKT/SCH FileLoad Values From CKT/SCH FilePrint ScreenPrint WindowExitAbout

The New option begins a new filter. M/FILTER promptsfor the type of filter to use, as well as the shape of the filter,and the process to use for the final layout. If the currentfilter has not been saved since the last modification,M/FILTER prompts before continuing.

All the data displayed on the screen and other informationwhich defines a particular filter are stored in files with a

M/FILTER Menus 105

default extention .MF$. The Open File option loads apreviously saved filter. Do not confuse these files withcircuit description files written for SuperStar which havethe default extension .CKT or schematic description fileswith the default extension .SCH.

The Save option saves the current filter data using thecurrent filename. If the filter has not been previouslysaved, or a filename has not been assigned,M/FILTER willprompt for one. The F2 beside Save in the menu simplymeans that the filter can be saved by pressing F2, ratherthan selecting the menu each time.

The Save As option saves under a new filename, or assignsa filename to a new filter file.

The Write CKT/SCH File option writes SuperStar circuitor schematic files, which can be loaded into SuperStar foroptimization.

The Load Values From CKT/SCH File option loads valuesfrom a previously saved circuit or schematic file. This alsoreplaces any current values that may have been optimizedusing SuperStar.

The Print Screen option dumps the entire screen to aprinter. Pressing Alt-F7 also selects this option.

The Print Window option dumps only the current windowto the printer. Pressing Alt-F8 also selects this option.

Choosing Exit (Return to SuperStar) will exit M/FILTERand return to the SuperStar environment. Selecting Exitto DOS or Exit to Windows will return to the operatingsystem.

The About option displays the Eagleware copyright noticeand the amount of available conventional memory.

106 M/FILTER Menus

TYPE MENU

Press Alt-T to select the Type menu. The options listedare:

TopologyShapeProcess

The Type menu options change particular filter charac-teristics without restarting the whole design.

The Topology option selects the general type of filter todesign (combline, hairpin, elliptic lowpass, etc.).

The Shape option selects the transfer function approxima-tion shape of the filter (Butterworth, Chebyshev, etc.)

The Process option selects the construction process usedfor the filter layout (Coaxial, Stripline, etc.)

SCHEMATIC MENU

Press Alt-C to select the Schematic menu. The optionslisted are:

Display ElectricalDisplay Phsical

The Schematic menu displays the current schematic(either the electrical or the physical version) in the sche-matic box.

The Display Electrical and Display Physical options select(Check mark is shown), or deselect the display options.

LAYOUT MENU

Press Alt-L to select the Layout menu. The options listedare:

Display LayoutPlot Layout

M/FILTER Menus 107

Write DXF FileWrite Viahole List

The Layout menu plots the current filter layout, displaythe layout, write a DXF format display file, and write aviahole data file.

The Display Layout option selects (Checkmark is shown),or deselects the layout display option.

The Plot Layout option plots the filter layout using aprinter or plotter.

Most options in the print/plot dialog box are self-explana-tory. Outlines only causes the output to not be filled in(useful for RubyLithe). Film Negative causes the file tobe plotted as white on black. A non-zero etch factor causesall traces to be wider by the amount given. A negative etchfactor is legal and may be useful to compensate for“spreading” when using a laser printer to print transpar-encies. The etch factor uses the units set up in theSetup/Units window.

The Write DXF File option writes a DXF format graphicsfile that is readable by many drawing packages. TheLayers and Colors subwindow customizes the DXF layersand line colors used in the DXF file. The etch factor isidentical to the etch factor described above for the Plotoption.

The Write Viahole List writes a file containing viaholecoordinates relative to a point that you choose.

UTILITIES MENU

Press Alt-U to select the Utilities menu. The optionslisted are:

N-HelpShow G-ValuesEdit G-Values

108 M/FILTER Menus

Show ErrorsRecalculateView Electrical VariablesView Physical Variables

The N-Help option assists in determination of the requiredorder to meet specific passband and stopband require-ments. This feature can be used prior to beginning thedesign process, and the filter should be one order higherthan suggested by N-Help.

The Show G-Values option shows the current filter’s G-Values.

The Edit G-Values option allows editing of G-Value diskfiles for user customized transfer approximations.

The Show Errors option shows all the errors accumulatedduring the last calculation.

The Recalculate option recalculates the filter layout andschematic based on the current parameters.

The View Electrical Variables option shows the values ofall the variables used in the electrical calculations.

The View Physical Variables option shows the values of allthe variables used in the physical filter model calcula-tions.

SETUP MENU

Press Alt-S to select the Setup menu. The options listedare:

Auto RecalcCapacitorsCross Hair SetupOutput BlockUnitsViaholes

M/FILTER Menus 109

The Setup menu allows setup of automatic recalculation,capacitor dimensions, layout window cross hairs cus-tomzation, SuperStar output format, length units, andviaholes configuration.

The Auto Recalc option selects manual or automatic recal-culation. In the manual mode, press F6 or the illuminatedCalc button each time filter parameters are changed. Inthe automatic mode the synthesis algorithms are auto-matically invoked each time a change is made. AutoRecalc is suggested for fast computer systems while man-ual recalculation saves waiting time each time a parame-ter is changed on slower machines.

The Capacitors option specifies the length of lumped ca-pacitors used in the layout as defined by the edge-to-edgeseparation of lines leading up to the capacitor.

The Cross Hair Setup option customizes the appearanceof the viahole cross hairs on the layout. To completelyremove the cross hairs from the layout, deselect each crosshair box. The auto size option forces the right and bottommargins to be equal to the left and top margins, respec-tively. Negative margins are legal and are often useful onthe left and right to allow extra lead line which will laterbe cut off.

The Output Block option selects the default format forCKT/SCH files. For example, to see a polar response plot,select POL, a display parameter and the desired polarchart radius. When SuperStar circuit files are written byM/FILTER, the parameters selected are used to set-up thedisplay window. Options are described in more detail inthe SuperStar manual.

The Units option specifies what units to use in the boardlayout. All lengths and displacements use the units cho-sen in this window.

110 M/FILTER Menus

The Viaholes option customizes the dimensions of theviaholes. Viaholes are only taken into account for micros-trip circuits.

LAYOUT WINDOW

The layout/schematic window shows the filter during thedesign process. The layout shown is exactly what the finalboard will look like. To view a schematic or layout, selectSchematic/Display Electrical, Schematic/Display Physi-cal, or Layout/Display Layout in the menu. The cursor inthe window displays current coordinates as a relativedistance from an origin that has been selected. To selecta new origin, click the mouse button at the desired loca-tion.

TUNING PARAMETERS

A tune percentage is shown on the bottom of the screen.The tuning percentage is increased by pressing F7 anddecreased by pressing F9. When in a parameter cell,increase/decrease a number by pressing Page Up/PageDown. The number is changed by the percentage shown.

M/FILTER Menus 111

Chapter 8

M/FILTER Operation

The following design example demonstrates the M/FIL-TER design process. In this example, we will design astepped lowpass filter with a cutoff frequency of 2 GHz.

Run M/FILTER by shelling from SuperStar. When theM/FILTER screen appears, click on the New Start buttonto choose a new filter type. Select Stepped Lowpass fromthe Topology screen and press Enter twice, or click on theOK button. Next, select Chebyshev from the Shape screenand click the OK button. Choose Microstrip as the filterprocess, and click OK. This completes the first step in theflowchart. Notice that the flowchart shows your progress,with interactive now highlighted.

ENTERING PARAMETERS

Tab to the Shape box, or click on one of the boxes in thegroup and enter the following numbers:

Order:7Fc, MHz:2000Ripple:0.0432Rin:50

Where Order is the desired order of the filter, Fc is thecutoff frequency in MHz, Ripple is the maximum rippleallowed, and Rin is the desired input resistance.

For this type of filter, the output resistance is uniquelydefined by the input resistance and the specified parame-ters. Move to the Topology box and enter the following:

Zmin:20Zmax:120

Zmin is the minimum impedance you feel is practical andZmax is the maximum impedance you feel is practical.More extreme values result in more ideal responses beforeoptimization and better stopband performance.

Now, move to the Microstrip box and enter these numbers:

εr: 2.55Tanδ: 0.0004Rho: 1Tmet: 0.71Rough: 0.055H: 31Lead: 100

εr is the dielectric constant, Tanδ is the dielectric losstangent, Rho is the resistivity (ρ), Tmet is the thickness ofthe metallization used, Rough is the metallization rough-ness,H is the height or thickness of the dielectric substratematerial, and Lead is the desired length of the filter leads.

Note: All lengths or displacements default to theunits specified in the Setup/Units menu option.

You have now told M/FILTER that you wish to design aseventh-order stepped low-pass filter, with a cutoff at 2GHz. This completes step two of the flowchart.

Now click the Calc button (or press F6). If you haveselected Show Layout in the Layout menu, a filter layout

114 M/FILTER Operation

appears on your screen. If the previously indicated pa-rameters were entered, the Show Errors box should beshown in gray. If the box is illuminated, check all parame-ter values. This completes step three of the flowchart.Your screen should now look similar to Figure 8-1.

Select the Write CKT button to save your filter in aSuperStar format. Choose Electrical CKT File and pressthe OK button. Type FIRST in the File box and pressEnter to name your circuit. Now, select Run SS to shell toSuperStar for analysis and optimization of the new filter.

USING SuperStar WITH M/FILTER

SuperStar computes and displays the plots that you se-lected in M/FILTER. Notice that S21 is plotted using theleft grid (using two different scales for the two traces) andS11 is plotted using the right grid. The cutoff frequencyis shown center-graph by default. Choose “Automatic”

Figure 8-1 Stepped-Z lowpass M/FILTER example screen.

M/FILTER Operation 115

from the Optimize menu to begin optimizing the electricalline lengths displayed near the bottom of the screen.

The dotted lines indicate the frequency response using thenewest optimized values. After several rounds, improve-ment halts. Press ESCAPE to stop the optimization. Thescreen should look similar to Figure 8-2. The plots nowreflect the optimized line lengths.

Important Note: This run was an electrical circuit anddoes not contain physical dimensions or losses. Since wewill do a physical circuit next, select Run M/FILTER fromthe Synthesis menu to return to M/FILTER and selectInteractive from the flowchart.

ELECTRICAL OR PHYSICAL?

M/FILTER now contains SuperStar optimized electricalline lengths. The next step is to create a SuperStar circuitfile using physical microstrip elements which accuratelymodel line loss, dispersion and discontinuities.

At this point a physical CKT or SCH file should be written.Note that SuperStar can optimize both electrical andphysical circuit parameters.

Select Write Physical CKT file from the Write CKT/SCHitem of the File menu, type FIRSTPHY for the filenameand run SuperStar. When SuperStar computes and dis-plays the response for the microstrip lowpass, press F3 tobegin optimization of the physical line lengths.

Notice the analysis and optimization of the physical modelis slower than optimization of the electrical description ofthe circuit. This is because the physical elements whichaccurately model microstrip behavior are quite complex.


NOTE: Physical circuits should be used in most cases.

WRITING DXF/GERBER FILES

Starting with Version 7, M/FILTER should no longer beused to create a layout. Instead, follow these steps:

Figure 8-2 SuperStar computed responses for the stepped-Zlowpass created by M/FILTER and optimized by SuperStar.


‘ FILE: TEST.CKT‘ TYPE: Stepped — Lowpass‘ Fc: 3000 MHz‘ PROCESS: MicrostripCIRCUITSUB ER=2.55 TAND=0.0004& RHO=1 TMet=0.71 ROUGH=0.06& UNITS=0.0254

MLI 1 2 W=WI H=H L=LIMST 2 3 O=SY NAR=WI W=Whi H=HMLI 3 4 W=Whi H=H L=L1MST 4 5 O=SY NAR=Whi W=Wlo H=HMLI 5 6 W=Wlo H=H L=L2MST 6 7 O=SY NAR=Wlo W=Whi H=HMLI 7 8 W=Whi H=H L=L3MST 8 9 O=SY NAR=Whi W=Wlo H=HMLI 9 10 W=Wlo H=H L=L4MST 10 11 O=SY NAR=Wlo W=Whi H=HMLI 11 12 W=Whi H=H L=L5MST 12 13 O=SY NAR=Whi W=Wlo H=HMLI 13 14 W=Wlo H=H L=L6MST 14 15 O=SY NAR=Wlo W=Whi H=HMLI 15 16 W=Whi H=H L=L7MST 16 17 O=SY NAR=Whi W=WOUT H=HMLI 17 18 W=WOUT H=H L=LOUTDEF2P 1 18 FILTEREQUATEH=31WI=85.793LI=100Whi=18.2333Wlo=411.155L1=?179.984L2=?115.275L3=?402.531L4=?122.968L5=?402.531L6=?115.275L7=?179.984WOUT=85.793LOUT=100WINDOW FILTER(50,50)GPH S21 -5 5GPH S21 -100 0GPH S11 -40 0GPH DLY 0 40FREQSWP 0 6000 101OPT0 3000 S11<-1004500 6000 S21<-30

Table 8-1 7th-order stepped-z lowpass CKT file


1. Write a physical Circuit file

2. From GENESYS,create a layout (Right-click on Designsin the workspace tree)

3. Choose Edit/Select All

4. Choose Layout/Connect Selected Parts

5. Choose File/Export/Gerber or DXF

[This section intentionally left blank.]


SELECTING OUTPUT OPTIONS

The Output parameters shown in SuperStar can be se-lected in M/FILTER. For example, to view a graph on theleft of S21 and a Smith chart on the right of S11, performthe following steps: Select Setup/Output Block from themenu bar. Click on the 1 button to choose the first plottype. Select GPH from the Type box to choose a rectangu-lar plot (GPH=Graph). Now choose S21 from the Optionsbox. Tab to the Range cells and select -5 to 5. This specifiesa plot of S21 from -5 to 5 dB. Next, click the 2 button andchoose GPH, S21, and -100 to 0. Click the 3 button andchoose SMH (Smith Plot), and S11. Click the 4 button andchoose None under Type. This means that a fourth plotwill not be shown. Now select Close to return to the mainscreen.


EQUATEH=31WI=85.793LI=100Whi=18.2333Wlo=411.155L1=?179.984L2=?115.275L3=?402.531L4=?122.968L5=L3L6=L2L7=L1WOUT=85.793LOUT=100

Table 8-2 Sample minimized equate block for Table 8-1


Chapter 9

M/FILTER Types

M/FILTER synthesizes thirteen filter topologies and sup-ports variations on several of the structures. Access to awide range of filter topologies is important because a giventype is best suited for a given range of applications. Astructure which is ideal for a narrowband bandpass mayyield impractical element values for a moderate band-width requirement. A filter which has desirable realiza-tion attributes may have poor stopband performance.There is no best choice.

These issues are much more critical in the bandpass classthan in the lowpass or highpass. This is why the greatestvariety of types in all Eagleware filter programs are asso-ciated with the bandpass class. The integrated designenvironment of M/FILTER and SuperStar allows quickevaluation of alternative designs to find approaches bestsuited for each application.

M/FILTER types are accessed from the Type/Topologymenu, or by selecting New Start. Available types include:

• Stepped Bandpass

• End Coupled Bandpass

• Edge Coupled Bandpass

• Hairpin Bandpass

• Combline Bandpass

• Interdigital Bandpass

• Elliptic Bandpass

• Stepped Lowpass

• Stub Lowpass

• Elliptic Lowpass

• Stub Highpass

• Direct Coupled Bandstop

• Edge Coupled Bandstop

FILTER SHAPES AND PROCESSES

M/FILTER supports numerous filter transfer approxima-tion shapes and manufacturing processes. Transfer ap-proximations are discussed in Appendix A . Availabletransfer functions are:

Elliptic

• Cauer-Chebyshev, Normal Terminations

• Cauer-Chebyshev, Equal Terminations

• Elliptic Bessel

• Elliptic User File

All-Pole

• Butterworth

• Chebyshev

• Bessel

• Transitional Gaussian to 6 and 12 dB

• Equiripple Phase Error of 0.05 and 0.5o

• Singly-Equalized

• Singly-Terminated Chebyshev & Butterworth

• All-Pole User File

Available manufacturing processes include:

124 M/FILTER Types

• Microstrip

• Slabline

• Stripline

• Coaxial

• General Electrical

FILTER PHYSICAL SIZE

At low frequencies the physical size of distributed filterscan be quite large. The most compact type is the comblinebut it requires lumped capacitors. The table below com-pares physical dimensions for 3rd and 7th order imple-mentations at 1 and 5 GHz for each of the topologies. Allfilters were designed with zero length 50 ohm leader lines.Dimensions are given in inches in the format L x W. Allbandpass filters were designed using a 10% bandwidth.Where applicable a resonator impedance of 50 ohms wasused. The substrate dielectric constant, εr, was 2.55 andthe board thickness was 31 mils.

Filter 1 GHz

Order=3

1 GHz

Order=7

5 GHz

Order=35 GHz

Order=7

Edge-Coup BP 16 x 0.52 32 x 1.0 1.6 x 0.52 3.1 x 1.0

Hairpin BP 4.0 x 1.7 8.2 x 1.7 1.1 x 0.50 2.5 x 0.49

Stepped LP 1.5 x 0.41 5.1 x 0.49 0.25 x 0.41 0.86 x 0.41

Stepped BP 18 x 0.42 38 x 0.91 3.5 x 0.42 7.2 x 0.84

Combline BP 1.2 x 0.44 1.2 x 1.0 0.35 x 0.44 0.35 x 1.0

Interdig BP 2.1 x 0.47 2.1 x 1.2 0.47 x 0.47 0.46 x 1.2

Elliptic LP 2.0 x 0.41 4.5 x 1.9 0.42 x 0.12 0.92 x 0.42

Elliptic BP 11 x 5.5 28 x 13 2.4 x 0.11 5.8 x 2.6

End-Coup BP 10 x 0.085 26 x 0.070 2.4 x 0.11 5.8 x 0.11

Stub LP 1.5 x 0.72 4.5 x 1.1 0.53 x 0.25 1.7 x 0.28

Stub HP 0.24 x 1.2 0.57 x 1.0 0.25 x 0.25 0.57 x 0.23

Edge-Coup BS 10 x 0.18 26 x 0.18 2.0 x 1.8 5.3 x 0.20

M/FILTER Types 125

FILTER EXAMPLES

The remaining portion of this chapter includes brief de-scriptions of available M/FILTER topologies. More de-tailed information on the suitability of each of thesetopologies for a given application and specific data impor-tant for each type is provided in HF Filter Design andComputer Simulation.

126 M/FILTER Types

EDGE COUPLED BANDPASS

The edge-coupled bandpass is a natural choice for narrow-band specifications, especially when a long and narrowshape is desired. The example layout above is rotated afew degrees (cross hair setup box) to force the input andoutput lines to lie on a horizontal axis.

The minimum bandwidth is limited by close spacing of theinput and output sections. This problem is reduced byusing Zres >50 ohms. This widens the spacings but in-creases dissipative insertion loss.

The practical bandwidth range is further extended byusing the tapped version which taps the leader directlyinto the first and last resonators.

Radiation is a severe problem in this structure. To reduceradiation the filter should be mounted in a channel whichis as narrow as possible and at least below cut-off through-

M/FILTER Types 127

out the passband frequency range. Higher resonator im-pedance also reduces radiation.

The Slide factor decreases the length of each resonatorwhich couples to adjacent resonators. This is generallyundesirable because it tightens the spacings and increasesspacing tolerance requirements. However, sliding the cou-pled sections is necessary in preparation for bending thefilter into a hairpin, so the factor was included as anoption. The slide factor is the number of degrees eachcoupled section is moved relative to resonator center. Thisnumber is usually zero for an Edge Coupled Bandpassfilter.

128 M/FILTER Types

HAIRPIN BANDPASS

The hairpin bandpass is mathematically identical to theedge-coupled bandpass with a slide factor and bend dis-continuities. Like the edge-coupled bandpass it is mostsuitable for narrowband applications. Spacing issues aresimilar to the edge-coupled. The practical bandwidthrange is further extended by using the tapped version .

As the frequency is increased a higher resonator imped-ance is desirable. Folding reduces radiation significantly.Folding also saves considerable space at lower frequen-cies. Resonator self-coupling is avoided by separatinghairpin arms by the greater of 3X the spacings or 5X thesubstrate thickness.

M/FILTER Types 129

STEPPED-Z LOWPASS

The stepped-impedance lowpass implements the seriesinductors of the lowpass prototype as high-imedance linesand the shunt capacitors as low-impedance transmissionlines. The responses are more ideal and the stopbandrejection is greater for extreme impedance ratios.

Zmin and Zmax are the minimum and maximum imped-ances to be used for synthesis of the filter. They should beset at the most extreme values that can be realized.

130 M/FILTER Types

STEPPED-Z BANDPASS

The stepped-impedance bandpass utilizes high-imped-ance resonators slightly longer than 180 degrees decou-pled from each other using low-impedance lines. Thisstructure provides better attenuation in the upper stop-band than in the lower stopband. Element values areunrealizable below about 20% bandwidth.

The structure tends to be very long except on high dielec-tric constant substrates. Zmin and Zres are the imped-ance of the wide decoupling lines and the half-waveresonators, respectively. Zmin values of 15 to 30 ohms andresonator line impedances from 80 to 120 ohms are rea-sonable values.

M/FILTER Types 131

COMBLINE BANDPASS

The combline bandpass is one of the most compact of alldistributed filters. It is used in both printed planar andmachined slabline. The air slabline version yields excep-tional Qu so this structure is well suited for narrowbandfilters. It has excellent stopband performance which im-proves with shorter Res θ, at the expense of Qu. Loadingcapacitors are required for each resonator, but this pro-vides a means of tuning.

Zres is the impedance of the resonators and Res θ is thephase length of the resonators which must be <90 and istypically 15<θ<45. The above example is tapped. A cou-pled input/output version is also available.

132 M/FILTER Types

INTERDIGITAL BANDPASS

Each resonator in the interdigital bandpass is 90 degreeslong and they are grounded at alternating ends. Theresonant line lengths eliminate the need for loading ca-pacitors. The longer line lengths result in even higherunloaded Q than the combline at the expense of narrowerstopbands.

Zres is the line impedance of the resonator fingers. Theinterdigital and combline bandpass use viaholes in mi-crostrip and stripline to ground one end of the resonators.

The above example is tapped. A coupled input/outputversion is available.

M/FILTER Types 133

ELLIPTIC LOWPASS

The elliptic lowpass uses high-impedance lines to emulatethe series inductors in the elliptic lowpass prototype andhigh and low-impedance stub lines to emulate series L-Cresonators to ground.

At higher frequencies the high-impedance lines becomeshorter and the stubs are likely to collide or couple to eachother. This problem is mangaged by using alternatingstubs (Alt Stubs), more moderate line impedances, or athinner substrate.

Zmin and Zmax are the minimum and maximum lineimpedances. More extreme values improve performancebut increase collision probability.

134 M/FILTER Types

ELLIPTIC BANDPASS

The direct coupled elliptic bandpass works best for band-widths greater than 10%. It tends to be physically largewhich makes it more practical for higher frequencies andhigher dielectric constant materials.

Realizability is improved with small passband ripple andlarge Amin. Zmin (typ. 20-40) sets the impedance belowwhich stubs switch to double stubs. Zmch (typ. 70-110)sets the impedance of the end matching sections. Rint(typ. 80-150) defines the internal filter impedance. Zinv(typ. 55-75) is the impedance of the impedance invertors.

M/FILTER Types 135

END COUPLED BANDPASS

The end-coupled bandpass is suited for narrowband appli-cations in mounted very narrow channels. As the band-width is increased above a few percent, the gaps(particularly at the ends) quickly become vanishinglysmall. Lumped capacitors may be substituted for linegaps at the ends or at all gaps.

Min G is the minimum gap spacing which is acceptedbetween resonators. If the required gap drops below thisvalue, the gap will default to the capacitor setup spacingso that a lumped capacitor may be used. WARNING: Thecapacitors don’t appear on the layout. Check the sche-matic window or ckt/sch file to see whether capacitors orgaps were used.

136 M/FILTER Types

STUB LOWPASS

The stub lowpass implements the series inductors of thelowpass prototype as high-impedance lines and the shuntcapacitors as open-end stub lines. Higher stub imped-ances result in longer stubs which cause finite transmis-sion zeros at the frequency where the line is 90 degreeslong. These notches can be used to enhance the stopbandperformance at particular frequencies.

Zstub is the stub-line impedance and Zmax is the imped-ance of the series lines. Zmax should be chosen as high aspossible and Zstub is selected for best rejection in thestopband of interest. A low value of Zstub is best for widestopbands.

M/FILTER Types 137

STUB HIGHPASS

Series capacitors are difficult to realize in distributedform. This popular highpass is a hybrid form which util-izes shorted shunt stubs to emulate shunt inductors andlumped capacitors for the series elements.

Zstub is the impedance of the stubs. It should be as highas practical to improve the passband bandwidth. Lead θis electrical length of the series lines which are requiredto mount the capacitors and separate the stubs. Lead θ isset as small as possible to avoid coupling between thestubs. Stubs spacings should be at least 5X the substratethickness. Alternating stubs without crosses provide thebest stub separation at the expense of filter size.

138 M/FILTER Types

EDGE COUPLED BANDSTOP

The edge-coupled bandstop works best for narrowbandapplications. With wide stopbands the spacings becomecritically small.

M/FILTER Types 139

Chapter 10

M/FILTER Error Messages

M/FILTER includes absorption algorithms which compen-sate the perturbations caused by transmission line discon-tinuities. These absorption algorithms significantlyimprove the responses of distributed filters and reducerequired subsequent optimization time.

These absorption algorithms compensate the discontinui-ties by adjusting the lengths of lines adjacent to thediscontinuity. If insufficient line is present to accommo-date absorption, then in the layout window the appropri-ate filter elements turn red and the Show Errors buttonilluminates red. Selecting the Show Errors button dis-plays a description list of one or more error messages. Ifabsorption fails at a given discontinuity, no compensationis attempted and the file is not corrupted, but simplyuncompensated. Therefore it is feasible to continue andobtain desired results by tuning or optimization in Super-Star. However, it is best to input alternative filter parame-ters which avoid absorption failure. In general, thinnersubstrates help avoid absorption failure.

End-effect discontinuities touch one line. Step disconti-nuities touch two lines. The step absorbs length from bothlines. Any or all lines which touch a discontinuity may betoo short to allow compensation.

The descriptive error messages are:

Line (W,L) connected to bend is too short to compensateTwo lines contact each bend. The length of line used tocompensate the adjacent bend is too short to absorb thebend. If this occurs in the hairpin try using a larger slidefactor and/or a higher resonator impedance.

Line (W,L) connected to cross is too short to compen-sateThe length of line used to compensate the adjacent crossis too short to absorb the cross. Four lines contact eachcross. Adjust line impedances or use a thinner substrate.

Line (W,L) connected to end is too short to compensateThe length of line used to compensate the adjacent end istoo short to absorb the end. One line contacts each end.For elliptic filters try using a higher value of Zmin. Fortapped combline and interdigital, continue with the de-sign and tune or optimize the length of the end resonators.

Line (W,L) connected to gap is too short to compensateThe length of line used to compensate the adjacent gap istoo short to absorb the gap. Two lines contact each gap.This problem is more likely to occur at higher frequencies.Try adjusting the impedance of lines which contact thegap.

Line (W,L) connected to step is too short to compensateThe length of line used to compensate the adjacent step istoo short to absorb the step. Two lines contact each step.For stepped-Z filters try increasing Zmin.

Line (W,L) connected to tee is too short to compensateThe length of line used to compensate the adjacent tee istoo short to absorb the tee. Three lines contact each tee.Adjust line impedances or use a thinner substrate.

142 M/FILTER Error Messages

Capacitor (C=) connected to viahole is too small tocompensateThe value of a capacitor connected to a viahole is too smallto absorb the viahole. One capacitor or line contacts eachviahole. For combline try using a shorter resonatorlength.

Line (W,L) connected to viahole is too short to compen-sateThe length of line used to compensate the adjacent viaholeis too short to absorb the viahole. One line contacts eachviahole. Try adjusting the impedance of the line contact-ing the viahole.

Error sliding resonators, try decreasing slide factorThe slide factor is too large and the synthesis algorithmshave failed. Try using a smaller slide factor. A higherresonator impedance may help improve the resonatoraspect ratio and decrease the need for a large slide factor.

Warning!!! Reduced Zmin to (value)To avoid synthesis failure, the low line impedance hasautomatically been adjusted lower to the specified value.This is only a warning. This message is unique to thestepped-Z bandpass. With other structures, too high avalue for Zmin does not cause synthesis failure but simplydegrades performance.

(W,L) in all the above error descriptions signifies the widthand length variable names for the line being adjusted tocompensate the listed discontinuity.

LAYOUT COLLISIONS

Certain filter parameter choices result in element colli-sions. This becomes immediately apparent in the M/FIL-TER Layout display window where the elements appear

M/FILTER Error Messages 143

to overlap. This problem is managed by adjustment ofinput parameters, for example decreasing Zmax.

These collisions are more likely at higher frequencies andthicker substrates. When they occur, it is likely that thesubstrate is too thick for the operating frequency. It isadvisable to critically review if the substrate is too thick(radiation and undesired coupling paths in the finishedcircuit become problematic).

144 M/FILTER Error Messages

Appendix A

Filter Shapes

For each filter type such as lowpass, bandpass, etc.there are a number of response shapes. The designof all filters is based on a lowpass filter with that

shape of response. This lowpass filter is called the lowpassprototype and the values of elements in that filter arecalled the prototype “G” values. The values are normal-ized to 1 ohm input impedance and a cutoff frequency of 1radian/sec [1].

To design a filter, FILTER computes these prototype val-ues, makes the transformation to the desired type andnormalizes to the specified impedances and frequencies.

FILTER computes the prototype G values for Butterworth,Bessel, Chebyshev, singly-equalized delay and ellipticCauer-Chebyshev shapes. Also FILTER allows storing offrequently used prototype G values in disk files which areautomatically read to design other filter responses. In-cluded on the FILTER disk are lowpass prototype G valuesfor several different filter responses. The included re-sponse types are discussed later in this chapter. Otherlowpass prototype files may be entered by the user usingthe editor in SuperStar, or many other word processors orASCII file editors.

Prototype G values may also be manually entered intoFILTER at runtime. Dozens of tables of prototype Gvalues have been published through the years for specific

applications, and more may be expected in the future.Many tables of values are given in the references cited inthis manual.

BUTTERWORTH

The Butterworth lowpass response is useful when matchand delay in the passband, particularly low frequencies,are important. The shape is characterized by monotoni-cally increasing attenuation in the pass band to 3 dB atthe cutoff frequency. Attenuation monotonically increaseswith increasing frequency in the transition and stopbands.Filters with infinite attenuation only at DC or infinitefrequency, and therefore which have no zeros of transmis-sion at finite frequencies, are called all-pole filters.

The Butterworth is a simple filter, with suitable charac-teristics for many applications. For straightforward filter-ing applications, the Butterworth is the filter response ofchoice. Its disadvantage is only fair selectivity. The fre-quency response of the Butterworth lowpass filter is givenby:

Atten = 10 LOG10[1 + (f/fc)2N] dB

where f = frequencyfc= 3 dB cutoffN = order

The equations usedin FILTER to com-pute the lowpassprototype G valuesfor the Butterworthfilter are given inreference [2].

The output imped-ance of the Butter-worth lowpass proto- Figure A-1 Butterworth responses

146 Filter Shapes

type filter is equal to the input impedance, therefore G(0),the first prototype G value, is equal to G(N+1), the lastprototype G value.

The normal definition for the cutoff of Butterworth filtersis the 3 dB attenuation frequency. FILTER allows the userto specify the desired attenuation at the requested cutofffrequency. For example, the user may specify a cutofffrequency at 1 dB attenuation. Any cutoff attenuationgreater than zero may be specified for the Butterworthresponse.

CHEBYSHEV

The Chebyshev lowpass response is characterized byequal attenuation ripple in the passband, with attenu-ation equal to the ripple at the cutoff frequency. TheChebyshev is an all-pole filter. The Chebyshev filter givesbetter selectivity than the Butterworth filter. The Cheby-shev filter is an excellent choice when passband attenu-ation and return loss ripple can be tolerated. Thefrequency response of the Chebyshev lowpass filter abovecutoff is given by:

Atten = 10 LOG101+εcosh2[N cosh-1(f/fc)] dB

where f = frequencyfc= 3 dB cutoffN = order

ε = 10RIPPLE/10 - 1

The equations used in FILTER to compute the lowpassprototype G values for the Chebyshev filter are given inreference [2].

The output impedance for Chebyshev prototype filters ofodd order are equal to the input impedance, therefore G(0),the first prototype G value is equal to G(N+1), the lastprototype G value.

Filter Shapes 147

For even order Che-byshev prototype fil-ters, the outputimpedance is lessthan or greater thanthe input imped-ance, depending onwhether the subtypeis ML or MC. Thedifference is relatedto the passband rip-ple and is greater forlarger passband rip-ple.

FILTER automatically determines and displays the out-put impedance on the lower right of the main window. Thehelp screen (accessed with F1) for the Shape subwindowindicates which even order filter types and subtypes havehigher and which have lower output impedance.

Two normal definitions for the cutoff of Chebyshev filtersare often used. Some contributors have defined the cutoffattenuation as 3 dB, and others define the cutoff attenu-ation as the passband ripple value, with the latter perhapssomewhat more generally accepted. We will define thecutoff attenuation as the ripple value. However, FILTERallows the user to specify any attenuation equal to orgreater than the ripple attenuation as the cutoff. Forexample, the user may specify a cutoff frequency for a .25dB ripple Chebyshev at .25, 1.07, 3, 6 dB, etc. attenuation.Any cutoff attenuation greater than the ripple may bespecified for the Chebyshev response.

Figure A-2 Chebyshev responses

148 Filter Shapes

BESSEL

The Bessel filter produces a maximally flat group delay inthe frequency domain. It is sometimes referred to as amaximally flat group delay filter and sometimes as aThompson filter.

Maximally flat group delay is often an advantage in pulsecommunication system applications. This filter has excel-lent characteristics in the time domain.

The disadvantage is extremely poor selectivity. However,for applications where good phase or time domain per-formance is critical, it is often the best choice.

FILTER will design Bessel filters through 10th order.Bessel filters through order 21 may be designed by userentry or file entry of lowpass prototype G values.

BLINCHIKOFF FLAT DELAY BANDPASS

Transformation of lowpass filters to bandpass filters re-sults in the modification of the group delay characteristics

Figure A-3 Blinchikoff Flat Delay Bandpass

Filter Shapes 149

of the lowpass prototype. Consequently, bandpass filtersdesigned using Bessel, minimum phase equiripple errorand other controlled delay prototypes do not exhibit thedesired delay characteristics. This phenomenon worsenswith increasing bandpass filter bandwidth. Some trans-form types, such as the top-C coupled bandpass, are worsethan others, such as the shunt-C coupled bandpass. Thereasons for this phenomena is discussed in the EQUALI-ZATION chapter.

Blinchikoff and Savetman [3][4] offered a solution to thisdilemma for 2nd and 4th order all-pole filters. The polesof the transfer function were optimized by computer forconstant delay over the passband directly as a bandpassfilter. The lowpass to bandpass transform is thereforeavoided. The process is not numerically efficient, but theeffort provides a useful set of constant delay bandpassfilters for 30 to 70% bandwidth.

The extremely desirable delay characteristics of a 4thorder Blinchikoff bandpass filter with 40% bandwidthcentered at 70 MHz are demonstrated in the accompany-ing response. As might be expected, the amplitude selec-tivity characteristics of the filter are poor.

SINGLY-EQUALIZED DELAY

All ladder, passive, filter structures are minimum-phase;the amplitude and phase responses are inseparably re-lated via the Hilbert transform. Selectivity and flat delaycannot be simultaneously achieved.

To resolve this difficulty, selective filters are sometimescascaded with non-ladder all-pass delay equalization net-works. Unfortunately several all-pass sections may berequired and each requires several components.

Developed by Eagleware, the singly-equalized prototypeoffers selectivity far better than Bessel and other control-

150 Filter Shapes

led phase prototypes but it is perfectly delay equalizedwith a single all-pass network. This prototype may beselected from the Shape dialog box. The theory behind thedevelopment of these prototypes is described as an exam-ple in HF Filter Design and Computer Simulation, pro-vided with FILTER.

SINGLY-TERMINATED

Sometimes a filter which is singly-terminated is required.FILTER will design Butterworth and Chebyshev filtersterminated on the input with a specified impedance andterminated on the output with either zero or an infiniteimpedance. The input and output of these filters may beswapped. Other filter shapes may be designed for singletermination by user or file entry of the lowpass prototypeG values. The Help screen in the Shape subwindow maybe used to determine which subtype for a given filter typewill have an infinite or a zero output impedance.

Since singly-terminated filters are not really matchingnetworks, the insertion loss of these filters is not 0 dB inthe passband. Consider a lowpass filter consisting ofseries inductors and shunt capacitors inserted between asource of 50 ohms and a zero impedance load. As thefrequency approaches zero, the capacitors effectively be-come open circuits and the inductors effectively disappear.How can these components match the source to the loadif they are effectively absent? The answer is they can not.Singly-terminated filters preserve the shape of the ampli-tude response and the shape of the voltage response, butwhen the power transferred between the source and loadis calculated or measured, the insertion loss is propor-tional to the difference in input and output impedances.

When writing SuperStar files for singly-terminated filtersin order to avoid infinite attenuation in the calculated lossof the passband,FILTER sets the output impedance at 398

Filter Shapes 151

or 1/398 times the input impedance, instead of infinity orzero. The response of a filter changes little when the ratiois greater than about 20. The ratio of 398 results in anattenuation offset of approximately 20 dB, so singly-ter-minated filters analyzed using SuperStar require addinga 20 dB offset to the scale of S21 and S12.

CAUER-CHEBYSHEV

Elliptic function filters have zeros of transmission at finiteas well as infinite frequencies. Zeros of transmission atfinite frequencies can reduce the width of the transitionregion, therefore increasing the selectivity or “sharpness”of the response. An important class of elliptic functionfilters is the Cauer-Chebyshev, which exhibits equiripplepassbands and equal minimum attenuation, Amin, in thestopband. FILTER designs Cauer-Chebyshev filters withuser specified passband ripple and stopband ripple. Theseroutines are based on work by Pierre Amstutz [5]. In theAmstutz paper, distinctly different routines were given foreven and odd order Cauer-Chebyshev prototype filters.The routines used different input data for determiningvalues in the odd or even case. The FILTER routinesremove this disadvantage.

FILTER computes prototype G values for both type B andtype C Cauer-Che-byshev filters. TypeB Cauer-Cheby-shev filters aresimilar to Cheby-shev filters in thatthe input and out-put impedances foreven order are dis-similar.

Figure A-4 Cauer-Chebyshev

152 Filter Shapes

A type C filter approximates the filter response for equalinput and output impedances for even order. The selectiv-ity suffers slightly for type C, but this is a minor inconven-ience when equal input and output impedance is required.

USER FILTERS

Specifying user file in the Shape subwindow allows enter-ing lowpass prototype G values at run time. This isconvenient for designing filters from G values found in theliterature or that you have developed.

The powerful optimizing routines in SuperStar can beused to develop prototype G values with a limitless varietyof amplitude or delay characteristics. An example of usingSuperStar to develop a new lowpass prototype class isgiven in the FILTER Examples chapter.

When G-file is selected, FILTER will first prompt for a fileunder which to store the new G values. To create a newfile, simply specify a non-existant filename. FILTER willthen display an editor in which you can enter the G file.The first line must contain a comment or note and mustnot contain data. Each remaining line (lines are sepa-rated by the <return> key) contains G values for a specificorder. The first number is the order (N). The G valuesfrom G(0) to G(N) follow. The exact number of requiredprototype G values must be specified. G(0) is the normal-ized input impedance. It is normally 1. For all-pole filters,G(1) through G(N) are the prototype values, and G(N+1)is the normalized output impedance.

For elliptic filters designed by FILTER, the number offinite frequency zeros of the lowpass prototype, M is givenby:

For N odd,

M = .5(N-1)

Filter Shapes 153

and for N even,

M = .5(N-2)

There are N+Mprototype G valuesfor elliptic filters.The normalizedoutput impedanceis G(N+M+1). Theform of the ellipticlowpass prototypefilter is given on the previous page. For even order filters,the final series branch is non-elliptic. The Cauer-Cheby-shev and many other elliptic function filters utilize thistopology. The general case for filters with zeros of trans-mission at finite frequencies may not utilize this topology.For example, the older class of m-derived filters havedesigner selected topologies.

OBSERVING G VALUES

Occasionally, the user may want to know the the internallygenerated G values. A typical application might be thesynthesis of a filter topology not included in FILTER, butfor which the user has synthesis procedures when the Gvalues are know.

To read the internally generated G values, first use FIL-TER to design any topology of filter with the desiredtransfer function shape. Next, select the display G valuesitem in the Utilities menu. FILTER displays the G valuesin a subwindow. Press Enter to select the Close buttonand return to the main window.

PROTOTYPE FILES

Some frequently used prototype G values have been sup-plied with FILTER. These files have the same format as

Figure A-5 Elliptic Cauer-Chebyshev prototype format

154 Filter Shapes

files which you manually create. The form of these filesis:

Remark line describes type and must be included.3 1 1 2 1 14 1 0.7654 1.848 1.848 0.7654 15 1 0.618 1.618 2 1.618 0.618 17 1 0.445 1.247 1.802 2 1.802 1.247 0.445 1

This particular file is for Butterworth prototype filters of3rd through 5th and 7th order.

The remark line is used to describe the type of lowpassprototype for reference. The remark line must be present.One line of data is used for each order. One or more ordersmay be in a file. The first number in a line is the order.The second number is G(0), the third G(1), etc. up toG(N+1), or up to G(N+M+1) for elliptic function filters.

When reading a file, if a data line for the specified filterorder is not found, the message “Data for order N not foundin file.” is displayed. Either edit the file or specify a newone. An incorrect number of data points in a line of dataadversely effects program operation so please carefullycheck prototype files you create.

We recommend using the extension “.PRO” for all-polelowpass prototype files and the extension “.PRE” for ellip-tic lowpass prototype files you create.

INCLUDED PROTOTYPE FILES

To begin your collection of special purpose lowpass proto-type filters kept as files, the FILTER disk contains anumber of lowpass prototype files. Included are:

• Linear phase 0.05 degree equiripple error: orders 2-10.

• Linear phase 0.5 degree equiripple error: orders 2-10.

• Transitional Gaussian to 6 dB: orders 3-8.

• Transitional Gaussian to 12 dB: orders 3-8.

Filter Shapes 155

• Singly-terminated Cauer-Chebyshev: orders 3-7. (Ripple =72 dB which is 24 files.)

• Bessel passband elliptic: orders 3-4 for Amin = 18, 24:orders 3-8 for Amin = 34, 42, 50, 58, 66, 70 dB.

The prototype files except Bessel passband elliptic areprovided with permission from reference [1], Handbook ofFilter Synthesis, by Anatol I Zverev, published by JohnWiley and Sons. This reference includes many other sin-gly-terminated Cauer-Chebyshev prototypes and otheruseful lowpass prototypes.

The Bessel passband elliptic stopband lowpass prototypesare provided with permission from reference [6], Elec-tronic Filter Design Handbook, by Arthur B. Williams andFred J. Taylor, published by McGraw-Hill.

LINEAR PHASE EQUIRIPPLE ERROR

Just as the Chebyshev prototypes are an optimum ampli-tude response solution, the linear phase prototypes arean optimum linear phase solution (constant group delay)given an allowable phase ripple. By allowing some phaseripple, improved selectivity is obtained. The two prototypefiles are named “LP0R05.PRO” and “LP0R5.PRO”. LP isan acronym for linear phase. 0R05 and 0R5 representrespectively 0.05 and 0.5 degrees phase ripple.

TRANSITIONAL GAUSSIAN

Also included on the disk are Gaussian to 6 dB (G06.PRO)and Gaussian to 12 dB (G12.PRO) transitional lowpassprototype filters for 3rd through 8th order. This class offilter approximates a Gaussian response to 6 or 12 dB andis a compromise of delay and selectivity characteristics.

Both the linear phase equiripple error and transitionalGaussian prototypes are doubly-terminated unsymmetri-

156 Filter Shapes

cal filters. The component values on the input and outputare not mirror images of each other.

SINGLY-TERMINATED CAUER-CHEBYSHEV

FILTER synthesizes doubly-terminated Cauer-Cheby-shev elliptic functions directly. However, it does not syn-thesize singly-terminated Cauer-Chebyshev functions.This class is useful for designing contiguous elliptic diplexfilters, so a number of prototype files for this class areincluded on disk.

The convention for naming these files is CCnNPPAA,where CC represents Cauer-Chebyshev, nN are the lowestand highest order included, PP is the reflection coefficientin percent, and AA is the approximate Amin in decibels.For the most part, the orders included are 3rd through 7th.The reflection coefficients are 1, 2, 4, 8, 10, 15, 20, and 25%,which represents a passband ripple of .00043, .0017, .007,.028, .044, .098, .18 and .28 dB respectively. Reference [1],which was so popular it has gone back into print, containsmany other prototype files.

BESSEL PASSBAND ELLIPTIC STOPBAND

As was discussed previously, Bessel filters have excellentdelay characteristics, but poor selectivity. The selectivityof flat delay filters can be improved by adding zeros oftransmission at finite frequencies. Elliptic lowpass proto-types for such a class of filters is given in reference [6].

The amplitude and delay responses for 5th order Bessel(solid curves) and elliptic Bessel Amin =50 dB (dottedcurves) filters with 1 MHz cutoffs are compared in theaccompanying figure.

PROTOTYPE FILE SELECTION ASSISTANCE

To assist in the management and use of lowpass prototypefiles, a list of available prototype files is available on the

Filter Shapes 157

help screen (accessed with F1) when FILTER prompts forthe prototype filename after you have selected the user fileshape option.

N-HELP

FILTER, A/FILTER, and M/FILTER can help you deter-mine the order required for Butterworth, Chebyshev andelliptic Cauer-Chebyshev filters.

Suppose you need a bandpass filter which passes 10.5 to10.9 MHz with a maximum ripple of .1 dB. The rejectionat 10.2 MHz and 11.2 MHz must be at least 50 dB. We willdetermine the minimum order required for a Chebyshevand a Cauer-Chebyshev filter.

Press F4, or select N-Help from the Utilities menu. De-termine the Chebyshev order first. Select the Bandpassand Chebyshev radio buttons. Enter “.1" for the rippleprompt. Enter ”10.5" and “10.9" for the Fl and Fu promptsrespectively.

Figure A-6 Bessel Passband Elliptic Stopband

158 Filter Shapes

You may then enter up to 10 separate stopband require-ments. FILTER will automatically determine which re-quirement is the most stringent and compute thenecessary order based on that requirement. In this case,at the F0 and A0 prompts, enter “10.2" and ”50". At thenext F1 and A1 prompts enter “11.2" and ”50". When youare finished entering stopband requirements, enter “0".The necessary order is computed and displayed as 5.39.The filter is therefore designed with the next higher inte-ger order of 6.

Next, determine the necessary order for a Cauer-Cheby-shev elliptic bandpass filter. Select the Cauer-Chebyshevradio button. Enter “50" at the prompt Amin, ”10.5" at theFl prompt and “10.9" at the Fu prompt.

For Cauer-Chebyshev bandpass filters, only two stopbandrequirements are entered, because the required stopbandattenuation is assumed equal to Amin. Enter the lowerand upper stopband requirements closest in frequency tothe passband. For elliptic lowpass filters, only one stop-band requirement is used.

Therefore, enter “10.2" at the Fsl prompt and ”11.2" at theFsu prompt. The required order is 4.03. Because this isvery close to 4, a 4th order filter might be chosen. Re-run-ning N-Help with Amin of 49 dB gives a required order of3.98, so you know that a 4th order filter will have between49 and 50 dB of attenuation.

Select the close button to return to the main window.

Filter Shapes 159

Appendix B

Noise Bandwidth

Filters are used in many electronic systems to bandlimit the noise, hopefully without distorting the sig-nal. The noise power referred to the input of a system

is given by:

PNi=kTBnF

where

k = Boltzman's constantF = the system noise figureT = the defining temperature of F, normally 290KBn = the effective noise bandwidth of the system.

The noise voltage refered to the input is:

where Req= the equivalent noise resistance.

Calculation of system performance parameters often re-quires knowledge of the effective noise bandwidth. Theeffective noise bandwidth is approximately equal to the 3dB bandwidth, but the actual value may vary significantlyfrom this value. The noise bandwidth is defined

e kTB FRN i n eq=

BH j

H j dn

m m

= z1

2

2

ωω ω

b ga f

where

H(jw)=the transfer function

Hm(jwm)=maximum value at the frequency, wm, of themaximum value

BUTTERWORTH NOISE BANDWIDTH

The noise bandwidth of a bandpass filter is equal to thenoise bandwidth of the lowpass prototype. Interestingly,the noise bandwidth of all-pole lowpass filters is equal to

π2Gn

, where Gn is the shunt capacitance at the open

circuit end of a singly-terminated lowpass filter of thattype. Because close form equations are known for singly-terminated Butterworth G values [2], calculating thenoise bandwidth of Butterworth filters is straightforward.The noise bandwidth for Butterworth filters is:

A similar process may be used for calculating the noisebandwidth of Chebyshev filters.

The problem with this approach is that it is very restric-tive. Equations for singly-terminated G values are knownfor only certain response shapes. Furthermore, practicalfilter responses are seldom ideal. What are the effects offinite-Q components, approximate bandpass transformsand standard component values?

GENERAL CASE

The noise bandwidth for the general case can be found byintegrating the actual filter response. FILTER and Super-Star automate this process. The filter response is com-

B BW

NN

n dB=FH

IK

32

2

p

psin

162 Noise Bandwidth

puted using SuperStar, and the output S-parameter datafile is written using the “Write S-data” option in theSuperStar File menu.

FILTER is then run and the Noise-BW routine is selectedfrom the Utilities menu or by pressing F5. The “*.OUT’filename is requested. The file wriiten above is specifiedand FILTER computes and displays the noise bandwidth.The maximum value of S21 in the output file and thefrequency at which this maximum value occurs are alsodisplayed. A typical output screen is given in Figure B-1.

NOISE BANDWIDTH EXAMPLE

Consider a 10.55 to 10.85 MHz 5th order shunt-C coupledButterworth bandpass filter constructed from inductorswith an unloaded Q of 120 and capacitors with an un-loaded Q of 1000.

Figure B-1 Typical output screen

Noise Bandwidth 163

The noise bandwidth computed by the equation givenearlier in the chapter is 305 KHz which is near the 300KHz 3 dB bandwidth. The response of the filter with thefinite-Q components is shown in Figure B-2. The finite-Qresults in significant response rounding, a 3 dB (from peakresponse) bandwidth of approximately 240 KHz and aninsertion loss of approximately 9.3 dB. Writing the Super-Star output file with F6 and integration of the noisebandwidth in FILTER results in an actual noise band-width of 251 KHz for the lossy filter. Notice the finite-Qcomponents constrict both the 3 dB and noise bandwidths.

FREQUENCY RANGE AND STEP SIZE

When the filter response is integrated, the majority of thecontribution to the area under the response curve is fromfrequencies for which the response is greatest. However,when the frequency range of the stopbands is extensiveand when the ultimate rejection is fairly low, contributionsto the noise bandwidth may occur from the stopbands.This is analogous to theproblem often encoun-tered in receiving systemswhen the IF filter is toclose to the front-end, andsignificant amplificationoccurs after the IF filter.

The value of the responsefor integration is taken tobe the average value atthe upper and lower fre-quencies. If the responsehas changed significantlybetween frequency points,the accuracy of the inte-gration is reduced. Thisproblem is avoided by us-

Figure B-2 Filter responsewith finite-Q

164 Noise Bandwidth

ing a large number of analysis frequency points whenwriting the S-parameter data. Typically 101 sweep pointsand a frequency range of about 3 times the passband isadequate.

Noise Bandwidth 165

Appendix C

File Formats

T his appendix describes the formats of various ASCIIfiles used or written by FILTER, EQUALIZE,MATCH and SuperStar. All of these files may be

created, viewed and edited using the editor in SuperStar,or other editors and word processors.

DEFAULT FILES

When the user finishes responding to input prompts,FILTER computes and displays the filter component val-ues. FILTER also writes the prompt responses to a diskfile labeled “DEFAULT.FI$”. When FILTER is restarted,default prompt values are read from the disk file. Thedefault responses to prompts are therefore the last re-sponses given by the user. This enhances user friendlinessand speeds the design process. While these default filesare ASCII, it is not recommended that the user modifytheir contents directly.

The user may also request FILTER to store the currentinputs in an .FI$ file with a name of the user’s choice. Theformat of these files is identical to the format of DE-FAULT.FI$. The .FI$ files are saved and opened from theFile menu of FILTER.

When you exit MATCH, your imput parameters are writ-ten to the disk file “DEFAULT.MA$”. When =MATCH= isrestarted, default prompt values are read from the disk

file. The default responses to prompts are therefore thelast responses given by the user. This enhances userfriendliness and speeds the design process. While thesedefault files are ASCII, it is not reccommended that theuser modify their contents directly.

LIST_OF . PRO

The file LIST_OF.PRO is a list of available lowpass proto-type G values for use with the user file Shape option. Thisfile is for documentation purposes only, and is not used byFILTER. If you add you own lowpass prototype files, youmay want to add the names of those files to this list. Thecurrent list as shipped with FILTERis:

All- pole with controlled delay from Zverez.G06.PRO G12.PRO LP0R05.PRO LP0R5.PROSingly-terminated Cauer-Chebyshev from Zverev.CC370142.PRE CC370152.PRE CC370172.PRECC370241.PRE CC370253.PRE CC370275.PRECC370441.PRE CC370451.PRE CC370472.PRECC370842.PRE CC370852.PRE CC370870.PRECC371042.PRE CC371052.PRE CC371072.PRECC371542.PRE CC371552.PRE CC371570.PRECC362042.PRE CC372052.PRE CC372073.PRECC362542.PRE CC372552.PRE CC372570.PRE

Bessel elliptic stopband from Williams and Taylor.BE347118.PRE BE347126.PRE BE387134.PREBE387142.PRE BE387150.PRE BE387158.PREBE387166.PRE BE387170.PRE

168 File Formats

Appendix D

GIC Transform Fundamentals

Several of the filter types designed by A/FILTER arebased on LC (inductor-capacitor) filters. These filtersare then transformed to remove inductors, leaving

only resistors, capacitors, and operational amplifiers.These types are very insensitive to component tolerancesbut are of medium to high complexity. They are often idealwhere large quantities of filters will be built.

All LC to active transforms use the generalized impedanceconverter (GIC). These transforms are referred to asLC/GIC transforms. A schematic of a GIC is shown inFigure D-1. Note that the GIC must always be groundedfor proper operation. The impedance to ground providedby a GIC is given by:

If a capacitor is substituted for Z4 and resitors are usedfor all other Z’s, then the equation becomes:

ZZ Z Z

Z Zinput = 1 3 5

2 4

ZsCR R R

Rinput = 1 3 5

2

This is the equation for an inductor with inductance

. Any LC filter containing grounded inductors canbe transformed using this element in place of thegrounded inductors. This equivalence is shown in FigureD-2.

The second kind of LC/GIC transformation is more com-plex. It is based on D Elements (sometimes referred to asfrequency dependent negative resistors). In a D Element,the basic GIC is implemented with capacitors for Z1 andZ3 and resistors for all other elements. This yields thefollowing equation:

This element cannot be used in an LC filter until a “1/stransform” is applied. In this transform, the entire filter

LCR R R

R= 1 3 5

2

ZR

s C C R Rinput = 52

1 3 2 4

Z1

Z2

Z3

Z4

Z5

Figure D-1 Basic schematic of a generalized impedanceconverter (GIC)

170 GIC Transform Fundamentals

is scaled by 1/s. This is similar to standard impedancescaling, except that the scaling factor is complex. Induc-tors with impedance of sL become resistors with resistance

of L ( ); Capacitors (1/sC) become D

Elements (1/s2C); Resistors (source and load, R) scale tocapacitors (R/s). Since the source and load resistors ofthese filters become complex, the actual terminating re-sistances become infinite (zero at the input, infinity at theoutput).

A good textbook for further information on GeneralizedImpedance Converters and their transforms is ElectronicFilter Design Handbook by Arthur B. Williams and FredJ. Taylor, © 1981, 1988 by McGraw-Hill.

sLs

L⋅ =1

R1

R2

R3

R5

C

R2

C R1 R3 R5

Figure D-2 Basic schematic of a generalized impedanceconverter (GIC)

GIC Transform Fundamentals 171

Appendix E

Training

Eagleware conducts training workshops and seminarson filter design and oscillator design. Sessions aredesigned for degreed engineers or individuals with

high frequency design experience who wish to enhancetheir design skills. A range of topics is covered including:

FILTER TOPICSFILTER FUNDAMENTALSCONVENTIONAL AND UNIQUE TRANSFORMSELLIPTIC FUNCTION FILTERSTHE MINIMUM “L” ELLIPTIC ZIG-ZAG BANDPASSSYMMETRY IN AMPLITUDE & DELAY RESPONSEFLAT DELAY FILTERS & GROUP DELAY EQUALIZATIONEFFECTS AND COMPENSATION OF FINITE-Q PARTSCOMPONENT PARASITICS & MODELSMICROWAVE DISTRIBUTED FILTERSCREATING NEW & UNIQUE LOWPASS PROTOTYPESNETWORK EQUIVALENTS & CUSTOM FILTERS

OSCILLATOR TOPICSLOOP OSCILLATOR THEORYNEGATIVE RESISTANCE THEORYBROAD TUNING VCOsQUARTZ CRYSTAL AND SAW OSCILLATORSPULLING SAWs AND CRYSTALSSTARTINGHARMONICSNON-LINEAR AND LIMITING EFFECTS

One day tutorials are given by Eagleware at seminarssponsored by RF Design magazine, Microwaves & RFmagazine, and Microwave Product Digest. Informationabout specific dates, times and registration for these tuto-rials is available from:

RF Design Magazine5660 Greenwood Plaza BlvdEnglewood, CO 80111TEL (303)793-0448

Microwaves & RF611 Route 46 WestHasbrouch Heights, NJ 07604TEL (201) 393-6286

Microwave Product Digest20 Mercer St., 3rd FloorHackensack, NJ 07601TEL (201) 488-3001

One-day to one-week workshops on filter design, oscilla-tors, and/or high frequency CAE may also be conducted atyour facility. For additional information contact:

Eagleware Corporation635 Pinnacle CourtNorcross, GA 30071PH. (678) 291-0995FAX (678) 291-0971

BOOKS AND VIDEO COURSES

Books and videos on circuit design which include examplesusing Eagleware software are available from:

Noble Publishingwww.noblepub.com

174 Training

Appendix F

References

FILTER REFERENCES

[1] H. J. Blinchikoff and A. I. Zverev, Filtering in the Timeand Frequency Domains, Krieger Publishing, Malabar,Florida, 1987.

[2] G. L. Matthaei, L. Young, and E. M. T. Jones, MicrowaveFilters, Impedance-Matching Networks, and CouplingStructures, Artech House, Dedham, Massachusetts, 1980

[3] R. Saal and E. Ulbrich, “On the Design of Filters bySynthesis,” IRE Trans. Circuit Theory, vol. CT-5, pp. 284-317, 327, Dec. 1958.

[4] F. Carassa, “Band-Pass Filters Having Quasi-Symmet-rical Attenuation and Group-Delay Characteristics”, AltaFrequenza, vol. XXX, No. 7, pp. 488-499, July 1961.

[5] G. Szentirmai, “The Design of Arithmetically Symmet-rical Band-Pass Filters,” IEEE Trans. Circuit Theory, vol.CT-10, pp. 367-375, September 1963.

[6] G. Szentirmai, “The Design of Arithmetically Symmet-rical Band-Pass Filters,” IEEE Trans. Circuit Theory, vol.CT-11, pp. 109-118

[7] W. M. Hummel, “Wide Band Linear Phase Band PassFilters,” Proceedings of the 20th Electronic ComponentsConference, 1970.

[8] H. J. Blinchikoff and M. Savetman, “Least-SquaresApproximation to Wideband Constant Delay,” IEEETrans. Circuit Theory, vol CT-19, pp. 387-389, July 1972.

[9] S.B. Cohn, “Direct-Coupled-Resonator Filters,” Proc.IRE, vol. 45, pp.187-196, February 1957.

APPENDIX REFERENCES

[1] A.I. Zverev, Handbook of Filter Synthesis, John Wileyand Sons, New York, 1967.

[2] G. L. Matthaei, L. Young, and E. M. T. Jones, MicrowaveFilters, Impedance-Matching Networks, and CouplingStructures, Artech House, Dedham, Massachusetts, 1980

[3] H. J. Blinchikoff and A. I. Zverev, Filtering in the Timeand Frequency Domains, Krieger Publishing, Malabar,Florida, 1987.

[4] H.J. Blinchikoff and M. Savetman, “Least-SquaresApproximation to Wideband Constant Delay,” IEEETrans.Circuit Theory, vol. CT-19, pp. 387-389, July 1972.

[5] P. Amstutz, “Elliptic Approximation and Elliptic FilterDesign on Small Computers,” IEEE Trans. Circuits andSystems, vol. CAS-25, No. 12, Dec. 1978.

[6] A.B. Williams and F.J. Taylor, Electronic Filter DesignHandbook, McGraw-Hill, New York, 2nd ed., 1988.

176 References

INDEX

AActive filter transforms 169Active lowpass minimum C filter 92Active lowpass minimum L filter 89Active single feedback lowpass filter94A/FILTER

Distributing/isolating gain 52Dual amplifier all pole bandpass 80Dual amplifier, max gain all pole

bandpass 81First example 45I/O matching buffers 51Low sensitivity all pole

bandpass 82Low sensitivity all pole highpass 70Low sensitivity all pole lowpass 60Minimum C all pole highpass 67Minimum C all pole lowpass 57Minimum C elliptic lowpass 63Minimum L all pole highpass 66Minimum L all pole lowpass 56Minimum L elliptic highpass 73Multiple feedback all

pole bandpass 78Multiple feedback all pole

highpass 69Multiple feedback all pole

lowpass 59Multiple feedback max gain

all pole bandpass 79Operation 45 - 53Reversing the pole order 53Simple first order RC section 52Single feedback all pole

highpass 68Single feedback all pole

lowpass 58State variable all pole

bandpass 83, 87

State variable all polehighpass 72

State variable all pole lowpass 62State variable elliptic

bandpass 85State variable elliptic highpass 75State variable elliptic lowpass 65Three pole sections 52Top C all pole bandpass 76Top L all pole bandpass 77Types 55Using followers to add gain 51VCVS all pole bandstop 86VCVS all pole highpass 71VCVS all pole lowpass 61VCVS elliptic bandpass 84VCVS elliptic highpass 74VCVS elliptic lowpass 64Voltage followers 51

BBandpass symmetry 22Bessel crystal filter 37Bessel definition 149Bessel passband/elliptic

stopband 157Blinchikoff definition 149Books and video courses 174

CCauer-Chebyshev definition 152Chebyshev definition 147Chebyshev terminations 147CKT files

Creating 6

DD element transform 169Default files 167Determining order

requirements 158

Discontinuity absorptionalgorithms 141

Dual amplifier max gainbandpass filter 100

EEagleware training sessions 173 - 174Exiting to SuperStar 7Exiting to DOS or Windows 7

FFile formats 167 - 168FILTER

Blinchikoff flat-delay bandpass 21Coupled all pole bandpass

types 15Full transform all pole bandstop 27Full transform elliptic bandpass 30Minimum C all pole bandpass 14Minimum L all pole bandpass 13Minimum L/C all pole highpass 12Minimum L/C all pole lowpass 11Minimum L/C elliptic highpass 29Operation 1 - 8Shunt C coupled all pole

bandpass 19Starting 1Symmetry preserving bandpass 22Top C coupled all pole

bandpass 17Top L coupled all pole

bandpass 18Tubular all pole bandpass 20Types 9 - 32

Filter symmetry example 38

GG-values 145

Viewing 154

HHelp 2, 45, 103

IInput fields 1, 45, 103

LLC/GIC transforms 169Linear phase equiripple error

prototypes 156

MM/FILTER

Changing units 110Combline bandpass 132Edge coupled bandpass 127Edge coupled bandstop 139Electrical vs physical output

files 116Elliptic bandpass 135Elliptic lowpass 134End coupled bandpass 136Entering parameters 113Error messages 141 - 144Hairpin bandpass 129Interdigital bandpass 133Layout collisions 143Layout window 111Menu commands 105Plotting layouts 108Stepped impedance

bandpass 131Stepped impedance

lowpass 130Stub highpass 138Stub lowpass 137Tuning parameters 111Types 123Using the flowchart 103Viewing variables 109Writing CKT/SCH files 116Writing DXF files 108

Mixed Coupling ElementsAccuracy 16Bandwidth Limitations 16Using 16

Monotonic attenuation 146Monotonic vs elliptic 10Multiple feedback lowpass

filter 98Multiplicity Ratio 22

NN-Help 158Noise

Bandwidth 5, 161Bandwidth example 163

180 Index

OOperational amplifiers

Gain limiting 53Uncontrolled voltages 89Viewing/specifying

parameters 50Optimizing A/FILTER

designs 91, 95Output

Adding plots 50Changing type 5, 49, 110

PPlace in EQUATE block xiiPrompts

Aa 3, 47Amin 135Do 48Er 114Fc 48, 113Fca 3, 47H 114Lead 114Lead Theta 138Lo 48Min G 136Order 3, 45, 47, 113Res Theta 132Rho 114Rin 4, 113Rint 135Ripple 3, 47, 113Rough 114Rout 4Slide 128Std C 48Std R 48Sum-G 48TanD 114Tmet 114Zinv 135Zmax 114, 130, 134, 137Zmch 135Zmin 114, 130 - 131, 134 - 135Zres 127, 131 - 133Zstub 137 - 138

Prototype files

List of 155 - 156, 168Using 154

QQuality Factor (Q)

Effective, calculating 6Specifying 6, 50

RR-X data files 168References 175 - 177Replacing optimized values 116

SSCH files

Creating 6Shape 46Singly-equalized delay

definition 150Singly-terminated

Cauer-Chebyshev 157Singly-terminated definition 151Symmetric transform

limitations 25

TTables

Active filtercomparison/contrast 88

Distributed filter sizesvs type 125

Elliptic vs monotonicselectivity 10

Topology 46Transitional gaussian

prototypes 156Transmission line

resonator filter 33Tuning active

sectional filters 96Tuning D-element filters 90

UUnits 4User defined prototypes

Creating 41, 153Using 43, 153

Using SuperStar withM/FILTER 115

Index 181

genesys v8 synthesis i: classic filter...

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