2011

Microwave Devices &Antennas

Project Report

Syed Asadullah Hussain 404

Amna Meer 442

M. Faizan Khalid 368

M. Ehtisham Asghar 367

Introduction:“A microwave filter is a two port network used to control the frequency response at a certain point in a microwave system by providing transmission at frequencies within the pass band of the filter and attenuation in the stop band of the filter.” [1]

There are two major techniques for designing a filter:

1. Image Parameter Method: uses cascading of two port filters to get desired frequency response. But response cannot be specified over a frequency range.

2. Insertion Loss Method: uses network synthesis techniques for filter design, so that frequency response can be specified over a fair range of frequencies.

Although Image Parameter Method is simpler, but as response cannot be specified over a frequency range so many iterations are needed for desired frequency response, which is quiet cumbersome. So we used Insertion Loss Method for Filter design as we can define our filter specifications well through this method.

The method of insertion loss uses network synthesis technique. The design is simplified in the beginning with low pass filter prototypes that are normalized in the beginning in terms of impedance and frequency. Transformations are then applied to convert the prototype design to the desired frequency range and impedance level. As our requirement is at microwave frequencies so lumped elements will not work ideally at these high frequencies so these lumped elements need to be transformed into distributed elements in order to observe required frequency response. The conversion of lumped elements to distributed elements is done using Richard’s transformation and the Kuroda identities.

Filter Design by Insertion Loss Method:In this method a filter’s response is defined by it ‘insertion loss‘or power loss. It is defined as the ratio of power available from source to power delivered to load.

= =

The basic steps in filter design are as follows:

The process defined above is explained and applied in detail of this report to design a ripple band pass filter of specifications:

Cut off Frequency: 2.8 GHz

Attenuation 25 dB at least

0.5 dB ripple in pass band

There are various topologies (configurations) for filters that can be used to implement the design for a certain low pass filter. The choice of these topologies depends on certain factors such as:

Type of filters, such as Chebyshive or elliptic

Bandwidth

Size

Power Requirements

While the choice for the fabrication for the filterHigher-order modes, Couplings, Dielectric loss and Temperature stability.circuits to design the filter.

Realization:Using the insertion loss method, we have gone through a series of steps and have arrived at the implementation of the low pass filter of the above mentioned specifications. closely resembles the Chebyshive’s response so we have used this filter response.

Prototype Design

Scaling & Tranforms

The basic steps in filter design are as follows:

The process defined above is explained and applied in detail of this report to design a ripple band

2.8 GHz

at least @ 4.7 GHz

ripple in pass band

There are various topologies (configurations) for filters that can be used to implement the design for a certain low pass filter. The choice of these topologies depends on certain factors such as:

filters, such as Chebyshive or elliptic

While the choice for the fabrication for the filter (substrate) depends on factors such as Size, order modes, Couplings, Dielectric loss and Temperature stability. We will u

we have gone through a series of steps and have arrived at the implementation of the low pass filter of the above mentioned specifications. Our filter’s response closely resembles the Chebyshive’s response so we have used this filter response. First the filter was

Specifications

Prototype Design

Scaling & Tranforms

Implementation

The process defined above is explained and applied in detail of this report to design a ripple band

There are various topologies (configurations) for filters that can be used to implement the design for a certain low pass filter. The choice of these topologies depends on certain factors such as:

depends on factors such as Size, We will use ladder

we have gone through a series of steps and have arrived at the Our filter’s response

First the filter was

designed using Lumped elements and then it was implemented using distributed elements, using Richard’s Transform and Kuroda Identities. Our filter is equiripple so the filter in pass band will have ripples of amplitude “1+k2”.

The Steps leading to this transformation are given below:

Step 1:First step is to find the order of filter, to find the order; first we will find the normalized frequency by using:

| || | -1

Using ωc (2*pi*2.8 GHz) and ω (2*pi*4.7 GHz), our normalized frequency is =0.5

So look the value of order, for 0.5 frequency in the graph of attenuation versus normalized frequency of equiripple filter prototype (0.5 dB). The curves in the graph are used to find the order of the filter and inour case it comes out to be 5th order.

Attenuation VS Normalized Frequency Graph [1]

Step 2:Table exists for designing the equal-ripple low-pass filters with normalized source impedance and cutoff

2.8GHz and can be applied to either ladder circuit. This design data depends upon the specified pass band ripple level

This table lists the elements values for normalized low-pass filter prototype having 0.5 dB. The values for the prototype are given below

Element Values for Equal Ripple LPF Prototype with g0 = 1, wc = 1, N = 1-10 [1]

Step 3:Next step is to design the prototype. There are two circuits. One is series circuit and other is parallel. We have selected the parallel combination of circuit in which capacitor is placed in parallel. There were three capacitors and two inductors. Thus the number of elements depends upon the order of the circuit.

Parallel Prototype beginning with Shunt Element

Step 4:Next step is the impedance scaling and transforming. In the prototype design, the source and load resistances are unity. A source resistance can R can be obtained by multiplying the impedances of the prototype design by R. Then if we let the primes denote impedances scaled quantities, we have the new filter component values given by:

. . .

With the aforementioned steps we reach at a prototype circuit for the Low pass filter with cut off frequency 2.8 GHz containing Lumped Elements.

Redundant Filter Synthesis:The Lumped Element circuit can be used to approximate the response of a low pass filter at low frequencies but at high frequencies the distance between filter components is not negligible so we have to use distributed elements for better approximation. The conversion from Lumped circuit elements to distributed circuit elements is done through Richard’s transform. While the circuit can be simplified for implementation through Kuroda Identities, these separate filter components through transmission lines. As these extra elements do not affect the response of the filter this process is called redundant filter synthesis.

Richard’s Transform:Richard’s Transform is used to synthesize a LC circuit using Open & Short circuited transmission lines.

The input impedance of a short circuit transmission line of characteristic impedance Z0 is purely reactive.

So an inductor can be replaced by a short circuited stub of length βl while a Capacitor can be replaced by an open circuit stub of βl.

V_ACSRC1

Freq=freqVac=polar(1,0) V

RR2R=50 OhmC

C6C=3.88 pF

CC4C=5.77 pF

LL4

R=L=6.98 nH

LL6

R=L=6.98 nH

RR1R=50 Ohm

CC5C=3.88 pF

Richard’s Transformation [1]

The circuit will be transformed through a series of steps:

The four kuroda’s identities use redundant transmission lines sections to achieve a more practical microwave filter implementation by performing any of following operations.

Four Kuroda Identities n2 = (1 + Z2/Z1)

Step 5: Physically separate transmission lines stubs by adding the additional transmission lines sections called

unit elements and are ⋋8 at cutoff frequency. The unit elements thus commensurate with stubs used to

implement the inductors and capacitors of the prototype design. These elements do not affect the filter’s performance since they are matched to source.

Adding Transmission Lines to both sides:

Step 6:The next step is to use Richard transformation to convert series inductors to series stubs andshunt capacitors to shunt stubs Transform series stubs to shunt stubs according to the characteristics impedances of a series stub is L, and shunt capacitor is 1/C. and all the stubs are ⋋

along. ω =ω It is usually more convenient to work with normalized quantities until the last

step in the design. The series stubs are very difficult to form so we have used one of the kuroda’s identities to convert this to shunt stubs. We have applied kuroda’s identity to both the ends of filter.

= 1 + = 1.300

= 1 + = 2.58

CC3C=1.7058

CC2C=2.58

CC1C=1.7058

LL2

R=L=1.2296

LL1

R=L=1.2296

TermTerm1

Z=50 OhmNum=1

TermTerm2

Z=50 OhmNum=2

CC5C=2.54

RR2R=1

TermTerm6

Z=1Num=6

RR1R=1

TermTerm5

Z=1Num=5

TLINTL4

F=1 GHzE=90Z=1.59

TLINTL3

F=1 GHzE=90Z=1.59

LL10

R=L=.630

CC6C=2.08

CC7C=2.08

LL7

R=L=1.0 nH

Multiplying by 50 and hence arriving at the final circuit:

Step 7:The calculated amplitude response is plotted along with the response of the lumped elements version. Note that the distributed element filter has a sharper cutoff. Also note that the distributed elements response has a response that repeats after every doubles of cutoff frequency.

TLINTL6

F=1 GHzE=90Z=1.63

TLINTL8

F=1 GHzE=90Z=1.63

CC12C=.388

CC11C=.388

TLINTL9

F=1 GHzE=90Z=1.59

RR4R=1

TLINTL7

F=1 GHzE=90Z=1.59

RR3R=1

CC10C=2.08

CC9C=2.08

TLINTL5

F=1 GHzE=90Z=1.59

CC8C=2.54

Term

Term7

Z=50 Ohm

Num=7

Term

Term8

Z=50 Ohm

Num=8

CC17

C=19.6

CC16

C=24

CC15

C=24

CC13

C=129

CC14

C=129

TLIN

TL14

F=1 GHzE=90

Z=79.5

TLIN

TL10

F=1 GHzE=90

Z=79.5

TLIN

TL12

F=1 GHzE=90

Z=81.5

TLIN

TL11

F=1 GHzE=90

Z=81.5

TLIN

TL13

F=1 GHzE=90

Z=1.59

Simulation:The Response for the lumped element circuit is given below:

Lumped Element Circuit

The Response:

The Distributed Element Circuit (Unoptimized):

Response:

Response of the unoptimized Distributed Element Circuit (Unzoomed & Zoomed at pass band to show the 5 dB ripple)

Attenuation

Optimization:Due to the fact that we didn’t get our required 25 dB attenuation @4.7 GHz so we used the optimization function of ADS to optimize the attenuation. We set our goal & Number of Iterations and then we simulate the results to observe the improvements.

But there is a trade off if we optimize attenuation cut off frequency will be affected and if we optimize cut off frequency attenuation will not be our desired value. So when we optimized attenuation of cut off frequency was affected.

Response (Optimized):

Hence attenuation was somewhat made closer to our desired value, but this was a desired characteristic to have a filter that has high attenuation in stop band so our goal was somewhat enhanced by this matter.

Results & Discussion:

Hence we have designed a Low pass filter using both Lumped and distributed elements of cut off frequency 2.8 GHz. We did not get our Desired Attenuation. The reasons for these imperfections were:

1. When choosing the order of the filter we chose approximately 5 by looking at the graph there wasn’t 100% precision in our selection. Because our order wasn’t exactly 5 so the choice for prototype circuit elements wasn’t 100% accurate hence the deviations occurred because of that.

2. Lumped Elements are realized at low frequencies and provide sharper roll off.3. Exact Goal cannot be achieved using optimization as there is a tradeoff between cut off

frequency and attenuation.4. The Higher attenuation is mostly a desired characteristic of low pass filters in stop band.

References:[1] Microwave Engineering David M. Pozar 3rd Edition

[2] Wikipedia.org