performance study of active continuous time filters
TRANSCRIPT
Performance Study of Active Continuous
Time Filters
A Graduate Project Report submitted to Manipal University in partial
fulfilment of the requirement for the award of the degree of
BACHELOR OF ENGINEERING
In
Electronics and Communication Engineering
Submitted by
Abhinav Anand
080907202
Under the guidance of
Ms Anitha H & Mr D V Kamath
Assistant Professor-Senior Scale Assistant Professor-Sel Grade
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
MANIPAL INSTITUTE OF TECHNOLOGY
(A Constituent College of Manipal University)
MANIPAL – 576104, KARNATAKA, INDIA
MAY 2012
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
MANIPAL INSTITUTE OF TECHNOLOGY
(A Constituent College of Manipal University)
MANIPAL – 576 104 (KARNATAKA), INDIA
Manipal
14.05.2012
CERTIFICATE
This is to certify that the project titled Performance Study of Active Continuous
Time Filters is a record of the bonafide work done by Abhinav Anand (Reg No.
080907202) submitted in partial fulfilment of the requirements for the award of the Degree
of Bachelor of Engineering (BE) in ELECTRONICS AND COMMUNICATION
ENGINEERING of Manipal Institute of Technology Manipal, Karnataka, (A Constituent
College of Manipal University), during the academic year 2011-12.
Ms Anitha H
Assistant Professor- Senior Scale
Project Guide
M.I.T, MANIPAL
Prof. Dr K. Prabhakar Nayak
HOD, E & C.
M.I.T, MANIPAL
i
ACKNOWLEDGMENT
Firstly, I would like to thank my project guide, Mr D V Kamath, Assistant Professor-Selection
grade, and Ms Anitha H, Assistant Professor-Senior scale, who, at each step, of this project,
guided me with their full insight and technical know-how that gave me the right direction to
accomplish this piece of work.
I would also like to thank my project partners who were a part and parcel of this project work
and always infused me with zeal to work even at difficult times.
This would be an apt opportunity to thank our director and the head of our department, Dr K.
Prabhakar Nayak, who disciplined me to complete my project work within the deadline. They
not only helped me to get insight on how to carry on with the research work in the right
direction but also helped me correct my mistakes during the course of the project work.
I would also grab this opportunity to thank all the teachers in my panel, who attended to my
presentations patiently and guided me at each and every step. During these presentations, all
the teachers always helped me to view the results obtained with an analytical approach and
helped me to broaden my perspective of thinking.
I would also thank the lab technicians who helped me immensely throughout the course of
project work and were always there to attend to any problem patiently.
Last but not the least, I would like to thank all the teachers of our department who have
imparted knowledge to us and have been of great help in this project completion.
ii
ABSTRACT
Continuous time active RC filters using Opamps have been widely used in various applications
such as telecommunication networks, signal processing circuits, communication systems,
control, and instrumentation systems for a long time. However, active RC filters cannot work
at higher frequencies (over 200 KHz) due to op-amp frequency limitations, and are not suitable
for full integration. They are also not electronically tunable and usually have complex
structures. Moreover, the performance of filters designed by the use of passive components
degrades at audio frequencies and the required resistances and inductances values calculated
from the mathematical expression are very difficult to meet from the market.
The most successful approach to overcome these limitations is the use of Operational
Transconductance Amplifier (OTA) with integrated capacitors to replace the conventional op-
amp in active RC filters. By controlling the bias current of OTA, one can change its trans-
conductance, which is very useful in designing of the active filters. OTA-C filters offer
improvements in design simplicity, parameter programmability, circuit integrability, and high-
frequency capability when compared to op-amp-based filters, as well as reduced component
count. OTA-C filters having good sensitivity performance can be realized. Hence OTA-C filter
structures have received great attention from both academia and industry and have become the
most important technique for high-frequency continuous-time integrated filter design. OTA-C
filters are also widely known as gm-C filters.
The project was commenced by study of the basic circuit elements realized using OTAs. Lower
order gm-C filters were studied in theory followed by the circuit realization and analysis in
Cadence Virtuoso and Spectre RF circuit simulation tools. Later, hardware design and
experimental verification were carried out. The results obtained were then compared with the
simulated responses of the filters.
The theoretical and simulated responses of the filters were conformant with the real time
responses obtained from experimental verification.
The OTA-C filters are emerging as a promising circuit element for the realization of high
frequency filter operation. Standardization of the filter circuits can also be accomplished using
OTAs.
Software used: - Cadence Virtuoso, Spectre RF and PSpice
Hardware used: - CA3080 OTA IC and passive elements.
iii
LIST OF TABLES
Table No Table Title Page No
3.2.1 Characteristics of IC CA 3080E 26
4.1.1 Ideal and practical phase shift of first order all-pass filter 31
4.2.1 Ideal and simulated phase shift of second order all-pass filter 34
4.2.2 Q-values for different gm2 of second order all-pass filter 34
4.2.3 Ideal and practical phase shift of second order all-pass filter 36
iv
LIST OF FIGURES
Figure No Figure Title Page No
2.2.1 Ideal and practical amplitude response of low pass filter 4
2.2.2 Ideal and practical amplitude response of high pass filter 4
2.2.3 Ideal and practical amplitude response of band stop filter 5
2.2.4 Ideal and practical amplitude response of band pass filter 5
2.2.5 Circuit symbol of SOOTA, DOOTA, MO-OTA 6
2.2.6 Internal architecture of OTA 7
2.2.7 Grounded Voltage Variable Resistor 9
2.2.8 Floating resistor and its equivalent circuit 9
2.2.9 Voltage Summer 10
2.2.10 Simulation of grounded inductor 10
2.2.11 First order low pass active filter using OTAs 11
2.2.12 Two admittance model 12
2.3.1 Pole-Zero pattern for first order all-pass filter 13
2.3.2 Fourth order current mode OTA-C all-pass filter 15
2.3.3 Block diagram of fourth order current mode OTA-C all-pass filter 16
3.2.1 Circuit design of first order current mode OTA-C all-pass filter 19
3.2.2 Circuit design of second order current mode OTA-C all-pass filter 21
3.2.3 Circuit design of fourth order current mode OTA-C all-pass filter 23
3.2.4 Pin diagram of CA3080E 25
4.1.1 Circuit diagram of first order current mode OTA-C all-pass filter 28
4.1.2 Circuit schematic of first order current mode OTA-C all-pass filter 28
4.1.3 Amplitude and phase response of first order current mode OTA-C
all-pass filter
29
4.1.4 Input and output waveforms of first order current mode OTA-C
all-pass filter
30
4.2.1 Circuit diagram of second order current mode OTA-C all-pass
filter
31
4.2.2 Circuit schematic of second order current mode OTA-C all-pass
filter
32
4.2.3 Amplitude response of second order current mode OTA-C all-pass
filter
32
4.2.4 Phase response of second order current mode OTA-C all-pass
filter
33
4.2.5 Phase response of second order current mode OTA-C all-pass
filter for different Ibias values
35
v
4.2.6 Input and output waveforms of second order current mode OTA-C
all-pass filter
35
4.3.1 Circuit diagram of second order current mode OTA-C all-pass
filter
36
4.3.2 Gain and phase response for fourth order at fc=1.5MHz using
behavioural model
37
4.3.3 Group delay for fourth order at fc=1.5MHz using behavioural
model
38
4.3.4 Gain and phase response for fourth order at fc=20MHz using
behavioural model)
38
4.3.5 Group delay for fourth order at fc=20MHz using behavioural
model
39
4.3.6 Gain and phase response for fourth order at fc=1.5MHz using
practical model
40
4.3.7 Group delay for fourth order at fc=1.5MHz using practical model 40
4.3.8 Gain and phase response for fourth order at fc=20MHz using
practical model
41
4.3.9 Group delay for fourth order at fc=20MHz using practical model 41
4.3.10 Phase response at fc=15MHZ for behavioural and practical model 42
4.3.11 Phase response at fc=50MHZ for behavioural and practical model 42
A.1 Schematic circuit in cadence of second order low pass filter 47
A.2 Amplitude response of second order low pass for different C 47
A.3 & A.4 Hardware circuit of first order current mode all-pass filter 48
A.5 & A.6 Hardware circuit of second order current mode all-pass filter 49
vi
Contents
Page No
Acknowledgement i
Abstract ii
List Of Tables iii
List Of Figures iv
Chapter 1 INTRODUCTION
1.1 Introduction 1
1.2 Motivation 1
1.3 Objective 2
1.4 Organization of project report 2
Chapter 2 BACKGROUND THEORY
2.1 Introduction 3
2.2 Literature Survey 3
2.3 Analysis of Transfer Functions 13
Chapter 3 METHODOLOGY
3.1 Introduction 18
3.2 Methodology 18
3.3 Tools Used 26
Chapter 4 RESULT ANALYSIS
4.1 First order current mode OTA-C all-pass filter 28
4.2 Second order current mode OTA-C all-pass filter 31
4.3 Fourth order current mode OTA-C all-pass filter 36
Chapter 5 CONCLUSION AND FUTURE SCOPE
5.1 Summary 44
5.2 Conclusion 44
5.3 Future Scope of Work 44
REFERENCES 46
ANNEXURES 47
PROJECT DETAILS 51
1
CHAPTER 1
INTRODUCTION
1.1 Introduction
In this age of digital revolution, talking about continuous time filters, i.e., analog filters seem to
be old-fashioned. But, though the digital technology may bring advantages over the analog
filters, it has to interact with the real world – the analog world. Though traditional, analog
filters seem to play significant role in modern day technology. For instance, bandlimiting and
reconstruction filters are analog filters, operating in continuous time. Hence, any system that
interfaces with the real world will find use for continuous-time filters.
This project mainly discusses about design of continuous time filters using OTA-C approach.
The passive LCR filters built with inductors, capacitors, and resistors are not suited for VLSI
integration, since no satisfactory way of making inductors on chip has been discovered. Active
filters offer the opportunity to integrate complex filters on-chip and have been around for some
time as a means of overcoming the disadvantages associated with passive filters.
1.2 Motivation
The development of integrated transconductance amplifiers (the so-called OTA, or Operational
Transconductance Amplifiers) led to new filter configurations. At present there is growing
interest in current-mode signal processing because of its advantages like increased band-width,
high dynamic range and reduced power supply requirements. The OTA has two attractive
features: its transconductance can be controlled by changing the dc bias current externally and
it can work at higher frequencies. As resistors demand large chip area, in recent years, active
filters which use only OTAs and capacitors have been widely studied. These filters are called
OTA-C filters. The voltage-mode single-output OTA-C (SO-OTA-C) approach is one of the
most successful methods for continuous-time integrated filter design at high frequencies. At
present there is growing interest in current-mode active filter design using active elements such
as OTAs, Dual Output-OTAs, Multiple Output-OTAs, Current Conveyors, etc.
The demands on filter circuits have become ever more stringent as the world of electronics and
communications has advanced. For example, greater demands on bandwidth utilization have
required much higher performance in filters in terms of their attenuation characteristics, and
particularly in the transition region between passband and stopband. This in turn has required
filters capable of exhibiting high Q, but having low sensitivity to component changes and
offering dynamically stable performance. In addition, the continuing increase in the operating
frequencies of modern circuits and systems reflects on the need for active filters that can
2
perform at these higher frequencies; an area where the OTA active filter outshines its active-
RC counterpart.
1.3 Objective
The main objective of the project work is to study the design, analysis and performance
evaluation of certain continuous-time filters using OTA-C approach. It includes study of
certain OTA-C filter structures and study of comparative merits like sensitivity, spread in the
component values, etc. The analysis of CT filter circuits using non-ideal OTA model is to be
carried out. Next step is to carry out the transistor-level simulation of OTA-C filters using tools
like Cadence, PSpice, etc. It is also intended to carry out experimental verification of a few
OTA-C filters using ICs like CA3080E.
1.3 Organization of the project report
The report is divided into five chapters.
It begins with the background theory that is required behind the basic technology and idea used
in the project. It contains the literature survey that has been done over a course of one month to
understand the essentials of a Operational Transconductance Amplifier (OTA) in realisation of
continuous time filters. It also gives an overview of transfer function of some of the filters
studied.
Chapter 3 discusses the design methodology used in our project work. It also includes brief
description of different simulation tools used.
In Chapter 4, the simulation and experimental results obtained were presented.
Chapter 5 summarizes the conclusions and scope for future work.
3
CHAPTER 2
BACKGROUND THEORY
2.1 Introduction
The chapter introduces the reader with the detailed background theory regarding the project. It
contains the literature survey that was done during project and general analysis of the filter
used.
2.2 Literature Survey
2.2.1 Filter Characterization
This section gives a brief insight to the various types of filter that can be designed. The filters
are characterized as follows
Continuous-Time and Discrete-Time:-
In a continuous-time filter, both the excitation e and the response r are continuous functions of
the continuous time t, i.e.
e = e (t); r = r (t)
In contrast, in a discrete-time or sampled-data filter the values of the excitation and response
are continuous, changing only at discrete instants of time. These are the sampling instants.
e = e (nT); r = r (nT)
where T is the sampling period and n a positive integer.
Passive and Active:-
A passive filter is made up of passive elements like resistors, inductors, capacitors,
transformers, etc. If the elements of the filter include amplifiers or negative resistances, this
will be called active.
2.2.2 Frequency response of the filters
Ideal filter response refers to Ideal transmission of a signal from its source to the receiver
requires the following two conditions to be satisfied:
1. The spectrum of the signal remains unchanged.
2. The time differences between the various components of the signal remain
unchanged.
4
The filters according to their frequency responses can be classified as lowpass, highpass,
bandpass, bandstop, allpass and arbitrary frequency response (equalizers).
Low-pass filter
In case of a low pass filter, all frequencies below the cutoff frequency ωc pass through the filter
without obstruction. The band of these frequencies is the filter passband. Frequencies above
cutoff are prevented from passing through the filter and they constitute the filter stopband.
A small error is allowable in the passband, while the transition from the passband to the
stopband is not abrupt. The width of this transition band (ωs-ωc) determines the filter
selectivity. Here ωs is considered to be the lowest frequency of the stopband, in which the gain
remains below a specified value.
Figure 2.2.1 (a) Ideal and (b) Practical amplitude response of low pass filter [3]
High-pass filter
In the high-pass filter the pass-band is above the cutoff frequency ωc, while all frequencies
below ωc are attenuated when passing through the filter.
Figure 2.2.2 Ideal and practical high-pass filter amplitude response [3]
5
Band-stop filter
This filter possesses two passbands separated by a stopband rejected by the filter. There are
also two transition bands.
Figure 2.2.3 Amplitude response of the ideal and practical band-stop filter [3]
All-pass filter
Ideally this filter passes, without any attenuation, all frequencies (0 to ∞). If its phase response
is linear, then it can operate as an ideal time delayer. In practice the phase can be linear, within
an acceptable error, up to a certain frequency ωc. For frequencies below ωc the allpass filter
operates as a delayer. It is useful in phase equalization.
Band-pass Filter
The passband lies between two stop-bands, the lower and the upper.
Figure 2.2.4 Amplitude response of ideal and practical bandpass filter. [3]
2.2.3 Operational Transconductance Amplifier (OTA)
The op-amp based active filters have been widely used in various low frequency applications
in telecommunication networks, signal processing circuits, communication systems, control,
and instrumentation systems for a long time. However, active RC filters cannot work at higher
frequencies (over 200 KHz) due to op-amp frequency limitations and are not suitable for full
integration. They are also not electronically tunable and usually have complex structures.
Currently the continuous-time designs use devices other than op-amps such as OTAs. The use
6
of the Operational Transconductance Amplifier (OTA) and capacitors to realize filters, namely
OTA-C filters has been a very successful approach. In OTA-C filters, the typical load is
usually capacitive. In the recent years OTA-based high frequency integrated circuits, filters and
systems have been widely investigated.
The OTA is represented symbolically as shown in fig 2.2.5. An ideal OTA is a Differential-
Input Voltage-Controlled Current Source (DVCCS), with infinite input and output impedances
and constant transconductance.
The output current equation is given as:-
(2.1)
where V+ and V
- are the voltages applied at non-inverting and inverting terminals respectively,
gm is the trans-conductance gain, Io is the output current and Iabc is the bias current.
Figure 2.2.5 Circuit symbol of SO-OTA, DO-OTA and MO-OTA
The important merits in favour of OTA-C filters are its gm value can be controlled by changing
the external dc bias current or voltage, and they can work well at higher frequencies. The on-
chip tuning is the most effective way to overcome fabrication tolerances, component non-
idealities, aging, and changing operating conditions such as temperature.
The OTA has been implemented widely in CMOS and bipolar and also in other technologies
like BiCMOS and GaAs. The typical values of transconductance are in the range of tens to
hundreds of µS in CMOS and up to mS in bipolar technology. The CMOS OTA can be used
typically in the frequency range up to of several 100 MHz.
Features of an OTA
Input Impedance (Zin) = ∞
Output Impedance (Zo) = ∞
OTA is used from 1Hz to several hundreds of MHz
Current consumption of OTA is only twice the Ibias value.
Slew Rate as high as 50v/µsec
g m
V + i
+
-
I o
V - i
g m
I + o
V - i
I - o
-
+V + i
-
++
I o+
-
+
V - i
V + i
-
g m
7
Internal Architecture of OTA
The fig 2.2.6 shows the simplified internal architecture of an OTA using bipolar transistors.
Transistors Q1 and Q2 form a differential pair. Current mirror Q3-Q4 accepts the control current
Ibias which can be adjusted by an external resistance Rext and control voltage Vc. Due to current
mirror Q3-Q4, we get I4=Ibias. The current I4 is divided at the emitters of Q1 and Q2. Thus
I1 + I2 = I4 (2.2)
Figure 2.2.6 Internal architecture of OTA
Current mirror Q5-Q6 duplicates I2 to yield I9=I2. The current I2 is in turn duplicated by the
current mirror Q9-Q10 to produce I10=I9=I2. Similarly, current mirror Q7-Q8 duplicates I1 to
yield I8=I1. By KCL we have,
I0 = I8 – I10 = I1 – I2 (2.3)
The voltage gain Av can be written as
Av =
=
= gm*RL (2.4)
By analysing the circuit, we get
8
⁄ and
⁄ (2.5)
where Vt = Thermal Voltage equivalent of temperature.
[
] (2.6)
Hence,
(2.7)
Applying KVL, we get
| |
(2.8)
Comparison between OTA and OPAMP
OTA OPAMP
1. Filters can work under much higher
frequencies.
1. Filters cannot work at higher
frequencies.
2. Wider bandwidth (few hundreds of
MHz)
2. Less bandwidth (few hundreds of
KHz)
3. Controllability of gm makes OTA
filters more versatile in tuning and
integration.
3. OPAMP filters are not electronically
tunable.
4. Useful to implement components like
resistor, negative resistor, inductor
etc.
4. Implementation of simulated inductor
requires more number of Op-amps.
Basic building blocks using OTAs
There are various passive elements which can be built using a single OTA or multiple OTAs.
Some of them are:-
9
1. Voltage Variable Resistor
(a) Grounded Voltage Variable Resistor-
Consider fig 2.2.7 which simulates grounded resistor using OTA. Applying KCL at
node A gives
Iin + Io = 0 (2.9)
Where I0 = -Vm * gm (2.10)
Substituting the value of Io from eqn. 2.10 in eqn. 2.9 we have,
(2.11)
Figure 2.2.7 Grounded Voltage Variable Resistor
(b) Floating Voltage Variable Resistor
(i) (ii)
Figure 2.2.8 (i) Floating resistor and its (ii) equivalent circuit
I01=gm1 * (V2-V1) (2.12(a))
I02=gm2 * (V1-V2) (2.12(b))
Assuming that V1 > V2, implies that the current flows from 1 to 2.
Therefore,
I12 = -I01=gm1 * (V1-V2) (2.13(a))
I12 = I02=gm2 * (V1-V2) (2.13(b))
10
Hence, Impedance (Z)
(2.14)
If gm1=gm2, then Z = 1/gm (2.15)
2. Voltage Summer
With the help of OTAs voltages can be added and hence summer can be implemented.
Figure 2.2.9 Voltage Summer
(2.16)
3. Grounded Inductor
With the help of multiple OTAs grounded inductor can be easily implemented and the
gains of the OTAs determine the inductance value.
Figure 2.2.10 Simulation of grounded inductor
11
Fig 2.2.10 shows the resulting circuit for grounded inductor
From 1st OTA, I01=gm1*V1 (2.17)
Now, I01=IC+I2-
=> I01=IC [Since, I2-=0 because I2
+=0] (2.18)
=> IC=gm1*V1 [From (2.17) and (2.18)] (2.19)
From 2nd
OTA, I02= -gm2*VC
=> I1 = -I02 = gm2VC = gm2*IC/sC
=> I1 = gm2*gm1*V1/sC [From (2.19)]
=> Zin=V1/I1= sC/ gm1*gm2
Therefore
(2.20)
2.2.4 Realization of first order filter using OTA
Consider a first order low pass filter as shown in fig 2.2.11 below.
Figure 2.2.11 First order low pass active filter using OTAs
The OTA block here acts as a resistor with resistance equal to 1/gm .
Therefore transfer function of active filter is
⁄
⁄ (2.21)
12
2.2.5 Dual Output OTA based current mode two admittance configurations
Figure 2.2.12 Two admittance model
Fig 2.2.12 illustrates the two admittance model which was used for the project and the
continuous filters were designed using the same.
The transfer function for this configuration is:-
( )
( ) (2.22)
2.2.6 Group Delay
Group delay is a useful measure of time distortion, and is calculated by differentiating
the phase response with respect to frequency. The group delay is a measure of the slope of the
phase response at any given frequency. Variations in group delay cause signal distortion, just
as deviations from linear phase cause distortion.
Given, a filter with frequency domain transfer function as
(2.23)
then the group delay is given as
(2.24)
Group delay has dimensions of time and is thus measured in seconds.
2.2.7 Quality Factor
Quality factor determines the rate of change of phase response. It is a dimensionless parameter.
For example, the transfer function of second order all-pass filter is given by
+
- +I o
g m1I
in
I in
-
Y p
Y n
13
(2.25)
Hence, Quality factor Q is given as
where ξ is the damping ratio of the second order
frequency domain transfer function. Higher the quality factor, steeper will be the response of
the filter. Similarly, low quality factor results in more gentle slope and early fall of the filter
response.
2.2.8 Phase response of all-pass filter
The phase response of a filter is defined as the plot of phase of the output signal with respect to
frequency.
In multi-pole filters, each of the poles add phase shift, so that the total phase shift will be
multiplied by the number of poles. For example, total phase shift at cut-off frequency for a two
pole system is 180, 270 for a three pole system, and so on.
2.3 Analysis of Transfer Functions
2.3.1 Location of poles and zeros of all-pass filters
For all-pass filter, the zeros and poles are mirror images of each other with respect to plane
in s-domain. For instance, in case of first order all-pass filter, the transfer function is given as,
(2.26)
Therefore, the pole-zero pattern is given as:-
Figure 2.3.1 Pole-zero pattern for first order all-pass filter
14
Similarly, the second order all-pass filter transfer function is given as
(2.27)
Transfer functions of the 1st order, 2
nd order and 4
th order current mode OTA-C all pass filters
were derived. The general transfer function of an nth
order all-pass filter circuit is given by
∑
∑
(2.28)
where P(s) is a polynomial of the complex frequency variable s with coefficients αi.
2.3.2 First order current mode OTA-C all-pass filter
When Yp = sC and Yn = R, the above admittance model (fig 2.2.12) behaves as a first order all-
pass filter. The transfer function of the above filter is
[
(
)
(
)] (2.29)
When gm in the eqn 2.29 is equal to 1/R then the above equation becomes the transfer function
of first order all pass filter.
Phase of the filter is given by arg H(s) which is,
(2.30)
At cut-off frequency, arg H(s) = 90°
2.3.2 Second order current mode OTA-C all-pass filter
When ⁄ and Yn = gm2, the admittance model (fig 2.2.12) behaves as a
second order all-pass filter. The transfer function of the above filter is
(
)
(
)
(2.31)
When gm1 = gm2, then a second order all-pass filter is realized. By realizing inductor using
OTAs, transfer function becomes
[
(
) (
)
(
) (
)] (2.32)
15
Phase of the second order all-pass filter is given by arg H(s)
[
] (2.33)
Cut-off frequency fo is given by
√
(2.34)
Quality Factor Qo is given by
√
(2.35)
At cut-off frequency fo, the phase shift obtained is 180°.
2.3.3 Fourth order current mode OTA-C all-pass filter
In this section we consider the realisation of fourth-order current-mode all-pass filters derived
from the general basic topology using ladder simulation approach. In this approach, the transfer
function of the filter is given by
(2.36)
where Y(s) is the input admittance function of a LC ladder network. The Y(s) provides the
position of poles which are mirrored in to the right-hand s-plane to generate exactly opposite
zero positions.
Figure 2.3.2 Fourth order current mode OTA-C all-pass filter
16
The current mode transfer function of the fourth order all-pass filter is given as
(2.37)
Where,
(2.38)
And I0= IAP4
Substituting eqn. 2.38 in eqn. 2.37 we get,
(
) (
) (
)
(
) (
) (
)
(2.39)
If Inductors L1 and L2 are realised using OTAs and capacitors, then eqn. 2.39 results into
(
) (
) (
)
(
) (
) (
)
(2.40)
The modified circuit of fig 2.3.2 is shown in fig 2.3.3
Figure 2.3.3 Block diagram of fourth order current mode OTA-C all-pass filter using
capacitors
With equal transconductance approach (gm1=gm2=gx1=gx2=gx3=gx4=g) the transfer function
becomes
(2.41)
17
where αi represents the co-efficient of filter designs. From eqn. 2.40 after rationalising we
obtained the α values as:
(2.42)
(2.43)
(2.44)
(2.45)
(2.46)
18
CHAPTER 3
METHODOLOGY
3.1 Introduction
This chapter presents the methods that were adopted during the course of the project. Initial
study of technical papers on OTA-C filters was followed by the simulation using Cadence
Virtuoso tools. Later, higher order filters were studied, simulated and analysed. First and
second order current mode OTA-C filters were realised on hardware.
For this purpose “CA3080 E” OTA IC was used. The entire circuit was rigged up on the
breadboard and the graph (output) obtained was observed on the CRO.
The results obtained from the hardware implementation were then found to be in accordance
with the expected result. The project was hence concluded on the note that the proposed
designs were correct and could be used for further references. The project also highlights the
wide use of gm-C filters and its ability to be used at high frequencies.
3.2 Methodology
This section gives an insight to the detail methodology that was adopted along with the design
issues and the tools used in the project. The following sections deals with each of these things
in detail.
3.2.1 Detailed Methodology
In this project, the design and implementation of first, second and fourth order current mode
OTA-C all pass filter has been considered. The study of transfer function for these OTA-C
filters has been carried out. CMOS OTA symbol was created in Cadence Virtuoso for realising
OTA-C filters. Simulation results were obtained using Spectre RF.
Certain circuits were also realised and simulated using PSpice. Various analyses like ac, dc,
parametric and transient analysis, etc. were carried out.
The phase response and gain response of the output were studied. It was then followed by
hardware implementation using the OTA, CA3080E, along with some passive elements.
Circuit design was carried out in accordance with the guidelines. The output was observed on
the CRO (Cathode Ray Oscilloscope) and it was compared with the theoretical results.
19
Similar approach was followed for second order current mode OTA-C all-pass filter and the
hardware implementation was carried out. Higher order filters were simulated and analysed in
PSpice. The netlist was written and simulated to study the responses and group delay of the
same. Comparison of simulation results for ideal and practical model at different frequencies
was also carried out using PSpice code. Then analysis of phase responses for different quality
factors was also carried out.
3.2.2 Circuit layout and design equations:
a. First order current-mode all-pass filter
The circuit was realised using single output OTA with one of their inverting and non- inverting
input shorted so as to obtain an inverting current. The circuit realisation is shown below:
Figure 3.2.1 Circuit design of first order current mode OTA-C all-pass filter
As shown in the fig 3.2.1 there are two stages in the circuit, the first stage acts as input current
generator and the second stage acts as the first order all-pass filter. Since we cannot have
current source as input, hence we have employed first stage of OTA as the voltage to current
converter.
The design equations used are as follows:
(
) (3.1)
(3.2)
20
Here Vy is the diode potential attached to pin 5 of the OTA IC. Also the supply voltages
applied to the circuit V+
and V- are +11.6 V and -11.6V respectively
.Design for the first stage (current generator):
Vm = 8.7 V and Rm = 47 KΩ
Gm= 8.3 mmho
Ibias = 0.432 mA
Design for the second stage (all-pass filter):
Cut-off frequency fc:
(3.3)
The design was carried out for a cut-off frequency of 600 kHz, since the IC used for hardware
implementation had a maximum bandwidth of 2MHz.
C= 560 pF
R= 470 Ω
gm= 1/R =2.13 mmho
Ibias = 0.11 mA
Vm= 5V
Rm= 150 KΩ
The phase equation for the first order all-pass filter is:
(3.4)
where, H(S) is the transfer function of the first order all-pass filter given in eqn 2.29
Accordingly the phase response was calculated and tabulated.
b. Second order current mode all-pass filter
Same approach (first order all-pass filter) was followed here and same single output OTA was
used to realize the circuit. The circuit realization is shown below:
21
Figure 3.2.2 Circuit diagram for second order current mode OTA-C all-pass filter
As shown in the fig 3.2.2 there are two stages in the circuit, first being voltage to current
converter stage which is also called the input stage. The second stage is the all-pass filter stage.
In the second stage, U3 and U4 amplifiers along with capacitor C2 are used as inductor and the
U5 and U6 are used in the filter section of the circuit. Inductor along with capacitor C1 forms
the feedback path for the second order filter.
The cutoff frequency expression for the second order all-pass filter
√
(3.5)
where g3 and g4 are the transconductance of the OTAs used as inductors.
The cutoff frequency chosen for the design was 190 KHz.
C1
V1
R6
R2
R3
R4R5
R1
0
C2
V2
V3
R7
R8
V4
0
0
0
0
U3
CA3080 OTA
+-
OU
T
U4
CA3080 OTA
+ -
OU
T
U5CA3080 OTA
+
-
OUT
U6
CA3080 OTA
+
-
OUT
U2
CA3080 OTA
+
-
OUT
U1
CA3080 OTA
+
-
OUT
OUTPUT
Ibias
Ibias
Ibias
Ibias
Ibias
Io
Iin
Iin
Ibias
22
Voltage to current converter
;
(
) (from eqn. 3.1)
(from eqn. 3.2)
Inductor design
,
,
C2=8nF
(
)
Filter design
,
,
C1=8nF,
(
)
Since the gain of the design was chosen to be one therefore,
With the help of these design equations the hardware implementation was carried out and the
output as observed in the CRO. The phase shift at cutoff frequency was observed and was
found to be in accordance with the theoretical values. The phase shift equation of second order
filter is given as:
[
] (3.6)
where, H(S) is the transfer function of the second order all pass filter given in eqn. 2.32
The filter was also analyzed in Cadence for various quality factors. This was done by varying
the bias current and performing a dc sweep to get gm of the mosfet used in OTA filter and then
calculating the quality factor using the formula (eqn. 2.35)
23
√
(3.7)
After this the effect of quality factor on phase response was studied and analysed.
c. Fourth order current mode OTA-C all-pass filter
After the second order implementation, further investigations were carried out on fourth order
filters. The circuit diagram for the fourth order filter is shown below:
:
Figure 3.2.3 Circuit diagram for fourth order current mode OTA-C all-pass filter
Above circuit has the transfer function as shown in previous chapter (eqn. 2.41):-
(3.8)
where αi represents the co-efficient of filter designs. From eqns. 2.42-2.46 we get following αi
values.
The general transfer function for nth
order all-pass filter is:
∑
∑
(3.9)
24
where A represents the gain of the filter and αi represents the co-efficient of filter designs.
Now using other set of equations for α (co-efficient) [2] calculation we get
; ; ; ;
The design values were chosen as
R1=34KOhm; R2=14.4 KOhm; R3=7.5 KOhm; R4=3.3 KOhm
Now since cutoff frequency of nth
order filter depends on the nth
root of the leading coefficient,
so using this relation the capacitances were calculated and thereby, the coefficients were
derived.
Using these values of coefficients the new capacitances were determined for the given circuit.
PSpice code was written for these filters for different cut off frequencies using the newly
determined capacitance values.
PSpice code was written using both behavioral (using voltage controlled-current source) and
practical model OTAs. Practical OTA was modeled in PSpice using 0.5µm MOSIS model
parameters, which are given in Appendix 4. The aim was to draw comparison between the two
and study their phase response and group delay. The plots obtained were then studied and
conclusions were drawn.
Design values for various cutoff frequencies are given below
fc= 1.5 MHz
C1=10.83pF, C2=16.91pF, C3= 6.78pF, C4= 2.3pF
gm= 70µs
fc= 20MHz
C1=0.822pF, C2=1.283pF, C3= 0.5143pF, C4= 0.1744pF
gm= 70µs.
The value of gm was determined by using Ibias as 17.2 µA.
25
3.2.3 Component Specification
CA 3080 E, belonging to the CA 3080 OTA family, is a differential input and a single-ended
output OTA. In addition, it has an amplifier bias input which may be used either for gating or
for linear gain control. It also has a high output and input impedance.
It has an excellent slew rate of about 50 V/µs, making it useful for multiplexer and unity gain
voltage followers. This is a product manufactured by Intersil and is easily available in the
market at much cheaper rate. The pin configuration is shown below
Figure 3.2.4 Pin diagram of CA3080E [1]
26
The typical characteristics of the IC are as follows: [1]
Table 3.2.1 Characteristics of IC CA 3080E
Characteristics Limits
Supply Voltage Range ±2 - ±5 V
Maximum Differential Input Voltage ±5 V
Power Dissipation 125mW maximum
Input signal current 1mA maximum
Amplifier Bias Current 2mA maximum
Forward Transconductance 9600µmho typical
Open Loop Bandwidth 2MHz
Unity Gain Slew Rate 50V/µsec
Common Mode Rejection Ratio 100dB typical
3.3 Tools Used
The software used for simulation was Cadence Virtuoso and netlisting for fourth order filter
was carried out using PSpice.
3.3.1 Cadence Virtuoso
Cadence is an Electronic Design Automation (EDA) environment that allows integrating in a
single framework different applications and tools (both proprietary and from other vendors),
allowing to support all the stages of IC design and verification from a single environment.
These tools are completely general, supporting different fabrication technologies. When a
particular technology is selected, a set of configuration and technology-related files are
employed for customizing the Cadence environment. This set of files is commonly referred as
a design kit.
The basic design flow in the cadence starts with the circuit schematic build up. First, a
schematic view of the circuit is created using the Cadence Composer Schematic Editor. Then,
the circuit is simulated using the Cadence Affirma analog simulation environment. Different
simulators can be employed, some sold with the Cadence software (e.g., Spectre) some from
other vendors (e.g., HSpice) if they are installed and licensed. The simulator used in this
project was Spectre.
27
Once circuit specifications are fulfilled in simulation, the circuit layout is created using the
Virtuoso Layout Editor.
All the entities in Cadence are managed using libraries, and each library contains cells. Each
cell contains different design views (the structure is similar –and physically corresponds - to a
directory (library) containing subdirectories (cells), each one containing files (views)). Thus,
for instance, a certain circuit (e.g. an ADC) can be stored in a library, and such library can
contain the different ADC blocks (comparators, registers, resistor strings, etc.) stored as cells.
Each block (cell) contains different views (schematic, layout, etc.).
The schematic is made using the components with this library and simulated with the
SPECTRE RF.
3.3.2 PSpice
PSpice is a simulation program that models the behaviour of a circuit. PSpice simulates analog
only circuits, whereas PSpice A/D simulates any mix of analog and digital devices.
Spice stands for Simulation Program for Integrated Circuits Emphasis. PSpice is the PC
version of Spice. PSpice has analog and digital libraries of standard components (such as
NAND, NOR, flip-flops, MUXs, FPGA, PLDs and many more digital components,). This
makes it a useful tool for a wide range of analog and digital applications. Several types of
analysis is possible in Spice which is done at a default temperature of 300K, though analysis at
different temperature can be carried out.
There are two ways to simulate any circuit. One is by writing the netlist and another is by
drawing the schematic. Though both approaches bear the same conclusion but former approach
gives the liberty to design complex circuits and analyse them in case model parts are absent in
the library. Though netlist can also be generated using the schematic drawing but it is always a
good approach to simulate the circuit using the netlist. Drawing schematics need to include
components from the standard libraries which are already present in the PSpice version. There
are many libraries which only get added as the versions improve but most common libraries are
Analog, Source, Eval, Abm, Special
Using these libraries, components are included for analysis. The schematic is drawn in Orcad
Capture and the analysis plots are observed in PSpice A/D.
28
CHAPTER 4
RESULT ANALYSIS
This section discusses the results that were obtained in the project work. It contains the plots
which were obtained using the Cadence Virtuoso and PSpice. The waveforms that were
obtained using hardware implementation of the filters are also presented in this section.
4.1 First order current-mode OTA-C all-pass filter
Figure 4.1.1 Circuit diagram of first order current mode OTA-C all-pass filter
4.1.1 Implementation on Cadence Virtuoso
Figure 4.1.2 Circuit schematic of first order current mode OTA-C all-pass filter
29
Figure 4.1.3 Amplitude and phase response of first order current mode OTA-C all-pass filter
Here gm of the OTA used in Cadence is 70µmho.
From eqn. 2.30 we have phase shift of first order all-pass filter as
Now,
When ω=0; arg H(s) is equal to 180 and this result can also be seen on the phase plot
shown in the fig 4.1.3.
Theoretical cut-off frequency, fo is
From the phase plot at this theoretical cut-off frequency, phase shift is 88.36 (180 -91.64 )
whereas from the phase shift equation it should be 90 which is in the acceptable range.
Also since gm = (1/R), therefore gain =1 which can be seen on the amplitude plot shown in the
fig 4.1.3.
30
4.1.2 Observations and Results of Hardware Implementation
(a)
(b)
(c)
Figure 4.1.4 Input and output waveforms at frequency (a) fc=600K (b) f=800K (c) f=300K
Fig 4.1.4 shows the output obtained on CRO for different frequencies.
(a) For cut-off frequency fc=600K phase shift obtained is
Phase shift ϕ = (0.7/3) * 360° = 85°
(b) For frequency f=800K phase shift obtained is
Phase shift ϕ = (0.6/2.8) * 360° = 77°
(c) For frequency f=300K phase shift obtained is
Phase shift ϕ = (1/3) * 360° = 120°
Ideal phase shift at cut-off frequency is 90°, at f = (fc/2) = 300K it is 127° and at f=2fc=600K it
is 74°
31
The above results are tabulated along with the ideal phase shift in the table given below
Table 4.1.1 Ideal and practical phase shift of first order current mode OTA-C all-pass filter
4.2 Second order current mode OTA-C all-pass filter
Figure 4.2.1 Circuit diagram of second order current mode OTA-C all-pass filter
Frequency Ideal Phase
(in degrees)
Simulated Phase
(in degrees)
300K 127 120
600K 90 85
800K 74 77
32
4.2.1 Implementation on Cadence Virtuoso
Figure 4.2.2 Circuit schematic of second order current mode OTA-C all-pass filter
Figure 4.2.3 Amplitude response of second order current mode OTA-C all-pass filter
33
Figure 4.2.4 Phase response of second order current mode OTA-C all-pass filter
From eqn. 2.33 we have phase for the second order all-pass filter as
[
]
From the above equation at ω=0 phase should be 180 which can be verified from the phase
response plotted in fig 4.2.4.
Cut-off frequency fo from eqn. 2.34 is given by
√
Theoretically, cut-off frequency comes out to be 1.114MHz and from the equation phase
should be 0 i.e. there should be a phase shift of 180 . From the fig 4.2.4 phase at 1.114MHz is
equal to 10 ; therefore phase shift is equal to 170 .
Also, since gm1 = gm2 therefore gain is equal to 1 which is justified by the amplitude response
curve plotted in fig 4.2.3.
Ideal phase and simulated phase for cut-off frequency (fc), fc/2 and 2fc are shown in the Table
4.2.1
34
Table 4.2.1 Ideal and simulated phase of second order current mode OTA-C all-pass filter
From eqn. 2.35 quality factor of second order all-pass filter is
√
And
√
Hence, in order to keep the cut-off frequency same and quality factor to be different,
values need to be varied.
We know that changing the Ibias value, changes the transconductance value of the OTA.
Hence, dc analysis was performed to get different transconductance values by varying Ibias. The
results of the analysis are tabulated below:-
Table 4.2.2 Q-values for different gm2
Quality factor determines the rate of change of phase response. Higher the quality factor,
steeper will be the response of the filter. Similarly, low quality factor results in more gentle
slope and early fall of the filter response. The simulation plot given below proves the above
mentioned statement.
Frequency Ideal Phase
(in degrees)
Simulated Phase
(in degrees)
10 kHz 179.84 180
1.114 MHz 0 10
3 MHz -124.60 -130
gm2 (µS) Ibias (µA) Q-factor
71.7228 10 1
23.4232 4.375 3.061
16.7954 2.5 4.27
35
Figure 4.2.5 Phase response of second order current mode OTA-C all-pass filter
for different Ibias
4.2.2 Observations and Results of Hardware Implementation
(a)
(b)
(c)
Figure 4.2.6 Input and output waveforms at frequency (a) f=20K (b) f=120K (c) f=195K
36
For hardware implementation of second order all-pass filter, the cut-off frequency was taken to
be fc = 190 KHZ.
At fc, the ideal phase shift between the input and output waveforms is 0 and the phase response
drops by 180 at cut-off frequency.
As mentioned earlier in eqn. 2.33 the theoretical phase equation for second order all-pass filter
is given as:-
[
]
The above results are tabulated along with the ideal phase shift values in the table given below
Table 4.2.3 Ideal and practical phase shift of second order current mode OTA-C all-pass filter
4.3 Fourth order current mode OTA-C all-pass filter
Figure 4.3.1 Circuit diagram of fourth order current mode OTA-C all-pass filter
Frequency (Hz) Ideal Phase-Shift
(degrees)
Practical Phase-Shift
(degrees)
20K 167 180
120K 86 90
195K -9 0
37
4.3.1 PSpice simulation using behavioural OTA model
In this section, the OTA blocks are replaced with ideal voltage controlled current sources to
study the ideal response of the fourth order all-pass filter.
The simulation plots of amplitude response, phase response and group delay of fourth order
filter for different cut-off frequencies are given below:-
a) Cut-off frequency fc=1.5MHz
Figure 4.3.2 Combined gain (in dB) and phase response plot for fourth order current mode
OTA-C all-pass filter at fc=1.5MHz using behavioural model
Frequency
1.0Hz 1.0KHz 1.0MHz 1.0GHz
1 P(I(V1)) 2 (20* LOG10(I(V1)/I(Iin)))
-800d
-600d
-400d
-200d
0d1
-2.0
-1.0
0
1.0
2.02
>>
38
Figure 4.3.3 Group delay for fourth order current mode OTA-C all-pass filter at fc=1.5MHz
using behavioural model
b) Cut-off frequency fc=20MHz
Figure 4.3.4 Combined gain (in dB) and phase response plot for fourth order current mode
OTA-C all-pass filter at fc=20MHz using behavioural model
Frequency
1.0Hz 100Hz 10KHz 1.0MHz 100MHz 10GHz
G(I(V1))
0s
200ns
400ns
600ns
800ns
Frequency
100Hz 10KHz 1.0MHz 40MHz
1 P(I(V1)) 2 (20* LOG10(I(V1)/I(Iin)))
-600d
-400d
-200d
0d1
-2.0
-1.0
0
1.0
2.02
>>
39
Figure 4.3.5 Group delay for fourth order current mode OTA-C all-pass filter at fc=20MHz
using behavioural model
4.3.2 PSpice simulation using practical model OTA
In this section, we use the practical model of OTA for realizing the fourth order all-pass filter.
The practical model of OTA takes into account, the limitations and non-idealities of the
transistors, comprised in the OTA, at higher frequencies.
The simulation plots of amplitude response, phase response and group delay of fourth order
filter for different cut-off frequencies are given below.
Frequency
1.0Hz 100Hz 10KHz 1.0MHz 100MHz
G(I(V1))
0s
20ns
40ns
60ns
40
a) Cut-off frequency fc=1.5MHz
Figure 4.3.6 Combined gain (in dB) and phase response plot for fourth order current mode
OTA-C all-pass filter at fc=1.5MHz using practical model
Figure 4.3.7 Group delay for fourth order current mode OTA-C all-pass filter at fc=1.5MHz
using practical model
Frequency
100Hz 1.0KHz 10KHz 100KHz 1.0MHz
1 P(I(V6)) 2 (20 * LOG10(I(V6)/I(Iin1)))
-600d
-400d
-200d
0d1
-5.0
0
5.02
>>
Frequency
100Hz 1.0KHz 10KHz 100KHz 1.0MHz
G(I(V6))
0s
200ns
400ns
600ns
800ns
41
b) Cut-off frequency fc=20MHz
Figure 4.3.8 Combined gain (in dB) and phase response plot for fourth order current mode
OTA-C all-pass filter at fc=20MHz using practical model
Figure 4.3.9 Group delay of fourth order current mode OTA-C all-pass filter designed for
fc=20MHz using practical model
Frequency
100Hz 10KHz 1.0MHz 40MHz
1 P(I(V6)) 2 (20* LOG10(I(V6)/I(Iin1)))
-600d
-400d
-200d
0d1
-10
0
10
-15
152
>>
Frequency
100Hz 1.0KHz 10KHz 100KHz 1.0MHz 10MHz
G(I(V6))
0s
20ns
40ns
60ns
42
4.3.3 Comparison of phase responses obtained using behavioural and practical OTA model
a) Cut-off frequency fc=15MHz
Figure 4.3.10 Phase response at fc=15MHz for behavioural and practical model
b) Cut-off frequency fc=50MHz
Figure 4.3.11 Phase response at fc=50MHz for behavioural and practical model
Frequency
1.0Hz 100Hz 10KHz 1.0MHz 100MHz
P(I(V2)) P(I(V3))
-800d
-600d
-400d
-200d
0d
Frequency
1.0Hz 100Hz 10KHz 1.0MHz 100MHz
P(I(V2)) P(I(V3))
-800d
-600d
-400d
-200d
0d
43
In fig 4.3.10 the cut-off frequency of practical model OTA is observed to be 14.43MHz while
the design value for cut-off frequency is chosen to be 15MHz. Similarly, in fig 4.3.11 cut-off
frequency of the practical model is observed to be just 39.5MHz, while the design value for
cut-off frequency is chosen to be 50MHz.
Hence, it is evident from the simulation results that the practical model of OTA deviates from
ideal characteristics as we move towards higher frequency range.
44
CHAPTER 5
CONCLUSION AND FUTURE SCOPE OF WORK
5.1 Summary
The objective of the project is to study and design continuous time filters which can work on
high frequencies. Programmable high-frequency active filters can be realized using OTAs.
Since the filters designed using passive elements are unable to work at high frequencies, and
have inherent ill-effects and non-idealities, this design brings a new horizon to high frequency
filter realisation. The simulation carried out in Cadence and PSpice and a valid realisation
using hardware with the help of OTA IC is the main objective of the project work.
This not only supports our hypothesis of versatility of gm-C filters but also opens a new avenue
for circuit optimization and designing.
5.2 Conclusion
The project was taken up to study and investigate the performance of gm-C filters. The
emphasis was to simulate the circuit and realize the same using hardware. The design and
simulation was carried out and the result was compared with the theoretical values. Simulation
of higher order filter was carried out at higher frequencies to investigate upon its performance
characteristics as compared to lower order filters. Parametric analysis was performed by
changing different component parameters to view the change in performance of the filters. The
results obtained give the evidence that OTA gm-C filters are quite stable at very high
frequencies. Moreover, gm-C filters eliminate the use of inductors in filters, which has been one
of the greatest challenges in the field of filter design.
The project work intended to bring out the advantage of using OTA for realizing all pass filters
over other traditional methods. In this era of technology, where digital filters are more in
demand than analogue filters, this project intends to accentuate the significance of analogue
filters by introducing new ideas of filter design using the current mode approach. The use of
OTA as a standard circuit element clearly depicts its versatility in the analogue domain.
Realization of passive elements using OTA is an unprecedented approach in the arena of
circuit design.
5.3 Future Scope
The study of design, analysis and verification of OTA-C continuous-time first order, second
order and fourth order current mode all-pass filters has been carried out. The OTA-C circuits
45
have been simulated using Cadence Virtuoso and Spectre RF tools and PSpice software. The
simulation results are in agreement with theory.
The circuits have been experimentally verified using discrete OTA ICs like CA3080E and
experimental observations obtained are in accordance with the theoretical results.
The design and simulation of first-order all-pass based quadrature oscillator can be carried out.
Hardware implementation of fourth order all-pass filter can be carried out. Study of other filter
structures in fully differential configuration may be of future interest. Higher order filters can
be studied, analysed and simulated. Other filter types such as notch filter, band-pass/ band-stop
filters can be realized using gm-C filters. The all-pass filters can be further implemented as
phase equalizers in various applications such as communication and bio-medical areas.
46
REFERENCES
Journal / Conference Papers
[1] CA3080 Datasheet by Intersil
[2] Dalibor Biolek, Josef Cajka, Kamil Vrba, Vaclav Zeman, “ Nth-order All Pass Filters
using Current Conveyors”, Journal of Electrical Engineering, Vol. 5, No. 1-2, 2002, 50-53
[3] B. M. Al-Hashimi, F. Dudek and M. Moniri, “Current-mode group-delay equalization
using pole-zero mirroring technique”, IEEE Proc.-Circuits Devices syst., Vol. 147, No. 4,
August 2000, 257-263
[4] Randall L. Geiger and Edgar Sánchez-Sinencio, “Active Filter Design Using Operational
Transconductance Amplifiers”, IEEE Ciruits and Devices Magazine, Vol. 1, pp. 20-32,
March 1985
[5] T. Tsukutani, Y. Sumi , Y. Fukui , “Electronically tunable current-mode OTA-C biquad
using two-integrator loop structure”, Frequenz , 60, pp. 53-56, 2006.
Reference / Hand Books
[1] J K Fidler, Yichuang Sun and T. Deliyannis, “Continuous Time Active Filter Design,
CRC Press LLC, 1999
[2] R. Jacob Backer, Harri W.Li, David E Boyce, CMOS Circuit Design, Layout and
Simulation, Wiley-IEEE Press , 3 edition, September, 2010.
[3] David A. Johns, Ken Martin, “Analog Integrated Circuit Design”, Johns Wiley & Sons,
ISBN 0-471-14448-7, 2002.
Web
[1] www.cadence.com
47
ANNEXURES
1. Basic implementation of second order low pass filter in Cadence
Figure A.1 Circuit schematic of second order low pass filter
Figure A.2 Amplitude response of second order low pass filter using different capacitor values
48
2. Hardware circuit of first order current mode OTA-C all-pass filter
Figure A.3
Figure A.4
49
3. Hardware Circuit of second order current mode OTA-C all-pass filter
Figure A.5
Figure A.6
50
4. 0.5µm MOSIS model parameters
0.5µm technology was used for designing of OTA in PSpice. The parameters for such
technology is shown below
NMOS LEVEL = 3 PHI=0.700000 TOX=9.6000E-09
+ XJ=0.200000U TPG=1 VTO=0.6684 DELTA=1.0700E+00 LD=4.2030E-08
+ KP=1.7748E-04 UO=493.4 THETA=1.8120E-01 RSH=1.6680E+01
+ GAMMA=0.5382 NSUB=1.1290E+17 NFS=7.1500E+11 VMAX=2.7900E+05
+ ETA=1.8690E-02 KAPPA=1.6100E-01 CGDO=4.0920E-10 CGSO=4.0920E-10
+ CGBO=3.7765E-10 CJ=5.9000E-04 MJ=0.76700 CJSW=2.0000E-11
+ MJSW=0.71000 PB=0.990000
PMOS LEVEL = 3 PHI=0.700000 TOX=9.6000E-09
+ XJ=0.200000U TPG=-1 VTO=-0.9352 DELTA=1.2380E-02 LD=5.2440E-08
+ KP=4.4927E-05 UO=124.9 THETA=5.7490E-02 RSH=1.1660E+00
+ GAMMA=0.4551 NSUB=8.0710E+16 NFS=5.9080E+11 VMAX=2.2960E+05
+ ETA=2.1930E-02 KAPPA=9.3660E+00 CGDO=2.1260E-10 CGSO=2.1260E-10
+ CGBO=3.6890E-10 CJ=9.3400E-04 MJ=0.48300 CJSW=2.5100E-10
+ MJSW=0.21200 PB=0.930000
51
PROJECT DETAILS
Student Details
Student Name Ankit Sureka
Register Number 080907180 Section / Roll No C/25
Email Address [email protected] Phone No (M) 9036587375
Student Name Abhinav Anand
Register Number 080907202 Section / Roll No C/27
Email Address [email protected] Phone No (M) 9036577939
Student Name Mayank Kumar Daga
Register Number 080907532 Section / Roll No D/61
Email Address [email protected] Phone No (M) 8971036348
Project Details
Project Title Performance Study of Active Continuous Time Filters
Project Duration 4 months Date of reporting 17th
January 2012
Internal Guide Details
Faculty Name Ms Anitha H
Full contact address
with pin code
Dept. of E&C Eng., Manipal Institute of Technology, Manipal – 576
104 (Karnataka State), INDIA
Email address [email protected]
Co-Guide Details
Faculty Name Mr D V Kamath
Full contact address
with pin code
Dept. of E&C Eng., Manipal Institute of Technology, Manipal – 576
104 (Karnataka State), INDIA
Email address [email protected]