This document describes the design of a 5th order Chebyshev low pass filter using operational transconductance amplifiers (OTAs). It begins by introducing filters and their frequency responses. It then discusses Chebyshev filters specifically, including their characteristics and a formula for determining the filter order based on design specifications. The document proceeds to describe the operational transconductance amplifier and reasons for using it to implement filter circuits. It provides the design process and calculations for a telescopic OTA and uses multiple OTAs in cascade to create the 5th order Chebyshev low pass filter. The filter is simulated and the results validate the design by achieving the desired cutoff frequency and ripple specifications. In conclusion, the document demonstrates the design of a

1. ISSN 2322-0929
Vol.03, Issue.02,
February-2015,
Pages:0119-0121
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Copyright @ 2015 IJVDCS. All rights reserved.
Telescopic OTA Based Design of 5th
Order Chebyshev Low Pass Filter
ARVIND SINGH RAWAT
1
, VIKALP JOSHI
2
, SUDHIR JUGRAN
3
, DR.SANJAY SINGH
4
1
Assistant Professor, Dept of ECE, University Dehradun, India.
2
Assistant Professor, Dept of EEE, DBIT, Dehradun, India.
3
Assitant Professor, Dept of ECE, Uttaranchal University, Dehradun, India.
4
Associate Professor, Dept of ECE, Uttaranchal University, Dehradun, India.
Abstract: The Operational Transconductance amplifiers are important building blocks for various analog circuits and systems
which were previously implemented by using OPAMP. Currently, research is on for implementation of OTA circuits that will
be highly linear, consumes less amount of power and operate at low power supply. Processing of a signal is not possible
without filters. Chebyshev filter is designed in this paper is based on OTA.
Keywords: Gain Bandwidth Product (GBW), Operational Transconductance Amplifier (OTA), Tanner EDA,
Transconductance.
I. INTRODUCTION
A filter is defined as an electric network, that passes or
allows unattenuated transmission of electric signal within
definite frequency range and stops or disallows transmission
of electric signal exterior this range. In active
implementation of filter, an active device has to be preferred
to a pleasing response of the filter. A variety of devices like
Operational Amplifier, Operational Transconductor
Amplifier (OTA) and Difference Differential Amplifier
(DDA), etc. can be used to design an active filter. After
broad study, of all the choices Operational Transconductor
Amplifier is preferred to design a Chebyshev filter. Amongst
all the architecture of OTA, on the basis of literature survey,
Telescopic OTA is preferred as it has high gain, high speed
low noise and low power consumption. The design
procedure for a single stage telescopic OTA is designed
using design equations. The circuit implemented is then
simulated on Tanner EDA tool. The simulated results are
validating the theoretical values.
Fig.1. Response of a low pass filter to various input
frequencies [2].
II. FREQUENCY RESPONSE
Simple filters are usually defined by their responses to the
individual frequency components that constitute the input
signal. There are three different types of responses. A filter's
response to different frequencies is characterized as pass
band, transition band or stop band. The pass band response is
the filter's effect on frequency components that are passed
through (mostly) unchanged. In fig.1, which shows the
frequency response of a low pass filter, ωp is the pass band
ending frequency, ωs is the stop band beginning frequency,
and As is the amount of attenuation in the stop band.
Frequencies between ωp and ωs fall within the transition
band and are attenuated to some lesser degree.[1]
III. CHEBYSHEV FILTERS
The word Chebyshev is known to a kind of filter
response, not a type of filter. Chebyshev filters have the
feature that they diminish the error between the idealised
filter characteristic and the definite over the range of the
filter, but with ripples in the passband. As the ripple
increases (bad), the roll-off tends sharper (good).The
response of Chebyshev filters is based on the minimization
of the maximum error in the complete passband, significant
in passband ripples with equal amplitude. The larger the
ripple amplitude accepted, the steeper the transition roll-off.
Chebyshev filters are also well-known as “equiripple” or
“minimax” filters due to their features. The Chebyshev low-
pass magnitude response can be described by
(1)
The function Tn(x) is a Chebyshev polynomial given by
(2)

2. ARVIND SINGH RAWAT, VIKALP JOSHI, SUDHIR JUGRAN, DR.SANJAY SINGH
International Journal of VLSI System Design and Communication Systems
Volume.03, IssueNo.02, February-2015, Pages: 0119-0121
The magnitude of Tn(x) oscillates between ±1 for
& grows as nx
for . If ε is passband ripple, „A‟ is the
stopband attenuation, ωo is passband edge frequency and ωs
is the stopband edge frequency, then the required filter order
can be determined as;
(3)
A. Order of Chebyshev Filter
Chebyshev filters are characterized by the parameters n, ε,
δ2 and the ratio Ωs/Ω p.
n = Order of filter
ε = Parameter related to ripple (δ1), δ1 = 10 log10 (1+ε2
)
Ωs/Ωp = Ratio of stopband and passband frequency
δ2 = the attenuation gain at stopband frequency
For a given set of specifications on ε, δ2 and Ωs/Ω p, the
order of the filter can be determined from the equation below
[3]
(4)
(5)
Where δ2 =
IV. OPERATIONAL TRANSCONDUCTANCE
AMPLIFIER (OTA)
The Operational Transconductance amplifiers are
important building blocks for various analog circuits and
systems which were previously implemented by using
OPAMP. Currently, research is on for implementation of
OTA circuits that will be highly linear, consumes less
amount of power and operate at low power supply. The
Operational Transconductance amplifiers (OTAs) are major
building blocks for different analog circuits and systems as
shown in Fig.3. [4]
Fig.2. Schematic of the Telescopic OTA with bias circuit
at the tail[5].
A. Design of Telescopic Cascade OTA
Taking following specifications into consideration to
design Telescopic OTA: Slew rate = 80 V/ μS Load
capacitance, CL = 0.5 pF Power dissipation < 3 mW Supply
voltages = ± 2.5V DC gain = 88 dB UGB = 65 MHz By
above specifications we can calculate aspect ratio for the
Telescopic OTA as shown in Fig.2.
B. Calculated Aspect Ratio
TABLE I: Calculated Aspect Ratios for the Telescopic
OTA
C. Schematic of OTA, Based On Calculated Aspect Ratio
and Defined Specifications
Fig.3. Schematic of the Telescopic OTA with bias circuit
at the tail.
D. OTA based design of Chebyshev Low Pass Filter
Fifth Order Chebyshev Low Pass Filter based on OTA:
The objective is to design a 5th
order low pass type 1
Chebyshev filter with following parameters;
Cut-off frequency = 10 KHz
Ripple in pass band = 1 dB
The design is based on the transfer function obtained from
the MATLAB;
(6)
E. Designing
To implement a fifth order low pass filter five OTAs has
been used. First & second OTAs forms a second order filter
followed by another second order filter formed by third &
fourth OTAs as shown in Fig.4. The third stage is simply a
single pole low pass filter with OTA gain of 4, same as we

3. Telescopic OTA Based Design of 5th
Order Chebyshev Low Pass Filter
International Journal of VLSI System Design and Communication Systems
Volume.03, IssueNo.02, February-2015, Pages: 0119-0121
did in designing third order filter. Since the two second order
filters are identical to the filters we used in fourth order filter
designing, so the values of parameters will be the same;
First 2nd
order filter; R= 7394 Ω & R1= 7232 Ω
Second 2nd
order filter; R= 1127 Ω & R2= 18929 Ω
Last stage is a simple low pass filter; hence the value of
resistance is found, where ωc= 2πfc= 18180 rad/s, we get R3=
18929 Ω.
Third OTA is a simple non inverting configuration; hence
for gain of 4 & resistance connected to ground being 100 Ω,
we get the value of R6 as R6 = 833.33 Ω.
Fig.4. Fifth Order Chebyshev LPF based on OTA.
V. SIMULATION RESULTS
On simulating above designed Chebyshev filter in T-
Spice we get following results:
Fig.5. Response of 5th
Order Chebyshev LPF designed in
fig.4.
It can be observed from the above frequency plot shown
in fig.5 that -3dB frequency is 9.83 KHz and calculated
frequency from section 4.1 is 10 KHz. Since both observed
and calculated frequencies are almost same which shows
successful design of 5th
order Chebyshev Type- I LPF.
VI. CONCLUSION
From the above design of 5th
order Chebyshev Type-I filter
we can analyze that cascading of filters leads to the higher
order filter with reduced transition band. On increasing order
of the filter transition band can be reduced but it may lead to
unstable the system due to large number of capacitors.
VII. REFERENCES
[1]. An Introduction to Analog Filters, Sensors Magazine
Online, July 2001.
[2]. A. Veeravalli, E. Sanchez-Sinencio, and J. Silva-
Martinez, “Transconductance amplifier structures with very
small transconductances: A comparative design approach,”
IEEE J. Solid State Circuits, vol. 37, no. 6, pp. 770–775, Jun.
2002.
[3]. John G. Prokis, Dimtris G. Manolakis, “Digital Signal
Processing: Principles Algorithm and Application”, Third
Edition, 2001
[4]. Shireen T. Sheikh, D.J. Dahigoankar, Hemant Lohana.
“Comparative Analysis of CMOS OTA” IOSR Journal of
VLSI and Signal Processing (IOSR-JVSP) ISSN: 2319 –
4200, ISBN No. : 2319 – 4197 Volume 1, Issue 3 (Nov. -
Dec. 2012).
[5]. Razavi Behzad, Design of Analog CMOS Integrated
Circuits (Tata McGraw-Hill .2002).