Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple (type I) or stop band ripple (type II) than Butterworth filters. Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the range of the filter,[citation needed] but with ripples in the pass band. This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials.

1. Chebyshev High Pass Filter
SAIKAT BHANDARI ENERGY STUDIES
TNU2015003100003
Electrical Circuit and Networks

2. INTRODUCTION
Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple (type I) or stop
band ripple (type II) than Butterworth filters. Chebyshev filters have the property that they minimize the error
between the idealized and the actual filter characteristic over the range of the filter,[citation needed] but with
ripples in the pass band. This type of filter is named after Pafnuty Chebyshev because its mathematical
characteristics are derived from Chebyshev polynomials.
Because of the passband ripple inherent in Chebyshev filters, the ones that have a smoother response in the
passband but a more irregular response in the stopband are preferred for some applications.
The Chebyshev filter has a smaller transition region than the sameorder Butterworth filter, at the expense of
ripples in its pass band. This filter gets its name because the Chebyshev filter minimizes the height of the
maximum ripple, which is the Chebyshev criterion. Chebyshev filters have 0 dB relative attenuation at dc. Odd
order filters have an attenuation band that extends from 0 dB to the ripple value. Even order filters have a gain
equal to the pass band ripple. The number of cycles of ripple in the pass band is equal to the order of the filter.
The zeros of this type of filter lie on the imaginary axis in the s-plane. The magnitude squared of the frequency
response characteristics of a type 1 chebyshev filter is given as
Where ϵ is a parameter of the filter related to the ripple in passband and Tn(x) is the Nth order chebyshev
polynomial

3. Design Steps
Determine the lowest order of Chebyshev filters that satisfy or exceed the specifications.
 Define the filter transfer functions using the equations
 Calculate the magnitude of the transfer functions for both filters at the frequencies
 Use Matlab to obtain the Bode plots (magnitude and phase) versus frequency from 1 Hz to 1 MHz for
both filters verify that these magnitudes agree with the values in the table. Use Matlab to obtain the
time response of both filters to a step function input.
 Choose the filter that is simpler (lower order). Determine a circuit that uses ideal op amps , resistors and
capacitors that will provide the required transfer function.
 Determine the values of the circuit elements. Simulate the circuit with PSpice. Use PSpice to obtain Bode
plots for the filter and verify that these magnitudes agree with the values in the table. Use PSpice to
obtain the time response of the filter to a step function input and verify that it agrees with the response
obtained with Matlab.
Chebyshev (type I) 2nd order high pass filter
Circuit diagram

4. Pspice circuit design

5. Matlab verification

6. chebyshev 5th
order high pass filter
Circuit diagram
Pspice circuit diagram

7. Result

9. Matlab verificaion
Conclusion
Implementation of chebyshev filter is very
import for signal processing and electronic
communication
Acknowledgement
I gratefully thanks prof. Bijoy Kumar Sinha. I
also thanks Souvik Pandey, shibaji kha, Avik Ghosh
and ECE lab, TNU.
REFERENCES:
1. A. I. Zverev, Handbook of Filter Synthesis,
John Wiley, 1967.
2. A. B. Williams, Electronic Filter Design
Handbook, McGraw-Hill, 1981, ISBN: 0-07-070430-9.
3. M. E. Van Valkenburg, Analog Filter
Design, Holt, Rinehart & Winston, 1982
4. M. E. Van Valkenburg, Introduction to
Modern Network Synthesis, John Wiley and Sons,
1960.
5. A. I. Zverev and H. J. Blinchikoff, Filtering
in the Time and Frequency Domain, John Wiley and
Sons, 1976.
6. S. Franco, Design with Operational
Amplifiers and Analog Integrated Circuits, McGraw-
Hill 1988, ISBN: 0-07-021799-8.
7. W. Cauer, Synthesis of Linear
Communications Networks, McGraw-Hill, New York,
1958.
8. Aram Budak, Passive and Active Network
Analysis and Synthesis, Houghton Mifflin Company,
Boston, 1974.
9. L. P. Huelsman and P. E. Allen,
Introduction to the Theory and Design of Active
Filters, McGraw Hill, 1980, ISBN: 0-07-030854-3.
10. R. W. Daniels, Approximation Methods
for Electronic Filter Design, McGraw-Hill, New York,
1974.
11. M Rashid, INTRODUCTION to Pspice