

Sixth Order High Pass Chebyshev Filter Lab
Objectives:
1. Implement the following filter with the given specifications:
A 6^{th} Order Chebyshev with 2dB ripple in the pass band; having a High Pass configuration
with a cutoff frequency of 2kHz, and 8dB of overall gain for the filter configuration. Use calculated
predictions and PSpice to verify the measured laboratory results.
Discuss the relationship between the filter stages and the effects each stage contributed to the design.
Procedure & Data:
For the given experiment the characteristics of a 6^{th} order Chebyshev high pass filter
with a 2dB ripple width was examined for its overall response, and individual stage response. The
filter required three stages, each stage consisting of a 2nd order high pass filter using a uA741
operational amplifier.
The filter specifications are as follows:
1. 6^{th} Order Chebyshev response
2. 2dB ripple width
3. High pass configuration
4. Cutoff frequency of 2kHz
5. Overall gain = 8.0 (so each stage gain, K = 2)
Conclusion and Discoveries:
1. It was discovered that each stage of the 6th order Chebysheb high pass filter produced the following.
a) Starting with stage one, the resistance values for R1 and R2, both in the positive feedback loop,
were large in comparison to the following stages and produced a response similar to a bandpass filter
a fc = 2kHz.
b) Moving on to the second stage, our values for R1 and R2 get even closer in value to each other,
but yet still large in comparison to the third stage. This second stage produced a response again
like the first stage, however the roll off was much less.
c) The third stages resistances values of R1 and R2 were very close in value to each other and produced
a response of a Butterworth filter.
2. When each stage was connected to create the 6^{th} order Chebyshev high pass filter, each
stage either provided gain and a sharp roll off point about 2kHz or provided a smooth bandwidth for
the circuit to operate in.
In closing the overall analysis of using hand calculations, Pspice and experimental measurements for
the given laboratory experiment allowed one to develop methods of analysis and continually checking
themselves. From these designs it was learned that by developing predictions and using simulations one
can better understand the output of the experimental measurements and the overall characteristics of
the circuit.
Implement the following two Filters with both having a 1dB ripple width Chebyshev
response and a stage Gain of 3.0
a) High Pass 2^{nd} Order, f_{c} = 1.5kHz
Figure 1: 2^{nd} Order Chebyshev HighPass Filter w/ 1dB RW
b) Band Pass 2^{nd} Order, f_{c} = 1.5KHz with Q = 10
Figure 2: 2^{nd} Order Chebyshev BandPass Filter w/ 1dB RW
Derive the transfer function and model the two circuits with Matlab or comparable
software tool, and show the Bode Plot, Step Response, and Impulse Response.
Verify the derivations and simulation results concur, then construct the circuits
and make measurements of the two circuits presenting both the frequency response
(i.e. Bode Plots) and the step response by using a square wave input.
Conclusions and Discoveries:
Using the Chebyshev response with a small ripple, 1dB in this experiment, provided a
steeper roll off then a similar Butterworth response with slight variation in the band
width. The overall analysis of deriving the transfer function and experimental measurements
in a laboratory environment allowed one to develop an understanding of the different responses
and applications for the highpass and bandpass filters.
Electrical Engineering lab key words: 6th order, sixth order high pass chebyshev filter, RW, gain
stage, cutoff frequency, bench test, feedback loop, percent error, step response, impulse response,
filter stage, ripple, passband, linear systems analysis.
