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Sixth Order High Pass Chebyshev Filter Lab


Objectives:

1. Implement the following filter with the given specifications:

A 6th 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.


Equipment:
1.
uA741 Operational Amplifier
2. AC / DC Power Supplies
3. Oscilloscope
4. Assorted Resistors


Procedure & Data:

For the given experiment the characteristics of a 6th 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. 6th 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)


First predictions were made to the circuit's response. In order to obtain the correct roll off each stage needed to provide a specific response to the final output. The approach used was to hand calculate each individual stages component values, and match them to the productions made. As expected each stages resistance values decreased starting with the first stage and through the third stage. Values for each stage are recorded in lab notes, page one.

Next the circuit was simulated using Pspice to determine the exact response expected. A model of each individual stage was constructed in Pspice and its output plotted in VdB. Once an understanding for each stage was developed a complete model of all stages was designed and its output plotted in VdB. (see Pspice simulations).

To confirm our initial predictions and Pspice simulations the circuit was constructed in a laboratory environment using resistors of ±5 percent error. Each stage was measured and compared to our simulated response. Then the overall Oh order high pass Chebyshev filter was measured and tested. Once we had a working model the impulse response for each stage and overall circuit was tested and plotted using a 100Hz input square wave at 2Vp AC.


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 6th 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 2nd Order, fc = 1.5kHz


Figure 1: 2nd Order Chebyshev High-Pass Filter w/ 1dB RW


b) Band Pass 2nd Order, fc = 1.5KHz with Q = 10


Figure 2: 2nd Order Chebyshev Band-Pass 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 high-pass and band-pass filters.


PSpice Results
Figure 1: PSpice 6th Order Chebyshev 2dB HPF
Output 1: PSpice Simulated Result 6th Order Chebyshev 2dB HPF
Figure 2: PSpice 1st Stage Chebyshev HPF
Output 2: PSpice Simulated Result 1st Stage Chebyshev HPF
Figure 3: PSpice 2nd Stage Chebyshev HPF
Output 3: PSpice Simulated Result 2nd Stage Chebyshev HPF
Figure 4: PSpice 3rd Stage Chebyshev HPF
Output 4: PSpice Simulated Result 3rd Stage Chebyshev HPF
Figure 5: Measured 6th Order Chebyshev HP Filter
Figure 6: Measured 1st Stage
Figure 7: Measured 2nd Stage
Figure 8: Measured 3rd Stage
Lab Notes
Lab Notes Page 1
Lab Notes Page 2
Lab Notes Page 3

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.

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