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Exam 2 - Operational Amplifier Filters

Examination two for the Linear Systems course tests the students understanding of the relationships between lumped elements and operational amplifiers in filter design. All calculations and work must be shown for full credit. This exam covers items such as filters, high-pass and band-pass, bandwidth, gain stages, filter response, ripple affects, and cascade operational amplifier stages.

Problem 1

When designing a filter one will be required to setup specific parameters and define variables required for the specific filter output response. For this problem, setup and implement a broad-band, band-pass filter with the following performance criteria:

a. Output Frequency (fo) = 10kHz
b. Bandwidth (BW) = 10kHz
c. Pass-Band Gain (ABP) = 16 in two stages
d. Butterworth Response
e. 4th Order Rolloff on both sides

Complete the design by drawing the circuit diagram with values labeled accordingly, and a block diagram depicting each stage of the two stages of the bandpass Butterworth filter.

Problem 2

In this problem students will be required to setup and implement a forth-order, band-pass filter with the following performance specifications:

a. Chebyshev Bandpass Filter Response
b. 3dB Ripple width
c. Band Pass Gain (ABP) = 4
d. Quiescent Value (Q) = 7.5

In your final design, show the schematic with all components labeled with the calculated values. Also, answer the following question:

e. What is the roll-off on each side of the output frequency (fo) for this circuit?

Problem 3

In this section you are to setup a Wein Bridge Oscillator with an output frequency (fo) equal to 4.7kHz. Set the values of the resistance and capacitance as necessary to produce the appropriate output response, and draw the schematic with values. Also, answer the following:

Question: Is oscillation guaranteed with the exact calculated gain and allowing for component tolerance error variation? Yes or No and why?

Solutions: Provided in the Exam Notes Calculations Section below.

Exam Calculations and Notes
Exam Notes Page 1
Exam Notes Page 2
Exam Notes Page 3
Exam Notes Page 4
Exam Notes Page 5
Exam Notes Page 6
Exam Formula Sheet

Engineering key words: Q value, filter, band pass, band reject, low pass, high pass, ripple width, oscillator, design principles, tolerances, gain, voltage, current, inductive, reactance, capacitive, resistive, impedance, Chebyshev, Butterworth, center frequency, decade, circuit schematic, specifications, spec, nth-order, computation, calculation, solution, answers, dB, filter design, passive components, active components, operational amplifier, op-amp, frequency, variables.

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