1. Dr. Holbert Dr. Holbert April 23, 2008
Lecture 23
Active Filters
Dr. Holbert
April 23, 2008
Lect23
EEE 202
EEE 202

2. Active Filters
To achieve a gain > 1, we need to utilize an op-amp based circuit to form an active filter
We can design all the common filter types using op-amp based active filters
Recall for an ideal op-amp that
V+ = V– I+ = I– = 0
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3. Op Amp Model V+ Non-inverting input + Rout Vo Rin + – –
A(V+ –V– ) V–
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4. Non-inverting Op-Amp Circuit+ – + + –
Vin Z2
Vout Z1 –
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5. Inverting Op-Amp CircuitZ2 Z1 – – + – +
Vin
Vout +
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6. An Integrator C R – + + + Vin – Vout –
Dr. Holbert
Lecture 23
An Integrator C R – + – + +
Vin
Vout –
H(jw) = 1/(sRC)
Earlier in the semester, we saw this op-amp based integrator circuit. What type of filter does it create? Does this help you to understand time and frequency domain interrelations?
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EEE 202
EEE 202

7. A Differentiator R C – + + + Vin – Vout –
Dr. Holbert
Lecture 23
A Differentiator R C – + – + +
Vin
Vout –
H(jw) = sRC
We also observed this op-amp based differentiator circuit. What type of filtering does it produce? How could we move the zero away from the origin?
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EEE 202
EEE 202

8. Practical Example
You are shopping for a stereo system, and the following specifications are quoted:
Frequency range: –6 dB at 65 Hz and 22 kHz
Frequency response: 75 Hz to 20 kHz ±3 dB
What do these specs really mean?
Note that the human hearing range is around 20 Hz to 20 kHz (audible frequencies)
Could you draw a rough Bode (magnitude) plot for the stereo system?
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9. MATLAB Filter Example How can we filter a real measurement signal?
One method involves using a numerical algorithm called the Fast Fourier Transform (FFT) which converts a time domain signal into the frequency domain
Start MATLAB, then download and run the ‘EEE202Filter.m’ file
Can you observe the reduction in the high frequency components in both the time and frequency domain plots of the output signal?
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10. MATLAB Filter Example (cont’d)
Can we extend the knowledge acquired about transfer functions and filtering?
How can we further reduce the high frequency component magnitudes? Show me.
How can we remove more high frequencies from the output signal? Show me.
Input
Signal
Fast
Fourier
Transform
Freq.
Domain
Filtering
Inverse
FFT
Output
Signal
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