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

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 Lect23 EEE 202

Op Amp Model V+ Non-inverting input + Rout Vo Rin + – – A(V+ –V– ) V– Lect23 EEE 202

Non-inverting Op-Amp Circuit + – + + – Vin Z2 Vout Z1 – Lect23 EEE 202

Inverting Op-Amp Circuit Z2 Z1 – – + – + Vin Vout + Lect23 EEE 202

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? Lect23 EEE 202 EEE 202

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? Lect23 EEE 202 EEE 202

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? Lect23 EEE 202

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? Lect23 EEE 202

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 Lect23 EEE 202