lab4_freq_resp_notes

# lab4_freq_resp_notes - ECE 209 Circuits and Electronics...

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Unformatted text preview: ECE 209: Circuits and Electronics Laboratory Notes for Lab 4 (Frequency Response of First-Order Active Circuits) 1. Comments on returned lab report. • Put units on tables and figures and show individual data points (i.e., not just interpolation). • In meters lab, positive error on R v is a good thing. Manufacturer gives worst-case specification. 2. First-order active filters. • Active filters allow for gain, simplicity, robustness, and can have hard “knees” without inductors. • Use standard inverting/non-inverting OA configuration, but use (equivalent) Laplace-domain impedances instead of simple resistances. • To quickly determine characteristic of filter (i.e., low-pass, high-pass, or bandpass) consider what happens to OA configuration’s “gain” at some sample frequencies. – In today’s lab, both filter’s have transfer function given by − Z F ( s ) /Z I ( s ). – In the low-pass filter, Z I ( s ) = R 1 and Z F ( s ) = R 2 bardbl ( sC ) − 1 . * Z F (0) ≈ R 2 for low frequencies — LF gain is − R 2 /R 1 (i.e., R 2 /R 1 with − 180 ◦ shift). * Z I ( jω ) ≈ 0 for high frequencies — HF gain is − /R 1 ≈ 0 (with − 180 ◦ − 90 ◦ shift). * First-order filter’s time constant τ must depend on C , but because V − is a virtual ground, the output does not “feel” the effect of R 1 . So time constant τ = R 2 C . * It is a low-pass filter with passband gain K = − R 2 /R 1 and time constant τ = R 2 C : H LPF ( s ) defines K τs + 1 = − R 2 R 1 sR 2 C + 1 . – In the high-pass filter, Z I ( s ) = R 1 + 1 / ( sC ) and Z F ( s ) = R 2 . * Z I (0) ≈ ∞ (i.e., “open” for VLF) — LF gain is − R 2 / ∞ ≈ 0 (with − 180 ◦ + 90 ◦ shift). * Z I ( jω ) ≈ R 1 for high frequencies — HF gain is − R 2 /R 1 (i.e., R 2 /R 1 with − 180 ◦ shift). * First-order filter’s time constant τ must depend on C , but because V − is a virtual ground, the input does not “feel” the effect of R 2 . So time constant τ = R 1 C ....
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lab4_freq_resp_notes - ECE 209 Circuits and Electronics...

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