EE201 Lecture 35 P 1 Frequency Response Definition Frequency response of a circuit is the graph of the ratio of the phasor output to the phasor input as a function of frequency Example plot the frequency response of the circuit below 0 01 F Vin Vout 1 Step 1 Find impedance of capacitor and resistor pair Zin R 1 j C 1 1 j0 01 EE201 Lecture 35 P 2 Step 2 Use voltage division to establish output to input ratio V out V in Magnitude 1 1 1 j0 01 j0 01 1 j0 01 H j High Pass 1 Filter 0 5 Phase 80 degrees 60 1 10 100 1000 1 10 100 1000 40 20 Frequency rad sec EE201 Lecture 35 P 3 Two plots one for magnitude and one for phase angle are needed because H j is a complex quantity Important frequencies for RC circuits 0 and H j0 0 90 H j 1 0 For magnitude H j 1 as H j 0 as 0 For phase H j 0o as H j 90 as 0 EE201 Lecture 35 P 4 Example Plot the frequency response for the circuit below Vin 1H Vout 1 Step 1 Find the impedance of inductor and resistor pair Zin R j L 1 j Step 2 Use voltage division to establish output to input ratio V out V in R R j L 1 1 j H j EE201 Magnitude Lecture 35 P 5 1 Low Pass Filter 0 5 0 01 1 10 100 0 Phase degrees 0 1 20 40 60 80 100 0 01 0 1 1 H j0 1 0 H j H j H j H j 10 Freq rad sec 100 H j 0 90 1 as 0 as 0 as 0 90 as 0 EE201 Lecture 35 P 6 Example Frequency response of RLC circuits 0 1 H 1 mF Vin Vout 1 Zin j Find ratio of phasor output to input Zin R j L 1 j C 1 j0 1 1 j0 01 By voltage division R V out V in R j L 1 j C Multiply by j0 001 j0 001 1 1 j0 01 1 j0 001 and reduce EE201 V out V in Lecture 35 P 7 j10 H j 2 4 j10 10 H j 0 as H j 0 as 0 H j 90 as H j 90 as 0 Look at other frequencies H j 0 01 as H j 1 H j 0 01 as as 10 rad sec 100 rad sec 1000 rad sec EE201 Lecture 35 P 8 Plotting magnitude and phase Band Pass Response Magnitude 1 Phase deg 1 10 100 1 10 100 1000 90 0 90 1000 10000
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