Recall that we used this idea earlier to calculate the DC voltage at the output

Recall that we used this idea earlier to calculate

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Recall that we used this idea earlier to calculate the DC voltage at the output. At high frequencies (F large), V out = V in
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23 M. Horowitz, J. Plummer, R. Howe Frequency Dependence of RC Circuit v in v out R C F V out /V in FRC j FRC j V V in out p p 2 * 1 2 * + = This circuit passes high frequencies but blocks low frequencies. Sometimes called a “high pass filter”.
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24 M. Horowitz, J. Plummer, R. Howe Analyzing RC Circuits Using Impedance (High Pass Filter) v in v out C=0.1 μ F FRC j FRC j FC j R R V V in out p p p 2 * 1 2 * 2 * 1 + = + = RC = 11ms; 2 p RC about 70ms 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 V out /V in F (Hz) R=11 k W
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25 M. Horowitz, J. Plummer, R. Howe Impedance of Other RC Circuits Series : Z eq = Z 1 + Z 2 = R 1 + R 2 R 1 R 2 R 1 R 2 C 2 C 1 C 2 C 1 Parallel: Z eq = 1 1 Z 1 + 1 Z 2 = R 1 R 2 R 1 + R 2 Series : Z eq = Z 1 + Z 2 = 1 j 2 π FC 1 + 1 j 2 π FC 2 = 1 j 2 π F 1 C 1 + 1 C 2 = 1 j 2 π F C 1 C 2 C 1 + C 2 Parallel: Z eq = 1 1 Z 1 + 1 Z 2 = 1 j 2 π FC 1 + j 2 π FC 1 = 1 j 2 π F C 1 + C 2 ( )
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26 M. Horowitz, J. Plummer, R. Howe Impedance of Other RC Circuits Series : Z eq = Z 1 + Z 2 = R + 1 j 2 π FC = 1 + j 2 π FRC j 2 π FC R R C C Parallel: Z eq = 1 1 Z 1 + 1 Z 2 = 1 1 R + j 2 π FC = R 1 + j 2 π FRC Check limits on these expressions!
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27 M. Horowitz, J. Plummer, R. Howe Learning Objectives for Today Generalize RC circuit analysis in the time domain Impedance is the relationship between voltage and current For a sinusoidal input Z = V/I so for a capacitor, Z = 1/2πFC or 1/j*2πFC Understand how to use impedance to analyze RC circuits Compute the “voltage divider” ratio to find output voltage Calculate series and parallel effective impedances
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  • Spring '20
  • Inductor, RC circuit, Electrical impedance

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