Lecture 191 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001

Lecture 192 Variable-Frequency Response Analysis As an extension of ac analysis, we now vary the frequency and observe the circuit behavior Graphical display of frequency dependent circuit behavior can be very useful; however, quantities such as the impedance are complex valued such that we will tend to graph the magnitude of the impedance versus frequency (i.e., |Z(j  )| v. f) and the phase angle versus frequency (i.e.,  Z(j  ) v. f)

Lecture 193 Frequency Response of a Resistor Consider the frequency dependent impedance of the resistor, inductor and capacitor circuit elements Resistor (R):Z R = R  0° So the magnitude and phase angle of the resistor impedance are constant, such that plotting them versus frequency yields Magnitude of Z R (  ) Frequency R Phase of Z R (°) Frequency 0°

Lecture 194 Frequency Response of an Inductor Inductor (L):Z L =  L  90° The phase angle of the inductor impedance is a constant 90°, but the magnitude of the inductor impedance is directly proportional to the frequency. Plotting them vs. frequency yields (note that the inductor appears as a short at dc) Magnitude of Z L (  ) Frequency Phase of Z L (°) Frequency 90°

Lecture 195 Frequency Response of a Capacitor Capacitor (C):Z C = 1/(  C)  –90° The phase angle of the capacitor impedance is –90°, but the magnitude of the inductor impedance is inversely proportional to the frequency. Plotting both vs. frequency yields (note that the capacitor acts as an open circuit at dc) Magnitude of Z C (  ) Frequency Phase of Z C (°) Frequency -90°

Lecture 196 Transfer Function Recall that the transfer function, H(s), is The transfer function can be shown in a block diagram as The transfer function can be separated into magnitude and phase angle information, H(j  ) = |H(j  )|  H(j  ) H(j  ) = H(s) X(j  ) e j  t = X(s) e st Y(j  ) e j  t = Y(s) e st

Lecture 197 Common Transfer Functions Since the transfer function, H(j  ), is the ratio of some output variable to some input variable, We may define any number of transfer functions –ratio of output voltage to input current, i.e., transimpedance, Z(jω) –ratio of output current to input voltage, i.e., transadmittance, Y(jω) –ratio of output voltage to input voltage, i.e., voltage gain, G V (jω) –ratio of output current to input current, i.e., current gain, G I (jω)

Lecture 198 Poles and Zeros The transfer function is a ratio of polynomials The roots of the numerator, N(s), are called the zeros since they cause the transfer function H(s) to become zero, i.e., H(z i )=0 The roots of the denominator, D(s), are called the poles and they cause the transfer function H(s) to become infinity, i.e., H(p i )= 

Lecture 199 Class Examples Extension Exercise E12.1 Extension Exercise E12.2