Transcript EEE 302 Lecture 19 - Arizona State University

EEE 302
Electrical Networks II
Dr. Keith E. Holbert
Summer 2001
Lecture 19
1
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 19
2
Frequency Response of a Resistor
• Consider the frequency dependent impedance of the
resistor, inductor and capacitor circuit elements
• Resistor (R):
ZR = R 0°
Phase of ZR (°)
Magnitude of ZR ()
So the magnitude and phase angle of the resistor impedance
are constant, such that plotting them versus frequency yields
R
Frequency
0°
Frequency
Lecture 19
3
Frequency Response of an Inductor
• Inductor (L):
ZL = L 90°
Phase of ZL (°)
Magnitude of ZL ()
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)
Frequency
90°
Frequency
Lecture 19
4
Frequency Response of a Capacitor
• Capacitor (C):
ZC = 1/(C) –90°
Phase of ZC (°)
Magnitude of ZC ()
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)
-90°
Frequency
Frequency
Lecture 19
5
Transfer Function
• Recall that the transfer function, H(s), is
Y ( s) Output
H (s) 

X( s )
Input
• The transfer function can be shown in a block diagram
as
X(j) ejt = X(s) est
Y(j) ejt = Y(s) est
H(j) = H(s)
• The transfer function can be separated into magnitude
and phase angle information, H(j) = |H(j)| H(j)
Lecture 19
6
Common Transfer Functions
• Since the transfer function, H(j), is the ratio of some output
variable to some input variable,
H( j ) 
Y( j ) Output

X( j )
Input
• 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, GV(jω)
ratio of output current to input current, i.e., current gain, GI(jω)
Lecture 19
7
Poles and Zeros
• The transfer function is a ratio of polynomials
N ( s) K ( s  z1 )(s  z2 ) ( s  zm )
H( s) 

D( s) ( s  p1 )(s  p2 ) ( s  pn )
• 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(zi)=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(pi)=
Lecture 19
8
Class Examples
• Extension Exercise E12.1
• Extension Exercise E12.2
Lecture 19
9