1. Network Functions Definition, examples , and general property
Poles, zeros, and frequency response
Poles, zeros, and impulse response
Physical interpretation of poles and zeros
Application to oscillator design
Symmetry properties

2. Definition, Examples , and General Propertyor
where
and

3. Resistor
Inductor
Capacitor
Sinusoidal steady state driving point impedance = special case of a network function

4. Example 1 Parallel RC circuit

5. Example 2 Low pass filter

6. Mesh analysis gives
Solve for I2

7. General Property
For any lumped linear time-invariant circuit

8. Poles, Zeros, and Frequency Response
phase
magnitude
Gain (nepers)
Gain (dB)

9. Example 3 RC Circuit Frequency Response
No finite zero
Pole at s = -1/RC

13. At At

14. Example 4 RLC Circuit Frequency Response
Zero at s = 0
Complex conjugate poles at

17. At
For and

18. At
For
General Case

19. Example 3 zeros 4 poles

22. Poles, Zeros, and Impulse Response
Example 5 RC Circuit
See section 6 Chapter 4 for derivation of h(t)

24. Example 6 RLC Circuit Fig 3.2 For Fig 3.3 For
See section 2 Chapter 5 for derivation of h(t)

25. Physical Interpretation of Poles and Zeros

26. Poles Any pole of a network function is a natural frequency of the
corresponding (output) network variable.
Using partial-fraction expansion
Residue at pi

27. If a particular input waveform is chosen over the interval [0,T]
For input current =
For i = 1
Natural frequency p1
If a particular input waveform is chosen over the interval [0,T]
then for t > T

28. Summary Any pole of a network function is a natural frequency of the
corresponding (output) network variable,
but any natural frequency of a network variable need
not be a pole of a given network function which has this
network variable as output.