Network Function Properties and Applications in Circuit Analysis

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 Property or where and

3. Capacitor Inductor Resistor 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. 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 frequencyof a network variable need not be a pole of a given network function which has this network variable as output.