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Network Functions

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. Definition, Examples , and General Property. or. where.

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Network Functions

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  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

  10. At At

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

  12. At For and

  13. At For General Case

  14. Example 3 zeros 4 poles

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

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

  17. Physical Interpretation of Poles and Zeros

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

  19. 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

  20. 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.

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