1. (C) P. D. Olivier 2001Frequency Response1 Noise Rejection Chapter 12

2. (C) P. D. Olivier 2001Frequency Response2 Consider the block diagram NOISEMechanical Electro-magneticThermal Always Noise

3. (C) P. D. Olivier 2001Frequency Response3 We will answer these questions two ways: By numerical simulation (Sysquake) Theoretically (derivation)

4. (C) P. D. Olivier 2001Frequency Response4 Numerical Experiments in Sysquake

5. (C) P. D. Olivier 2001Frequency Response5 Theoretical Development: Is the conjectured relationship always true? Consider the steady state frequency response of a stable system described by the transfer function T n (s).

6. (C) P. D. Olivier 2001Frequency Response6

7. (C) P. D. Olivier 2001Frequency Response7 Fundamental Theorem of Linear Systems : The steady- state output of a stable system described by a transfer function G(s) and excited by a pure sinusoid of Magnitude M and frequency omega is another pure sinusoid of frequency omega, the magnitude is product of the magnitude of the input sinusoid and the magnitude of the transfer function evaluated at j*omega The phase is argument (angle) of the transfer function evaluated at j*omega How is linearity in this theorem?

8. (C) P. D. Olivier 2001Frequency Response8 InputOutput Frequency AmplitudeM Phase angle

9. (C) P. D. Olivier 2001Frequency Response9 Fundamental Theorem of Linear Systems Frequency analysis (Noise rejection etc) Phasor Analysis Vibration Analysis etc

10. (C) P. D. Olivier 2001Frequency Response10 PHASOR ANALYSIS Consider a series RLC circuit excited by an AC source at arbitrary frequency. Phasor impedences: Input: Frequency: Solving for the Phasor current: Input:

11. (C) P. D. Olivier 2001Frequency Response11 Converting back to time domain