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lect26_sinusoid

# lect26_sinusoid - EE 42/100 Fall 2010 Sinusoidal...

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Department of EECS University of California, Berkeley EE 42/100, Fall 2010 Sinusoidal Steady-State and Linear Systems Prof. Niknejad

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EECS 42/100 Spring 2010 Prof. A. Niknejad Department of EECS University of California, Berkeley The Magic of Sinusoids Since most periodic (non-periodic) signals can be decomposed into a summation (integration) of sinusoids via Fourier Series (Transform), the response of a LTI system to virtually any input is characterized by the frequency response of the system: Any linear circuit With L,C,R,M and dep. sources Amp Scale Phase Shift
EECS 42/100 Spring 2010 Prof. A. Niknejad Department of EECS University of California, Berkeley Example: Low Pass Filter (LPF) Input signal: We know that in SS: Amp shift Phase shift

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EECS 42/100 Spring 2010 Prof. A. Niknejad Department of EECS University of California, Berkeley LPF the “hard way” (cont.) Plug the known form of the output into the equation and see if it can satisfy KVL and KCL Since sine and cosine are linearly independent functions: IFF
EECS 42/100 Spring 2010 Prof. A. Niknejad Department of EECS University of California, Berkeley LPF: Solving for response… Applying linear independence Phase Response: Amplitude Response:

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EECS 42/100 Spring 2010 Prof. A. Niknejad Department of EECS University of California, Berkeley LPF Magnitude Response Passband of filter
EECS 42/100 Spring 2010 Prof. A. Niknejad Department of EECS University of California, Berkeley LPF Phase Response

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EECS 42/100 Spring 2010 Prof. A. Niknejad Department of EECS University of California, Berkeley dB: Honor the inventor of the phone… The LPF response quickly decays to zero We can expand range by taking the log of the magnitude response dB = deciBel (deci = 10)
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lect26_sinusoid - EE 42/100 Fall 2010 Sinusoidal...

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