EE40 Lecture 10 - The jw Mind Trip Express

# EE40 Lecture 10 - The jw Mind Trip Express - ee forty...

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ee forty lecture ten the jω mind trip express Neel Shah 7/15/11

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Class stuff Regrades HW1 and HW2 regrades due with HW3 HW3 and HW4 regrades will be due with HW5 HW5 regrades will be due with HW6 Won’t have regrade option on HW6 – sorry Final project proposals due today on bSpace Makeup lab section after lecture today Midterm 2 is Wed 7/27
A More Complex Example + - R 1 R 2 C 1 V in V out = ?? C 2 t=0

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A More Complex Example
Another Example + - R 1 R 2 C 1 V in V out = ?? C 2 t=0 Assume dV in /dt = 0… Does this circuit have the same governing equation or a different one?

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A Hairier Example + - R 1 R 2 C 1 V in V out = ?? C 2 t=0
A Hairier Example

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Sinusoidal Steady State The differential equations we have covered offer a general solution given any input Works especially well in digital switching analysis We will cover this topic later A lot of times we want to restrict our analysis to sinusoidal inputs for linear circuits only All of audio is just a sum of sinusoids So is all of RF communication Any periodic signal can be expressed as a sum of sinusoids If our circuit is linear then we can use superposition
Fourier Superposition Let’s say we wanted to filter an audio source + - L R C 1 V audio V out = f(V audio ) C 2

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Fourier Superposition The audio is a sum of different instruments L R C 1 + - V drum V out = f(V drum )+f(V guitar )+f(V piano ) C 2 + - V guitar + - V piano
Fourier Superposition Our signal is a sum of different frequencies L R C 1 + - V freq1 C 2 + - V freq2 + - V freq3 V out = f(V f1 )+f(V f2 )+f(V f3 )

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Let’s replace our DC source with an AC source ω is the angular frequency ω = 2πf, where f is a regular frequency in Hz And plug it into our differential equation Solving for V O is nasty… The New Steady State + - V S C R O
The New Steady State But it illustrates some neat things The steady state response of this circuit is sinusoidal Just like the steady state response was constant before

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## This note was uploaded on 09/09/2011 for the course EECS 40 taught by Professor Chang-hasnain during the Summer '08 term at University of California, Berkeley.

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EE40 Lecture 10 - The jw Mind Trip Express - ee forty...

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