# Berkeley ELENG 105 - Lecture 17 Frequency-Domain Analysis (14 pages)

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## Lecture 17 Frequency-Domain Analysis

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## Lecture 17 Frequency-Domain Analysis

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Pages:
14
School:
University of California, Berkeley
Course:
Eleng 105 - Microelectronic Devices and Circuits
##### Microelectronic Devices and Circuits Documents

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EE105 Fall 2005 Microelectronic Devices and Circuits Lecture 17 Frequency Domain Analysis Announcements Homework 7 due today Homework 8 due next week Lab 6 this week Reading Chapter 10 10 1 2 1 Lecture Material Last lecture Common drain amplifier Review phasors This lecture Frequency domain analysis Bode plots 3 RC Circuit with Sinusoidal Input iR vs t vc t R iC C vs t Vs cos t set phase of source to zero use as the reference vc t Vc cos t solution is a sinusoidal signal with the same frequency but with a different amplitude and phase shifted with respect to the source 4 2 A Better Technique It is much more efficient to work with imaginary exponentials as representing sinusoids since these functions are direct solutions of linear differential equations d e j t j e j t dt Note that EEs use j 1 1 2 rather than i since the symbol i is already taken for current 5 Using Imaginary Exponentials dv RC c v c v s dt Substitute Result v s t v s e j t v c t v c e j t j v c e j t v c e j t v s e j t 6 3 Finding the Amplitude Ratio j v c e j v c e j e j t v s e j t j e j e j v c v s use to find amplitude and phase vc 1 e j v s j e j e j 1 j Amplitude Ratio Answer is a real number so take magnitude vc 1 vs 1 2 7 Graphical Result for Amplitude Ratio 1 0 0 707 0 5 1 10 1 10 8 4 Amplitude A New Representation We are interested in very small ratios e g Vc Vs 0 0001 Therefore we use a log plot but we also define a new function called the deciBel after Alex Graham Bell Vc Vs dB 20 log10 Vc Vs Examples Vc Vs 0 0001 Vc Vs dB 80 dB Vc Vs 0 707 Vc Vs dB 3 dB 9 Finding the Phase j e j e j v s v c a real number Use Euler s formula to convert to rectangular form j cos j sin cos j sin v s v c Collect real and imaginary parts latter must be zero Im cos sin 0 tan 10 5 Graphical Result for Phase 1 10 1 10 0 45 90 11 Finding the Real Waveform How to connect the imaginary exponential solution to the measured waveform v t Conventionally v t is the real part of the of the imaginary exponential Re ve j

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