Lab5-SupplementalNotes

Lab5-SupplementalNotes - Electrical Measurement Laboratory...

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1 Electrical Measurement Laboratory Experiment #5 Frequency Response V s + - V o + - R sC 1 s s o V sRC V sC R sC V + = + = 1 1 1 1 Sinusoidal input with frequency f ω j s = f π 2 = () sRC V V s H s o + = = 1 1 j H j H RC j V V j H s o = + = = 1 1 2 1 1 RC j H + = ( ) RC j H 1 tan ) ( =
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2 Transfer Function I o sRC V V + = 1 1 Æ Input output relation is a function of frequency. Æ The input and output have the same frequency, but a different magnitude and phase (This is a fundamental property of linear circuits). Æ We define the transfer function: sRC s I o + = = 1 1 ) ( V V H I V o V ) ( s H I o s V H V ) ( = Transfer Function Æ At frequency ω I o j V H V ) ( ω = ( ) ( ) I I h o o j θ = V H V ) ( h I I o o j + = V H V ) ( ) cos( ) ( I I t A t v + = ) ( s H )) ( cos( ) ( ) ( j t j A t v I o H H + + = Æ Same frequency ω Æ Amplitude is multiplied by |H(j ω )|. Æ Phase is shifted by the angle of |H(j ω )|. Æ H (s) is not a phasor!
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3 Frequency Response Measurement 1. Hold the input sinusoid at a constant amplitude. 2. Vary the frequency. 3. For each frequency value, measure the amplitude at the output as well as phase shift. Single Input Frequency + - ) cos( ) ( 1 1 1 t A t v ω = () ) ( cos ) ( ) ( 1 1 1 1 θ + = t j H A t v o Linear Electrical Netowork ) ( s H + ) ( ) ( 1 1 j H =
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4 Single Input Frequency + - ) cos( ) ( 2 2 2 t A t v ω = () ) ( cos ) ( ) ( 2 2 2 2 θ + = t j H A t v o Linear Electrical Netowork ) ( s H + ) ( ) ( 2 2 j H = Multiple Inputs + - ) cos( ) ( 1 1 1 t A t v = ) ( cos ) ( 1 1 1 1 + t j H A Linear Electrical Netowork ) ( s H + + - ) cos( ) ( 3 3 3 t A t v = + - ) cos( ) ( 2 2 2 t A t v = ) ( cos ) ( 2 2 2 2 + + t j H A ) ( cos ) ( 3 3 3 3 + + t j H A = ) ( t v o Principle of linearity
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5 Decibel Scale for Power Æ
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This note was uploaded on 12/22/2010 for the course ECSE ECSE 291 taught by Professor Khazaka during the Winter '03 term at McGill.

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Lab5-SupplementalNotes - Electrical Measurement Laboratory...

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