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INC 112 Basic Circuit Analysis Week 13 Frequency Response
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What is the change of vL(t) when the frequency of the voltage source change?
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ω |vL| (magnitude) A
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Log ω |vL| (magnitude) Log scale of frequency A
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Linear Scale & Log Scale 1 2 3 4 5 6 0.1 1 10 100 1000 Linear Scale Log Scale
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What is the frequency response of vc(t) Log ω |vc| (magnitude) A
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Input & Output System Input Output Input is usually what we can control. Output is usually what we are interested in.
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What is the frequency response of vc(t) Input = voltage source Output = vc(t)
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Frequency Domain Frequency domain is another point of view of things in the world. Some analysis are easier done in frequency domain than time domain.
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Metaphor of Frequency Domain (1,1,1) (2,-3,0) Time Domain Frequency Domain
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Time Domain Frequency Domain
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Transfer Function Transfer function = ratio of output and input in frequency domain System H(s) System H(s) Input Output U(s)Y(s) Transfer function Note: Transfer function describes characteristic of a system.
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Example: Obtaining Transfer Function input is v(t) output is vc(t)
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Change all components to Phasor (frequency domain)
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Kirchoff’s Voltage Law
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Transfer function
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Frequency Response System Input Output Freq 10Hz Amplitude = 1Phase = 0 Freq 100Hz Amplitude = 1Phase = 0 Freq 800Hz Amplitude = 1Phase = 0 Freq 10Hz Amplitude = 0.96 Phase = 12 Freq 100Hz Amplitude = 0.82 Phase = 44 Freq 800Hz Amplitude = 0.53 Phase = 56
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Frequency Response Plot Note: log frequency and log magnitude Magnitude Phase
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The HP 35670A Dynamic Signal Analyzer obtains frequency response data from a physical system.
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Fourier Series “Any periodic signal can be written in the sum of sine wave signals at different frequency.”
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Filter Log ω |vc| (magnitude) We want to get rid of the signal 3sin(9t) ω=5ω=5 Cut-off frequency
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Example Find vc(t) Use superposition to consider the effect of two different frequencies
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For 2sin(t)
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For 3sin(9t)
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Finally, we add vc(t) from both frequencies
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Power Line Systems 3 phases systems have three wire called “line” which are sine wave with phase shift 120 from each other Power Plant Line 1 Line 2 Line 3 3 phases, 3 wires
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Power Plant Line 1 Line 2 Line 3 3 phases, 4 wires Neutral L1-N = 220Vrms, L2-N = 220Vrms L3-N = 220Vrms L1-L2 = 381Vrms,L2-L3 = 381Vrms,L1-L3 = 381Vrms
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Star Connection ( Y-connection) Load Each load get 220 Vrms
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Delta Connection ( Δ-connection) Load Each load get 381 Vrms
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