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INC 112 Basic Circuit Analysis

INC 112 Basic Circuit Analysis. Week 13 Frequency Response. Frequency Response. What is the change of vL(t) when the frequency of the voltage source change?. |vL| (magnitude). A. ω. Log scale of frequency. |vL| (magnitude). A. Log ω. Linear Scale & Log Scale. Linear Scale. 6. 5.

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INC 112 Basic Circuit Analysis

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  1. INC 112 Basic Circuit Analysis Week 13 Frequency Response

  2. Frequency Response What is the change of vL(t) when the frequency of the voltage source change?

  3. |vL| (magnitude) A ω

  4. Log scale of frequency |vL| (magnitude) A Log ω

  5. Linear Scale & Log Scale Linear Scale 6 5 4 1 2 3 Log Scale 1000 100 0.1 1 1000 10

  6. What is the frequency response of vc(t) |vc| (magnitude) A Log ω

  7. Input & Output System Output Input Input is usually what we can control. Output is usually what we are interested in.

  8. What is the frequency response of vc(t) Input = voltage source Output = vc(t)

  9. 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.

  10. Metaphor of Frequency Domain Frequency Domain Time Domain (1,1,1) (2,-3,0)

  11. Time Domain Frequency Domain

  12. Transfer Function Transfer function = ratio of output and input in frequency domain Input Output System H(s) U(s) Y(s) Transfer function Note: Transfer function describes characteristic of a system.

  13. Example: Obtaining Transfer Function input isv(t) output isvc(t)

  14. Change all components to Phasor (frequency domain)

  15. Kirchoff’s Voltage Law

  16. Transfer function

  17. Frequency Response System Output Input Freq 10Hz Amplitude = 0.96 Phase = 12 Freq 100Hz Amplitude = 0.82 Phase = 44 Freq 800Hz Amplitude = 0.53 Phase = 56 Freq 10Hz Amplitude = 1 Phase = 0 Freq 100Hz Amplitude = 1 Phase = 0 Freq 800Hz Amplitude = 1 Phase = 0

  18. Frequency Response Plot Magnitude Phase Note: log frequency and log magnitude

  19. The HP 35670A Dynamic Signal Analyzer obtainsfrequency responsedata from a physicalsystem.

  20. Fourier Series “Any periodic signal can be written in the sum of sine wave signals at different frequency.”

  21. Cut-off frequency Filter We want to get rid of the signal 3sin(9t) |vc| (magnitude) ω=5 Log ω

  22. Example Find vc(t) Use superposition to consider the effect of two different frequencies

  23. For 2sin(t)

  24. For 3sin(9t)

  25. Finally, we add vc(t) from both frequencies

  26. Power Line Systems 3 phases systems have three wire called “line” which are sine wave with phase shift 120 from each other Line 1 Line 2 Line 3 Power Plant 3 phases, 3 wires

  27. Power Plant Line 1 Line 2 Line 3 Neutral 3 phases, 4 wires L1-N = 220Vrms, L2-N = 220Vrms L3-N = 220Vrms L1-L2 = 381Vrms, L2-L3 = 381Vrms, L1-L3 = 381Vrms

  28. Star Connection ( Y-connection) Load Each load get 220 Vrms

  29. Delta Connection ( Δ-connection) Load Each load get 381 Vrms

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