* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture 13
Chirp compression wikipedia , lookup
Linear time-invariant theory wikipedia , lookup
Loudspeaker wikipedia , lookup
Pulse-width modulation wikipedia , lookup
Power inverter wikipedia , lookup
Buck converter wikipedia , lookup
Transmission line loudspeaker wikipedia , lookup
Spectrum analyzer wikipedia , lookup
Spectral density wikipedia , lookup
Mains electricity wikipedia , lookup
Variable-frequency drive wikipedia , lookup
Alternating current wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Power electronics wikipedia , lookup
Opto-isolator wikipedia , lookup
Three-phase electric power wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Ringing artifacts wikipedia , lookup
Utility frequency wikipedia , lookup
Phase-locked loop wikipedia , lookup
INC 111 Basic Circuit Analysis Week 13 Frequency Response Frequency Response Frequency response is a study of how the change of frequency affect the voltage or current. + R Asin(ωt) AC - + vL(t) - L What is the change of vL(t) when the frequency of the voltage source change? + R Asin(ωt) AC - Change to phasor + vL(t) - jL vL A R jL 1. When L R R + L A∟0 AC - + vL(t) - jωL To sketch graph, we look at 3 points jL jAL vL A R jL R jL jR j A A A 0.707 A45 2. When L R vL R jL R jR 1 j 3. When L R jL jL vL A A A R jL jL + R Asin(ωt) AC - + vL(t) - L |vL| (magnitude) A ω Linear Scale & Log Scale Linear Scale 1 2 3 4 5 6 Log Scale 0.1 1 10 100 1000 1000 Log scale of frequency |vL| (magnitude) A Log ω + R Asin(ωt) AC - + vC(t) - C What is the frequency response of vc(t) + R Asin(ωt) AC - + vC(t) - Change to phasor C R + A∟0 AC - + vC(t) - 1/jωC 1 1 jC vC A A To sketch graph, we look at 3 points 1 1 jRC R j C 1 1 vC A A A 1. When RC 1 1 jRC 1 2. When 3. When RC 1 RC 1 1 1 vC A A 0.707 A 45 1 jRC 1 j 1 1 A vC A A 1 jRC jRC jRC R + Asin(ωt) AC - + vC(t) - C What is the frequency response of vc(t) |vc| (magnitude) A Log ω Input & Output Input System Output Input is usually what we can control. Output is usually what we are interested in. + R Asin(ωt) AC - + vC(t) - C What is the frequency response of vc(t) Input = voltage source Output = vc(t) System = RC circuit Measure Frequency Response Input Freq 10Hz Amplitude = 1 Freq 100Hz Amplitude = 1 Freq 800Hz Amplitude = 1 System Output Phase = 0 Freq 10Hz Amplitude = 0.96 Phase = 12 Phase = 0 Freq 100Hz Amplitude = 0.82 Phase = 44 Phase = 0 Freq 800Hz Amplitude = 0.53 Phase = 56 Frequency Response Plot Magnitude Phase Note: log frequency and log magnitude The HP 35670A Dynamic Signal Analyzer obtains frequency response data from a physical system. 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. Metaphor of Frequency Domain Frequency Domain Time Domain (1,1,1) (2,-3,0) Time Domain R L 2 sin 2t 2 s 4 C Frequency Domain R sL 1/sC Transfer Function Transfer function = ratio of output and input in frequency domain Input System H(s) U(s) Transfer function Output Y(s) Y ( s) H (s) U (s) Note: Transfer function describes characteristic of a system. Example: Obtaining Transfer Function input is v(t) output is vc(t) Change all components to Phasor (frequency domain) Kirchoff’s Voltage Law I ( s) V ( s ) LsI ( s ) RI ( s ) Cs 1 I (s) V ( s) 1 Ls R Cs 1 VC ( s ) I ( s ) Cs 1 VC ( s) LC V (s) s 2 R s 1 L LC Transfer function Fourier Series “Any periodic signal can be written in the sum of sine wave signals at different frequency.” Filter + 2sin(t)+3sin(9t) AC AC - R + vC(t) 2sin(t)+3sin(9t) + C We want to get rid of the signal 3sin(9t) |vc| (magnitude) Cut-off frequency ω=5 Log ω Example Find vc(t) 1Ω + vC(t) 2sin(t)+2sin(9t) + AC 0.2f Use superposition to consider the effect of two different frequencies 1Ω + 2sin(t) AC - + vC(t) - 1Ω + 0.2f AC 2sin(9t) - + vC(t) - 0.2f For 2sin(t) 1 + 2∟0 AC - + vC(t) - -j5 1 1 5 j5 jC j 1 0.2 j j5 5 90 Vc 20 2 0 j5 1 5.1 78.69 1.96 11.31 vC (t ) 1.96 sin( t 11.31 ) For 3sin(9t) 1 + 2∟0 AC - + vC(t) - -j0.556 1 1 0.556 j 0.556 jC j 9 0.2 j j 0.556 0.556 90 Vc 20 2 0 j 0.556 1 1.144 29.07 0.972 60.93 vC (t ) 0.972 sin( 9t 60.93 ) Finally, we add vc(t) from both frequencies vC (t ) 1.96 sin( t 11.31 ) 0.972 sin( 9t 60.93 ) AC 1Ω + vC(t) 2sin(t)+2sin(9t) + 0.2f Other topics • Three-phase circuits • Magnetically Coupled circuits • Transformer Power Line Systems 3 phases systems have three wire called “line” which are sine wave with phase shift 120 from each other Line 1 220 2120 Line 2 220 20 Line 3 220 2240 AC AC AC Power Plant 3 phases, 3 wires Power Plant Line 1 220 2120 Line 2 220 20 Line 3 220 2240 AC AC AC Neutral 3 phases, 4 wires L1-N = 220Vrms, L2-N = 220Vrms L3-N = 220Vrms L1-L2 = 381Vrms, L2-L3 = 381Vrms, L1-L3 = 381Vrms Star Connection ( Y-connection) AC Z Z AC Z AC Load Each load get 220 Vrms Delta Connection ( Δ-connection) AC AC Z Z AC Z Load Each load get 381 Vrms