Experiment-5 Phasor Analysis, Gain and Phase Response of a RC Circuit Circuit Lab. Experiment-5 Phasor Analysis, Gain and Phase Response of a RC Circuit

Quiz A(t)=5.sin(100pt) B(t)=sin(100pt-p) Draw the graphic of signals. Write the phasor forms.

x(t)=A.cos(wt+q) Amplitude Phase Shift Angular Frequency time (variable)

Phasor Diagram Phasor Form: A=A1Ðf

Example 1 Es(t)=10.sin(wt) V(t)=5.sin(wt+30o) V=5Ð30o 5 2 I(t) = 2.sin(wt+120o) I=2Ð120o 5 2 120o 30o

Example 2 A(t)=3.sin(wt+90o) A=3Ð90o Es(t)=10.sin(wt) A(t)=3.cos(wt)

Euler’s Formula ejx=cos(x) + jsin(x)

Example 3 E(t)=10.sin(wt) Vc(t)=? Ic(t)=? Ic(t) Vc(t)=E(t)=10.sin(wt) VC=10Ð0o Ic(t)=C.dVc(t)/dt = 10.C.w.cos(wt)=10.w.C.sin(wt+90o) IC=10.w.CÐ90o

VC=10Ð0o IC=10.w.CÐ90o IC 10wC 10 VC

Circuit Gain and Phase Response

Gain: R=1 kW C=100 nF

Phase: R=1 kW C=100 nF

Example: |Vo|=|Vi|.|H(jw)|=10.(0.8467)=8.467 V (p) R=1 kW, C=100 nF, |Vi|=10 V (p) f=1 kHz Gain ?, Phase? Gain: |Vo|=|Vi|.|H(jw)|=10.(0.8467)=8.467 V (p)

Phase: Time Difference ? 360o  1ms 32.14o  x X = 89.28 ms

Phasor Diagram Vi 10 32.14o 8.46 Vo

Time Domain

Measurement Setup f Hz 1 kW 100 nF 10 V (p) or 5 V (p-p) Vo Vi GDS-1102 SFG-2120 f Hz 50 W OUT Vo Vi 1 kW 100 nF 10 V (p) or 5 V (p-p)

Measure Calculate f (Hz) |Vi| |Vo| Time Diff. Gain Phase 100 750 1200 1600 2000 3000 5000 8000 16000

Plot f vs. Gain f vs. Phase