1. 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

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

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

4. Phasor Diagram
Phasor Form: A=A1Ðf

5. 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

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

7. Euler’s Formula
ejx=cos(x) + jsin(x)

8. 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

9. VC=10Ð0o
IC=10.w.CÐ90o IC
10wC 10 VC

11. Circuit Gain and Phase Response

13. Gain:
R=1 kW
C=100 nF

14. Phase:
R=1 kW
C=100 nF

15. 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)

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

17. Phasor Diagram Vi 10
32.14o
8.46 Vo

18. Time Domain

19. 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)

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

21. Plot
f vs. Gain
f vs. Phase