Circuit Lab.
Experiment-5
Phasor Analysis, Gain and Phase Response of a RC Circuit
Quiz
• A(t)=5.sin(100t)
• B(t)=sin(100t-)
–Draw the graphic of signals.
–Write the phasor forms.
x(t)=A.cos(wt+)
Amplitude
Angular Frequency
time
(variable)
Phase
Shift
Phasor Diagram
Phasor Form: A=A1
Example 1
• Es(t)=10.sin(wt)
• V(t)=5.sin(wt+30o)
• V=530o
• I(t) = 2.sin(wt+120o)
• I=2120o
530o
2120o
Example 2
• Es(t)=10.sin(wt)
• A(t)=3.cos(wt)
• A=?
3
A(t)=3.sin(wt+90o)A=390o
Euler’s Formula
ejx=cos(x) + jsin(x)
Example 3Ic(t)
E(t)=10.sin(wt)Vc(t)=?Ic(t)=?
Vc(t)=E(t)=10.sin(wt) VC=100o
Ic(t)=C.dVc(t)/dt = 10.C.w.cos(wt)=10.w.C.sin(wt+90o)
IC=10.w.C90o
10wC
IC
VC
10
VC=100o
IC=10.w.C90o
jwC)sin(j)cos(wC
)sin(j)cos(
wCI
VZ
oo
oo
o
o
C
CC
1
909010
0010
9010
010
Circuit Gain and Phase Response
jwτ1
1
jwRC1
1
RjwC
1jwC
1
(jw)V
(jw)VH(jw)
i
o
22 21
1
wτ1
1
jwτ1
1H(jw)
fRC)(
Gain:
R=1 kC=100 nF
Phase:
R=1 kC=100 nF
)fRCarctan()arctan()( oo 20wτ0jw(jw)V
(jw)V
i
o
Example:R=1 kC=100 nF, |Vi|=10 V (p) f=1 kHz Gain ?, Phase?
Gain:
8467039481
1
1041
1
1021
1
10100101021
1
21
1 H(jw)
2221
29332
..
)(
)....(fRC
|Vo|=|Vi|.|H(jw)|=10.(0.8467)=8.467 V (p)
)lagging(..
).arctan(
)....arctan(
)fRCarctan()(
ooo
o
o
o
143214320
200
10100101020
20jw933
Phase:
Time Difference ?
msf
TPeriod
kHzf
11
1
360o 1ms
32.14o x
X = 89.28 s
Phasor Diagram
Vi10
Vo8.46
32.14o
Time Domain
Measurement Setup
50 OUT
SFG-2120
1 k
100 nF
GDS-1102
f Hz
10 V (p) or
5 V (p-p)
Vo
Vi
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
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