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