16.360%20Lecture%203

1
16.360 Lecture 3

• Phasor

VR(t)
Vs(t) V0Sin(?t?0),
VR(t) i(t)R,
Vs(t) VR(t) VC(t),
V0Sin(?t?0)
i(t)dt/C i(t)R,
Integral equation,
Using phasor to solve integral and differential
equations
2
16.360 Lecture 3

• Phasor

Vs(t) V0Sin(?t?0)
j(?0 - ?/2)
)
Re(V0 e
3
16.360 Lecture 3
Time
Phasor

• Phasor

j?
1
),
Re(I
j?
j?
VR(t)
time domain equation
V0Sin(?t?0)
i(t)dt/C i(t)R,
phasor domain equation
V
I R
,
4
16.360 Lecture 3
VR(t)

• Phasor domain

V
I R
,
I
R 1/(j?C)
V0Sin(?t?0)
i(t)dt/C i(t)R,

,
R 1/(j?C)
Back to time domain
j?t
Re (
e
)
R 1/(j?C)
5
16.360 Lecture 3

• An Example

VR(t)
Vs(t) V0Sin(?t?0),
VR(t) i(t)R,
Vs(t)
VL(t)
i (t)
Ldi(t)/dt,
VL(t)
Vs(t) VR(t) VL(t),
V0Sin(?t?0)
Ldi(t)/dt i(t)R,
differential equation,
Using phasor to solve the differential equation.
6
16.360 Lecture 3

• Phasor

j?t
di(t)/dt
Re(d I e
)/dt
j?
),
Re(I
time domain equation
V0Sin(?t?0)
Ldi(t)/dt i(t)R,
phasor domain equation
j?
)L
Re(I
7
16.360 Lecture 3

• Phasor domain

I R
j?L
V
I

,
I
R (j?L)

,
R j?L)
Back to time domain
j?t
Re (
e
)
R (j?L)
8
16.360 Lecture 3

• Steps of transferring integral or differential
  equations to linear
• equations using phasor.

1. Convert the given expressions to cosine function
2. Express time-dependent variables as phsaor.
3. Rewrite integral or differential equations in
   phasor domain.
4. Solve phasor domain equations
5. Change phasors variable to their time domain value

9
16.360 Lecture 3

• Waves in phasor domain

Recall waves, traveling wave in time domain
In phasor domain
x direction
- x direction
10
16.360 Lecture 3

• A question

Whats this?
Answer a traveling wave in phasor domain
Complex amplitude
11
16.360 Lecture 3

• Electromagnetic spectrum.

Recall relation ?f v.

• Some important wavelength ranges

1. Fiber optical communication ? 1.3 1.5?m.
2. Free space communication 700nm 980nm.
3. TV broadcasting and cellular phone 300MHz
   3GHz.
4. Radar and remote sensing 30GHz 300GHz

12
Relations for Complex Numbers
Learn how to perform these with your
calculator/computer
13
(No Transcript)
14
Summary