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# Representations of AC signals

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(1)

ω

ω

0

ω

### ) d

Component at ω Angular frequency ω =2πf

1

1

2

2

1

1

2

2

1

1

1

2

2

2

1

1

1

2

2

2

### t

H(ω) : transfer function

(2)

## Phasor(相子)

0

### υ t = Vt +

phase: φ depends on the zero point of time

0

0 ω φ

j t+ j

−1

= j

ωt+φ

Re Im

0

0 0

ω φ

t j j

φ

Re Im

jωt

(3)

### Ex.

Plot the phasors of the following signals.

4 ) cos( 5

sin cos

3 3

2 2

1 1

### ω υ

+

=

=

=

t I

i

t V

t V

4 5 3 3

2 2

3 2 2

1 1

π π

j j

e I

jV e

V V

=

=

=

=

I V

V φ

Re Im

V

V1 V2

I3

time V1

V2

I3

V1 leads V2 by π/2; V1 leads I3 by 3π/4; Or V1 lags V2 by3π/2; V1 lags I3 by5π/4。

(4)

Calculate

4

2 1

ω

π

t j

j

Re Im

V V1 V2

(5)

C

C

j t j j j

j

j

ω π φ π

φ

φ

2 0

0 0

0 0

C C

V I

Re Im

φ

(6)

L

L

j t j j j

j

j

ω π φ π

φ

φ

2 0

0 0

0 0

L L

V I

Re Im

φ

(7)

i

o

i

i

o

o

i o

(8)

H

L

B

dB

BODE PLOT（波德圖）

i o

i i

(9)

i o

υ

υ

i o i

i

i o p

p

(10)

1 2 3

3 2

1 υ υ υ υ υ υ

υ

υ

(11)

RC 電路

i

i

o

o

(12)

i

o

i

o

2 / 1 2 2

2

1

2 /

1 − 45°

°

− 90

ω j s

sRC s

s s T

i o

=

= +

= 1

1 )

( ) ) (

( V

V

(13)

2 2 2

2 2 2 2

/ 1 2 2 2

(14)

0

(15)

i

o

2 / 1 2 2

2

1

2 /

1

90°

i

o

RC s

s sRC

sRC s

s s T

i o

/ 1 1

) (

) ) (

( = +

= +

= V V

(16)

0

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