Time Domain vs Frequency Domain

6.002x

CIRCUITS AND
ELECTRONICS

Time Domain versus
Frequency Domain Analysis

Reading: Section 13.6.3 and Pages 819 – 823 of A & L.

1

Review

2

One Circuit, Different Filters

Review

+ Vc –

L

Vi +
–

C

R

3

Review Q indicates peakiness
+ Vc –

L

Vi +
–

C
R

Vc
Vi 1

1

Mapping back to time domain is easy

+ Vc –
L
Vi

C

+
–

R

2

Vc
ωo
= 2
Vi s + 2α s + ω o 2

1

Let’s use Q to compare time domain and frequency domain
Frequency domain

L
Vi +
–

Time domain
L

C

R

vI

+
–

C

R

2

Overdamped case:

α > ωo

Or

Frequency domain

Vi +
–

C

ωo 1
<
2α 2
Q=

Time domain
+ vC –

+ Vc –
L

Q=

vI +–

R

L

C

ωo =
2α =

R

Unit step

Sinusoid

v I = Vi cos ω t

v I = u (t )
vC

Vc
Vi

ωo

ω

ωo
2α

t

1

1
LC

R
L

Underdamped case:

α < ωo

Or

Frequency domain

Vi +
–

C

ωo 1
>
2α 2
Q=

Time domain
+ vC –

+ Vc –
L

Q=

vI +–

R

L

C

ωo =
2α =

R

Unit step

Sinusoid

v I = Vi cos ω t

v I = u (t )
vC

Vc
Vi

ωo

ω

ωo
2α

t

1

1
LC

R
L

Critically damped case:
Frequency domain

Vi +
–

C

Q=

ωo 1
=
2α 2
Q=

Time domain
+ vC –

+ Vc –
L

Or

α = ωo

vI +–

R

L

C

ωo =
2α =

R

Unit step

Sinusoid

v I = Vi cos ω t

v I = u (t )
vC

Vc
Vi

ωo

ω

ωo
2α

t

1

1
LC

R
L