MAE 140: Linear Circuits – Winter 2013 Circuit Demonstration #4

Active Second-order Low-pass Filter

2

311

ALM324N

100kR1

100k

R2

10nF

C

10nFC

100kR

100kR

GND

GND

VoutVin VbVa

Vb

Vb

Circuit Analysis

2

311

ALM324N

100kR1

100k

R2

10nF

C

10nFC

100kR

100kR

GND

GND

VoutVin VbVa

Vb

Vb

KCL at A: 01

1 1Voltagedivision: (1 )1 1

1 1 2Voltagedivision: , 11 2 1

Va Vin Va Vout Va VbR RCs

CsVb Va Va Va RCs VbRCsR Cs

R RVb Vout Vout KR R K R

− − −+ + =

= = ⇒ = +++

= = = ++

Filter Transfer Function

2 2 2

0

( )( )( ) (3 ) 1

2lim ( ) DCgain 1 , 1 31

lim ( ) 0s

s

Vout s KT sVin s R C s K RCs

RT s K KR

T s→

→∞

= =+ − +

= = = + ≤ <

=

Bode Diagram

100 101 102 103 104 105 106 107-400

-300

-200

-100

0

100

Frequency [Hz]

Mag

nitu

de [d

B]Bode Diagram

R =1kR =10kR =50kR =100k

100 101 102 103 104 105 106 107-200

-150

-100

-50

0

Frequency [Hz]

Phas

e [d

egre

e]

20 kHz20

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