active second-order low-pass...
TRANSCRIPT
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
New circuit components � LM324 OpAmp, Capacitors and dual potentiometer
Constructed Circuit � Audio mixer + Active filter
Constructed Circuit, with connectors, and volume and cut-off frequency controllers