low pass filter

1. MAE140:Linear Circuits –Winter 2013
Circuit Demonstration #4
Active Second-order Low-pass Filter
3
1
1
A
LM324N
R1
100k
R2
100k
10nF
C
10nF
R
100k
R
100k
GND
GND
V
out
Vin
Vb
V
a
Vb 2
Vb

2. Circuit Analysis
3
1
1
A
LM324N
R1
100k
R2
100k
10nF
C
10nF
R
100k
R
100k
GND
GND
V
out
Vin
Vb
V
a
Vb 2
Vb
KCL at A:
1
Voltagedivision:
Voltagedivision:
R R
1
Cs
1
Cs
Cs
R1
Va Vin Va Vout Va Vb
   0
Va 
1 RCs
Va  Va  (1 RCs)Vb
Vb 
R  1
Vb  Vout 
1
Vout, K 1
R2
K R1
R1 R2

3. Filter Transfer Function
K
Vin(s) R2
C2
s2
R1
s0
s
T(s) 
Vout(s)

 (3 K)RCs 1
limT(s)  DCgain  K 1
R2
, 1 K  3
limT(s)  0

4. Bode Diagram
10
0
10
1
10
2 3 4
10 10 10
5
10
6
10
7
-400
-300
-200
100
0
-100
Frequency [Hz]
Magnitude
[dB] Bode Diagram
R =1k
R =10k
R =50k
R =100k
10
0
10
1
10
2 3 4
10 10 10
5
10
6
10
7
0
-50
-100
-150
-200
Frequency [Hz]
Phase
[degree]
20 kHz
20

5. New circuit components
⚫LM324OpAmp, Capacitorsand dual potentiometer

6. Constructed Circuit
⚫Audio mixer + Active filter

7. Constructed Circuit, with connectors, and volume and
cut-off frequency controllers