This document describes the design process for an active low pass filter. It includes: 1) Specifying the filter requirements including passband, stopband frequencies and gains. 2) Calculating the element values using Butterworth and Chebyshev approximations. 3) Verifying the frequency response meets specifications. 4) Optimizing values using standard capacitor sizes. 5) Testing elements with ±5% tolerance. The result is the filter circuit with all calculated element values that meets the design specifications.

1. Active Filter Design
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Design Services

2. Contents
Slide
#
1. Filter Design
Category..............................................................................
2. Active Filter Design Flow-Chart.............................................................
3. Passive Low Pass Filter
Design...............................................................
3.1
Specifications : ..................................................................................
3.2
Calculation : ......................................................................................
.
3.3
Verification : ......................................................................................
.
3.4
Optimization : ....................................................................................
3.5 Elements
test : ...................................................................................
3
4
5
5
6
7
8-9
10-11
12
2All Rights Reserved Copyright (C) Bee Technologies Corporation 2009

3. 1.Filter Design Category
Available Filter Types
• Low Pass Filter
• High Pass Filter
• Band Pass Filter
• Band Reject Filter
Approximation
• Butterworth
- No ripple
- Smooth roll-off (rate of 20dB/decade for every pole)
• Chebyshev
- Pass-band ripple specification would be required.
- Steeper roll-of
Topology
• Passive
- High frequency range (> 1 MHz)
- Source and load impedance specifications would be required
• Active
- Low frequency range (1 Hz to 1 MHz)
- Unity-Gain Sallen-Key configuration (see Figure 1.0)
Number of Order
• 2nd
-10th
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R 1 R 2
C 2
0
C 1
in
+
-
U 1
A M P S I M P
o u t
Fig.1.0 Unity-Gain Sallen-Key Active Filter (2nd
-Order Active LPF)

4. 2.Active Filter Design Flow Chart
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2. Circuit design and calculation2. Circuit design and calculation
3. Verification3. Verification
4. Optimize with standard capacitor value4. Optimize with standard capacitor value
5. Elements test (± 5%)5. Elements test (± 5%)
Meet the spec?Meet the spec?
No
Yes
Satisfy?Satisfy?
Yes
YESYES
Result :
Filter circuit with all element values
Result :
Filter circuit with all element values
Use 1% CapacitorUse 1% Capacitor
1.Customer’s
specification
1.Customer’s
specification
No

5. Fr equenc y
100Hz 1. 0KHz 10KHz
db( v ( out ) )
- 40
- 30
- 20
- 10
0
3.Active Low Pass Filter Design (1/5)
3.1 Specifications :
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Figure 2 Low-pass filter response and specification
Pass-band Region
Stop-band Region
Pass-band edge frequency = 1 MHz
Pass-band gain = -3 dB
Stop-band edge frequency = 2.5 MHz
Stop-band gain = -30 dB
•Pass-band edge frequency : 1 kHz (fCutoff)
- Pass-band gain : -3 dB
•Stop-band edge frequency : 2.5 kHz
- Stop-band gain : -30 dB
•Load and Source Condition :
- Source Type : Voltage
- Filter Load Impedance : 50 Ω
- Resistance in the filter : 5 kΩ
STEP1.Customer’s
specification
STEP1.Customer’s
specification

6. R 1
5 k
R 2
5 k
R 5
5 0
0
C 1
2 9 . 4 2 n F
0
C 2
3 4 . 4 4 n F
R 3
5 k
R 4
5 k
C 3
1 2 . 1 8 n F
0
C 4
8 3 . 1 7 n F
+
-
U 2
A M P S I M P
o u tV s o u r c e
0
in
+
-
U 1
A M P S I M P
3. Active Low Pass Filter Design (2/5)
3.2 Calculation :
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Figure 3.1 Low-pass filter circuit with calculated element-values
(Butterworth approximation).
Figure 3.2 Low-pass filter circuit with calculated element-values
(Chebyshev approximation).
•R1 = R2 = R3 = R4 = 5kΩ
•C1 = 29.42nF
•C2 = 34.44nF
•C3 = 83.17nF
•C4 = 12.18nF
STEP2. Circuit
design and
calculation
STEP2. Circuit
design and
calculation
•R1 = R2 = R3 = R4 = 5kΩ
•C1 = 47nF
•C2 = 82nF
•C3 = 5.1nF
•C4 = 220nF
R 1
5 k
R 2
5 k
R 5
5 0
0
C 1
4 7 n F
0
C 2
8 2 n F
R 3
5 k
R 4
5 k
0
C 3
5 . 1 n F
C 4
2 2 0 n F
+
-
U 3
A M P S I M P
o u t 2
+
-
U 4
A M P S I M P

7. Fr equenc y
100Hz 1. 0KHz 10KHz
db( v ( out ) ) db ( v ( out 2) )
- 60
- 40
- 20
- 0
3. Active Low Pass Filter Design (3/5)
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 7
Figure 4 Response and specification of the calculated circuits.
Butterworth (1MHz,-3.013dB)
Chebyshev : (1MHz,-2.818dB)
(2.5MHz,-44dB)
(2.5MHz,-31.858dB)
3.3 Verification :
• Frequency Response Simulation
Pass-band Ripple (-1.23dB) •Pass-band edge frequencies : 1 MHz
•Pass-band gains : -3 dB 
•Stop-band edge frequencies : 2.5 MHz
•Stop-band gains : < -30 dB 
•Butterworth Approximation
- No ripple 
- Roll-off rate is 80dB/decade 
•Chebyshev Approximation
- Pass-band ripple : -1.23dB 
- Steeper roll-of 
— Butterworth Approximation
— Butterworth Approximation
STEP3.
Verification
STEP3.
Verification

8. 3.4 Optimization :
- Use standard capacitor values (E-24 Capacitor Values)
- Optimize inductor values
R 1
5 k
R 2
5 k
R 5
5 0
0
C 1
3 0 n F
0
C 2
3 3 n F
R 3
5 k
R 4
5 k
C 3
1 2 n F
0
C 4
8 2 n F
+
-
U 2
A M P S I M P
o u tV s o u r c e
0
in
+
-
U 1
A M P S I M P
3.Passive Low Pass Filter Design (4/5)
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Figure 5.1 Low-pass filter circuit with optimized element-values (Butterworth approximation).
Figure 5.2 Low-pass filter circuit with calculated element-values (Chebyshev approximation).
STEP4. Optimize with
standard capacitor value
(then verify)
STEP4. Optimize with
standard capacitor value
(then verify)
•R1 = R2 = R3 = R4 = 5kΩ
•C1 = 47nF
•C2 = 82nF
•C3 = 5.1nF
•C4 = 220nF
R 1
5 k
R 2
5 k
R 5
5 0
0
C 1
4 7 n F
0
C 2
8 2 n F
R 3
5 k
R 4
5 k
0
C 3
5 . 1 n F
C 4
2 2 0 n F
+
-
U 3
A M P S I M P
o u t 2
+
-
U 4
A M P S I M P
•R1 = R2 = R3 = R4 = 5kΩ
•C1 = 30nF
•C2 = 33nF
•C3 = 12nF
•C4 = 82nF

9. Fr equenc y
100Hz 1. 0KHz 10KHz
db( v ( out ) ) db ( v ( out 2) )
- 60
- 40
- 20
- 0
3.Passive Low Pass Filter Design (4/5)
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Figure 6 Response and specification of the optimized circuits.
3.4 Optimization :
• Frequency Response Simulation
•Pass-band edge frequencies : 1 MHz
•Pass-band gains : -3 dB 
•Stop-band edge frequencies : 2.5 MHz
•Stop-band gains : < -30 dB 
•Butterworth Approximation
- No ripple 
- Roll-off rate is 80dB/decade 
•Chebyshev Approximation
- Pass-band ripple : -1.23dB 
- Steeper roll-of 
Butterworth (1MHz,-3.06dB)
Chebyshev : (1MHz,-2.818dB)
(2.5MHz,-44dB)
(2.5MHz,-31.521dB)
Pass-band Ripple (-1.23dB)
— Butterworth Approximation
— Butterworth Approximation

10. 3.5 Elements test :
- ± 5% test for each capacitor value.
R 1
5 k
R 2
5 k
R 5
5 0
0
C 1
4 7 n F
0
C 2
8 2 n F
R 3
5 k
R 4
5 k
0
C 3
5 . 1 n F
C 4
2 2 0 n F
+
-
U 3
A M P S I M P
o u t 2
+
-
U 4
A M P S I M P
R 1
5 k
R 2
5 k
R 5
5 0
0
C 1
3 0 n F
0
C 2
3 3 n F
R 3
5 k
R 4
5 k
C 3
1 2 n F
0
C 4
8 2 n F
+
-
U 2
A M P S I M P
o u tV s o u r c e
0
in
+
-
U 1
A M P S I M P
3. Active Low Pass Filter Design (5/5)
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Figure 7.1 Low-pass filter circuit with ± 5% of the capacitance-values (Butterworth approximation).
Figure 7.1 Low-pass filter circuit with ± 5% of the capacitance-values (Chebyshev approximation).
STEP5. Elements test
(± 5%)
STEP5. Elements test
(± 5%)
•R1 = R2 = R3 = R4 = 5kΩ
•C1 = 47nF (± 5%)
•C2 = 82nF (± 5%)
•C3 = 5.1nF (± 5%)
•C4 = 220nF (± 5%)
•R1 = R2 = R3 = R4 = 5kΩ
•C1 = 30nF (± 5%)
•C2 = 33nF (± 5%)
•C3 = 12nF (± 5%)
•C4 = 82nF (± 5%)

11. Fr eque nc y
1 00Hz 1. 0KHz 1 0KHz
db( v ( o ut 2 ) )
- 6 0
- 4 0
- 2 0
- 0
Fr eq ue nc y
1 00 Hz 1. 0KHz 10 KHz
db ( v ( ou t ) )
- 60
- 40
- 20
- 0
3.Passive Low Pass Filter Design (5/5)
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Figure 8 Response and specification when the element values are error with ±5%.
3.5 Elements test :
• Frequency Response Simulation, compare to -5% and +5% of all element values.
Butterworth
— +5%
— standard values
— -5%
Pass-band gain (-3 dB)
Cutoff frequency : 0.9486M, 1M, 1.0485M
Chebyshev
— +5%
— standard values
— -5%
Cutoff frequency : 0.9564M, 1M, 1.0567M
Pass-band gain (-3 dB)

12. R 1
5 k
R 2
5 k
R 5
5 0
0
C 1
4 7 n F
0
C 2
8 2 n F
R 3
5 k
R 4
5 k
0
C 3
5 . 1 n F
C 4
2 2 0 n F
+
-
U 3
A M P S I M P
o u t 2
+
-
U 4
A M P S I M P
R 1
5 k
R 2
5 k
R 5
5 0
0
C 1
3 0 n F
0
C 2
3 3 n F
R 3
5 k
R 4
5 k
C 3
1 2 n F
0
C 4
8 2 n F
+
-
U 2
A M P S I M P
o u tV s o u r c e
0
in
+
-
U 1
A M P S I M P
•R1 = R2 = R3 = R4 = 5kΩ
•C1 = 47nF (± 5%)
•C2 = 82nF (± 5%)
•C3 = 5.1nF (± 5%)
•C4 = 220nF (± 5%)
•R1 = R2 = R3 = R4 = 5kΩ
•C1 = 30nF (± 5%)
•C2 = 33nF (± 5%)
•C3 = 12nF (± 5%)
•C4 = 82nF (± 5%)
3.Passive Low Pass Filter Design
3.6 Result :
• Low-pass filter circuit with all element values.
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 12
Figure 8.1 Low-pass filter circuit with all element-values (Butterworth approximation).
Figure 8.1 Low-pass filter circuit all element-values (Chebyshev approximation).
± 5%
± 5%
± 5%
± 5%
± 5%
± 5%
± 5%
Result : Filter circuit
with all element values
Result : Filter circuit
with all element values
± 5%