1. Submitted By: Alex Kremnitzer
Date: 05-11-2011
Date Performed: 05-18-2011
Lab Partners: Curtis Raatz
Sarah Woodbury
Butterworth Active Bandpass Filter
using Sallen-Key Topology
Technical Report 5
Milwaukee School of Engineering
ET-3100 Electronic Circuit Design

2. 1
Abstract
The design of an Active Butterworth Filter with Sallen-Key topology was
calculated, simulated and prototyped. The simulated and tested prototyped
circuit verified the validity of the design.
Signals below the critical frequency of the High Pass Filter were
attenuated. Signals above the critical frequency of the Low Pass Filter were
attenuated. The frequency response (attenuation) in the Bandpass region was
flat. The value for Q was less than 1 which is what would be expected for a
broadband bandpass filter. All values were within expected tolerances except
the cutoff frequency of the Low Pass Filter was greater than expected.
The use of active filters has the advantage of the avoidance of inductors,
the reduction of circuit loading and the shape of the frequency response, cutoff
frequencies and Q value can be varied.
Introduction
The design constraints were to create a unity gain Active Bandpass Anti-
Aliasing Filter to be used for an audio application. A 6th
order Butterworth Filter
was to be used to filter out high frequency signals above the audio range
(22kHz) and a cascaded 2nd
order Butterworth Filter to reduce the low
frequency content of the signal below 40Hz. The filter input impedance was to
be greater than 1k and constant from 10Hz to 40kHz.
The Butterworth filter is designed to have a flat response in the passband
region. The filter topology used was the Sallen-Key. The upper critical
frequency of the filter was chosen as 22kHz since this was just above the
maximum frequency limit of human hearing said to be at 20kHz ideal.
The frequency response of the filter was tested by applying an input
signal from a signal generator which was swept from 10Hz to 100kHz. Plots of
the simulated and measured frequency response were made and reviewed
against the design constraints.

3. 2
The circuit shown in the Appendix was constructed. Capacitor
measurements were taken using a Fluke Model PM6304 RCL Meter. Resistor
measurements were taken using an Agilent 34401A Digital Multi Meter. In the
lab, the output signal amplitude measurements were taken using a Agilent
54622D Digital Oscilloscope. The circuit power was supplied with ±10VDC
using an Agilent E3631A Power Supply. The applied input signal was a 2.0Vpp
Sinusoidal Wave from an Agilent 33220 Function Generator. The amplitude of
the output signal was measured on the oscilloscope while the frequency of the
input signal was swept from 4Hz to 100kHz. The frequency was also recorded
when the signal was at the critical upper and lower frequency as determined by
an amplitude of 0.71VDCpk (-3dB).
The following formulas were used in the design of the Butterworth
Active Band-Pass Filter Circuit:
Design Criteria:
Input Buffer Filter:
(Design Criteria: The filter input impedance was to be greater than 1k and constant
from 10Hz to 40kHz.)

4. 3
LM741 Output Resistance Vs Frequency
Low Pass Filter Design Calculations:
2nd Order Unity-Gain LPF Sallen-Key Topology (For Reference)

5. 4
6th Order Unity-Gain LPF Sallen-Key Topology
Unity Gain 6 Pole LPF Active Filter Design Using Frequency and Impedance Scaling and Look-up tables;
Butterworth Filter with Sallen-Key topology.
High Pass Filter Design Calculations:
2nd Order Unity-Gain HPF Sallen-Key Topology

6. 5
Unity Gain 2 Pole HPF Active Filter Design Using Frequency and Impedance Scaling and Look-up tables;
Butterworth Filter with Sallen-Key topology.
Bandpass Filter Calculations:
General Formula For Error Analysis:
Simulation Validation
Table 1: BPF, Calculated versus Simulated Results

7. 6
Table 2: Frequency Roll-Off, Calculated versus Simulated Results (Ideal)
Table 3: Frequency Roll-Off, Calculated versus Simulated Results (Actual)
Figure 1: Simulated Frequency Response, Ideal Values

8. 7
Analysis of Simulation Results
See Table 1 and Figure 1. The simulated results were within expected
values for the frequency response of the filter design. The upper and lower
critical frequencies were within 5% of calculated using ideal component values.
The bandpass region was flat as would be expected for a Butterworth filter.
Critical Frequency High Pass Filter. See Table 1 and Figure 1. The
calculated value for the lower critical frequency was 40Hz and the value
calculated from simulation results was 40.39Hz having an error of 0.98%. The
error increased to 3.93% when using the actual circuit component values in the
simulation.
Critical Frequency Low Pass Filter. See Table 1 and Figure 1. The
calculated value for the upper critical frequency was 22kHz and the value
calculated from simulation results was 22.05kHz having an error of 0.21%. The
error increased to 1.30% when using the actual circuit component values in the
simulation.
Bandwidth (BW): See Table 1 and Figure 1. The calculated value for the
bandwidth was 21.96kHz and the value calculated from simulation results was
22.01kHz having an error of 0.21%. The error increased to 1.30% when using
the actual circuit component values in the simulation.
Center Frequency (fcenter): See Table 1. The calculated value for the
center frequency was 938Hz and the value calculated from simulation results
was 944Hz having an error of 0.59%. The error increased to 2.61% when using
the actual circuit component values in the simulation.
Quality Factor (Q): See Table 1. The calculated value for Q from was
0.042 and the value calculated from simulation results was 0.0439 having an
error of 0.38%. The error increased to 1.29% when using the actual circuit
component values in the simulation. The Q value is less than 1 which is what
would be expected for a broadband bandpass filter.

9. 8
Frequency Roll off: See Tables 2 and 3 and Figure 1. High Pass Filter;
The roll off of the High Pass Filter was designed to be 40dB per decade and
using ideal values the simulated rolloff overall was less than 4.9% overall of
calculated. The error decreased to -3.2% using actual values in simulation. Low
Pass Filter; The roll off of the Low Pass Filter was designed to be 120dB per
decade and using ideal values the simulated rolloff overall was -5. 5% of
calculated. The error increased to -6.8% using actual values in simulation.

10. 9
Design Validation and Testing
Table 4: Component Value Error Analysis
Table 5: Calculated versus Measured Values
Table 6: Frequency Roll-Off, Calculated versus Measured Results

11. 10
Figure 2: Measured Frequency Response
Figure 3: High Pass Filter Section
Figure 4: Low Pass Filter Section

12. 11
Analysis of Testing Results
Component Values
The values of all components measurements are shown in Table 4. All
component were within their expected values except for C4 (-27.86%), C5
(15.0%), C7 (-27.32%) and C8 29.33%) All these capacitors were from the Low
Pass Filter section however their variance did not greatly affect the expected
cut-off frequency and roll off of that portion of the Band Pass Filter, as shown
in Tables 5 and 6.
Circuit Analysis
Critical Frequency High Pass Filter. See Table 5 and Figure 3. The
measured critical frequency (-3dB) of the High Pass filter section was
calculated to be 40Hz but was measured to be 90Hz, causing an error of 125%.
The design calculations of the High Pass Filter were verified to be correct and
there was small error in the actual circuit components. Table 1 verifies that there
was a minimal change in the cut-off frequency in simulation between using
ideal and actual values. After reviewing the users manuals on the Oscilloscope
and Function Generator, it was noticed that the user’s manual’s specifications
are based on a 30 minute warm-up period before measurements should be taken,
which was not observed.
Critical Frequency Low Pass Filter. See Table 5 and Figure 4. The
measured critical frequency (-3dB) of the Low Pass filter section was calculated
to be 22kHz but was measured to be 22.4kHz, having an error of 1.82% which
is acceptable.
Bandwidth (BW): See Table 5 and Figure 2. The calculated value for the
Bandwidth using measured values was 22.31kHz while it was calculated to be
21.96kHz and an error of 1.59% which is acceptable.
Center Frequency (fcenter): See Table 5. The calculated value for the
center frequency using measured values was 1420Hz while it was calculated to
be 938Hz resulting in an error of 51.36%. The variance in the center frequency
was caused by the error in the critical frequency of the High Pass Filter. Since
the center frequency is calculated as the geometric mean of the upper and lower
critical frequencies.

13. 12
Quality Factor (Q): See Table 5. The calculated value for Q from
measured values was 0.04 and was the same as calculated. It is less than 1
which is what would be expected for a broadband bandpass filter.
Frequency Roll off: See Table 6 and Figure 2. The roll off of the High
Pass Filter was designed to be 40dB per decade but was measured to be 25dB
per decade with an error of 37.5%. The roll off of the Low Pass Filter could not
be analyzed over a full decade as the output signal measurements were taken up
to 100kHz as the highest frequency. With a critical frequency of 22kHz, to
obtain a full decade, measurements should have been taken past 220kHz. With
the roll off analyzed over ¼ decade, it was measured to be -27.37 and an error of
-8.8% when compared to the calculated value of -30dB per ¼ decade. The
design criteria was reviewed to see if the requirements of the filter order were
misinterpreted (reversed) but after review, it appeared to be correct
Conclusion
The simulated and tested prototyped circuit verified the validity of the
Butterworth Sallen-Key topology Active Filter design. The calculated and
measured frequency response were of the same symmetry.
Signals below the 40Hz critical frequency of the High Pass Filter were
attenuated however the circuit measured at a critical frequency of 90Hz and an
error of 125%. Signals above the 22kHz critical frequency of the Low Pass
Filter were attenuated and the tested circuit had a maximum error of 1.82%. The
frequency response (attenuation) in the Bandpass region was flat. The frequency
rolloff was as expected. The value for Q was less than 1 which is what would be
expected for a broadband bandpass filter.
The use of active filters has the advantage of the avoidance of inductors
which tend to be large when in the audio frequency range. The use of
operational amplifiers also reduce the circuit loading which passive components
would cause. An improvement in the design would be to use tighter tolerances
on components or use variable capacitors and resistors so the shape of the
frequency response and cut-off frequencies plus the Q factor can be adjusted.