ECE 3200
Sallen-Key
S13
Part 3
There are many common analog filters, each with advantages and disadvantages. For
the third part we will examine a different filter type. For this example we will design a
4th Order Bessel low pass filter at 1 kHz with unity gain. The Sallen-Key architecture with
gain is shown in the circuit below.
As in the previous documents the transfer function for the Sallen-Key is:
( )
(
)
To build the 4th order Bessel we will use a table detailing the required values to force the
transfer function coefficients to meet the required shape. From the table [1] the
optimal parameters for the 4th Order Bessel filter are.
f01
Q1
f02
Q2
1.419
0.522
1.591
0.806
Unlike the Butterworth Filter the Bessel filter has a scaled frequency as well as optimal
Q.
The denominator of the 4th order transfer function for the Bessel follows the form:
(
) (
)
We need two Sallen-Key arranged opamps. Following the procedure of the previous
documents the first stage will be:
(
)
and
For design simplification we will let R 1 = R2 and select a standard value for C1, 4.7nF.
(
)
The second stage will follow the same pattern as the first using the same assumptions.
1
ECE 3200
Sallen-Key
(
S13
)
The Bessel filter’s frequency response is shown below.
References
[1] S. Franco. Design with Operational Amplifiers and Analog Integrated Circuits 3 rd ed.
McGraw-Hill, 2002.
2