Page 139 - Analog and Digital Filter Design

1 36 Analog and Digital Filter Design

An example of denormalizing a Sallen and Key lowpass filter will now be given.
Let us just consider a single second-order stage from a fifth-order Chebyshev
filter having 0.5dB passband ripple. The pole locations for this stage are 0.1057
f j0.95497. The frequency scaling factor for this filter to have a 10 kHz cutoff
frequency (Fc) is 2 nFc = 62,832 rad/s.

The equations to find the capacitor values for a normalized lrad/s cutoff
1
frequency are: C'1= - and C'2 = ~ 0? + w?. In these equations, substituting
0
0 = 0.1057 and o = 0.95497 gives the result C'1 = 9.46074 and C'2 = 0.1145.

.
To find the frequency scaled component values use C = - = lOkR
If
R
2nfi R
(suitable for a source of about loon), and the frequency scaling factor 21rF,. =
62.832 rad/s, are substituted into the above equation, this gives:
9.46074
C1= = 15.057 nF = 15nF
62,832 .lo'
0.1145
c2 = = 182.23pF = 180pF
62,832.10''
Finally, RI = R2 = R = 10kR.

State Variable Lowpass Filters

This circuit design has a lower sensitivity to the op-amp's gain-bandwidth
product limitation, and section Q factors of up to 200 are possible. It does,
however, need three op-amps, as shown in Figure 4.12.

I
R3
Rl
C
II C
I II
II R

ov
ov
Figure 4.12
State Variable
Lowpass
(All-Pole) Output