Page 138 - Analog and Digital Filter Design

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Analog Lowpass Filters

Butterworth response, its maximum passband frequency is 1 MHz/25 = 40 kHz.
If, instead, a 1 dB Chebyshev response is wanted, the maximum passband fre-
quency is limited to I MHd172.5 = 5.8 kHz.

These frequency limits are for a maximum error in the passband of ZdB. If
no error is acceptable, the frequency limit will be much lower. Although the
frequency limit can be raised by using an amplifier having a greater gain-
bandwidth product, it can lead to instability. Usually, amplifiers with a high
gain-bandwidth product have a minimum gain for stability. For example, the
OP37 amplifier has a gain-bandwidth product of 63MHz, but at a minimum
gain of five.

Denormalizing Sallen and Key Filter Designs

In active filter designs the resistor values used should all be in the range I kQ to
100 kR where possible. If resistor values are lower than 1 kR there map be a
problem with loading of op-amp stage outputs. Loading can cause distortion
and increases the supply current. If resistor values are much higher than lOOkR
there may be problems with noise pickup. High impedance circuits can capaci-
tively couple with external electric fields. These unwanted signals can then inter-
fere with the wanted signal. Also, thermal noise voltage generated by the circuit’s
resistors increases in proportion to their resistance.

Active filters are based on a lowpass normalized filter model, using 1 R source
and load resistors and a cutoff frequency of 1 rad/s. Denormalization is quite
simple: (1) scale the impedance; the input impedance will tend towards 1 R as
the frequency approaches the passband cutoff point; and (2) scale for frequencl
by denormalizing the capacitance value.

Impedance scaling is simply multiplying the resistor values by a value that gives
a suitable input impedance. If you are driving the filter from a 600R source it
is probably better to make the input impedance high. say 56 kR (about 100 times
600R). and then provide a separate 600Q resistive termination to match the
source. This makes the input impedance correct for all frequencies. If 600R
resistors were used in the filter, the impedance would only be correct close to
the cutoff frequency. The input impedance of an active filter changes Lvith fre-
quency because of the shunt and feedback capacitance.

Scaling the capacitor values can now be carried out using the following equa-
C‘
tion: C = ~ . Where C’ is the normalized value calculated earlier. and R is
2x6 R
the denormalized value chosen to give a suitable input impedance