Page 298 - Analog and Digital Filter Design

Selecting Components for Analog Filters 295

The other method of in-circuit adjustment is suitable for wider bandwidth
filters. The frequency response of the whole filter can be examined on a
spectrum analyzer if a white noise source or a tracking signal generator is
available. The inductors in the circuit can be adjusted to give the correct fre-
quency response.

The usefulness of a white noise source should not be underestimated. A white
noise source generates all frequencies with equal average power. Therefore the
average output spectrum is equal to the filter’s transfer function.

Operational Amplifiers

The operational amplifier, or op-amp, is the active device in an active filter. Its
characteristics may change with temperature, but those most affected are the
DC offset, bias current, and so forth. The AC characteristics, which are of
primary interest here, are less affected by temperature.

The greatest problem in designing an active filter is that the op-amp is not ideal.
The ideal op-amp has infinite input impedance, zero output impedance, and a
flat frequency sesponse with linear phase. Most practical op-amps have very high
input impedance, and this does not cause us many problems. The output imped-
ance is not zero and can be up to about 1OOLl. This is not often a problem
because negative feedback is used to limit the gain of the op-amp, and this also
makes the effective output impedance close to zero. There is, however, an
assumption: that the gain bandwidth of the op-amp is far higher than that
required by the circuit. If the gain-bandwidth product limit is approached, the
output impedance rises.

This brings us nicely to the final problem. If the op-amp has insufficient gain-
bandwidth product, excessive phase shifts occur and the circuit can show
peaking in the frequency response. Gains of 20dB close to the cutoff frequency
can occur unless care is taken in the design. A good frequency response can be
obtained by utilizing an op-amp that has a gain-bandwidth product many times
that of the filter’s cutoff frequency. A rule-of-thumb value is 10 to 100 times the
cutoff frequency. Operational amplifiers in high-order filters work better if their
gain-bandwidth product is about 100 times the cutoff frequency.

Filters with a sharp frequency response such as 1 dB Chebyshev types require a
greater op-amp performance than filters with a gentle response such as Butter-
worth. The gain-bandwidth product is also known as the unity gain frequency,
or FU. Empirical formulae have been developed by me’ to find a suitable value
for FU in a number of active filters where the passband insertion loss or ripple
was less than 2dB.