Page 232 - Op Amps Design, Applications, and Troubleshooting

214 ACTIVE FILTERS

The ratio fc/bw is called the Q of the circuit. The higher the Q, the sharper the cut-
off slopes of the filter.
The term Q is also used with reference to low-pass and high-pass filters, but
it must be interpreted differently. The output of some filters peaks just before the
edge of the passband. The Q of the filter indicates the degree of peaking. A Q of 1
has only a slight peaking effect. A Q of less than 1 reduces this peaking, while a Q
greater than 1 causes a more pronounced peaking. There is usuaEy a trade-off
between peaking (generally undesired) and steepness (generally desired) of the
slope. The high- and low-pass filter designs in this chapter use a Q of 0.707, which
produces a very flat response.

5.2 LOW-PASS FILTER

Figure 5.2 shows one of the most common implementations of the low-pass filter
circuit. This particular configuration is called a Butterworth filter and is character-
ized by a very flat response in the passband portion of its response curve.
Ideally, a low-pass filter will pass frequencies from DC up through a specified
frequency, called the cutoff frequency, with no attenuation or loss. Beyond the cutoff
frequency, the filter ideally offers infinite attenuation to the signal. In practice, how-
ever, the transition from passband to stopband is a gradual one. The cutoff fre-
quency is defined as the frequency that passes with a 70.7-percent response. This,
of course, is the familiar half-power point referenced in basic electronics theory.

5.2.1 Operation

Let us try to understand the operation of the low-pass filter circuit shown in Fig-
ure 5.2 from an intuitive or logical standpoint before evaluating it numerically.
First, mentally open-circuit the capacitors. This modified circuit is shown in Fig-
ure 5.3, which is essentially how the circuit will look at low frequencies when the
capacitive reactance of the capacitors is high. We can see that this amplifier is con-
nected as a simple voltage follower circuit. Resistor R 3 is included in the feedback
loop to compensate for the effects of bias currents flowing through R x and R 2. For
low frequencies, then, we expect to have a voltage gain of about unity.

FIGURE 5.2 A tow-pass Butterworth
filter circuit.