The basic multiple-feedback band-pass filter is useful for Qs up to about 15 with “moderate” gain. Band-pass circuits normally have lower damping and higher Q values than the usual low-pass or high-pass responses. In fact, these circuits are progressively harder to build and tune as the damping goes down and the Q goes up. Experience has shown that a high-performance, high-Q band-pass active filter cannot be built with a single op amp. Component-tolerance problems, sensitivity problems, or severe gain restrictions provide insurmountable barriers as you try to increase the circuit Q of single op amp circuits beyond a certain point. Therefore, single op amp versions of this filter may be used only for low-Q applications (Qs in the 2 to 5 range). Fortunately, Q values of 2 to 5 are ideal for many audio applications, including equalizers and tone controls. Higher Q circuits find use at IF and RF frequencies.
Figure 3-20 shows a single-stage, multiple-feedback band-pass filter where the op amp is connected in the inverting mode. Resistor R3 from the output to the inverting input sets the gain and the current through the frequency-determining capacitor, C1. Capacitor C2 provides feedback from the output to the junction of R1 and R2. CI and C2 are always equal in value. Resistor R2 may be made
adjustable in order to adjust the center frequency which is determined from:
When designing a filter of this type it is best to select a value for C1 and C2, keeping them equal. Typical audio filters have capacitor values from 0.01µF to 0.1µF which will result in reasonable values for the resistors. We will design a filter for 10 kHz and assume a Q of 3 and a stage gain of 2. The three resistors values are then determined from the following equations:
As previously stated, a single-stage active filter of this type results in low Qs (2 to 5). Filters which provide a very narrow passband must have a much higher Q than possible with a single section using one op amp. This may
be achieved by using several cascaded stages. Another method to achieve higher Q is the use of positive feedback. Figure 3-21 shows a positive-feedback band-pass filter using four op amps which make up two sections.
While looking rather complex at first, this circuit may be analyzed by examining each filter section separately. The complete filter is comprised of two identical sections, section “A” and section “B”. Each section uses an op amp connected as a multiple-feedback band-pass filter as we have described in the preceding paragraphs. This is followed by a second op amp used as a phase inverter to achieve positive feedback to the input of the first op amp. This stage has a gain of only 0.7. While the 16 kΩ positive feedback resistor gives us a gain of about 10.7, it is reduced to about 7.5 due to the 0.7 gain of the phase inverter stage. The resulting overall gain of section “A” is 4.
When section B is cascaded to section A we have the complete two stage (4 op amp) filter with an overall gain of 16 and Q of 69. The scope photo in Figure 3-22 shows the bandwidth of both stages cascaded. The measured bandwidth with an fo of 100 kHz is 2.3 kHz at the – 3 dB or half-power points.