The three-amplifier implementation of the state-variable filter in Figure 1 provides for second-order bandpass, highpass, and lowpass responses. The strength of the circuit, however, is in the bandpass response (VOUT/VIN), in which it's easy to achieve high gain (G) and high Q. These two characteristics are important in applications in which selectivity is a key parameter in the filter. The application value of the circuit becomes even greater when DPPs (digitally programmable potentiometers) control and vary the bandpass filter's center frequency, f0, and passband gain, G. The independent control of a bandpass filter's parameters is a rarity among traditional filter-circuit techniques.
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| Figure 1. | Using digitally programmable potentiometers, you can control a passband filter’s center frequency and gain. |
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For the filter, IC1 functions as a summing amplifier, and IC2 and IC3 function as integrators. Three potentiometers, DPP1, DPP2, and DPP3, program the center frequency and passband gain of the filter. The 100-tap ON Semiconductor potentiometers, DPP1 and DPP2, are electronically ganged to program the frequency, f0, and DPP3 programs the gain, G. The center frequency is
and the gain is
where p represents the relative position of the wiper from one end (0) of the potentiometer to the other end (1). R represents the DPP's end-to-end resistance. The gain and Q are related by
The increment/decrement interface of the CAT5113 DPP allows for real-time, closed-loop applications, in which you can continuously vary the center frequency of the filter to track an input signal or to accommodate a system-level requirement. For the values shown, the center frequency varies from less than 200 Hz to more than 6 kHz with gain values as high as 25.
