Single resistor tunes lowpass filter
Any tunable, second-order, active RC-filter section requires at least two thoroughly matched variable resistors. But the lowpass implementation in Figure 1 provides for wide-range cutoff-frequency control using only a single variable resistor, R. In addition to the resistor, this filter comprises an operational amplifier, IC2, which serves as a unity-gain buffer; two capacitors, C1 and C2; and a single-pole, double-throw analog switch, IC1, driven by a periodic sequence of square-wave switching pulses applied to the SW input. Thanks to the high-frequency periodic switching, you can simultaneously control the time constants of both C1 and C2 in their recharging processes using only R. The approximate voltage-transfer function of the filter, assuming that the switching frequency is much higher than the filter's cutoff frequency, is:
where ωP=1/(R is the pole frequency; Q= is the quality factor; Θ=τ/T is the online time ratio (duty cycle); π is the pulse width; and T is the switching period.
Obviously, controlling R results only in variations of pole frequency and does not affect the quality factor. So, you can tune this filter over a wide frequency range, preserving its passband gain and ripple. You can achieve a stable value of Θ by using a binary counter. A high-resolution, digitally programmable potentiometer is probably the most appropriate choice for R in this filter. Figure 2 shows the filter's frequency response, simulated in PSpice. This design tunes the cutoff frequency over 20 Hz to 20 kHz by varying the resistor value from 1.2 MΩ to 1.2 kΩ, with C1=10 nF, C2=1 nF, Θ=0.5, and a switching frequency of 500 kHz. Using this method, you can also implement a high-order lowpass filter by cascading second-order sections or by joining them to multiple-feedback structures.