Design Ideas: May 23, 1996

Programmable filter uses parallel processing

Alex Belousov,
Rego Park, NY

The circuit in Figure 1 uses an easy trick to produce a stable highpass filter. The trick is to simply take a lowpass filter and subtract the filter output from input signal. The mathematical basis for this method is

K(s)=1-1/(1+ts)=ts/(1+ts),

where K(s) is the filter's overall transfer function, and 1/(1+ts) and ts/(1+ts) are the typical, respective transfer functions of the lowpass and highpass filters.

This approach has several advantages. First, the lowpass filter itself has excellent stability and noise immunity.

Second, parallel-signal processing using this circuit topo-logy enables you to avoid cascading many op amps, which increases the phase margin and potential instability. (There is no common feedback loop in the circuit.) Finally, you can simultaneously use the lowpass and highpass filter outputs.

The lowpass filter in Figure 1 comprises a multiplying DAC (MDAC) and two op amps. The filter includes three major parts: a voltage-controlled current source with a differential input (IC_1A and R₁ through R₄), a digitally controlled current divider (MDAC), and an inverting integrator (IC_1B and C₁). This configuration provides high accuracy and stability combined with relative simplicity. (The circuit uses only two op amps.)

The time constant is digitally programmable: t=R₂C₁/D, where D is the MDAC's transfer coefficient. The cutoff frequencies are the same for both lowpass and highpass filter outputs. IC_1C and two pairs of resistors, R₅ through R₈, perform simple analog subtraction.

The filter suits the audio-frequency range of 20 Hz to 20 kHz. For the maximum D, which is approximately equal to 1, the cutoff frequency is approximately 20 kHz. For higher frequencies, the parasitic capacitance of the MDAC and the dynamic performance of the op amp may degrade overall filter accuracy.

The circuit uses the quad LF347 op amp and AD7541A MDAC, but similar components are applicable. R₁ through R₄ must be precise. R₅ through R₈ also must be precise, or at least ratio-matched (R₅/R₆=R₇/R₈). To increase the potential stability of the lowpass filter, R₃ has a slightly lower value than the other resistors. C₁ must be a good quality capacitor with low dielectric losses. (DI #1872)

To create a stable highpass filter, this circuit simply uses IC1C and associated resistors to subtract the output of a quality lowpass filter from the input signal.