Variable frequency high slope filter with one
potentiometer or DAC
Ing. Peter Bobek - April 16, 2014
Analog variable frequency filters require the use of variable passive components. The higher the
slope of the filter, the greater the number of needed variable passive components. These elements
are most often potentiometers. For example, low-pass Butterworth filter with 18dB/octave slope
requires a three-gang potentiometer. If we need to retune low-pass and high-pass filter at the same
time, the necessary number of potentiometer's resistive tappers doubles.
This is also true when we need to retune multiple identical filters simultaneously. These multi-gang
potentiometers are expensive and hard to find. Another problem is their gang error which is in
practice around 3 db. These potentiometers are usually quite bulky. In addition, worn out
potentiometers generate "zipper" noise.
Another way to realize these filters is to use active components instead of variable passive
components. The most suitable element is voltage controlled amplifier - VCA. A variable of VCA
circuit is gain that varies depending on an external control voltage.
VCA cells are the most commonly designed as current-in/current-out devices with exponential
response to voltage-sensitive control ports.
Gain of VCA cell is:
Figure 1. Typical VCA circuit
The input voltage Vin is converted into the input current Iin through the resistor R. VC is a control
voltage modulating the gain. VCA controls gain by converting an input current signal to a bipolar
logged voltage, adding a dc control voltage VC, and reconverting the summed voltage back to a
current through an antilog circuit. The VCA output current Iout is converted to a voltage Vout via an
op-amp based I-V converter, as shown in Figure 1, where the conversion ratio is determined by the
feedback resistor connected between the output and inverting input. The signal path through the
VCA and the output opamp is non-inverting because VCA is inverting. If Vc pin is held at ground, the
output current will equal the input current.
On a decibel scale (Figure 2), the relationship between the control voltage and the gain is linear:
The response scale varies by VCA manufacturer. For example: SSM2164 -33mV/dB, SSM2018 30mV/dB, THAT2180 +/-6,1mV/dB.
Figure 2. Gain vs. control voltage for SSM2164
Let´s start with example of a first order low-pass filter:
Figure 3. 1-pole Low-pass filter based on operational amplifier
Cutoff frequency of the filter is:
Cut-off frequency change of this filter is most often done by resizing resistor RS. If we put voltage
controlled amplifier to the previous circuit, filter schematic will be as follows:
Figure 4. 1-pole low pass filter based on VCA
This is typical first order low pass filter, but with cutoff frequency dependent on VCA gain. If gain is
unity, VCA behaves as short and cutoff frequency depends only on Rs and Cs values. If the gain is
greater than 1, VCA acts as a negative resistor (cutoff frequency increases). If the gain is less than 1,
VCA behaves like a resistor (cutoff frequency decreases).
With VCA, filter cutoff frequency is given as:
where G is VCA gain.
Figure 5. Frequency response of the filter in figure 4
State variable filter
If we want to VCA control both low-pass and high-pass filter simultaneously, it is preferable to use a
state variable filter (Figure 6). State variable filter is made up of integrator (OA2) and a
summing/differencing amplifier (OA1); signals from all stages are used for feedback. These filters
show low component value sensitivity and are simple to design.
Figure 6. 1-pole State variable filter based on VCA
When VC is zero, the cutoff frequency is determined by the circuit RSCS pair and decreases with a
slope dependent on the gain constant of VCA as VC increases.
If VCA gain in dB is nonzero, the shifted corner frequency fC2 is:
For known gain-control constant GC, shifted frequency will be:
where VC is VCA control voltage.
For example, if VCA has -50mV/dB gain-control constant and VC is equal to 1V, the cut-off frequency
will be 1/10 of the cut-off frequency of the RSCS pair.
The following formula expresses the control voltage necessary to change the cutoff frequency from fC
given by RS and CS to the desired value fC2.
From the previous equation, it can be seen that VC controls the cutoff frequency with an exponential
response.
For high slope filter, we must increase filter order. Figure 7 shows dual channel fourth-order
Linkwitz-Riley state-variable filter controlled by one potentiometer or digital/analog converter. In
one channel there are now four integrators plus the summing/differencing stage, to which feedback
from all four integrators is returned. IC3 works as a buffer and drives all eight VCA´s control ports.
Voltage from potentiometer or DAC is applied to the inverting input. This voltage is attenuated or
amplified by IC3´s gain, which can be set by resistors R13 and R14.
Figure 7. Dual channel high slope variable frequency filter
Figure 8 shows frequency response of the filter in figure 7. Both low pass output and high pass
output are plotted. Center gain is 0dB and corner frequency is set by RS and CS to approximately
1kHz. If the gain is doubled, cutoff frequency is also doubled (approx. 2kHz). Similarly, if the gain is
halved, cutoff frequency is also halved (approx. 500Hz).
Figure 8. Frequency response of fourth-order variable LR filter for 3 different gains of VCA.
Because precision E192 resistors as well as matched capacitors and high speed op-amps are used in
the final design, the measured characteristics are very accurate.
Figure 9. VCA controlled filter as part of a more complex system
References:
SSM2018 Datasheet
THAT2180 Datasheet