Variable frequency high slope filter tutorial based on potentiometer or DAC implementation

Analog variable frequency filters require the use of variable passive components. The larger the slope of the filter, the more variable passive components are required. Many of these components are potentiometers. For example, a low-pass Butterworth filter with a slope of 18 dB/8 frequency requires the use of a three-potentiometer potentiometer. If we need to re-tune the low-pass and high-pass filters at the same time, the necessary number of potentiometer resistor taps will double.

This is also the case when we need to re-tune multiple identical filters at the same time. These sets of potentiometers are very expensive and difficult to find. Another problem is their group error, which is about 3dB error in actual use. The volume of these potentiometers is also usually large. In addition, potentiometer wear produces "zipper" noise.

Another way of implementing these filters is to use active components instead of variable passive components. The most suitable component is a voltage-controlled amplifier - VCA. The variable of the VCA circuit is the gain, which changes according to the external control voltage.

VCA cells are most often designed as current-in/current-out devices and are exponentially responsive at voltage-sensitive control ports.

The gain of the VCA unit is:

Figure 1: Typical VGA Circuit

The input voltage Vin is converted into the input current Iin. VC by the resistor R as a control gain of the modulation gain. The VCA control gain process is to convert the input current signal into a bipolar logarithmic voltage, add it to the DC control voltage VC, and then convert the added sum voltage back to the current through the antilogarithmic circuit. The VCA output current Iout is converted to a voltage Vout by an op-amp-based IV, as shown in FIG. 1, where the conversion ratio depends on the feedback resistance connected between the output and the inverting input. The signal paths through the VCA and output op amps are in phase because VCA is inverting. If the VC pin is connected to ground, the output current will equal the input current.

If you use the decibel scale (Figure 2), the relationship between control voltage and gain is linear:

The response scale provided by each VCA manufacturer is different. For example, SSM2164 is -33mV/dB, SSM2018 is -30mV/dB, and THAT2180 is ±6,1mV/dB.

Figure 2: The relationship between gain and control voltage of SSM2164

Let's start with the first-order low-pass filter example:

Figure 3: Single-pole low-pass filter based on op amp

The cutoff frequency of this filter is:

The cutoff frequency of such a filter is often changed by adjusting the resistance RS. If a voltage-controlled amplifier is used in the previous circuit, the filter schematic will become as follows:

Figure 4: Single-pole low-pass filter based on VCA

This is a typical first-order low-pass filter, but the cutoff frequency depends on the VCA gain. If the gain is 1, the VCA behaves like a short circuit and the cutoff frequency depends only on the Rs and Cs values. If the gain is greater than 1, VCA is equivalent to a negative resistance (cutoff frequency increases). If the gain is less than 1, VCA is equivalent to a resistor (decrease in cutoff frequency).

After using VCA, the cutoff frequency of the filter is equal to:

Where G represents the VCA gain.

Figure 5: Frequency response of the filter in Figure 4

If we want to use the VCA to control both low-pass and high-pass filters, it is best to use a state-variable filter (Figure 6). The state variable filter consists of an integrator (OA2) and a sum/difference amplifier (OA1). Signals from all stages are used for feedback. These filters have low sensitivity to component values ​​and the design is simple.

Figure 6: Single-pole state variable filter based on VCA

When VC is 0, the cutoff frequency is determined by the circuit RSCS pair. As VC increases, the cutoff frequency decreases with the slope that depends on the VCA gain constant.

If the VCA gain in dB is a non-zero value, the shifted corner frequency fC2 is:

For the known gain control constant GC, the transfer frequency is:

VC stands for VCA control voltage.

For example, if the VCA has a gain control constant of -50 mV/dB and VC is equal to 1 V, then the cutoff frequency will be 1/10 of the cutoff frequency of the RSCS pair.

The following formula expresses the control voltage required to change the cutoff frequency from fC to the target value fC2, where fC is determined by RS and CS.

As can be seen from the above formula, VC controls the cutoff frequency with an exponential response characteristic.

For large slope filters, we must increase the order of the filter. Figure 7 shows a dual-channel, fourth-order Lincitz-Rayleigh state-variable filter controlled by a potentiometer or digital/analog converter. In one channel, there are 4 integrators plus sum/difference circuits, and feedback from all 4 integrators is returned to the sum/difference circuit. IC3 acts as a buffer, driving all 8 VCA control ports. The voltage from the potentiometer or DAC is applied to the inverting input. This voltage is then attenuated or amplified by the gain of IC3, and the gain of IC3 is determined by resistors R13 and R14.

Figure 7: Dual-Channel Large Slope Variable Frequency Filter

Figure 8 shows the frequency response of the filter shown in Figure 7, which also shows the low-pass output and the high-pass output. The center gain is 0 dB, and the corner frequency is set to approximately 1 kHz by RS and CS. If the gain is doubled, the cutoff frequency will be doubled (about 2 kHz). Similarly, if the gain is halved, the cutoff frequency will also be halved (about 500 Hz).

Figure 8: Frequency response of a fourth-order variable LR filter at three different VCA gains

Figure 9: VCA controlled filter as part of a more complex system

Because the precision E192 resistors and matched capacitors and high-speed op amps were used in the final design, the measured characteristic data was very accurate.