Adjust op-amp gain from -30 dB to +60 dB with one linear pot

A good manually adjusted audio gain stage is characterized by:

Low noise and low distortion,
A 20 kHz bandwidth,
A wide gain adjustment range (e.g. 90dB), and
Logarithmic (at least pseudo-logarithmic) control characteristic to
Efficiently span that wide gain range with good resolution (not too twitchy)

Figure 1’s circuit checks all these boxes.

Figure 1 Low noise DC to 20 kHz audio gain stage based on the OP37 with pseudo-logarithmic gain adjustment.

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Figure 1 is based on the OP37 which has an impressive list of specs. They include a 60 MHz gain-bandwidth, making 20 kHz bandwidth compatible with gain up to 3000x = +70 dB, noise ~3 nV/Hz1/2 which is less than the thermal noise of a 600 Ω resistor, ~20 µV input DC offset, etc.

Figure 1 exploits these impressive features while also accommodating one quirk. To ensure stability, the OP37 requires a minimum closed loop gain of 5 = 14 dB. Satisfying this requirement is assured by the R2:R3 ratio.

Minimum closed loop gain = R3/R2 + 1 = 4.03 + 1 = 5.03

But a minimum gain of 14dB for the entire circuit would be incompatible with many audio applications, which often require a minimum adjustable gain < 1, or even approaching zero. This is the reason for the R1/R2 variable voltage divider, which sets a lower minimum-gain without incurring the cost of a dual potentiometer.

Grounding the pot wiper creates two mechanically linked but electrically independent variable resistors. The bottom half (ccw) cooperates with R1 to form a variable input attenuator with an (input) gain of:

GI = 2ccw/(1 + 2ccw)

ccw = fraction of R2 between ccw limit and wiper position

So GI, the attenuator’s gain, goes from near zero to 2/3 as ccw goes from 0 to 1.

Meanwhile, the top half of the pot forms a variable feedback network with R2. This network sets the OP37’s closed loop (output) gain:

GO = (8.06/2cw + 1)

cw = fraction of R2 between wiper and cw limit

Cascading these two ratios (both controlled by the R2 pot), results in a total IN-to-OUT gain product of:

I/O gain = (2ccw/(1 + 2ccw))(8.06/2cw + 1)

Figure 2 shows the plot of the pseudo-logarithmic result with good log conformity from -10 dB to +40 dB.

Figure 2 Pseudo-logarithmic GIGO gain versus R2 wiper position 0 to 1 = fully CCW to fully CW.

To optimize noise performance, R1 and R3 should be metal film types to avoid carbon-resistor excess (1/f) noise, and R2 should be a cermet type.

Stephen Woodward’s relationship with EDN’s DI column goes back quite a long way. Over 100 submissions have been accepted since his first contribution back in 1974.

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