Digital pot can control gain over a 90 dB span like an electromechanical

A short while back, I published a design idea that uses a single linear pot to control the gain of a high performance OP37 decompensated op-amp over an unusually wide (-30 dB to +60 dB) range.

Figure 1 shows the circuit.

Gain = (R2ccw/(R1 + R2ccw))(R3/R2cw + 1).

Figure 1 Grounded wiper makes R2 serve as both input attenuator and output gain set.

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Recently I started wondering whether a digital pot (Dpot) would work in place of Figure 1’s mechanical R2. Figure 2 shows what seemed like a likely Dpot topology.

Gain = (R2ds/(R1 + R2ds + Rw))(R3/(R2(1 – ds) + Rw) + 1)

Figure 2 R2 has the same function as in Figure 1 with DC bias from R4 R5 C2 to accommodate bipolar signals. But what about Rw wiper resistance effects?

On closer inspection, it turned out not to be so very promising after all. This is due to wiper resistance interfering with the isolation of the two halves of R2 that made the original circuit work in the first place. Figure 3 shows the fix I eventually resorted to.

Figure 3 Positive and negative feedback loops around A2 combine to create active negative resistance = -R4.

A2 and its surrounding network are the basis of the trick. They generate an active negative resistance effect that subtracts from Rw and, if adjusted so R4 = Rw, can theoretically (the engineer’s least favorite word) cancel it out completely. 

A quick method for dialing out Rw is to write the Dpot setting to zero, provide a ~1v rms input, then trim R4 for output null.

Here’s some negative resistance math. Note Vp# = voltage signal present at A2 pin #. 

1. Let Iw = wiper signal current, then
2. Vp6 = Vp2 – R4*Iw
3. Vp2 = Vp3 (negative feedback)
4. Vp3 = Vp6/2 (positive feedback)
5. Vp6 = Vp6/2 – R4*Iw
6. Vp6 – Vp6/2 = Vp6/2 = -R4*Iw
7. Vp6 = -2*R4*Iw
8. If R4 = Rw, then IR4 = IRw
9. -2*R4*Iw = -(R4 + Rw)Iw
10. Vw = Vp6 + (Iw*R4 + Iw*Rw) = -Iw(R4 + Rw) + Iw(R4 + Rw)
11. Vw = 0 (Rw has been cancelled out!)

 Gain = (R2ds/(R1 + R2ds))(R3/(R2(1 – ds)) + 1)

Figure 4’s red curve compares Figure 2’s behavior with an (uncompensated) Rw = 150 Ω (plausible for the Microchip Dpot illustrated), while the black curve shows what happens if R4 = Rw = 150 Ω. Compare it to the performance of the original (Figure 1) circuit using a mechanical pot as shown in Figure 5.

Of course, how perfect Rw cancellation over the full range of Dpot settings can be is no better than Rw match over the Dpot’s 257 different taps at the 2.5v DC bias provided by R5R6. Typical matching within a given pot’s resistor array seems good, but this is not the manufacturer’s promise, which only speaks to a factor of +/-20% or so. But reducing Rw by a factor of 5 is still useful.

Figure 4 Red curve plots uncompensated Rw (~150 Ω), note the 20 dB loss from both ends of the span. Black curve plots the case where Rw is compensated with negative resistance (R4 = Rw = 150). 

Figure 5 Gain curve using the mechanical pot is identical to Dpot with negative resistance Rw compensation.

Footnote: Subsequent to publishing the mechanical pot version of this idea, I learned that Mr T. Frank Ritter had anticipated it by more than 50 years in his “Controlling op amp gain with one potentiometer,” published in “Electronics Designer’s Casebook”, 1972, McGraw Hill. 

So, I hereby offer a belated but enthusiastic tip of my hat to Mr. Ritter. I’ve always admired pioneers!

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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