Volume Control and Attenuation Figure 1 shows how the ratio between two voltages, typically an input voltage and output voltage, are expressed in decibels.

Note that the levels are always expressed as gain. Attenuation is the same a negative gain: for example, -3db of gain is the same as 3dB of attenuation. Figure 2. shows a simple two-resistor network and how the input voltage and output voltage are related to the resistor values.

For example, if R2 is 47K and you want 3dB of attenuation:

Vout
-------- = 0.708 for -3db Gain
Vin

47K
------------- = 0.708
R1 + 47K

47K
-------------- = R1 + 47K
0.708

66384 = R1 + 47K

19384 =  R1

Use a 20K resistor for R1 as the closest standard value. Figure 3. shows a single resistor providing attenuation.

Here the series resistor is R1 and the amplifier input impedance is R2. For example, a 20K series resistor will provide 3dB of attenuation for an amplifier that has an input impedance of 47K. Figure 4 adds a shunt resistor to the attenuator.

This is starting to get a little more complex, but as we will see later, R5 may not exist and thus will drop out of the equation. In any event, you may choose R4 to be any value you want and then calculate a value for R3. The value of R3 plus the value of R4 (in parallel with R5, if it exists) will determine the total input impedance. Therefore you should choose R3 to provide an appropriate total input impedance. A value of 10K or greater should be fine. Figure 5 shows a simple series volume control.

If the volume control is set at maximum, then R3 = 0, and we have Vout = Vin.  If the volume control potentiometer is large compared to the amplifier input impedance, the smaller amplifier input impedance will dominate the parallel combination and most of the effect of the volume control will be in the first few degrees of rotation. If the volume control potentiometer is small compared to the amplifier input impedance, the smaller volume control impedance will dominate the parallel combination and there will be better control across the the entire rotation. However, there is a trade-off - the total input impedance of the combined volume control potentiometer and amplifier will vary between a maximum equal to the value of the potentiometer, and a minimum of the value of the volume control in parallel with the input impedance of the amplifier. For example, for a 50K volume control and a 47K amplifier input impedance, the combined input impedance will vary between 50K and 24.2K. So it is best to keep the volume control large enough to get an appropriate total input impedance, and the amplifier input impedance much larger than potentiometer for good control. If the amplifier is very large, say the grid of a tube  (R5 does not exist), then the combined input is that of the volume control potentiometer and that input impedance is constant, irrespective of the setting of the potentiometer. Figure 6 shows a simple series volume control for a differential amplifier.

This is the same as two of the volume control potentiometers of figure 5, one for the positive signal and one for the negative signal. The total input impedance is twice that of figure 5, and all of the conditions for the single-ended amplifier volume control hold for the differential amplifier volume control. Figure 7 shows a shunt volume control.

If the volume control is set at maximum, then the attenuation is the same as in figure 4. As with the simple series volume control shown in figure 5, the volume control potentiometer should be small compared to the amplifier input impedance. However, now the volume control potentiometer alone does not determine the total input impedance - the series resistor also adds, with a maximum of the series resistor plus the volume control potentiometer, and a minimum of the series resistor plus the parallel combination of the potentiometer and the amplifier input impedance. So for example, with a 50K series resistor, a 50K potentiometer and a 47K amplifier input impedance, the total input impedance will vary between 100K and 74.2K. This allows a large total input impedance with a smaller volume control potentiometer. The trade-off now is the amount of additional attenuation due to the series resistor. One advantage of the shunt volume control over the simple series volume control is that the potentiometer is minimally in the circuit and the series resistor can be a high-quality resistor, thereby improving the quality of the sound. Figure 8 shows a shunt volume control for a differential amplifier.

This is the same as two of the shunt volume controls of figure 7, one for the positive signal and one for the negative signal. The total input impedance is twice that of figure 7, and all of the conditions for the single-ended amplifier volume control hold for the differential amplifier volume control. Figure 9 shows a bridged shunt volume control for a differential amplifier.

This is similar to the volume control shown in figure 8 except that the volume control is not referenced to ground. The total input impedance varies between a minimum of the sum of the two series resistors, to a maximum of the sum of the two series resistors plus the parallel combination of the potentiometer in parallel with the amplifier input impedance.  The advantage of this configuration over that of figure 8 is that this one requires only one potentiometer, rather than two potentiometers. Also, from my experience, this one sounds better than the one in figure 8. Figure 10 shows the amplifier input impedance.

The input impedance of a single ended amplifier is that of the input resistor, R5. The input impedance of a differential amplifier is that of the sum of the two input resistors, R5 + R8. Note that R5 and R8 may be absent, with the volume control potentiometer directly feeding the grids. In this case, R5 and R8 simply drop out of the equations for determining the attenuation.

There may be a transformer, either before the volume control or between the volume control and the amplifier. The transformer will reflect the the impedances as the square of the turns ratio. For example, if the transformer ratio is 1:2, and the impedance on the "2" side is 100K, the impedance on the "1" side will be 25K. Figure 11 shows an example of simplifying a resistor network.