Understanding AC/DC, Series/Parallel, Resistance and Impedance
Page 1, 2, 3,

LYNN EAR

Figure 1b: Parallel circuit configuration and formula plus Ohm’s Law
(click image for larger view).

Like the water analogy, a variable resistor can be viewed as a valve, although vacuum tubes and transistors are much more efficient when “heavy lifting” is required. In a recording console, for example, the effect and aux sends are examples of variable resistors in the form of rotary potentiometers (pots).

Most pots are three-terminal devices. Typical connections to a linear fader are detailed in Fig. 2. The input is at the top, output via the middle terminal (called the “wiper”) and the bottom terminal is the signal common, typically connected to ground. The wiper divides the resistor into two parts: The ratio of the bottom resistor to the total resistance determines the amount of input signal that is output. The very first example in the table on p.116 is the easiest to visualize.

The table defines 16-bits of dynamic range in 6dB increments as represented by the change in voltage and the equivalent resistance for a 10-kilohm fader.

A mechanically linear fader may also be electronically linear when a DC control voltage is used for VCA-type automation. The table on p. 116 shows how an audio taper pot differs. Starting with 10 volts at the top of a 10-kilohm fader, each 6dB drop represents a 50% voltage reduction from the previous value. While the first drop from 10 volts to 5 volts is half the electrical value, you know that the wiper knob will not be halfway down.

Test No. 3: Imagine a fader that is both mechanically and electrically linear. Put in 10 volts at the top, set it halfway and get 5 volts out. The fader comes in three resistance options—1,200 ohms, 4,800 ohms and 10 kilohms. The equivalent circuit is a series resistor pair consisting of…(Answer No. 3: 600, 2,400 and 5 kilohms, respectively.)

Test No. 4: The resistive element in an audio taper pot is “logarithmic,” matching the ear’s nonlinear sensitivity to level changes. It’s hard to avoid the math, but I encourage those with access to a scientific calculator to engage the dB formula at the lower right corner of Fig. 2. Divide any two voltages from the table, take the log and multiply by 20. Compare your answers with those in the table. It feels good, doesn’t it? I used to do this on a slide rule!

MIX MASTER

Figure 2: A photo-schematic of an open linear fader. The formula for calculating dB from two voltages is shown in the lower right corner
(click image for larger view).

In a mixer, an IC op amp may have to feed several effect sends as well as the primary fader. If four pots will be connected to an op amp, then it is important, for the sake of efficiency, to choose an optimal resistance value that, when combined in parallel, isn’t so low as to overload the op amp or so high as to be vulnerable to stray capacitance (next month’s topic).

For ease of head calculation, I chose four 2,400-ohm resistors. Combine the first two pairs into a single pair of 1,200-ohm resistors and then combine those into one 600-ohm load. This, too, is a magic number, vintage gear having input and output impedances of 600 ohms and being referenced to 0 dBm. The Power formula (in Fig. 1a) states that P equals E-squared divided by R. In this case, E is 0.775 volts.

Test No. 5: Apply .775 volts to the load and determine the power. (Answer No. 5: 1 milliwatt.)

Note: One mW is the reference for 0 dBm, 4 dB below “nominal” level for professional equipment.

Many op amps can comfortably drive a 600-ohm load. But within a mixer module, only the output amps need to be prepared to work this hard and only when driving vintage-style equipment. Typical pot values are between 5k and 10 kilohms. Four 10-kilohm pots represent a 2,500-ohm load to the op amp.

Test No. 6: Can you calculate the power if 0.775 volts appear across a 2,500-ohm load? (Answer No. 6: 0.24 milliwatts.)

Reprinted with permission from

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