SynthMaker How a voltage divider works
A voltage divider is two resistors in a row, and the output, taken from between them, is the input times R2 / (R1 + R2). Two equal 10 kΩ resistors give exactly half, 6 dB quieter; a volume knob is the same idea with one resistor you can turn.
circuit Divider setting level: 10k, from 100 to 100k R1 in out 10k R2 out gnd level # Rload out gnd 10kendPress Play to see the wave after the circuit, at out.
What you're hearing
Voltage is the push. It's the difference in electrical pressure between two points, measured in volts (V). Like water pressure, it only means something between two places: here, between a point and ground, which we call 0 V. A sound in a circuit is a voltage that swings up and down hundreds or thousands of times a second.
Current is the flow. It's how much charge moves through a part each second, measured in amps (A). Small circuits use thousandths (mA) or millionths (µA). Current only flows round a complete loop: out from the input, through the parts, back through ground.
Resistance is how hard a part makes it, and Ohm's law ties the three together. Resistance is measured in ohms (Ω): 10 kΩ is 10,000 Ω. Ohm's law says the voltage across a resistor is the current through it times its resistance: V = I × R. Push 1 V across 20 kΩ, and 1 V ÷ 20 kΩ = 50 µA flows.
A divider shares the voltage out. Here R1 (10 kΩ) and R2 (10 kΩ as set) sit in a row from the input to ground, 20 kΩ in all. With 1 V at the input, 50 µA flows through both, so each one has 50 µA × 10 kΩ = 0.5 V across it. The output is the point between them, so it gets R2's share: Vout = Vin × R2 / (R1 + R2) = 1 V × 10 kΩ / 20 kΩ = 0.5 V. Half the voltage is 6 dB down: 20 log (0.5) = −6.0 dB. That's the same sum that sets many pedals' bias to 4.5 V: two equal resistors across a 9 V battery.
Turn R2 and it's a volume knob. The knob runs R2 from 100 Ω to 100 kΩ. The bigger R2 is, the bigger its share:
| R2 (the knob) | out, no load | out, 10 kΩ load | out, 1 MΩ load |
|---|---|---|---|
| 100 Ω | 0.0099 V (−40.1 dB) | 0.0098 V (−40.2 dB) | 0.0099 V (−40.1 dB) |
| 1 kΩ | 0.091 V (−20.8 dB) | 0.083 V (−21.6 dB) | 0.091 V (−20.8 dB) |
| 10 kΩ | 0.50 V (−6.0 dB) | 0.33 V (−9.5 dB) | 0.50 V (−6.1 dB) |
| 100 kΩ | 0.91 V (−0.8 dB) | 0.48 V (−6.4 dB) | 0.90 V (−0.9 dB) |
The output can never be more than the input, because R2's share can never be more than all of it. A divider only turns things down.
Whatever you connect is part of the divider. Anything plugged into the output is a resistor from the output to ground, side by side with R2. Two resistors side by side act as one smaller one: 10 kΩ and 10 kΩ make 5 kΩ. So with a 10 kΩ load and R2 at 10 kΩ, the bottom is really 5 kΩ, and the output falls from 0.50 V to 5 kΩ / 15 kΩ × 1 V = 0.33 V. With R2 at 100 kΩ, it falls from 0.91 V to 0.48 V: the top of the knob stops working. That's loading. A 1 MΩ load, a hundred times bigger than the divider's resistors, changes almost nothing. The rule: whatever follows a divider should be much bigger than it.
Try this
- Turn level from 10 kΩ up to 100 kΩ, then down to 100 Ω, and watch the Scope. The wave keeps its shape and only changes height. You hear it get quieter, never louder than the input.
- Press "10k load". The sound drops at once, and the top half of the knob does little. Then press "1M load": it's back, almost exactly as before.
- Open it in SynthMaker to change the parts. Make R1 and R2 different sizes and work out the output first, then check it on the Scope.
The parts list
circuit Divider setting level: 10k, from 100 to 100k R1 in out 10k R2 out gnd level # Rload out gnd 10kendThe last line is the load. Remove the # to put it in.
How we checked it
Checked against ngspice, a standard circuit simulator: every value in the table, with and without a load, matches ngspice's to the digits shown (resistors alone are exact).
Build it step by step
- The manual: Your first circuit: how a parts list is written, one part per line.
- The lesson: A distortion pedal from six parts (opens in a new tab). Its first part, a 2.2 kΩ resistor into two diodes, is a divider whose bottom half changes with the voltage.
- The video: This distortion pedal is six lines of text: a real circuit, simulated. It loads only when tapped.
- Further on: An amp from one OTA, pushed until it growls (opens in a new tab) uses a divider, 100 kΩ into 220 Ω, to bring a sound down to a few thousandths of a volt.
Further reading
- The formula, loaded dividers and where they're used: Wikipedia: Voltage divider.
- V = I × R and where it comes from: Wikipedia: Ohm's law.
- Why half the voltage is −6 dB: Wikipedia: Decibel.
- Water as a picture of voltage and current, and where the picture fails: Wikipedia: Hydraulic analogy.