Superposition: solving one source at a time
A linear circuit with several sources can be solved with one source left in at a time, and the results added. A tool for understanding sensor circuits with an offset.
In a linear circuit, the effect of each source can be calculated separately and added.
Method
- Keep one source and short the other voltage sources, open the other current sources
- Calculate the voltage or current at the point of interest
- Repeat for every source and add the results
Example: a bidirectional current-sensor input
If a current sensor's output swings ±1 V but the ADC only reads 0 to 3.3 V, two resistors mix the signal with a 1.65 V reference.
- With only the signal: output = signal × 1/2
- With only the reference: output = 1.65 V × 1/2 … work out each and add, and you get "half the signal + an offset".
Split up like this, you can see at once how the gain and the offset each change when the resistor ratio changes.
Limits
Superposition holds only for linear elements (resistors, capacitors, inductors, op-amps in their linear region). It cannot be used once a diode or a saturated transistor is involved. Also, power goes as the square of the current, so it must not be added by superposition. Add currents or voltages first and then calculate power.