Thevenin and Norton equivalent circuits
Reduce a complex circuit to one source and one resistor. It shows how well a sensor or divider can drive the next stage.
Seen from two terminals, any linear circuit can be replaced by one voltage source with one series resistor (Thevenin) or one current source with one parallel resistor (Norton).
How to find them
- Vth: the voltage with the terminals left open
- Rth: the resistance seen from the terminals after shorting voltage sources and opening current sources
Example: a voltage divider
A divider with 12 V, R1 = 30 kΩ and R2 = 10 kΩ has
- Vth = 3.0 V
- Rth = 30k ∥ 10k = 7.5 kΩ
So this divider is the same as "a 3 V source with a 7.5 kΩ resistor attached". Connect a circuit with a 10 kΩ input resistance and the output is not 3.0 V; it falls to 3.0 × 10/(7.5+10) = 1.7 V.
Output impedance and input impedance
This idea is the basis of impedance matching.
- The output resistance of the side sending a signal should be small
- The input resistance of the side receiving it should be large
A difference of 10 times or more usually makes the effect small. If the difference is not enough, put an op-amp buffer (voltage follower) in between. It is the same reason an MCU ADC datasheet states a "maximum source impedance".