The Millman equivalent circuit
Many circuits have more than one voltage source.
For example:
- Banks of batteries for emergency lighting
- Parallel power generators,
and so on.
Each of these sources of voltage has a different internal resistance.
All these sources of voltage are connected to the same load. Look at the first picture (The original circuit diagram)
The Millman's Theorem shows us an easy way to obtain an equivalent circuit (the second chart).
In order to use the Millman's Theorem, we have to reconstruct the circuit (if posible) into a circuit of parallel branches consisting of a voltage source and a series resistance (impedance) or a current source and a parallel resistance (impedance). We'll use the first option.
1 - We find RM. RM is the equivalent parallel resistor value of all resistors that are in series with the voltage sources.
1/RM = 1/REq = 1/R 1 + 1/R2
For Example: If we have a circuit with two voltage sources, each one with a resistor in series (R1 and R2). We can find the parallel resistor of R1 and R2.
If the circuit has 3 o more voltage source, the process would be the same.
2 - VM is obtained using the following formula:
VM = (V1/V1 + R2/R2) / (1/R1 + 1/R2)
The new circuit consists of a voltage source in series with a resistor (The Millman equivalent circuit). This circuit will be connected in series with the load resistor (RL)
The Voltage source has the value of the VM and the resistor has the value of the RM. The last picture shows the Millman equivalent Circuit connected to RL
