Millman’s Theorem | Limitations & Applications

Millman’s Theorem

Case-1

The theorem states that if several ideal voltage sources V₁, V₂, V₃,……., V_n in series with resistances R₁, R₂, R₃,…….., R_n, are connected in parallel then the circuit may be replaced by a single voltage source V_out in series with the resistance R_eq. Let us consider a circuit having three sources i.e. n=3.

Case-2

The theorem states that if several ideal current sources I₁, I₂, I₃,……., I_n are in parallel with resistances R₁, R₂, R₃,…….., R_n, are connected in series then the circuit may be replaced by a single ideal current source I in parallel with the resistance R_eq such that

where 

R_eq = R₁+R₂+R₃+………………………+R_n

Limitations of Millman’s Theorem

1. Not applicable to the circuits consisting of impedances between the independent source.
2. Not applicable to the circuits consisting of dependent source between the independent source.
3. Not useful to the circuits consisting of less than two independent sources.

Applications & Advantages of Millman’s Theorem

1. This Theorem is very convenient for determining the voltage across a set of parallel branches, where there are enough voltage sources present to prevent solution via regular series-parallel reduction method.

2. It is easy to apply as it doesn’t require the use of simultaneous equations.

3. The Millman theorem is mostly applied for circuits with several operational amplifiers representing complex circuit topology.