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Appelication of superposition theorem

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What are the practical applications of superposition theorem, Thevenin's theorem, Norton's theorem, and maximum power transfer theorem?

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Roy Vardhan, Bsc from The College and University Experience (2019)

Answered Jun 11

Hi.

Superposition theorem:Superposition theorem:

The superposition theorem must be used when solving steady state models of circuits. That is, when you have a DC and an AC source together, and the circuit is in the steady state, you must use superposition. Apart from this, the superposition theorem is needed in order to make the other circuit theorems true.

Thevenin and norton theoremThevenin and norton theorem

The above state that any linear circuit across its two points can be reduced to two, equivalent (at their terminals) sources. In the thevenin form: The voltage source VSVS in series with a resistance RTHRTH and the norton form a current source ISIS in parallel with a resistance RNRN

There is an equivalence between the norton and thevenin theorem, in that its just a simple conversion of a practical voltage to current source.

VThevenin=INorton⋅RThevenin/nortonVThevenin=INorton⋅RThevenin/norton

The internal resistance, is the same for both (hopefully that is clear).

The uses of thevenin and nortons theorems are:

Reducing a circuit with larger parts to one with smaller parts: Since the thevenin norton theorem allows for terminal equivalency, a larger circuit with more resistors and other components, can be reduced to a simple thevenin/norton equivalent.Simplifying analysis at certain terminals of interest. Suppose a relation such as a transfer function is needed, for some frequency response analysis, the circuit can be simplified to a Thevenin or Norton circuit with an internal impedence and connected the load. It can greatly simplify the analysis as the transfer function can now be easily found. In one example you can do thevenin trasnform of a capacitor in parallel with some resistors and in series with another, to find the cuttoff frequency and reduce it down to one simple circuit!Transient analysis: You would use a thevenin or norton transfer around your inductors and capacitors, when the transient response is sought.

Maximum power transfer theorem: DC and sinusoidal steady stateMaximum power transfer theorem: DC and sinusoidal steady state

The theorem for DC (resistances only) states that the output power at the load is the maximum when the load resistance is equal to a source resistance. So if you want to maximise the power at your output terminals, you would use this theorem and a thevenin or norton equivalent, and then find the maximum power transfer resistance.

Sinusoidal steady state: Power factor correction and maximum powerSinusoidal steady state: Power factor correction and maximum power

Reactive elements: L and C, have something known as reactive power. Due to the phase differences between current and voltage in L,C elements and due to the passive sign convention, for L,C elements in sinusoidal steady state, they act like sinks (absorbing energy from the network) and sources (returning energy to the network).