Circuit Theory/Source Injection

Source injection is a trick used when parallel/series combinations don't exist in a circuit.

Source injection helps find the overall impedance of a circuit from V_s/I_s. Vs and Is are found in the phasor/complex frequency domain using node or mesh analysis.

• 
  original complicated circuit, want to look at just the red part
• 
  want to reduce middle resistors into one equivalent resistor
• 
  remove middle part from circuit, inject source of 1 volt, find source current and compute the equivalent resistance

mupad screen shot of code node analysis of the source injected circuit

Suppose have a complicated circuit, want to break it up into smaller sections, find a clump of passive devices in the middle of it, want to find their equivalent, but can not combine in series or parallel.

This type of problem has to be done with source injection (or Y Δ Transform .. but that is later).

One is really not physically injecting anything into the circuit, one is just pretending so that node analysis can be used to find the overall real (in phasor/complex frequency domain) impedance.

For the circuit above, the node analysis shows that the overall current is:

$I_{s}=0.2542735043$

This means that:

$R_{eq}={\frac {V_{s}}{I_{s}}}={\frac {1}{0.2542735043}}=3.9328ohms$