# 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.

<File:Example24a.png%7Coriginal> complicated circuit, want to look at
just the red part <File:Example24b.png%7Cwant> to reduce middle
resistors into one equivalent resistor <File:Example24c.png%7Cremove>
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:

$$R_{eq} = \frac{V_s}{I_s} = \frac{1}{0.2542735043} =  3.9328 ohms$$

