Part 5
Sources, conductances and shorthands
Current sources, dependent sources of all four kinds, conductance as a value, and the parallel-resistor shorthand.
Last updated 2026-09-11
Current sources
j takes the same four fields as e, and its current flows from the first node to the second, inside the element. A source written j,0,1 therefore pushes current into node 1.
j,0,1,3'm
r1,1,0,1/g
r2,1,0,2'kTwo things are happening in three lines. The source drives 3 mA into node 1; and r1's value is 1/g, so the answer comes back in terms of a conductance. There is no conductance element — a conductance is a resistance written as its reciprocal, and the algebra takes care of itself.
Dependent sources
There is no letter for them. An e or a j whose value names an answer is dependent, and that covers all four textbook types:
| Value looks like | |
|---|---|
| VCVS | e2,3,0,5*v2 |
| VCCS | j2,3,0,g*v2 |
| CCVS | e2,3,0,r*ir1 |
| CCCS | j2,3,0,beta*irb |
The controlling quantity is just an answer name, so it may be any answer in the circuit, and it may appear inside a larger expression.
The parallel shorthand
In a resistor's value only, a bracketed list is that group in parallel:
e,1,0,9
rp,1,0,[1'k,2'k,2'k]1 kΩ ‖ 2 kΩ ‖ 2 kΩ is 500 Ω, so 18 mA. The entries may be symbols, and the list may be any length.
It saves describing three elements and three nodes when the group is not the thing you are studying. When it is the thing you are studying, describe them separately so each reports its own current.