Sources, conductances and shorthands

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.

A 3 mA source feeding two resistors in parallel, one of them given not as a resistance but as a conductance \(g\). We write the source with its arrow pointing into node 1, j,0,1, name the resistors r1 and r2, and give the first the value 1/g, since there is no conductance element and a conductance is a resistance written as its reciprocal:

j,0,1,3'm
r1,1,0,1/g
r2,1,0,2'k

Run in DC, the voltage across the pair comes back in terms of that conductance:

The algebra took care of the reciprocal 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:

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. A 9 V source across three resistors of 1 kΩ, 2 kΩ and 2 kΩ side by side, the three written as one element we call rp:

e,1,0,9
rp,1,0,[1'k,2'k,2'k]

Run in DC, the current through the group is

which is 18 mA: 1 kΩ ‖ 2 kΩ ‖ 2 kΩ is 500 Ω. 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.