Mutual inductance and transformers

m — mutual inductance

m names two inductors, not two nodes:

m1,l1,l2,0.01

Those are the names of two l elements already in the circuit, and the last field is M in henries. It may be a symbol, and it may carry an SI prefix.

An m has no answers of its own. It is a statement about two other elements; its effect turns up in their currents.

The dots are the node order

Symbulator cannot draw a dot, so the first node you name in each coupled inductor is its dotted end. That is the whole convention, and it is the one most likely to hand you a correct-looking wrong answer.

e,1,0,10
l1,1,0,0.03
l2,2,0,0.03
m1,l1,l2,0.01
r2,2,0,30

At ω = 1000 the current in r2 comes back as

Write the second coil as l2,0,2 instead — the same coil, the other way round — and the answer is exactly its negative, -0.0621 + 0.0552j. Same magnitude, opposite sign, no error message. Nothing will warn you.

So: read the schematic, decide which end of each coil carries the dot, and name that node first in both coupled elements.

t — the ideal transformer

t1,n1,n2,turns1,turns2

The two-node form names the top terminal of each side and grounds the other two:

e,1,0,120
t1,1,2,10,1
rl,2,0,5

Ten to one, so 12 V across the load and

An ideal transformer has no leakage, no magnetising current and no losses. For a real one, model it as coupled inductors with m instead — that is the same choice you make on paper.

Four terminals

When neither side sits on ground, name all four with bracketed pairs:

t1,[tl,bl],[tr,br],[10,1]

[tl,bl] is the left port, top terminal first; [tr,br] the right. The turns must then be bracketed too. The two-node form is exactly this with both bottoms on 0.

A transformer reports a current at each live terminal rather than one current, since the two sides carry different ones. The names are the element's name followed by the node's: for t1 with ports at nodes 1 and 2, they are it11 and it12.

The same bracketed-pair form works on two-port blocks; see Two-ports.