Created by Created August 24, 2012 Last modified August 24, 2012 Tags

### Summary

A way to make a pair of inductors with an adjustable coupling factor.

To run the simulation:

Simulate > Time Domain > Run Time-Domain Simulation

or

F5

### Description

A way to make a pair of inductors with an adjustable coupling factor.

This simulation compares a behavioural transformer to an inductive transformer. In this example both transformers have a:

1:3 turns ratio. 100mH primary inductance. coupling factor of 0.95.

Turns ratio: TR=3

Coupling factor: k=0.95

Primary inductance: Lpri=100uH

Primary mutual inductance: Lmpri1 = Lpri*k

Primary leakage inductance: Leakpri = Lpri*(1-k)

Secondary leakage inductance: Leaksec = Lpri(1-k)TR^2

If the turns ratio is 1:TR then the gains of CCCS1 and VCVS1 are TR. Note that the inductive transformer ratio (N) is equal to 1/TR. Take care not to be confused by this! For more information on the CL transformer symbol see:

https://www.circuitlab.com/circuit/vehv3p/understanding-the-cl-transformer-symbol-01/

https://www.circuitlab.com/circuit/zjq2qt/understanding-the-cl-transformer-symbol-02/

https://www.circuitlab.com/circuit/857879/understanding-the-cl-transformer-symbol-03/

For each component, Right click > Edit parameters to see the how the component value, coupling factor and turns ratio are used in the associated expressions.

It may help improve convergence to include some resistance in the leakage inductances to represent the primary and secondary winding resistances. These can be scaled with the primary inductance and turns ratio as required.

The simulation is run for long enough for the startup transient to settle.

To run the simulation:

Simulate > Time Domain > Run Time-Domain Simulation

or

F5