Mutual Inductor (Transformer;Transient analysis)

A mutual inductance in SPICE is defined by specifying the coupling coefficient K between the two inductors. The syntax is as follows:


 
 

Kname Inductor1 Inductor2 value_of_K    

The value of K must be larger than 0 but smaller than 1. Spice does not support perfect coupling (k=1). The above statement must always be together with the statements for the two inductors. An example is given in the figure below. The coupling coefficient K can be calculated as K=M/sqrt(L1xL2)=0.81.
 
  The SPICE statements to define the above coupled coils are as follows.
 

 

 




L1 3 5 10M

L2 4 7 3M

K L1 L2 0.81

The DOTS are always associated with the first node of the inductances (i.e. node no. 3 of L1 and no. 4 of L2). Also SPICE will assign the positive node voltage to the first node of the inductance (i.e. the DOT) and use the passive sign convention for the current direction as indicated in the figure above. For an example circuit see under the section



The syntax for a mutual inductance is as follows:

Kname Inductor1 Inductor2 value_of_K

In which K is the value of the coupling coefficient that determine the mutal inductance: M=K.sqrt(L1xL2). An example of a complete SPICE file for the circuit given below follows.

(K=M/sqrt(L1xL2)=0.693)

Vin 1 0 sin(0 5 159.15 0 0)

Rs 1 3 100

Rl 4 0 500

L1 3 0 10M

L2 4 0 2M

K L1 L2 0.693

.TRAN 0.1M 10M

.PRINT TRAN V(3) V(4)

.PLOT TRAN V(3) V(4)

.END

Remarks:

1. SPICE always needs a reference node numbered 0. One can never leave any node floating. For that reason we have connected the two coils together to node 0 (or put a large resistor between it). As there is no current flowing through this section, the circuit will not change by connecting these nodes.
2. SPICE does not allow to connect a voltage source in parallel with an inductor, as it thinks that the voltage source is short circuited. You can place a small resistor (ex. 0.001 Ohm) in series with the voltage source to overcome this problem.