Electronic Design

A Spice Model For The Ideal Transformer

The ideal transformer may be described as a two-port device that provides a constant voltage gain and a current gain inversely proportional to the same constant. Such a device is required in certain types of system or analog simulation work. For example, in acoustics modeling, electric analogies are used to simulate acoustic circuits, while ideal transformers model the transformation of air pressure and velocity with changes in tube apertures sizes.

Spice doesn’t provide a specific statement to model an ideal transformer. Instead, Spice provides a coupled-inductor model in the K statement that includes self and mutual inductances. A two-port transformer modeled in this way would have the configuration shown in Figure 1.

The problem with this transformer model is that the inductances add secondary loading to the circuit and therefore produce irrelevant effects in some simulation work. Larger inductance values may be chosen to overcome this loading effect. However, the diminishing impedance value of these inductors as the frequency is lowered implies that there’s a lower frequency bound to which this will work. As a consequence, the coupled-inductor model doesn’t simulate an ideal transformer at zero hertz (dc). At dc, any source connected to the input of the transformer will see a resistance of zero due to the inductors L1 and M. Also, the transformer’s output voltage will be 0 V.

An alternative approach models the transformer as a two-port linear network (Fig. 2). A current-controlled current source and a voltage-controlled voltage source are connected back to back to form the ideal transformer. The resulting output equations are of the correct form and the model works properly in Spice.

In the Spice listing, the Spice model for a current-controlled currentsource, the F statement, requires the use of a 0-V dc source to sense the current in the second port (see the listing). The turns ratio “a” has been set to 10 in this instance, but must be changed in both the E and F statements for other applications. A load RL, equal to 1000 O, has been added to provide a current path at the transformer’s output.

The output file of a Spice run should produce a current from the source VIN equal to 100 mA. The voltage across and the current through RL are equal to 10 V and 10 mA, respectively, at all frequencies, including 0 Hz.

For multiple-secondary transformers, a number of ideal transformers can be connected in parallel with their primaries connected either in parallel or series as required.

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