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Variable K Transformer Model
Ever wanted to vary the K value in a transformer but couldn't? Well you can if you use the equivalent circuit below. This is an equivalent circuit for the transformer primitive.
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The general transformer equations are as follows:
Basic transformer equations:
(Z1 + S*LP)*I1 + S*M*I2 = V1
S*M*I1 + (Z2 + S*LS)*I2 = 0
Definition of Terms
I1 is the current flowing the primary
I2 is the current flowing in the secondary
V1 is the primary input voltage
Z1 is any impedance in series with the primary
Z2 is any impedance in series with the secondary
LP is the primary inductance
LS is the secondary inductance
M is the mutual inductance between LP and LS
These transformer equations are implemented in the circuit above. The utility of this equivalent circuit is that its part values can be expressions and thus varied during a run, whereas in current Micro-Cap implementations (through Micro-Cap 7.0), the transformer parameters (L1, L2, and K) cannot be time-varying expressions.
Here is the transient analysis of the circuit above.
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The transient analysis above and the AC analysis below show identical plots for both the primitive and the equivalent circuit model outputs, demonstrating the electrical equivalence of the transformer equivalent circuit.
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With this equivalent circuit in mind we'll now modify the circuit by changing the K value from a constant to a variable. This is done by simply changing its .define statement as follows:
Old: .DEFINE K .98
New: .DEFINE K 1.0*(10U-T)/10U
The new expression for K causes it to vary linearly over time.
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Here is what the transient analysis for 5us looks like.
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Having gone through the exercise of how to do a transformer variable K expression, we thought it would be a good idea to simply add it to MC7. So we did. Micro-Cap 7 Version 7.02 or later has this capability built in. Prior versions would only allow a constant K value. Now, you can simply write an expression for the transformer K value. A typical transformer with an expression looks like this:
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If you have Micro-Cap 7 Version 7.0 or 7.01 you can update by downloading the MC7.ZIP file from our web site at www.spectrum-soft.com
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