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# Modulated Transformers and Gyrators

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# Modulated Transformers and Gyrators

Next to transformers and gyrators wit a fixed transformation ratio and gyration ratio, in bond graphs also modulated transformers (MTF) and modulated gyrators (MGY) are supported. In these models the transformation ratio of gyration ratio are equal to a (fluctuating) value provided by an input signal. In the table below the effort and flow equations are shown.

 MTF-element bond graph element equation effort-in causality f1 = (1/u) f2 e2 = (1/u) e1 effort-out causality f2 = u f2 e1 = u e2 MGY-element bond graph element equation effort-in causality f1 = (1/u) e2 f2 = (1/u) e1 effort-in causality e1 = u f2 e2 = u f1

The directions of the flow and effort are partly fixed for a modulated transformer. Like the 1 junction and the 0 junction, the causality is constraint. For a transformer, an effort-in causality on the incoming bond results in an effort-out causality on the outgoing bond and vice-versa. For a gyrator, an effort-in causality on the incoming bond results in an effort-in causality on the outgoing bond and vice-versa.