Modulated Transformers and Gyrators

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Modulated Transformers and Gyrators

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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

MTFElementEffortIn

f1 = (1/u) f2

e2 = (1/u) e1

effort-out causality

MTFElementEffortOut

f2 = u f2

e1 = u e2

MGY-element

bond graph element

equation

effort-in causality

MGYElementEffortIn

f1 = (1/u) e2

f2 = (1/u) e1

effort-in causality

MGYElementEffortOut

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.