"Determination of the coupling factor"

Determination of the coupling factor

Simple network model of the transfer measurement with the HP3577A

Determination of the coupling factor using this model and the measurement results

We will now determine the coupling factor of the two coupled inductors. To this end, we determine the Laplace transform of the voltage transfer from the source "V1" to the voltage at node "out". We use numeric analysis and substitute s=2πjfm, where fm is the measurement frequency. Since the coupling factor has no numeric value it will remain symbolic in this gain expression. We then solve the coupling factor by equating this expresion with the measured value..

The transfer function is a function of the coupling factor:

(1)At=0.0006918kcs3.877105s+1

The squared magnitude of this transfer at the measurement frequency of this circuit is obtained as:

(2)Atsq=17.84kc2

The measured value Asq of the squared voltage transfer at this frequency amounts:

(3)Asq=4.266106

Solving Asq=Atsq yields:

(4)kc=0.000489

Modeled magnitude characteristic

Substitution of the value of kc in At yields:

(5)At=3.383107s3.877105s+1

The figure below shows the magnitude plot. It should correspond with the one measured with the network analyser. If not, the values of the model parameters are incorrect, or the model is too simple and a more elaborated model should be used.

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Last project update: 2024-03-04 22:12:16