# Small signal transfer function of the transformer and weakly coupled wireless coils

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#### bhl3302

##### Full Member level 6
Small signal transfer function of the transformer and weekly coupled wireless coils

Hi All, I am curious about the small signal transfer functions of transfomer and the weekly coupled wireless coils. Would anyone teach me how to write the transfer functions?

(1) In the left side of this picture, it is a transformer with the turning ratios N1:N2. When this transformer is used in the loop of a power converter, for example, flyback, how can we write the transfer function of it?
(2) In the right side of this picture, we have a pair of weekly coupled wireless coils. If I have some series and parallel connections on both sides to some R and C components, how can I derive the transfer function Vout(s)/Vin(s) when we have such a pair of coils?

In addition, would you refer to some books/papers that I can read for more details?

Thank you!

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#### FvM

##### Super Moderator
Staff member
Re: Small signal transfer function of the transformer and weekly coupled wireless coi

Generally, there's nothing specific about small signal versus large signal transfer function as long as long as involved magnetic cores are operated below saturation. The coupled coil equivalent circuit is a basic transformer circuit with low coupling coefficient k respectively high leakage inductance.

#### bhl3302

##### Full Member level 6
Re: Small signal transfer function of the transformer and weekly coupled wireless coi

Generally, there's nothing specific about small signal versus large signal transfer function as long as long as involved magnetic cores are operated below saturation. The coupled coil equivalent circuit is a basic transformer circuit with low coupling coefficient k respectively high leakage inductance.
Hi FvM, thank you! The purpose of opening this thread specifically to address the TF questions and to look for the references. Now I have the following questions and would you help me?
(1) For the transformer, if we have N1:N2=1: x, in the small signal transfer function, does that mean we can just thread it as a voltage controlled voltage source, with the gain equal to x? I tried to look for the answer but surpringly I cannot find any place in telling the transformer's TF.
(2) Regarding the wireless coils, I did have one question that SunnySkyguy has advised me. As you can see from the following picture, he used a series inductance to connect between the primary coil and the secondary coil, in emulating the coupling. This model works well but I do not understand why it should be modeled like this.

Do you have any suggestions (papers/books) that I can read to understand this? Thank you!

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