# Equivalent circuit of a simple transformer?

EDIT: My question is: How can you translate the first circuit into one that uses simple (linear) electrical elements and, as a result, can be solved using mostly Kirchhoff's laws?

I am trying to analyse how the frequency of the input voltage affects the amplitude of the output voltage in the following circuit.

simulate this circuit – Schematic created using CircuitLab

Everything we need to know is given: $$\V_{in}\$$, angular frequency $$\ω\$$, $$\a\$$, $$\R\$$ and $$\C\$$. I think this circuit is supposed to work like a band-pass filter, but I am not used to working with transformers. That is why I am trying to find the equivalent circuit of this element. Is the next circuit equivalent to the above? Likely, it is not, because transformers are supposed to change the voltage across the secondary coil, at the cost of current. If not please suggest the correct one, or explain a better way of understanding the circuit (What kind of impedances might occur, if the transformer is not ideal?).

simulate this circuit

What kind of impedances might occur, if the transformer is not ideal?

Ignoring high frequency parasitic capacitance, the transformer equivalent circuit is this: -

Picture from here.

So your interpretation is somewhat erroneous: -

• Your "L" matches my Lm (magnetization inductance)
• Your "R" matches my Rp (primary copper losses)
• Your "R1" matches my Rs (secondary copper losses)
• Your "aL" is not relevant
• My "Rc" represent the cores losses)

Given that your tuning capacitor is on the secondary, it will series resonate with "my" Ls and this is the main componentry that produces resonance. However, the primary leakage inductance (for a transformer) is just as relevant and what folk normally do is lump primary and secondary leakage inductance together and calculate resonance based on that.

My Rp and Rs will dampen the effect of resonance making it less peaky.

• Since the transformer in your circuit is ideal the rule $Vp/Vs = Is/Ip = Np/Ns$ applies, where the subscript $p$ indicates the primary coil, $s$ the secondary and $N$ is the number of turns, right? To be clear, I named $Vp$ the voltage across the left part of the ideal transformer (not "your" primary voltage) and $Vs$ the voltage across the second part. Dec 28, 2019 at 17:54
• @BramFran I seem to be having trouble reading your full comment on my ancient PC but I can fully see it on my mobile.... You mention Vp but I have no idea what you are referring to nor what you are trying to imply. I don't see the terms Vp or Vs in your question at all???? I see Vin and Vout. Dec 28, 2019 at 18:06
• Take a look at this this image. I am using the circuit of your answer. Dec 28, 2019 at 18:11
• Yeah.... but what are you trying to imply or what is your question? Also, if you are going to refer to a doctored version of the picture in my answer, please add it as an obvious edit section below your original question text and images. Dec 28, 2019 at 18:14
• Given that $Vp, Vs, Is, Ip, Np, Ns$ are the quantites shown on this image is it true that $Vp/Vs=Is/Ip=Np/Ns$? Dec 28, 2019 at 18:17

The summation of flux, in the core, implements a negative feedback system.

The source resistance is key to the feedback.