Primary/Secondary Transformer Impedance, and Impedance Matching

Question

I need to select the proper transformer to use in a device to convert from a hi-z input to a lo-z input. As far as I understand transformers have no impedance, rather a percent impedance which is actually a voltage, expressed as a % of rated voltage, that is required to circulate rated current through the transformer.

When I shop for audio transformers they list primary and secondary impedances. Am I to assume theyre providing me two parts of a ratio that is the % impedance, and that as a parameter it doesnt have a direct effect on my use case of wanting to go from hi-z to low-z? Also it lists the impedance as "CT" which is center tapped as I understand. i also dont understand why the values are provided as center tapped primary and secondary impedances.

Here is an example transformer that calls out primary/secondary impedance. https://www.mouser.com/ProductDetail/Triad-Magnetics/TY-250P?qs=Yx4IQMNd5u7UhIpi75ZQsw%3D%3D

Thank you

Answer 1

For an ideal transformer, you're perfectly correct.

However, you've not got a catalogue of ideal transformers, you've got a catalogue of 'audio transformers', that is, transformers designed for use in an audio amplifier or distribution system.

The listed impedances are the ones the transformers have been designed for.

Designing a wideband audio transformer is quite difficult, more so than designing a single frequency transformer. To push the low frequency end down, you need high primary inductance compared to your operating impedance, which needs lots of turns and a large core. To push the high frequency end up, you need a high SRF, which needs low self capacitance, which needs the number of turns minimised and a large core. To maintain a low loss at the operating impedance you need thick wire. To have a low cost, you need thin wire and a small core.

Transformer designers first decide on a target impedance range, power and bandwidth range, then optimise a design, and place it in the catalogue.

Answer 2

Let's consider an ideal transformer with just two coils: Primary and secondary.

The key characteristics of a transformer is the ratio between the number of turns of wire creating primary and secondary coils.

The easy to understand part is that the voltage between the coils follows the respective numbers of turns:

If a primary coil has p turns and the secondary coil has s number of turns then the ratio is \$r=s/p = Vs / Vp\$ where the Vp and Vs are Primary and Secondary voltages.

The currents, however, are transformed by 1/n (to keep the power at the input the same as the power at the output). (Remember: We are discussing *ideal transformer" with no losses)

Now, let's define the primary side impedance:

\$Zp=Vp/Ip\$

you may see that the secondary impedance is:

\$Zs = (Vp*r)/(Ip/r) = Zp* r^2\$

The impedance is "transformed" by \$r^2\$ (squared) where r is the ratio between the number of primary and secondary turns.

Answer 3

Consider a cascaded arrangement of an op amp followed by a 12:1 step-down transformer followed by an 8 ohm speaker.

The impedance that the op amp "sees" will be 144*8 ohms. This is because, moving right to left from speaker to op amp across the transformer, the voltage has increased by a factor of the turns ratio but the current has decreased by the same factor (by the turns ratio). Since R = V/I it means that inserting the transformer in between the op amp and the speaker has increased the impedance that the op amp "sees" by a factor of the turns ratio squared.