# Why are a transformer's high and low impedance reported directly?

For context I've looked at DI boxes for audio applications. Passively operated ones use a transformer to step a source voltage down as well as provide an impedance bridge for a potentially high-impedance source to a low-impedance input for maximum voltage transfer efficiency - desirable in audio applications. A bridging impedance is Z_load >> Z_source, usually a ratio of 10 or so.

The DI circuits are basically equivalent to only a transformer (see the "block diagram" section here and below). However, products in this space often report input and output impedances. One reports 140 kOhm in and 150 Ohm out for a 1 kHz signal, with a turns ratio of 11.5 (see the transformer specs here and below).

To my knowledge, transformers only have an impedance ratio which is the square of the turns ratio. So in a voltage divider, a transformer would only shift the apparent impedance of the load, unlike say when using an active buffer amplifier that has set input and output impedances. But then the ratio of the reported impedances of the transformer (140k / 150 = 930), does not match the square of the turns ratio either (130).

Here is a simple schematic of the system:

simulate this circuit – Schematic created using CircuitLab

So above, the load impedance of 1 kOhm would ideally present as 100 kOhm to the source, providing a bridging impedance.

Is there something else at play or have I misunderstood the issue? Is it only a matter of marketing and the transformer not being ideal? Thank you.

• If your linked images/documents are relevant to the question you should embed them and cite their source. Commented Jan 25 at 8:22
• @Andyaka Improved now! Let me know if you still think it needs something. Commented Jan 25 at 8:36

Is there something else at play or have I misunderstood the issue?

I don't see any problem with the data sheet for the transformer: -

12 squared is 144 and, for an ideal transformer with a 12:1 step down ratio and a 1 kΩ load, the input impedance would be 144 kΩ. I have no idea where the 150 Ω load comes from that you mention: -

One reports 140 kOhm in and 150 Ohm out for a 1 kHz signal

The 150 Ω actually comes from an analysis of test circuit 1 using the 6.8 kΩ drive resistor and the series 4.6 kΩ primary resistance. When converted to the secondary (by dividing by 144), the impedance is 79 Ω. Then, add this to the secondary resistance and you get 142 Ω. Consider also that the primary and secondary have a little bit of leakage inductance and you can readily see that the output impedance of test circuit 1 is nominally 150 Ω.

Relevant info: -

• @Felix if you load test circuit 1 with 150 ohms, I expect the signal level will drop by 50%. That's what they mean. Commented Jan 25 at 9:12
• @Felix see the addition to my answer. If we are done here, please take note of this: What should I do when someone answers my question. If you are still confused about something then leave a comment to request further clarification. Commented Jan 25 at 9:27
• Thank you for the excellent explanations! I think I've got it now. (I also deleted the previous comments, because they don't add anything anymore) Commented Jan 25 at 9:39

"To my knowledge, transformers only have an impedance ratio which is the square of the turns ratio." Only in textbooks. Real transformers are complicated beasts. Magnetizing and leakage inductance, capacitance, resistance, eddy currents, hysteresis, ...

Real transformers are usually engineered to behave approximately like textbook transformers in their intended application. Part of this is designing for a specific impedance. Operation at a different impedance will impact other characteristics like frequency response and power handling capability.

• Oh, that's definitely good to note! Although it is slightly hand-wavey. Of course, they are never ideal, but should I expect a transformer to perform meaningfully worse if it was tested at 1kOhm load but I connected a 10kOhm one instead? A hundred? If so, what is it about the design that's tailored to that load? Commented Jan 25 at 21:45
• @Felix What's tailored? Turns count, wire gauge, core geometry, core material, insulation. If you change the impedance that changes voltage and current, so you should derate the power to keep those below what they'd be for rated power at design impedance. At high impedance, magnetizing inductance and capacitance shunt current at low and high frequencies, so bandwidth suffers. At low impedance, leakage inductance gets in the way at high frequencies and resistance wastes energy. It's hard to be quantitative with so many variables in play. Commented Jan 25 at 22:22
• Fair enough :P still, thanks for explaining a bit further! I'll just have to test how the response changes if I want to find out. Commented Jan 25 at 22:32

The numbers do add up. The test and measurement are given in the assumptions of the testing.

If the transformer has 11.52 turns ratio, it approximately converts impedance with ratio of 133. Since the test is done at 1kohm load on secondary, the primary should look like 133 kohms load. And it is listed as 141 kohms, in range of 130 to 150 kohms, so pretty accurately matches the assumption.

• Thank you! That does make sense, but it leaves the question of the reported output impedance (see the discussion under the other answer) and whether it's useful to report absolute values or not. It doesn't seem like it. Commented Jan 25 at 9:12
• @Felix The transformer is not ideal. If you have a device with zero output impedance driving the primary, the secondary output cannot have zero output impedance, it will be typically 63 ohms. Commented Jan 25 at 9:22
• Oh okay! So to summarise: the input/output impedance values are not related. The input impedance is reported with a specific load impedance, and given another load, the input impedance would change according to the ratio. The output impedance is still relevant for very low impedance sources, which would present as bigger to the load because of the inherent impedance in the transformer. Yeah? Commented Jan 25 at 9:29
• @Felix I would approach this not from being relevant to the primary input, but for what kind of loads you can expect the secondary output to work. If you put a 8 ohm speaker or 63 ohms headphones as load to the secondary with output impedance of 63 ohms, you must understand why you don't get the assumed voltage based on turns ratio. It's no different than AC mains transformers. If you have a transformer rated at 1A and rated voltage, you will not get the rated voltage but less if you put a 2A load there, and you definitely would not even try a 10A load on a 1A transformer. Commented Jan 25 at 9:40