….but, Rothwell Audio Products explanations also go into further detail in the next section, which would definitely imply caution against SUT use in a current based phono stage, due to geometrically increasing impedance:
”the transformer turns ratio and impedance ratio
The turns ratio of a transformer is the ratio of the number of turns of wire on the primary winding to the number of turns of wire on the secondary winding, and the voltage on the primary is stepped up (or down) by the same ratio as the turns ratio and appears on the secondary. A transformer with a 1:10 turns ratio for example will step up a voltage at its primary by a factor of ten. However, since transformers are totally passive devices with no power supply to draw energy from, no extra power can be produced by a transformer and an increase in voltage will be accompanied by a corresponding decrease in current. This is what gives rise to the concept of the impedance ratio. The impedance ratio is the square of the turns ratio and makes an impedance on the secondary winding of a transformer appear to a source feeding the primary as that impedance transformed by the square of the turns ratio. The transformer itself doesn’t have an impedance, rather an impedance on one side of it will look like a different impedance from the other side (it works in both directions). In the case of, for example, a 1:10 step-up transformer, a 20k impedance on the secondary winding will appear to be a 200 ohm impedance on the primary winding (20,000 divided by 10 squared equals 200). A 1:2 step-up transformer with a 100k load on the secondary would appear to have an input impedance to a source driving the primary as 25k (100k divided by 2 squared equals 25k).
So, it would seem logical that a cartridge with an output voltage of, for example, 0.5mV, when used with a step-up transformer with a 1:10 turns ratio, would produce 5mV at the transformer’s output. Yes, it would if the cartridge’s source impedance (also known as its internal impedance or its coil impedance) was zero. In practice, with low impedance cartridges of about 10 ohms or less and low ratio transformers (less than about 1:20), the transformer’s output voltage is very close to the cartridge’s output voltage multiplied by the turns ratio and can be safely used as a good first order approximation for guidance. However, the cartridge’s source impedance may be low but it is never zero, and the transformed secondary load needs to be considered for a more accurate analysis. Consider as an example a transformer with a 1:10 ratio and a cartridge with a 10 ohm coil. If the load on the transformer secondary is an MM phonostage with a 47k impedance, that load appears to the cartridge as 470 ohms (47,000 divided by 10 squared) and must be driven by the 10 ohm coil. The 470 ohm load and the 10 ohm source form a potential divider (the “pre-set volume control” described in the previous section) with some of the cartridge’s voltage dropped across its own internal 10 ohm impedance. The proportion dropped internally is 10/(470+10) = 0.0208, which is not very much at all – just 0.2dB. The deviation from the first order approximation is small and probably not worth worrying about, but it is there. It’s when higher turns ratios are used with higher source impedances that the potential divider effect becomes significant. Consider a cartridge with a 40 ohm coil and a transformer with a 1:30 ratio. The 47k load on the secondary now appears as 52 ohms from the primary side. When driven by a 40 ohm source the voltage divider is formed by 52 ohms and 40 ohms. Therefore the proportion of signal dropped across the cartridge’s coil is 40/(40+52) = 0.43, which is very significant – nearly half the voltage produced by the cartridge is lost internally. Whereas only 0.2dB was lost in the previous example, here the signal loss is 5dB, and instead of achieving a signal voltage at the output of the transformer of 30 times the cartridge’s output, the output is only 0.43x30 times the cartridge’s output, ie a voltage step-up of effectively just 13 times, not 30 times. Clearly, increasing the transformer turns ratio by a factor of X doesn’t increase the output voltage by the same factor. As the turns ratio increases, the increase in the output voltage gets less and less as the load on the cartridge becomes more and more significant until a point is reached where increasing the turns ratio further actually causes the output voltage to drop.
The point at which the maximum possible voltage at the transformer’s output is achieved occurs when the transformed load is equal to the source impedance. In the case of a 47k secondary load (the usual load impedance of an MM phonostage) and a 40 ohm MC cartridge, the turns ratio would have to be 1:34.28 to get the absolute maximum output voltage. This is because 40x34.28x34.28 = 47000
It’s this that gives rise to the misguided notion that the transformer must “match” the cartridge impedance. Yes, it may be true that matching the impedances gives the maximum possible voltage at the transformer’s output, but in a hi-fi system we’re not looking for the absolute maximum voltage from the transformer, we’re looking for a voltage suitable to be fed into the following MM phonostage and we’re looking for maximum fidelity. This rarely (if ever) achieved by matching the impedances. The signal voltage suitable for an mm phonostage to handle is about 5mV. A higher voltage into the phonostage will reduce headroom and increase distortion. A lower voltage will compromise the signal-to-noise ratio. Trying to achieve 5mV into the phonostage (with maximum fidelity) should be the aim of a step-up transformer.
The big mistake most often made when selecting a transformer for a moving coil cartridge is to overlook the voltage required at the phonostage’s input and instead try to make the impedances match so that, for example, a cartridge with a 5 ohm source impedance sees a 5 ohm load at the transformer’s input. This approach takes the cartridge’s impedance as the most important factor when in reality it should be the cartridge’s output voltage.
To demonstrate how far wrong the “matched impedance” approach can be, take as an example an Ortofon Vivo Red cartridge with a 5 ohm source impedance. In order to "match the impedance”, the 47,000 ohms on the secondary side of the transformer would have to appear as 5 ohms on the primary side. That means that the impedance ratio must be 9400 (because 47,000 divided by 5 equals 9400) and therefore the turns ratio must be the square root of 9400, which is 97. So we must find a step-up transformer with a turns ratio of 1:97. However, the Vivo Red’s output voltage is 0.5mV and the voltage fed to the phonostage by a 1:97 transformer would 24mV. That would be enough to overload most phonostages and would be a long way from optimal. A much better approach to finding a suitable transformer ratio would be to work with the cartridge’s output voltage. The Vivo Red has an output of 0.5mV and the phonostage requires about 5mV for the best performance, therefore a ratio of 1:10 would appear to be much better. The first order approximation suggests a 1:10 ratio would give us 5mV. Does that still hold true if we also consider the cartridge’s 5 ohm source impedance and the load impedance presented by the transformer? Yes. A 1:10 transformer with a 47k load on its secondary winding presents a load of 470 ohms to the cartridge. The voltage divider formed by the 5 ohm source impedance and the 470 ohm reflected load means that only 5/(470+5) is dropped across the cartridge’s internal impedance and the actual voltage at the transformer’s output is 4.95mV, ie extremely close to the estimate using the approximate method. The 470 ohm load seen by the cartridge is perfectly compatible with Ortofon’s recommended load of >10 ohms. The “impedance matching” method of using a 1:97 ratio transformer would give the cartridge a 5 ohm load impedance, which is outside the manufacturer’s recommendation. Also, for the reasons explained below, a 1:97 transformer would have a seriously compromised performance compared to a 1:10 transformer.
Now consider a different cartridge, the Dynavector Karat17D3 with a 38 ohm coil. Using the impedance matching approach to find the best transformer ratio we end up with a ratio of 1:35 and the cartridge’s 0.3mV output becomes 5.25mV at the the transformer’s output. This time, the “impedance matching” approach appears to have worked out well, but is is really the best turns ratio? Maybe not, because Dynavector’s recommended load is 100 ohms and a 1:35 transformer would give the cartridge a 38 ohm load. In this instance a lower turns ratio would be better. For example, a 1:20 transformer would give the cartridge a load of 117.5 ohms and have an output of 4.5mV. Also, a 1:20 transformer is likely to have better performance than a 1:35 transformer, as explained below.”
