moving coil stepup transformers explained 
Stepup transformers for moving coil cartridges are the most esoteric and misunderstood items in the world of hifi, and this partly explains why they are so seldom used. This is a great shame because the use of a good transformer gives the best possible performance from a moving coil cartridge. This article is intended to demystify the subject and allow the reader to select a suitable transformer with confidence. Apologies in advance if some of the maths becomes a bit baffling and causes more confusion rather than less. Despite the apparent complexity, the conclusions are quite simple and you could just skip to the bottom of the page for the recommendations. the cartridge operating principle why use a transformer at all? cartridge loading the transformer turns ratio and impedance ratio So, it would seem logical that a cartridge with an output voltage of, for example, 0.5mV, when used with a stepup 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 “preset 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 stepup 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. 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 stepup 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. real world transformers transformer loading 




Transformer ringing The oscilloscope screen shots in figure 1 above illustrate ringing and the effects of different loads on the transformer's secondary winding. The transformer ringing which can be seen as peaks at the corners of the waveform in figure 1 is a common problem and arises from inductive and capacitive elements (leakage inductance and interwinding capacitance) combining to produce resonance. The capacitance of the cable connecting an mc stepup transformer to the following phonostage also plays a part, which is why the interconnecting cable should be a low capacitance design and kept as short as is practical. Ringing can be found in many commercial moving coil stepup transformers, regardless of price. Sometimes the ringing occurs at very high frequencies and is reasonably well damped and therefore quite benign, but often it occurs at a much lower frequency or rings for such a long period that it can cause quite audible effects. Even expensive transformers from wellknown audiophile brands often exhibit poor performance as regards ringing. Figure 2 below shows oscilloscope screen shots of a stepup transformer from a manufacturer of expensive valve amplifiers. The input signal is again a 1kHz square wave from a 10 ohm source. Figure 2a shows the transformer's output when there is no load and the overshoot is quite clear to see. Figures 2b to 2e show the 1kHz waveform with different loads on the transformer's secondary. A 47k load has barely any effect on ringing, but as the load is reduced through 22k, 10k and 5k1, the ringing is progressively damped. At 5k1, the ringing is gone but the signal level is reduced. With this particular transformer, the signal loss with the 5k1 load is not as bad as the signal loss suffered by the first transformer, but any loss of signal should be avoided. Note however that the top and bottom of the waveform are very flat, indicating that this transformer has very good low frequency performance. Figure 3 is a closer look at the corner of the waveform and shows clear ringing which lasts for several cycles before subsiding. The frequency of the ringing is about 100kHz  well above audibility  so there's no chance of actually hearing a ringing sound, but it is clear that the signal produced by the signal generator is being severely deformed. Figure 4 shows the output from a 10kHz square wave input. The waveform is hardly recognisable as a square wave at all and it is not difficult to imagine what effect such deformation could have on a music signal. The leading edges of crash cymbals, ride cymbals and snare drums or the attack of plucked strings could easily lose integrity and become a confused jumble of sound. When several percussive instruments are playing together, as is very common, separation between the instruments will not be helped by the severe ringing shown in figure 4. 



Fortunately, ringing can be totally eliminated without sacrificing signal level by loading the secondary winding correctly with a resistorcapacitor network, not a simple resistor (though far too many commercial stepup transformers totally neglect this). Although lower values of resistive load on the secondary do tend to reduce ringing, as illustrated above, loading with a correctly optimised resistor/capacitor network will produce far superior results. Since different transformers are constructed with different core materials, wire thickness, number of turns and winding techniques, the optimum load network will be different for each, and the only way to determine the correct network is through measurement. 


listening tests and empirical results the transformer/cartridge selection method recommended by Rothwell Aim for about 5mV into the phonostage and look for the turns ratio which will produce that with the cartridge in question. Too high a voltage will compromise headroom (though bear in mind that valve designs have huge headroom), and too low an output will result in a compromised signal/noise ratio. 5mV is a good target figure to aim for. The range from 4mV to 6mV covers a +/ 3dB spread either side of 5mV. The range from 3mV to 8mV covers a +/ 4.5dB spread around the 5mV target. Don't worry about trying to get exactly 5mV, and adjust your calculations accordingly if your phonostage is more sensitive than usual. If your phonostage states its sensitivity as 3.5mV for example, use that as your target figure instead of 5mV. Having found a likely match using just the cartridge output voltage and transformer turns ratio, you can check that the transformed impedance is acceptable, though it almost certainly will be. Assuming a standard MM phonostage load of 47k, a turns ratio of 1:10 will give the cartridge a load impedance of 470 ohms and a turns ratio of 1:20 will give the cartridge a load impedance of 117.5 ohms (in the absence of any load modifying components). further examples All the Audio Technicas will work well with 1:10 transformers and produce enough voltage for a typical MM phonostage. They will also work well with 1:20 transformers, producing voltages of 7.3mV, 6.4mV and 6.4mV respectively. The Denons are unusual in having high source impedances but quite low output voltages. A more detailed analysis of Denon cartridges can be found here, but the summary is that 1:20 is a good ratio for them. Lyra make excellent cartridges but their recommended loadings appear confusing. On their website they say that the recommended load "directly into MC phono input : 91ohms  47kohm", but then go on to say "recommended load via stepup transformer : 5  15 ohm". Taken literally, this makes no sense, but probably means the transformer should be designed for a source impedance of 5  15 ohms rather than presenting a load of 515 ohms to the cartridge. Whatever they mean, their cartridges work well with 1:10 transformers. Finally, there are many cartridges made before about 1990 which have much lower outputs than the modern cartridges in table 1 above (below 0.2mV). In theory they should be used with higher stepup ratios than 1:20, but experience has shown that 1:20 is still sufficient in many cases. The superior performance of lower turns ratios remains attractive and transformers with significantly higher ratios should be approached with caution. The author has encountered one mc stepup transformer with a turns ratio of 1:100. Its bandwidth with a 10 ohm source was well below 20kHz. 
Rothwell Transformers Headamps summary further reading FAQs about magnetic sheilding A detailed paper about core materials Lundahl’s Transformer Design Philosophies 
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