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.
the cartridge operating principle Moving magnet cartridges, as their name implies, contain magnets which are moved by the stylus’ cantilever, and the movement induces the signal voltage in fixed coils in close proximity to the magnets. In moving coil cartridges the roles are reversed, so now the magnets are fixed and the coils move. The big advantage of moving coils is that the coils are much lighter than the magnets, so they are much more responsive to the motion of the stylus. The big disadvantage is that the output voltage of moving coil cartridges is about 20dB lower than that of moving magnets, so an extra 20dB of gain is required. The extra gain can be provided by the phonostage amplifier or by a transformer. The most commonly found solution is to increase the gain in the phonostage, but stepup transformers are still the best solution where cost is no object.
why use a transformer at all? The distortion produced by audio transformers is of a completely different nature to that produced by a transistor amplifier. The harmonic distortion in transformers is greatest at the lowest frequencies and falls rapidly as the frequency rises, whereas in transistor amplifiers distortion is more usually distributed evenly across the audio spectrum. More importantly, intermodulation distortion tends to be lower in transformers than it is transistor amplifiers. The outcome is that although transformers aren't absolutely free of distortion (nothing is), the distortion is very much more benign than the distortion produced by transistor amplifiers. This explains why the sound produced when a moving coil cartridge is used with a good transformer is so sublime and can create an open and spacious soundstage with amazing separation between instruments. The case against transformers is simply one of cost. Transistors can be as cheap as a few pennies (or less when bought in sufficient quantities) whereas transformers always cost a lot more, by as much as a factor of several thousand, due to the expensive materials used in the core and the cost of the copper windings in terms of both material and labour.
cartridge loading Before considering how to match a moving coil cartridge with a transformer, it is worthwhile considering the effects of different loads on moving coil cartridges. Most modern moving coil cartridges have a source impedance of about 10 ohms or less, with a very small inductance of a few microhenries. The inductance is so low that it can be virtually ignored. In theory, such a low source impedance should be able to work into almost any load without any ill effects on performance. The usual rule for audio equipment in general is to feed the signal into a load ten times greater than the source impedance to avoid any signal loss, and this is a good way to choose a suitable load for a moving coil cartridge. Given a typical source impedance of 10 ohms, 100 ohms is a good choice for load impedance. This is well in line with the recommendations from cartridge manufacturers (see the table of data below). Anything above 100 ohms should be equally suitable. However, one thing to consider is the effect of the current drawn from the cartridge. As the load impedance is reduced, the current drawn from the cartridge increases. This current flowing through the coils sets up a tiny magnetic field which opposes the motion producing it due to Lenz's law and will impose a force which opposes the movement of the stylus. This is analagous to the back EMF in moving coil loudspeakers where the motion of the coil sets up a magnetic field in opposition to the loudspeaker's permanent magnet and which damps the motion of the coil. Just as a low amplifier output impedance maximises the damping of the loudspeaker cone, so a low load impedance on an moving coil cartridge will damp the motion of the stylus. However, although a near zero output impedance for an amplifier is both feasible and beneficial, a zero load impedance on a cartridge would silence it, so there has to be a limit to how low the load impedance can be. Unfortunately there seems to be no concensus on how significant the effect of stylus damping is, or even whether or not stylus damping is a good or bad thing. In fact, the effect seems to be so poorly appreciated that this author has only ever seen it refered to once, and that was by Graham Slee. He recommends a higher than usual load impedance to minimise the damping effect, but many people recomend a load impedance much closer to cartridge's source impedance for optimum sound (though without any convincing rationale for the recommendation). The recommendation of Rothwell Audio Products is in line with Ortofon, Audio Technica and most other cartridge manufacturers  that 100 ohms is a good value for nearly all cartridges, but that the exact value is not critical as long as it is well above the cartridge's source impedance. One thing is certain, and that is that the load impedance should not be equal to the cartridge's source impedance. The idea that having the load impedance equal to the source impedance achieves perfect "matching" is totally wrong and is the most commonly held myth about moving coil cartridges. It also gives rise to most of the confusion surrounding stepup transformers and how to select the correct one for any given cartridge.
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 signal 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 stepup 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 stepup 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). These calculations assume a theoretically perfect transformer with infinite primary inductance, zero leakage inductance, zero coil winding resistance, infinite core permeability, zero interwinding capacitance etc., all of which are impossible to achieve. The big mistake most often made when trying to select a transformer for a moving coil cartridge is to try to make 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 is totally wrong, but for now we will follow the flawed logic to see where it takes us. Take as an example an Ortofon Cadenza Bronze cartridge with a 5 ohm source impedance which we want to put through a stepup transformer and feed into a moving magnet phonostage with an input impedance of 47k. In order to "match" the impedances, the 47,000 ohms on the secondary side of the transformer should 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. This would be impossible  they simply don't exist (for reasons which will be revealed later). Ok, so lets look for a transformer with the nearest ratio to 97 that we can find. The nearest would most likely be a 1:30 transformer. With this transformer, the impedance ratio would be 900 (30 squared), so the 47k on the secondary would appear to be 52 ohms on the primary. However, 52 ohms is much higher than the 5 ohms we were trying to achieve, so what can be done? The solution which can be found recommended all too often in cyberspace is to reduce the input impedance of the following moving magnet phonostage to a lower value so that it appears to be 5 ohms on the primary side of the transformer. Lets do the calculation. 5 ohms multiplied by the impedance ratio of 900 equals 4500 ohms. That means that reducing the phonostage's input impedance to 4k5 and using a 1:30 transformer would present the cartridge with a 5 ohm load and everything would be perfectly matched, right? No! In reality, absolutely everything about this apparently correct deduction is wrong! Unfortunately, there are many articles on the internet which advocate this very approach using the same logic to arrive at the same disastrous results.
what's wrong with the "matching" calculations? Let's analyse the errors in the above example. Firstly, as explained earlier, the load impedance that a cartridge is fed into should not be equal to its source impedance. If you examine Ortofon's specifications for the cartridge in the example above you'll see that they recommend a load of 50  200 ohms. That means that almost any load impedance over quite a wide range will be fine and complies with the general rule mentioned above that the load impedance should be 10 times the source impedance to minimise signal loss. The 52 ohm load that the 1:30 transformer would have presented would have been within the recommended range. A 5 ohm load would have been well outside the manufacturer's recommended range and would have adversely affected the cartridge's output. The other disaster resulting from the calculations above was to place a 4k5 load on the transformer's secondary winding. The realities of realworld transformers makes that a bad idea.
real world transformers If it was possible to make transformers where the coil windings had zero resistance, where the inductance of the primary coil was infinite, where the transformer's core had no limit to its maximum flux density, where no capacitance existed between coil windings, etc., etc., it would be possible to make truly astounding transformers which could perform like the theoretically perfect transformers which can tolerate any load impedance and remain unaffected. However, in the real world, we have to live within the constraints nature places upon us and work with materials that do have resistance, capacitance, finite permeability etc. All transformers have limitations, and trying to optimise one aspect of a transformer's design will usually have a detrimental affect on another. For example, trying to improve a transformer's bass response by increasing the number of turns on the primary winding will either result in a reduced stepup ratio (if the secondary turns are kept the same) or increased secondary coil resistance and capacitance (if the secondary turns are increased to maintain the turns ratio). The resistance and capacitance in the secondary winding place limits on the bandwidth and the load that can be tolerated without signal loss. A transformer which works well into a 47k load may not work nearly so well into 4k5, as explained below.
