moving coil step-up transformers explained

Step-up transformers for moving coil cartridges are the most esoteric and misunderstood items in the world of hi-fi, 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 step-up 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 step-up 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 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). These calculations assume a theoretically perfect transformer with infinite primary inductance, zero leakage inductance, zero coil winding resistance, infinite core permeability, zero inter-winding 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 step-up 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 step-up 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 real-world 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 step-up 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.

transformer loading
The oscilloscope screen shots in figure 1 above illustrate what can happen when a transformer works into difference load impedances.
Figure 1 shows a step-up transformer being fed a 1kHz square wave from a 10 ohm source impedance (typical of an MC cartridge’s source impedance). Square waves are a useful tool because a perfect square wave contains a combination of all frequencies. An imperfectly reproduced square wave shows how the amplifier or transformer has limited the bandwidth. If the top of the square slopes down to the right, that indicates the low frequency limitations. If the corners are rounded off, that indicates high frequency limitations.
Figure 1a shows the output with a 47k ohm load on the secondary of a fairly modest transformer. The slope on the top and bottom of the waveform is caused by the low frequency limit of the transformer due to inadequate primary inductance. The peaks at the corners of the waveform are due to transformer ringing, also known as overshoot. (Ringing, and the best way to cure it, will be dealt with in more detail later.) Figures 1b, 1c and 1d show what happens to the waveform when the secondary load is reduced to 22k, 10k and 5k1 respectively. The slope of the waveform straightens out as the impedance is reduced and the corners lose the unwanted peaks, but the overall signal level also drops significantly. The level with the 5k1 load is about 10dB less than the level with the 47k load. This shows that although the performance of the transformer can be improved by reducing the load impedance, the benefit comes at the expense of a serious loss of signal level. Since the point of using a step-up transformer with a moving coil cartridge is to gain an extra 20dB or so of signal level, any loss due to incorrectly loading the transformer is unacceptable.

The problem of 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 inter-winding capacitance) combining to produce resonance. The capacitance of the cable connecting an mc step-up transformer to the following phonostage also plays a part, which is why the interconnect should be a low capacitance design and kept as short as is practical. Ringing can be found in many commercial moving coil step-up transformers, regardless of price. Sometimes the ringing occurs at very high frequencies and is resonably 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 well-known audiophile brands often exhibit poor performance as regards ringing.
Figure 2 below shows oscilloscope screen shots of a step-up transformer from a manufacturer of expensive valve amplifiers. The input signal is again a 1kHz square wave. Figure 2a shows the transformer's output when there is no load and the overshoot is quite clear to see. 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, seperation between the instruments will not be helped by the severe ringing shown in figure 3.

Figures 2b to 2e show the 1kHz waveform with different resistive loads on the transformer's secondary. A 47k load damps the ringing slightly and as the load is reduced through 22k, 10k and 5k1, the ringing is progressively damped more. 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.

Fortunately, ringing can be totally eliminated without sacrificing signal level by loading the secondary winding correctly (though far too many commercial step-up transformers totally neglect this). However, the optimum load is unlikely to be merely resistive, and 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.
Figure 5 below shows the transformer of figures 2 and 3 after an optimised load network has been applied, again with a 1kHz square wave input. The ringing has been eliminated and the signal level available into a 47k load has been maintained.
Figure 6 shows the effect of applying a non-optimum loading network. In this case the incorrect component values (out by only a few nanofarads and a few kilohms) have resulted in quite a peculiar deformation of the waveform. This illustrates the need to get the loading network right rather than copying a network which is optimised for a different transformer.
As an aside, the use of silver wire for the windings might appear impressive but does little or nothing for performance due to the fact that silver has only marginally less resistance than copper and the limiting factors in transformer performance are due to the finite size and permeability of the core, leakage inductance and inter-winding capacitance, none of which are improved by the use of silver wire. However, it does have a significant impact on cost. It should go without saying that elaborate cases with 3D milled aluminum front panels or gold plated turrets, while very nice to look at, also have no benefit for audio performance but, again, do have an impact on cost.

listening tests and empirical results
There is much ill-informed advice on the internet suggesting that any load can be placed on the secondary winding of a step-up transformer and the transformed load will appear on the primary without any ill effects. This is not true, as can be seen from the screen shots above. Some transformers can handle a range of resistive loads on their secondaries and maintain acceptable performance, but many cannot and all will be affected to some extent by varying the load. Exactly how a transformer will respond to different loads depends on what core material has been used and what shape and size it is, how many turns of wire are on the primary and secondary, the thickness of the wire, the winding techniques employed, etc. The result is that different transformers respond differently to varying the load.
There are various articles on the internet which state or imply that the audible effects of altering the load on a transformer's secondary winding are due to the different transformed loads seen by the moving coil cartridge. In an article about step-up transformers on the 6moons website (http://www.6moons.com/audioreviews/stepup/primer.html) Tom Miccolis states "...you may wish to experiment with lowering the primary impedance value in order to witness what affect it has on the resultant sound from your system. This can be accomplished by using resistors in parallel across the secondary side of the transformer." Why would you want to do that? If you want the cartridge to see a lower impedance, the sensible thing to do is place the extra load on the primary side of the transformer, not the secondary. Placing the load on the secondary side of the transformer does change the load seen by the cartridge, but it is more likely to have an effect on the transformer's performance than the cartridge's because the transformer is much more sensitive to loading than the cartridge is, as has already been shown. The same article contains other errors and misleading information, such as stating step-up ratios as 20:1 instead of 1:20, and much worse, stating that "resistor loading can cause ringing on the signal". On the contrary, resistor loading damps ringing, not causes it, as is clearly illustrated in the screen shots above.
In truth, a step-up transformer can only be fully optimised with a very specific load on its secondary. If it works open circuit or into too high a load impedance, it will almost certainly display ringing on its output. If it works into too low an impedance, it will not suffer from ringing on its output but will possibly have a reduced high frequency response and the signal voltage will not be stepped up as much as it would be otherwise.
This is borne out by experiments and listening tests, even by people who do not fully understand the technicalities of transformer loading. In another article about step-up transformers on the internet (http://www.high-endaudio.com/RC-Step-ups.html), Arthur Salvatore concludes that transformer loading is crucial to optimising performance (quite true) and after describing the results of his empirical experiments with resistor loading the Bent Silver transformer he states that "when the resistor value is too high, the sound will normally be bright, forward, light and lean" and goes on to say that "when the resistor value is too low, the sound will normally be dark, recessed and compressed". He also says that with a slightly reduced load impedance the sound had "greater separation", but reducing the resistor value too far caused the volume to drop too much.
All of Mr Salvatore's results were predictable and all concur with results of the transformer loading experiments described above. At first the reduced load impedance is damping out the ringing in the transformer and causing the sound to become clearer and less bright sounding. Further reductions in the load cause the high frequencies to balance better with the low frequencies (as predicted by the square wave flattening out in figure 1 above) and reducing the load impedance even further causes the signal level to drop to such an extent that the transformer is no longer stepping up sufficiently to be any use. The correct way to load the transformer would have been with a resistor/capacitor network, which, in fairness, the author does allude to, and which could have eliminated ringing and maintained the step-up ratio. Nevertheless, his empirical results concur very well with both theory and measurement.

the transformer/cartridge selection method recommended by Rothwell
Our recommended procedure for the purpose of assessing the compatibility of any cartridge/transformer combination is to work initially with a cartridge's output voltage rather than its source impedance. The method is to calculate what the cartridge's output signal will be after it has been stepped up by the transformer. A cartridge with an output of 0.5mV and a step-up transformer with a 1:10 turns ratio will give an output of 5mV. This is just about the right signel level for the input of a moving magnet phonostage. 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 compromised signal/noise ratio. 5mV is a good target figure, but anything in the range of 2.5mV to 10mV is within acceptable limits. Having found a good match for cartridge output and transformer turns ratio, check that the transformed impedance is acceptable. 47k is virtually universal as the input impedance of moving magnet phonostages, and dividing this figure by the square of the turns ratio will give the load impedance that the cartridge sees (except in the case of Rothwell transformers, where the load impedance is maintained at 100 ohms by primary loading as detailed below). With a 1:10 transformer, the load impedance seen by the cartridge will be 470 ohms. Is this within the cartridge manufacturer's recommended range? Check their specifications to see. A 1:20 transformer will present a load impedance to the cartridge of 117 ohms and a 1:30 transformer will present a load of 52 ohms. 52 ohms may be on the limit, or below, what a manufacturer recommends, which is one of the reasons why 1:30 is considered too high a ratio for most modern cartridges and is best reserved for the few remaining cartridges with outputs of 0.1mV or 0.2mV. The inevitable compromises in transformer design mean that a 1:30 ratio will also most likely suffer from either low primary inductance, resulting in poor bass response, or high winding capacitance resulting in limited high frequency response or excessive ringing.

some examples
The table below shows the specifications for a range of modern low output moving coil cartridges. The use of modern rare earth magnets has resulted in most moving coil cartridges having a reasonably healthy output of around 0.4mV or 0.5mV whilst maintaining a low source impedance. This makes the signals they produce much easier to handle than the cartridges from 40 years ago (neodymium magnets weren't invented until 1983) so the problems of yesteryear are thankfully not such a problem now.
Take as a first example the Audio Technica ATOC9ML3. With a specified output voltage of 0.4mV, a 1:10 transformer will produce an output of 4mV, which is a very good level for an mm phonostage. The load impedance on the cartridge will be 470 ohms, which is higher than Audio Technica's recommended 100 ohms but a higher value is generally better than a lower one.
Take as another example the Ortofon Xpression. If used with a 1:20 transformer, its 0.27mV output will become 5.4mV, which is again ideal for an mm phonostage. The 117 ohm load on the cartridge is clearly compatible with Ortofon's recommendation of anything above 10 ohms.
Some of the cartridges with higher source impedances, such as the Benz Micro LP-S, should be used with lower ratio transformers. A 1:10 ratio transformer with the LP-S would give an output voltage of 5.1mV and load the cartridge with 470 ohms. Again, this would be a good match, but higher turns ratios would be less suitable.
The figures for the Denon cartridges look slightly odd compared to the rest of the table. If the figures are correct, the output voltages look a little low for the higher than normal source impedances of 40 ohms (possibly due to the use of relatively weak magnets and more turns of wire on the coils), but a 1:20 transformer would give an output voltage of 5mV with the DL-103R and present it with a load of 117 ohms. The voltage is again ideal for a mm phonostage and the impedance is only very slightly higher than Denon's recommendation, which is probably only meant to be a ballpark figure anyway.
The Dynavectors and Koetsus have a good output voltage level and low source impedance and should be compatible with transformer turns ratios of between 1:10 and 1:20. However, they will be seeing load impedances quite a bit higher than the recommended value of 30 ohms. In practice this is most unlikely to be an issue and, again, the recommended load is likely to be ballpark figure rather than a hard and fast rule. It’s also possible that the figure is meant to be read as “30 ohms or more”. Many Dynavectors and Koetsus are in use all over the world into 100 ohm load impedances and give superb performance.
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 step-up transformer : 5 - 15ohm". Taken literally, this makes no sense. Why would a cartridge be happy into a 100 ohm load if it is presented by an amplier but not if it is presented by a transformer? The only logical conclusion is that they mean the transformer should be designed for a source impedance of 5 - 15 ohms. That would make perfect sense and it can be safely said from experience that Lyra cartridges are an excellent match for Rothwell transformers.

Rothwell Transformers
The MC1 has a step-up ratio of 1:12.9 and the MCL has a step-up ratio of 1:20. In both cases the input impedance is 100 ohms. This is because loading is used on the primary side of the transformer as well as the secondary side to maintain a 100 ohm load. The extra load makes the input impedance compatible with a very wide range of cartridges and has the added benefit of smoothing out any non-linearities in the input impedance caused by the real-world practicalities of transformer design such as non-zero leakage inductance and interwinding capacitance.
The secondary windings of both the MC1 and MCL have optimised loading networks so that when fed into a 47k moving magnet phonostage the bandwidth and voltage gain are maximised and ringing eliminated. Do not use any additional loading on the secondary of either the MC1 or MCL in order to try to improve cartridge loading or cartridge matching as prescribed by dubious advice found on the internet.
The higher step-up ratio of the MCL makes it more suitable than the MC1 for cartridges with outputs on the low side (and vice versa for slightly higher than average output cartridges) but both transformers are suitable for the vast majority of cartridges on the market today. The only cartridges which are on the margins of compatibilty are the very low output cartridges of less than 0.2mV (from Audio Note, for example) and the Denon DL-304 which has an output of 0.18mV and a source impedance of 40 ohms. Even so, they are on the margins rather than totally unsuitable and it is worth trying them and judging compatibility by ear if at all possible. Sometimes the specs can be misleading and lead to the rejection of combinations which work well in practice. With all cartridges in the range of 0.3mV - 0.7mV and a recommended load impedance range which covers 100 ohms (ie the vast majority of modern cartridges), either the MC1 or MCL will be an ideal match.

summary
1) Output voltage and source impedance are clearly defined parameters of a cartridge, but the recommended load impedance is not. A load impedance which is equal to the cartridge’s source impedance does not mean that the cartridge is perfectly matched to the load. The very minimum load impedance on the cartridge should be at least three times the source impedance. Ten times the source impedance is safer, but the exact value is not critical.
2) Turns ratios of less than 1:10 are usually too low to step up the cartridge’s output sufficiently.
3) Turns ratios of more than 1:20 are usually too high to be compatible with most modern cartridges and should be used only with certain cartridges of very low output.
4) Loading the transformer does have an effect on the load seen by the cartridge, but any change in sound quality is more likely to be due to altering the performance of the transformer, not the cartridge.
5) Complicated calculations involving impedance transformations and specific recommended loads are usually unnecessary.

further reading
an excellent article on the website of Jensen transformers
http://www.jensen-transformers.com/an/Audio%20Transformers%20Chapter.pdf
This article is excellent and can be taken as gospel. However, it is quite technical.

FAQs about magnetic sheilding
http://www.magnetic-shield.com/faq/interference.html

A detailed paper about core materials
www.sowter.co.uk/pdf/GAVS.pdf
This is probably way more information and detail than you need, but you may find it interesting

Lundahl’s Transformer Design Philosophies
http://www.lundahl.se/pdfs/papers/design_philosophies.pdf
Lundahl supply the transformers used in the MCL