Below is a description from Andy Grove covering how Audio Note (UK)

matches cartridges to Step Up Transformers: -

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"​Matching of low impedance moving coil cartridges presents a major problem: noise. Taking the example of a cartridge with a 1 ohm internal impedance, that equates to an equivalent noise voltage of 0.126nV/ rt(HZ) or about 18nV in a 20kHz bandwidth, and about a 60dB signal to noise ratio compare to a 30uV signal from the cartridge. In practice it will always be worse.

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Although physically possible to design a solid state stage to amplify such a small signal, without drowning the music in hiss, requires pretty extreme measures, and designers often resort to multiple paralleled transistors running at high current, and a large DC blocking capacitor and/or a differential stage, which doubles the transistor requirement to achieve the same noise figure.

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In audio, the solution to this low impedance problem is almost always to use a transformer, and many high end ribbon and dynamic microphones also use a transformer to raise the signal level out of where transistors or valves struggle.

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However, just like a microphone, a cartridge is an electro-dynamical system which requires matching for optimum signal transfer. For optimum power transfer we usually think about a 1:1 source and sink match, which is why you have 50ohm and 75ohm cables, connectors and systems. When designing with valves, especially single ended stages, the optimum power is transferred out of the valve at a theoretical 1:2 ratio, but in practice a ratio of 1:3-4 is usually chosen. That’s why a 300B often uses a 2k5 to 2k7 transformer primary.

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It’s the same with moving coil cartridges. Due to the mechanics of the cantilever, and the electrical characteristics of the armature winding, the optimum load impedance usually works out at about 3-5 times the generator impedance of the cartridge, and that is often estimated by using the dc coil resistance.

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Of course there are exceptions, and there is scope for tuning, but usually what happens is, too low = rolled off high frequencies and sat on feeling, and too high = insufficient damping and the sound is too light and vague.

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But, the transformer itself is an energy transfer device, much like our 50ohms or 75ohms cables, and mis-termination leads to reflections, ringing and frequency anomalies, so the transformer itself has to be designed to work with a certain source impedance and to run into a given load.

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Usually this works out quite will with traditional cartridges using ferrite, alnico or field coil magnets, there is a natural relation between the cartridge output, the transformer step-up ratio, and the loading, to work into a moving coil phono stage. It’s not surprising as these three parts all grew up together. However, neodymium and samarium cobalt magnets can be quite hot, which makes matching more problematic. If this is the case, it’s often necessary to mismatch the transformer impedance wise, to get it to work ratio wise.”