A recent classic from Don.
The optimum design of a modulator and final is more involved than simply calculating the modulation transformer impedances and turns ratio based on the published impedance properties of the tubes.
If a common power supply is used for modulator and final, regardless of the impedance level, the modulation transformer needs to have a turns ratio of about 1.4:1, or a 2:1 impedance ratio. The only case in which a "multi-match" transformer, with a choice of several turns ratios, is useful is when separate supplies are used for modulator and final, and different plate voltages can be applied to the modulator and final tubes. Otherwise, an appropriate fixed-impedance transformer is satisfactory, and may actually give better performance.
The reason is simple. In a class-B or AB circuit, the peak audio voltage capability of each tube is roughly 80% of the DC power supply voltage. It is very difficult to drive the grid of a tube hard enough to bring the instantaneous plate voltage below about 20% of the DC plate voltage. One of the reasons is that, to get the tube to conduct to saturation, substantial positive voltage must be applied to the grid, and this peak grid voltage is likely to be close to 20% of the plate voltage. With a triode tube, it is impossible to bring the plate voltage below the grid voltage, no matter how hard the tube is driven.
With two tubes in push-pull, the total peak a.c. (audio) voltage across the primary of the modulation transformer is the sum of the peak voltages generated by each of the two tubes. If we assume the figure of 80% of the DC plate voltage, that means that the the total peak audio voltage developed by the modulator tubes cannot exceed 1.6 times the DC plate voltage. Therefore, for exactly 100% modulation capability, the turns ratio, total primary to secondary, would be approximately 1.6:1, or 2.56:1 impedance ratio. But to avoid distortion near the 100% modulation point, we need some head-room, so that the tube is not being driven to saturation right at the instant that 100% modulation occurs; therefore it is preferable to have a little less step down, maybe 1.4:1 or 1.5:1. If you are looking for extended positive peaks, a ratio of 1.3:1, 1.2:1 or even 1:1 would be necessary.
Where the plate-to-plate impedance comes in, involves how much current is run on the final. By Ohm's law, modulation impedance = plate voltage/plate current. This impedance is reflected back to the modulator tubes via the transformer. So you need to choose a plate current that will give the proper modulating impedance that when reflected back to the modulator tubes through the transformer, will allow the modulator tubes to work into a satisfactory plate-to-plate load.
There is nothing sacred about the p-to-p load recommendations given in the tube charts; they are just that, recommendations. With most good tubes, the p-p load they work into can be varied considerably, maybe as much as 2 to 1 and still get good results. When working the tubes into a lower p-p load impedance, the peak plate current will be higher, the plate dissipation will increase and the stage may become less efficient. Taken to extreme, the linearity of the tube may suffer. But within reason, the main thing to watch for is plate dissipation and maximum peak plate current. The maximum peak output from the tubes may be reduced when one veers too far from the recommended p-p impedance, but if peak plate current and plate dissipation are kept within the manufacturers ratings, the tube will perform just fine. The same goes for running at a higher-than-recommended p-p load. In this case, for 100% modulation capability at the full power rating, the DC plate voltage will be increased. Again, this causes no problem as long as the maximum plate voltage rating of the tubes is not exceeded. The tube may run more efficiently at a higher p-p load, but if too much step down is used in the transformer, the peak output capability and therefore modulation capability will be reduced.
The third factor to be considered is the nominal impedance rating of the modulation transformer itself. This is determined by the amount of iron in the core, the type of iron used, and the number of turns in each winding. Most good transformers can be run at least +/- 100% of the nominal value, again as long as maximum current and voltage ratings are not exceeded. If you get too far away from the nominal impedances, frequency response may be affected. Running a transformer at a much higher impedance than normal will limit low-frequency response due to the lower inductance of a low impedance winding. Conversely, running a transformer at a much lower impedance than recommended may limit the high frequency response due to the combination of stray inductances and capacitances in the windings. Also, the core is more likely to saturate on peaks due to higher currents through the windings. But within reason, the transformer should work OK.
In fact, this is the principle of operation of the multi-match "universal" modulation transformers. The same turns ratios are used for many different sets of impedance walues. The CVM-5 for example is rated for something like a range of 2000 to 20,000 ohms on both the primary and secondary. Looking at the charts, you will see the same turns ratio connections repeated over and over to transform widely different impedance levels.
So, getting back to the topic, if a common power supply is to be used, a mod transformer turns ratio of somewhere between 1.2:1 and 1.4:1 should be used, and tube types, DC plate voltage, final amplifier plate current and nominal modulation transformer ratio should be juggled for the best fit. Some compromise may be necessary, regarding both performance and power output, when one is limited to using components on hand.
Calculating the mod xfmr turns ratio based on published modulator impedances and final amplifier plate voltages/currents listed in the tube charts may or may not meet the above criteria. If not, it is better to push the load and modulating impedances a little beyond the tube chart recommendations, or live with slightly less power output capability, than to veer too far from the optimum modulation transformer turns ratio as described above when using a common power supply for the modulator and final.