MC LOADING & STEP UP DEVICE

Step 1: Find out the winding ratio of the trannie.
e.g. 20dB = 1:10; 26dB = 1:20; 30db = 1:31.6; etc.
(there are more on the web, no need to calculate...)

Step 2: Find out the 'natural impedance' of the trannie.
Ratio^2 * phono-pre input impedance
e.g. 31.6 * 31.6 * 47k ohm = 47 ohm for a 30dB trannie
(this will be what the cart sees if you do not use secondary or primary loading of the trannie)

Step 3: Check for phono-pre over load
e.g. of cart V = 0.25mV; cart DCR = 6 ohm
[cart output V * ratio]* [load impedance/(load imp + cart DCR)] =
e.g. [0.25 * 31.6] * [47 / (47+6)] = 7.9mV * 0.887 = 7.0mV

try for max. input value not to exceed ~ 7.5mV

With a 26dB, you will have a higher 'natural impedance' i.e. 117.5 ohm (and not 47 ohm as with a 30 dB item) which in turn might require secondary or primary loading to lower the impedance that the cart will see.

Secondary trannie loading is reflected 'back' to primary, by dividing the secondary R by the square of the winding ratio.
But first you have to get the correct value e.g. if 18k ohm is loaded on the secondary then:
47k*18k / 47k+18k = 13.01k ----
then reflected = 13.01k / 31.6*31.6 = 13ohm that the cart will now see.

But secondary loading will ALSO have the effect of damping the trannie, as more current is pulled on the secondary side, this may be just what is needed -- but it may be also not a good thing --- only testing & listening will tell.

If primary loading is indicated (if e.g. secondary gets too dull) then:
e.g. 18ohm load R with 47ohm 'natural impedance' =
47*18 / 47+18 = 13 ohm again what the cart sees.

I hope this will be enough to give you a starting point for checking the various option.
Cheers,

Axel, thanks very much for the primer. I now understand these SUT impedance calculations. Using your formulae, I was able to recalculate the 3 Ohm input impedance for the Auditorium A23 Hommage T1 MC transformer that is referenced in Art Dudley's recent column based on the winding ratio (1:30) and the secondary coil impedance (2.8k ohms) specified in the column.

Very educational.

Cincy Bob -- Art Dudley's writeup was perhaps worded a bit misleadingly, and I want to make sure it's clear that the load impedance seen by a cartridge working into that transformer is NOT 3 ohms. It is, to a close approximation, the input impedance of the phono stage or preamp which is connected to the secondary side of the transformer, divided by the square of the turns ratio. In other words, typically 47,000 ohms divided by 933 in this case, or 50 ohms.

The voltage gain would correspond to the turns ratio, which is just over 30 times (actually 30.54, the square root of 933). The voltage gain expressed in db is 20 times the log of 30.54, or 29.7db.

I'm not certain, but I suspect that the 3 ohm and 2800 ohm figures he mentions are dc resistances, which will result in a slight but insignificant attenuation of the signal.

Axel -- I second the thank you which Bob offered for your excellent post.

Regards,
-- Al

In other words, typically 47,000 ohms divided by 933 in this case, or 50 ohms.

I should have added, of course, that the 50 ohms would be less if load resistors are added.

Regards,
-- Al

Here is the excerpt from Art Dudley's write-up:

Aschenbrenner's Hommage T1 measures somewhat differently, with a primary coil impedance of about 3 ohms and a secondary coil impedance of 2.8k ohms

I assumed that the secondary coil impedance was equivalent to a secondary trannie loading that is reflected back to primary as discussed in Axel's post above. The math seemed to confirm this:

47k*2.8k / 47k+2.8k = 2,643 / 933 = 2.83 ohms

Is it coincidence that the mathematical result agrees with the "primary coil impedance of about 3 ohms" that is cited in the write-up?