[Eric T]

Just in case someone else needs help figuring out the best place to tap a Hammond 125 series universal replacement transformer when the secondary impedance isn't showing on the chart (available here: http://www.hammondmfg.com/125.htm), I have decided to post this fairly simple bit of math:

The chart does not show where a 5 ohm secondary impedance should be tapped to get 17,000 ohms primary impedance. Hammond also doesn't show the turns ratio for each tap, so you need to figure that out in order to decide the closest match for the original.

On the chart, you see that tapping the secondary at 1 & 3 with a 6 ohm voice coil impedance will get you 21,600 ohms impedance at the primary. The primary to secondary impedance ratio is the turns ratio squared.

pri/sec = turns²

So you divide 21,600 (primary) by 6 (secondary) to get 3,600.
21,600 ÷ 6 = 3,600

Then you find the square root of 3600 to get the turns ratio, which is 60.
√3,600 = 60

Now I'm looking for a 58:1 turns ratio and a primary impedance of 17,000 ohms, so I did the math on the two closest tap points on the chart and found that I'll get 60:1 at taps 1 & 3 and about 53:1 at 2 & 4.

At 1&3:
60² = 3,600
3600 x 5 = 18,000

And at 2&4:
53² = 2,809
2,809 x 5 = 14,045

So I go with tapping the secondary at 1&3 to get a primary impedance of 18,000 ohms to go with the 5 ohms secondary impedance.

Yes, I know that was easy to estimate just by looking at the chart for my situation, but not everybody is going to have as cut-and-dried choices. Punching a few numbers on the calculator is easier than hooking up the transformer and playing the trial-and-error game.