Everything for Electronics

# From the Q&A

With TJ Byers

## Reflections Of A Transformer

### Question:

I am using a RadioShack 70-volt audio transformer (32-1031) for matching the impedance between an LF353 opamp and a low-impedance spring reverb driver coil. I've had the best results using the lowest resistance tap (10W) on the primary and the 16-ohm tap on the secondary. Do you know how to convert the input tap markings from wattage to impedance values for the purpose of substituting other transformers?

Forrest Cook
via Internet

The impedance ratio between the primary and secondary of a transformer is equal to the square of the turns ratio, or

Zprimary = Zsecondary x (turns ratio)2

which means that if we know the secondary impedance (we do) and the turns ratio (we don't), we can calculate the primary impedance. Here's what we know:

Eprimary = 70 volts
Zsecondary = 16 ohms
Pprimary = Psecondary = 10 watts

Since we don't know the turns ratio, that's the first order of business. It can be calculated from the primary and secondary voltage ratio, which is

Eprimary          Nprimary

Esecondary     Nsecondary

For example, if the ratio of the primary to secondary is 10:1, then the voltage on the secondary is 1/10 the voltage on the primary. Place 10 volts on the primary, and you get one volt on the secondary; 20 volts translates into two volts. Simple enough. Now we know the primary voltage (70 volts), but not the secondary voltage. However, we do know the power (10 watts) and the secondary impedance (16 ohms), which will give us the secondary voltage using the formula.

P = E2/R or E2 = PR
E2 = 16 x 10 = 160
E = 12.65

turns ratio = Eprimary/Esecondary  = 70/12.65 = 5.53

Zprimary = Zsecondary * (turns ratio)2
Zprimary = 16 * (5.53)2 = 16 * 30.6
Zprimary = 490 ohms

Here's another formula that's often used to calculate transformer impedance that eliminates the extra step of determining the turns ratio:

Zprimary / Zsecondary = (Eprimary / Esecondary)2
Zprimary = (Eprimary / Esecondary)2 * Zsecondary
Zprimary = (70/12.65)2 * 16
Zprimary = 30.6 * 16 = 490 ohms

Both methods show us that the impedance seen by the LM353 amplifier is approximately 500 ohms, a standard audio transformer impedance.