If the transducer is a piezo, it will exhibit strong impedance variation with frequency. There will be no one fixed optimum source impedance other than zero (or as close to zero as you can get). Also, if it is a piezo, you won't be varying the frequency very much. The best drive happens when excited at the resonant frequency. Because of the relatively high impedance, you may need a significantly high drive voltage. Typically a conventional audio power amplifier is not a good driver because they are designed to drive a low impedance (usually 4 ohms to 32 ohms).
Some piezo transducers are resonant above audio. But, if it is for underwater use, the frequency can be as low as 2KHz. You have to know the resonant frequency! If it is for echo-ranging, then transient response is critical.
This is not a very clear response, but it is very significant challenge to design a "generic piezo driver". Much more specific design guidelines can be provided if you can specify the piezo resonant frequency, the impedance at the resonant frequency, and the desired output power.
Jim Wagner Oregon Research Electronics
Given its size, that is likely to be an audio coupling transformer, rather than an AC mains transformer - assuming its core is separate metal laminations.
(If it has a ferrite core, then it may be designed for high frequency use, in a PSU, but it looks like metal laminations).
Audio coupling transformers usually fall into 2 classes : wide bandwidth for pro audio use (ideally 20Hz to 20kHz) or telephony, usually 300 to 3400Hz. The measurements you have made so far suggest the latter.
The transformer's performance is mainly determined by three quantities (and their interaction with the circuitry around it)
- Turns ratio (determines voltage gain)
- Primary inductance (determines LF performance)
- Leakage inductance (determines HF performance)
It's also worth knowing three more quantities:
- Primary resistance (measured at DC, presumably 1 ohm from your question)
- Secondary resistance (measured at DC)
- Leakage capacitance (can be indirectly determined)
Turns ratio is close to the best voltage ratio you measure, probably 3.6:1.
The ratio of secondary to primary resistances will be approximately the turns ratio squared (not exact, it depends on the nearest wire gauge) so your secondary R is probably about 13 (10 to 16) ohms.
Primary inductance is measured across the primary (duh!) with the secondary open circuit. If you can't measure inductance directly, you can connect a known capacitor in parallel and find the resonant frequency.
Now the primary inductance is effectively in parallel with the load (its purpose is to magnetise the core, generating the flux that communicates signal to the secondary). So it, combined with the source impedance of your signal generator, (actually that source impedance plus the 1 ohm primary resistance) form a series R-L circuit - which is the high pass filter you have observed. (600 ohms is a traditional source impedance in audio work, your signal generator may be different, maybe 50 ohms if it covers radio frequencies)
simulate this circuit – Schematic created using CircuitLab
You can improve the LF performance by driving the transformer from a low source impedance (e.g. an audio power amplifier) reducing R1.
You can't eliminate the primary resistance (R2) for perfect LF performance, but I've seen transformers driven from negative source impedances to partially cancel it. (Not a common trick : as you can probably guess, unstable when the transformer is replaced with a better one!)
Now the leakage inductance is measured in the same way, but with the secondary shorted. Smaller is better; it determines the high frequency performance of the transformer.
simulate this circuit
The leakage inductance forms a series L-R circuit with the load, which is R3 / turns SQUARED. So to get good high frequency response, keep R3 high.
But there is a practical limit on this : the leakage capacitance C1 resonates with leakage inductance, limiting the high frequency response, and providing a frequency response peak. Use this peak to determine the capacitance. It can be controlled (damped) by reducing the value of R3 or a separate Zobel network
Best Answer
The turns ratio will give you the impedance ratio and the voltage ratio. The choice of turns depends on the core type and size and the expected voltage that you need to drive through the transformer so that it does not saturate.
Typically one tried to have an equal size coil for primary and secondary for an isolation transformer. There will be some clever calculation to work out the optimal power transfer for a given coil size as more turns will eventually increase the DC resistance too high.
Your turns ratio will be quite high so the primary will be very fine wire. Winding so much on a toroid may be uneconomical in production volumes, pot cores and E-I stacks are still common.
Here is a link to two reference manuals Wolpert's and Whitlocks that can offer you some further guidelines. You will need to find out the parameters of the core you plan to use and see if you can cope with the required turns in the toroid.