Transformer with unmatched turns?
In your application, you wish to discover if the primary winding is centre-tapped, or if it is non-symmetrical. Many of these type transformers are wound with very fine wire. It is possible to measure wire resistance to get an estimate of turns ratio. If your ohmmeter has too poor resistance resolution, a bridge setup can measure wire resistance ratio of XFMR1 windings with considerable precision:







simulate this circuit &ndash; Schematic created using CircuitLab

In this case R2 (150 ohms) is included to limit current flow in the transformer wire. Adjust R1 until AM1 reads zero current. A voltmeter can be substituted, but will be less sensitive to the null point.
Upon adjusting AM1 to read zero current, remove R1 from the circuit, and measure resistance from wiper to one end, and resistance from wiper to the other end. If these resistances are equal (about 500 ohms), then your transformer is centre-tapped.

Why would a transformer not be centre-tapped? An intermediate-frequency amplifier is tuned to have a desired bandwidth. Its source and load impedance must reduce the tuned Q down to this desired bandwidth. An offset tap may allow the transistor amplifier to achieve a matched-impedance gain, while also loading Q to the desired bandwidth.
Your push-pull (balanced) amplifier benefits from symmetry. It will still work with a non-symmetric load, but one transistor will work much harder, and will distort before the other. If it is unbalanced, second-harmonic distortion will be significant: if it is balanced, even-order distortion is minimized (odd-order distortion becomes dominant).