The regulation characteristics of a transformer can be specified by three complex parameters, commonly the magnetizing admittance, and the primary and secondary impedances. The paper shows that for practical purposes a no-load admittance, a source impedance, and a complex ratio, form a more convenient system of parameters. The relationship between the two systems is set out diagrammatically.The advantages of this approach become pronounced when an exact theory is required. The theory is applied to the interpretation of test results on a transformer supplying a variable-resistance load. It is shown that even when the no-load current is large, the primary and secondary current vectors can be represented as terminating upon a common circular locus.