Hier ist die Bedingung für den Stromtrafo angegeben:
Der Abschlußwiderstand der Sekundärspule muß in Bezug auf die Induktivität ausreichdend klein sein. (kein Leerlauf, Kurzschluß wäre ideal für die Stromübertragung, nur nicht zum Messen)

http://www.sensorsmag.com/articles/0799/26/main.shtml

Current Transformers
In the case of an ideal transformer, the above description would be the end of the story. Nonideal transformers, however, require a few additional design considerations. For current measurement at low to moderate frequencies (<10 kHz), the most important considerations are mutual coupling and secondary reactance. Mutual coupling is the degree to which the flux generated by the primary winding passes through the secondary, and vice versa. For an effective transformer, try to get as high a degree of mutual coupling as possible. Fortunately, common architectures (e.g., toroids and E-cores) readily provide high degrees of coupling.
Appropriate amounts of reactance are also required for the transformer to behave in a close-to-ideal manner; the reactance of the secondary circuit at the frequencies of interest must be significantly higher (>10 *) than its total resistance. Otherwise the transformer's secondary current will not accurately reflect the primary current.