[OP here]
To clarify my questions:
I'm building an AM broadcast receiver to be used in a non-standard application. It will use an existing wideband COTS software defined radio product that does not provide tuning information to the ferrite antenna. So I'dlike to be able to get enough antenna gain across the broadcast band from the antenna to avoid having to tune the antenna to resonance on each frequency. But space limitations dictate use of a ferrite.
This non-standard application DOES require knowledge of the antenna delay vs. frequency.
There's nothing fundamentally wrong with using an untuned antenna.
Gain is cheap nowadays, and AM reception is generally dominated by
external noise, not receiver noise figure. A good opamp or jfet will
get you below 1 nV/rootHz noise, so resonant gain isn't necessary. If
delay matters, it's better to not resonate the antenna.
An untuned loop, or an untuned ferrite rod, would work, far below
self-resonance. A few-turn loop would act like an almost ideal H-field
probe, and its gain and delay behavior are calculable.
What are you trying to do? Do you expect to have a lot of signal? Is
the transmitter nearby?