Wideband loops work by extracting signal current independent of frequency. You will find the theory completely different from traditional tuned loops. 

Two challenges present themselves when you try to use a traditional tuned loop as a wideband antenna. First is the self-resonance effect. Second is the frequency dependency of the signal voltage generated.

It turns out that if you short the loop ends together, operating the magnetic loop antenna as a closed loop or shorted circuit current transducer gets rid of both challenges and provides a very wideband antenna. Here’s how wideband loops work.

From Ohm’s Law, you know that current is equivalent to a voltage divided by an impedance. As shown above, the numerator voltage is a function of frequency, magnetic flux and loop area, or ƒ(ωBA).Think of this voltage as the driving force. At the same time, loop impedance – the denominator – opposes the force. Impedance in this circuit is comprised of loop reactance ωL, resistive losses in the loop R_LOOP and finally the resistance of the load resistor used to short the loop and collect current, R_LOAD.

Now, it turns out that with a properly designed loop, the loss and load resistances become very small compared to loop reactance. Your magic relationship to make a wideband loop is ωL >> R_LOAD > R_LOOP. When this relationship holds, that is when resistances are very much less than reactance in the denominator, the resistive terms effectively disappear. And, since you are then left with ω in both numerator and denominator, the frequency effect cancels out.

So, at the end of all this, you are left with loop current depending on magnetic flux generated by a passing signal, the area of the loop and the inductance of the loop. Increasing loop area and/or decreasing loop inductance will provide more signal to your receiver.

How Wideband Loops Work – Check the Assumptions

Does the relationship ωL >> R_LOAD > R_LOOP hold for a typical receiving loop? Pretty much, yes. For my one meter diameter aluminum test loop, there are three resistances involved in the loop. First is DC loss resistance which is negligible at around 100 μΩ. Second is radiation resistance, which increases with frequency but is typically less than one ohm. Third, and the main contributor is AC skin effect loss, which also increases with frequency but remains well under 100 mΩ.

On the other hand, inductive reactance ranges from 2 to 500 Ω. So, as long as my load resistance is very small (under 5 Ω and preferably much less) you will find that the inductive reactance remains an order of magnitude larger than either loss or load resistance.

The secret sauce is obtaining a very low load resistance at the amplifier input. If you can do this, the wideband loop will provide signal current independent of frequency over a very wide range of frequencies. The takeaway from this analysis is that none of the typical tuned loop amplifiers will work as they rely on high input impedance to extract voltage. You need something completely different.

If you want a deeper dive into the theory, check this article from Jochen Bauer.