With a VLF receiving loop, you usually do not need conventional 50-ohm impedance matching.
At VLF (say 10-30 kHz), your loop is electrically tiny. Its impedance is dominated by the inductance of the loop plus the resistance of the wire:
Z = R + j(2 x pi x f x L)
For your approximately 1.34 m loop using about 150 m of 22 SWG wire, the inductance could be several mH depending on the winding geometry.
For example, if the inductance were 5 mH at 20 kHz:
XL = 2 x pi x 20,000 x 0.005
XL = approximately 628 ohms
TUNING THE LOOP
A capacitor can be used to cancel the inductive reactance of the loop.
The resonant frequency is:
f = 1 / (2 x pi x sqrt(L x C))
At resonance:
XL = XC
The inductive and capacitive reactances cancel, leaving mainly the resistance of the loop.
For example, with:
L = 5 mH f = 20 kHz
the required capacitor would be approximately:
C = 1.27 nF
Therefore a capacitor decade box covering the nF range would be very useful for experimenting with the loop.
Note that 10 uF would be far too large to resonate a several-mH loop at 20 kHz.
RECOMMENDED ARRANGEMENT
Loop | | Tuning capacitor | | High impedance preamplifier | | Sound card / ADC | | Spectrum Lab
You generally do NOT need:
Loop -> 50-ohm matching network -> receiver
A high-input-impedance, low-noise preamplifier is usually preferable because a low impedance such as 50 ohms can heavily load the loop and reduce its Q and received signal.