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How do I measure the inductance of this air round coil attached to the antenna of a tube radio? I have read something about LC tank circuit here but im not sure how I would apply it. Would I use the resistor already attached to the coil and probe it with my oscilloscope? Inductance is an unfamiliar territory for me and any assistance or advice would be great!!

enter image description here

I have the tube radio schematic below.

enter image description here

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    \$\begingroup\$ What equipment do you have available (in addition to the oscilloscope)? \$\endgroup\$ – Spehro Pefhany Dec 6 '17 at 5:19
  • \$\begingroup\$ I hope you realize that probing this radio with an oscilloscope is very dangerous. An oscilloscope's ground and the radio chassis ground may be at very different potentials. It is a serious shock hazard. Use a 1:1 isolation transformer on the 120V power line. \$\endgroup\$ – glen_geek Dec 6 '17 at 13:40
  • \$\begingroup\$ Thanks for this info!! I actually detached the antenna so it won't be connected to the radio circuit when I probe it. \$\endgroup\$ – Chris Manning Dec 6 '17 at 13:43
  • \$\begingroup\$ Am curious what your intentions are. L2 transformer is not required. Most installations did not use an external long-wire antenna. The loop antenna mounted on the back-board is required for radio reception if no external antenna is used....this is the way most folks used this radio in strong-signal urban regions. \$\endgroup\$ – glen_geek Dec 6 '17 at 17:06
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Most of L2 winding appears to be clumped onto one end of a 3300 ohm resistor. This resistor value does not seem to be included in the schematic. One end of L2 goes to the Ant screw terminal on the back panel. Schematic suggests that this winding of L2 should have about 8 ohms DC resistance, which you should be able to measure with a multimeter. The other end of L2 goes to the ground lug of the Phono jack (also mounted on the back panel, next to the Antenna screw terminal).
back panel RCA radio
The schematic also shows a link winding for L2, suggesting it has fewer turns. This makes L2 an air-wound transformer having four wires in total. Your photo is unclear, but I guess that this link winding goes up to two tie points mounted on the back panel. The measured resistance of this link winding should be smaller than the 8 ohm resistance of L2 primary.
Just to be clear, the loop antenna L1 is also in the photo. It should have two ends, one of which seems to be dangling, unconnected. This is a very important part of the radio, resonating with the big variable capacitor C20.

On to measure L2 inductance

L2 probably hasn't much inductance: estimating how much may influence how it should be measured. Some multimeters claim to measure "L", but give inaccurate results for small values, or are inaccurate where an inductor is lossy (like this one).
Jerry's suggestion to resonate L2 with a capacitor might be a good method. A function generator and oscilloscope are required, and a known-value capacitor. You might try this circuit:

schematic

simulate this circuit – Schematic created using CircuitLab

The 3.3K resistor is the one on whose body L2 is wound. You might try different values of capacitance for C1...something like 0.001uF - 0.01uF. Adjust function generator frequency watching for oscilloscope voltage to rise to a maximum. This voltage will likely be quite small. Start at the high-frequency end of your function generator's range.
\$ L_2 = {1 \over {(2PI F)^2C_1}} \$ where F is frequency (Hz), C1 is capacitance (farads), and L2 is inductance (henry).

Normally, the loop antenna L1 is the main source of radio signal. The small link winding of L2 might add some additional signal from an external long-wire antenna. If no antenna is connected (the usual case), the link winding of L2 is a very low impedance: almost a short circuit. The main purpose of L2 is to electrically lengthen an external antenna, (which was usually too short), and couple its signal into the main resonator: L1.

These direct-AC-line-connect radios would not pass safety code today. Although RCA was careful to not allow an external direct connection to their "ground" symbol, many component failures could cause such a deadly connection. In any case, the shields around I.F. transformers are potentially "hot". I would not plug anything into that back-panel phono jack. And I've learned the hard way that probing around circuits like this with an oscilloscope is very perilous: I still have my thumb, but a 'scope probe ground clip didn't survive.

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The obvious starting point would be to count (or estimate as accurately as possible) the total number of turns, length, and average diameter. Then plug them into the standard equation:

L = N2r2 / (228r + 254len)

Where:

N = number of turns
r = radius of coil in meters
len = length of coil (also in meters)

...and the result will be in millihenries.

Oh, and since it's apparently operating at RF, you'll need to de-rate that by a couple of percent or so to compensate for skin effect in the wire.

I think the intent is that the resistor only acts as a physical support, without affecting its inductance much, but I could be wrong about that. If you want to measure, you could build an LC tank circuit with a capacitor of known value, measure the resonant frequency, and compute the inductance from the normal equation, fr = 1/[2π√(LC)]

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