Roy, W7EL wrote:
"---feedpoint impedance of 35-j370 at 3.8 MHz. Choose an inductor value
and let me know what the output : input current ratio would be for that
inductor at the base of the antenna. Assume that the inductor is
physically small."

I`ll assume the inductor has no resistance, loss or radiation.

No loss or radiation means the inductance only delays current in the
antenna circuit by the phase angle impedance makes with resistance in
the circuit.

We need 370 ohms of inductive reactance to counteract the capacitive
reactance of the too short antenna. That calculates to 10.926
microhenry.

The current into the resonant antenna circuit is E/R = E/35

The current into the too short antenna alone is E/Z = E/ 371.65

The output : input ratio of the inductor is very nearly one because the
coil is lossless and its size is insignificant in terms of wavelength.

Best regards, Richard Harrison, KB5WZI

Hm. Let's suppose the inductor had a loss resistance of, say, 35 ohms
(equal to the resistive part of the antenna input Z). What would the
ratio be then? This is assuming the loss is dissipative and not "loss"
due to radiation.

Roy Lewallen, W7EL

Richard Harrison wrote:
. . .
The output : input ratio of the inductor is very nearly one because the
coil is lossless and its size is insignificant in terms of wavelength.