OK, based on your suggestions and the calculations you have posted, I can visualize the transformer. It will be small enough to hold in one hand.
Here is what I have done so far:
I will be using 750 KHz as my center frequency as an example. This frequency is used by the famous WSB.
WSB is a 50,000 watt clear channel broadcasting station in Atlanta, GA.
The antenna is located in Tucker, GA according to Wikipedia.
L = Total length of coiled wire
L = f/w = 299,792,458 (meter / second) / 2 * PI * 750,000 (/second)
= 299,792,458 / 2 * 3.14159 * 750,000 (meters) = 63.62 meters = 63.62 meters * .3048 ft / meter
= 19.39 feet
L = Length of each turn = 19.39 feet / 20 = 0.9695 feet = 11.63 inches
Circumference C = L; Diameter = Circumference / PI = 3.7 inches
H = Coil height = 0.2 * Diameter = 0.2 * (11.63 inches / PI)
= 0.74 inches
Max diameter of wire. Space between strands of wire is 62 percent of wire diameter.
20 turns take 0.74 inches ===> 1 turn takes 0.74 inches / 20 = 0.037 inches
0.037 inches = 162 percent of wire diameter ===> 100 percent of wire diameter = 0.037 / 1.62
Wire diameter = 0.02286 inches (max.)
AWG 23 has a diameter of 0.0226 inches / 0.573 mm.
AWG 23 has resistance of 66.79 ohms / Km. which is 20.36 mOhms / ft.
For 19.39 ft, the coil will have 395 mOhms or 0.395 Ohms resistance.
I thought it would be larger than this. So much for my intuition.
There is a reason why science has been successful and technology is widespread. Don't be afraid to do the math and apply the laws of physics.