Jerry, WA6E wrote:
"Just take two resonant antennas on whatever frequency you want, aim one
towards the repeater and the other towards your house.

Connect them with good coax as short as possible but the length must be
a multiple of 1/4 wave at the desired frequency."

Yes./ Maybe an even-multiple of 1/4wave. Odd-multiples may be
particularly bad.

Suppose the two antennas are identical, mounted high and in the clear.
The radiation resistance of one antenna matches the other, so we have a
matched source and load in both directions. Maximum power can be
intercepted and re-radiated.

A 1/4-wavelength transmission line inverts the impedance presented. A
too low impedance at one end becomes a too high impedace at the opposite
end and vice versa.

A 1/2-wave length of transmission line reoeats the impedance presented
to it at its opposite end, no matter what the Zo of the line is. If the
terminations are matched, a repetition through the line is exactly what
you want.

Best regards, Richard Harrison, KB5WZI