Connect antenna to FM circuit
For maximum power transfer to the antenna you should match your output circuit to the impedance that your circuit &quot;sees&quot; at the output: cable + antenna.
Coaxial cables have an impedance of 50/75/100 Ohm no matter how long the cable it is.
Antennas have an impedance of 50/75 Ohm only if you install the antenna according to the manufacturer's specifications. For example you may be asked to put a ground plane.

Example:
if your &quot;cable + antenna&quot; system has, at the frequency of your oscillator, an impedance Z:
Z = 44 + 12j

Than you have to add an impedance matching circuit that has an impedance Z*:
Z* = 44 - 12j

Use a coaxial connector to bring the signal from the circuit to the coax cable.
The matching circuit is usually made of L and C components.

There are many programs (some are free, some are open source, some are on-line, some need a commercial license) that can build your matching network.
Optenni Lab
MatchCalc™ RF Design Calculator (QORVO)
RF Impedance Matching Calculator (Analog Devices)
You may also Google this: &quot;RF matching circuit synthesis program&quot; or &quot;Synthesis of passive LC networks to match complex loads to sources&quot;
Optenni is considered the king of all.
Radio Amateurs have their program but I forgot the name.
I got no affiliation to any of the companies I mentioned.

To measure the impedance of your &quot;cable + antenna&quot; system you need an antenna tester or a Vector Network Analyzer.