Calculation of resistor and capacitor values
Basically you have a source impedance that is approximately equal to R2 i.e. 200 ohms and you want to drive a 50 ohm coax that presumably will be terminated in 50 ohms to avoid reflections at the high frequencies (up to 3 GHz).

If you want the lowest frequency to pass to be (say) 10 Hz then C2 has to have a reactance of no more than 50 ohms at 10 Hz i.e. C2 is 318 uF minimum.

You have it shown at 10 nF so it is massively too small. On the other hand you cannot use a 330 uF capacitor to drive 3 GHz so you have to parallel up capacitors to spread their respective self-resonant-frequencies but, at 3 GHz the 330 uF capacitor is going to cause local reflections due to its very large size.

I think this problem is under-constrained or you're expectations need massaging.