in the reference cited by @tomnexus are the calculations that I wanted. Thanks

@rclocher3 It is the most accepted answer so far, regardless of whether it is the only one, it brought me very close to the place I would like to be, which is to know a calculation as you mentioned well.

those spacecraft were built in 1977 !! amazing, I would like to see the schematic circuits! only discrete components i guess ..

@Phil I mean to find concrete examples of this type of communication, this is the point. en.wikipedia.org/wiki/Interstellar_communication

@tomnexus The original VCO has a range of 50Mhz around 1450Mhz approx. My intention is to lower it to 1090Mhz open loop and then modify the PLL in some way.

@tomnexus I added a photo of the circuit, I have not simulated it. With a resistance of 15K in the base the circuit works well in 1450Mhz. What I want to do is make it oscillate at 1090Mhz without changing the resonator, just adding a capacitor in parallel as seen in the photo, but it doesn't work. I'm going to try lowering the base R to 3K. How do you know that $S_ {11}$ > 1?

more in this post eevblog.com/forum/rf-microwave/…

@tomnexus R=74.5 and 10uF is a low pass filter for the power supply. It is very common to see this as a filter in commercial circuits

@tomnexus The circuit is working in a commercial microwave equipment. I am researching the subject at the moment, so what I am reading is studied with the concept of negative resistance oscillator.

you have some example of filters with discrete parts for MW? Thanks

@Phil In this paper they mention filters built with "lumped elements" A New Design of Lumped Element Bandpass Filter in L-Band