Hi @kevinz,
Your first impression of “circular reasoning” is somewhat correct!
In applied electronics we break this circle using an approach which is know as interactive develpment.
A first approximation is done, and them depending upon the departure of the physical (realization) components from ideal, a forthcoming interaction is made and the results checked, and if the design still unsatisfactory, a new round is done.
Some answers to yours interests can be approached by educated guesses and overall analysis.
For example, in the (still example circuit, but it serves for this argument) filter subject of this thread, it is imediate that the voltage C1 needs to withstand is the voltage necessary to deliver 100 W to the 50 Ω load¹.
Also, as the simulation goes to a more real life situation you’ll need to ascertain what is the harmonic content the output stage of your transmitter (section if XMTR) and as a function of current FCC regulations what minimum attenuation would your filter need.
Another issue is that the output impedance of the power output stage is not very well modeled by a 50 Ω load (the overall efficiency would be low), on the other hand a definitive and “correct” impedance for this non linear piece of circuit is hard to come by, reason why it is normally approximated, in general taking in account the operating class of the output power device.
In the zipped project attached for simulation, the ‘in’ label is at the junction of R1 and L1, look at the dip of the voltage as the frequency progresses!
Also, note that except if you are willing to implement your power filter with air inductors, present use of toroidal cores brings the Q of the inductors to the neighborrough of 80.
The dissipation factor of generally available capacitor can be between 0.025 and 0.001 (rougly 40 ≤ Q ≤ 1000).
Far better would be if could get better behaviour models for your inductors and capacitors, as some manufacturers publish this info, some even as Spice models.
HTH
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As the complexity of the circuit (higher order filter) the approach may get cumbersome, so circuit simulation becomes an accelarator tool.
[1] I’ll postpone a whole (and fascinating) issue of the impact of a non ideal 1:1 SWR on a real life (antenna) load!