filter of the frequency multipliers
Little or tall people, all use LPF instead BPF because they have wider range for rejected frequencies, LPF usually don’t have parasitic resonances, usually for the same number of poles LPF has less inband insertion loss and less ripple than BPF.
Well, in a purely abstract sort of way, one needs to drive and load a non-linear device with very specific impedances AT EACH AND EVERY FREQUENCY. A lowpass filter can be easily designed to be an open circuit at all frequencies above its cuttoff frequency, so that makes your job easy in that you know you are presenting an open circuit for all those frequencies.
For example, if you are using a varactor diode as the non-linear element, if you drive it thru a lowpass filter, and have the desired harmonic come out thru a bandpass filter, you can restrict RF currents to flow only at those two frequencies, and form one boundary set of impedance conditions that optimize that multiplier design.
If you instead tried to drive it with a bandpass filter, due to parasitics and foster's reactance theorem, it is hard to restrict currents from flowing at some intermediate frequencies. This might lead to oscillating instabilities, or at least less conversion efficiency.
Rich
