# There is no math for adding the functions of two parallel filters. Or is it?

I want to add two "parallel" functions. Each of them describes the frequency response of that individual filter. Put in other words, I want to see what the frequency response looks like when the two parallel filters are summed together.

Filter 1 is f(x) and filter 2 is g(x). So I go f(x)+g(x) must = the frequency response of the filters in parallel. No. Ofcourse not. Instead I get the frequency response of the filters added together like they were in series. Which they are, according to the math. Is there a solution for calculating (and graphing) filters that are in parallel?

I must be looking at the problem in a completely wrong way. The solution feels obvious and simple, yet, I cannot find it.

• What are these filters? A parallel combination behaves very differently if they are op-amp based filters with a high input impedance and zero output impednce, or passive LC filters designed to see a matched termination on their ports. – Neil_UK Mar 6 at 16:08
• Can you give a more concrete example? Like, what are f(x) and g(x), and can you show a schematic? I'm wondering if you may be a bit weak on the concepts of frequency-domain design and transfer functions. – TimWescott Mar 6 at 16:11
• They are passive LC filters with matched termination. Basically I don't want the functions to add magnitude when "interacting" with each other. Just blend together. Just like a passive LC circuit. Just imagine a voltage divider, with several taps of different ratios. Now connect two wires at different taps to gnd. They are in parallel. One of the wires will have the highest potential. Even if the wire with least potential is disconnected, the voltage will read the same as if it were not. They don't add. Thats my circuit simplified; a voltage divider. – Cape Zoloh Mar 6 at 17:26
• The filters will interact, because of finite input and finite output impedances. You must include that in the modeling, and to achieve the isolated behaviors, you must provide that on both input and output. – analogsystemsrf Mar 6 at 17:27
• Please post a schematic and give us a one-line summary of your education in EE. This is a solved problem in RF design (as @ThePhoton pointed out); I think the best guidance we can give you is what classes to take. – TimWescott Mar 6 at 17:41

f(x) $$\\cdot\$$ g(x) is the resultant effect of two filters that are in series.