Filter Design (Low Pass Prototype Method)

In the Low Pass Prototype Method for filter design, after choosing the order N and the tolerance of the filter according to the design specifications, we have to look at some tables with the normalized impedances gk, with k = 1,...,N+1.

My doubt is about g0 and gN+1. Do you know what they represent and how to choose their values?

• What do you mean by binomial filter? can you provide a reference for that? Jun 24, 2019 at 21:24
• I mean a Butterworth filter. mwl.diet.uniroma1.it/people/pisa/RFELSYS/L08_FILTERS.pdf Jun 24, 2019 at 21:55
• Please edit your question rather than just clarifying in the comments. Jun 25, 2019 at 0:51

g0 and gN+1 are the impedances that are driving the filter and loading the filter respectively.

Normally they are the same, and 90% of people on the planet use 50 ohms for the final filter, because it's a de facto standard, a reasonable value, and makes the filters easy to test, and to incorporate into other equipment. Another common value is 75 ohms, because it's a better match for the video and receiver industry.

In some cases, a filter is used to match a finite impedance to zero or infinity (short or open circuit), use tables with g0 and gN+1 set to zero or infinity as needed. An even order Cheby filter can also be used to get finite ratios between g0 and gN+1, again use the tables with them set to the desired ratio.

I'll illustrate how/why you might use a filter with an infinite impedance on one port. Let's say you wanted to drive a capacitive load (say a Kerr cell or piezo transducer) with a reasonably flat frequency response. You could design a filter with an infinite gN+1, then reduce the value of the final shunt capacitor to absorb the value of the capacitive load. The finite input impedance of the filter is now much easier to drive than the large capacitance of the original load. Obviously the filter bandwidth has to be adequate for the frequency range you intend to drive, and the final capacitor has to be large enough to absorb the load, these set limits on the filter design.

• I have another question related to the design of this kind of filters. How can I design them if the source and load impedance are not 50 Ohm? The filter's frequency response will be the same? I thought that if it is not the same, it is possible to build a proper matching network, but maybe there is a better design procedure for these filters in this case Jul 14, 2019 at 5:43