# Minimizing reflection coefficient of a low-pass filter

I'm trying to figure out (with not a lot of success) as to what I need to consider when I want to minimize reflection coefficient below a certain point. I'm trying to design a low-pass shunt stub filter with reflection coefficient below -12 dB (and a given $$\f_C\$$, but that part is easy).

Here's an example of a fifth-order Chebyshev low-pass filter with ideal components.

The reflection coefficient will spike in two spots of the pass-band on Chebyshev's prototype filters like so:

I tried different orders of Chebyshev filters and I tried swapping the filter design to Buttersworth/Bessel, but they all had their own characteristic reflection coefficients that way exceeded the desired value (example, Bessel's reflection coefficient would be very big towards f=0 Hz and would decline somewhat fast, though it was still too high of a value from what I desired).

So I have a few things I'm pondering about it.

If my pass-band is whatever it is, do I usually have to care about the reflection coefficient at extremely border cases (just at the cut-off frequency or after it or at near-zero frequencies when the cut-off frequency is at GHz scale)

What things should I consider when I want to minimize reflection coefficient up to a point?

And if someone thinks that I've fundamentally approached the problem in a bad manner, that'd be great to know as well.

• Chebyshev filters have staggered high Q resonance points to achieve the desired equal ripple in the pass band creating S11 zeros with two Pi filter loops for a 5th order LPF with 6dB loss.With Q's > 5 the sensitivity will be much greater than Bessel and much higher Group Delays . Bessel has the lowest Q's<1 but Cheby, has the steepest skirts due to the last pole Q So you spec must consider what you need for SNR S21 loss with PB ripple, group delay and S11 loss You cannot optimize one thing like S11 without affecting all the other parameters. .10th order reduces sensitivity to tolerances – Tony Stewart EE75 Mar 3 '19 at 0:16

If you are building a lossless filter, the only way that you can prevent power from going to the load is to reflect it back to the source. And a filter's response is continuous with regard to frequency (and keeping in mind that a dip down to $$\-\infty\$$dB is accompanied by a phase reversal, so the actual number is going through zero in a continuous manner).

So yes, you're fundamentally approaching this in the wrong way. If you want to maintain the load impedance on the source within limits then you need a diplexer, so the out-of-band energy from the source gets burnt up in a load resistor. This is not usually a thing for transmitting applications -- the only place that I've seen it (in my admittedly hobby approach to RF design) is between a mixer and an IF strip in a radio designed for the lowest possible 3IM products in the mixer.

• kudos for clarity – analogsystemsrf Mar 3 '19 at 2:32

Try an Inverse Chebychev LPF

This one at 2.5 GHz 0.02dB ripple.

You'll need to reduce the ripple so as to improve the reflection coefficient in band.

I suggest you to play a little bit with this filter tool: www.iowahills.com/Downloads/Iowa%20Hills%20RF%20Filters.zip

That way you'll get more familiar with the influence of design parameters on the frequency response of your filter.

In my opinion, if you don't need linear phase, you may consider using an elliptic filter. The topology is the same as Chebyshev II, but it exhibits much better out-of-band rejection.

• The only ting that matters is that I have attenuation of -3dB or greater at the pass-band (up to 2.6 GHz) and smaller than -10dB at the stop-band which is at 3.3 GHz and that the reflection coefficient is good enough. – Grak Mar 3 '19 at 8:10
• I arbitrarily set my R(load) to 50 Ohm in my ADS simulations, but in the demo tool 5th order Chebyshev can only be 32.5 Ohm, I think that's why my ADS simulations are suffering from high reflection coefficient. How can or should I figure out the R(load) at different orders? – Grak Mar 3 '19 at 12:39
• Well, it seems that's a bug. You'll need to set RLoad to 50 Ohm manually and press Calc – Andrés Martínez Mera Mar 4 '19 at 15:56
• Alternatively, you may find other filter design tools in the Internet. See, for example, calculatoredge.com/electronics/ch%20pi%20low%20pass.htm – Andrés Martínez Mera Mar 4 '19 at 15:58