Broadband filter matching design

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I have a 3rd order differential, passive low-pass filter prototype I'd  
like to wideband-match into a load. Source impedance is on the order of  
10 ohms single-ended equivalent and the load on the order of 100 ohms.

If I try to use the LC filter itself to match those two the calculator  
(this is for single-ended) e.g.:


shows insertion loss is unacceptably high. A wideband matching  
transformer somewhere in-line seems necessary.

But there are a lot of variables here, what impedance the prototype  
should be normalized to, how to scale the values of the filter prototype  
if say the inductance ends up unreasonably small, whether the matching  
transformer comes at the source end or the load end and what impedance  
it should match into, etc.

Just generally looking for advice on how to design a topology of this  
type to minimize insertion loss and loading of the source

Re: Broadband filter matching design
Well yeah, at DC you can only get out whatever voltage or current that you  
put in.  If that's what you want, then that's what you want, and the minimum  
insertion loss is the ratio of impedances, simple as that.

It could be better around the transition band (over a bandwidth on the order  
of the reciprocal ratio of impedances), but not wideband.  Obviously,  
matching doesn't work at DC.

If you need better, and can afford a transformer (and loss of DC response),  
then yeah, you can bring that down to 0dB minimum insertion loss.


Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design
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Re: Broadband filter matching design
On 1/17/2021 1:30 PM, Tim Williams wrote:
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Thanks Tim. Not sure if it would be better to put the matching  
transformer at the input or output port; here I have a 3rd order  
Legendre filter going from 10 to 75 and then a transformer on the output  
port into a 150 ohm load.

This is for a 5-level stepped sine inverter at a couple MHz, floating load.

I haven't prototyped this one yet the last version I built was OK but I  
mucked up the H-bridge switching timing so it gave the correct output  
but the efficiency stunk. Working on re-designing the output filter  
while I'm at it. The differential inductor is #2 material powdered iron  
toroid and the common-mode choke and transformer would be like a 43  
material ferrite I guess.

Efficiency of this looks a lot better in the sim so far than when the  
switch timings are wrong but definitely not sure if this is an optimal  
filter design...





Re: Broadband filter matching design
On Saturday, January 16, 2021 at 7:38:22 AM UTC-8, bitrex wrote:
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First, a note on "insertion loss" nomenclature. The RF-Tools graphing is in
correctly calling "transducer loss" insertion loss. Note that at DC, the vo
ltage at the input is the same as the voltage at the output (across the loa
d) and this is also the voltage across the load when the filter is not *ins
erted." So, the filter has no insertion loss at DC (or the peaks of the rip

Transducer loss and insertion loss are only the same thing when the load an
d source impedances are equal. I am not criticizing RF-Tools?I can'
t because I have been just as sloppy in casual conversation, but I did want
 to raise the point.[1]  Your filter did not have "high insertion loss," bu
t regardless, I think you are saying you want to extract as much power as p
ossible out of your 10 ohm source.

 mean you don't really need a low-pass response, which includes DC. I menti
on this because bandpass filters have innate impedance transforming capabil
ity. This transforming quality is inversely related to the fractional bandw
idth required. You said it was a "sine inverter at a couple MHz." Tell me w
hat you really need (what is the center frequency and minimum bandwidth). T
ell me about your rejection and reflection coefficient masks too.

If you need a wide bandwidth, you probably are into a transformer, but even
 with that you may be able to reduce the transformation amount.

Out of curiosity, why a Legendre filter?  I've never had a reason to use th
at approximation, so its usage naturally leads to my question.

[1] Even the titans can get it wrong. Blinchikoff and Zverev get it wrong i
n "Filtering in the Time and Frequency Domains" (pp.274-275). Besser and Gi
lmore get it right ("Practical RF Circuit Design," pp.194-196, p.418). Dani
els gets it right ("Approximation Methods for Electronic Filter Design," pp
.293-294). Geffe gets it right ("Simplified Modern Filter Design," pp.76-78
). Kuo gets it right ("Network Analysis and Synthesis," pp.429-431).

Re: Broadband filter matching design

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Try the non-linear solver in MS Excel.

There is, today, no real need to be concerned with any of the historical  
traditional methods of design filters. They were invented, essentially,  
because closed form solutions were required to make the problems tractable.  
Computers make this a complete non issue.

One can setup Excel  to take a graph shape, and get it to minimise or  
maximise a function subject to twiddling any number of variables. One can  
set it up to proportionally minimise error, for example error =  
a*phase_error + (1-a)*gain error.

It can be anything you want, and the solver just blindly spits out the best  
values, for example, once setup, the RLC values of a filter.

A point worth noting is that for example, a Bessel filter is the traditional  
way to achieve a linear phase filter. However, this filter was never the  
"best", it was just a convents way of getting a "good" filter. Brute force  
computation  gets a better result. For a second order filter an analytical  
calculation gave the well known result 2/pi. Today, brute force for 100th  
order is trivial.

Pretty much the whole rational of Butterworth, Chebychev, elliptic etc has  
all been superseded. The "best" filter performance is never a standard  

The key point here, is that one doesn't need to have much knowledge of  
filter design at all. Even throwing down a random topology of components can  
work. The solver just spits out the optimum values to match the desired  

I have used the method to generate chebychev coefficients for linearizing a  
varactor of a VCXO

-- Kevin Aylward - SuperSpice

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