Stepped impedance lowpass filter - how to compensate lengths?

[Yansi]

Hi!

I have just fallen in love with experimenting with microwave stuff  Just out of my stupid curiosity, I am trying to design a stepped impedance lowpass filter. I have tried to obtain some useful sources of information round the web. One of them, a lecture from a Prof. T.L.Wu mentions "compensation of parasitic elements". However I do not fully understand, what that means and how to compensate for a filter with arbitrary length of elements.

I have attached the presentation.  On page 3 down, the two equations with tangents, underlined red. Do I understand it right I should put there a sum of every other (L versus C) elements?

So for example, If I have a 7th order filter, I have 4 capacitors and 3 inductors.  To compensate a length of any "L" transmission line in the filter, I have to put there a sum of tangents of all four capacitors in the filter, and do similar with the C length compensation?

Here's a link to the presentation: http://ntuemc.tw/upload/file/20110321102525847f2.pdf (Sorry, it didn't allow me to attach it)

Thank you for help,
Yan

[Yansi]

So this is the way I have understood how to calculate the lengths. Taking the formula from page 3 of the PDF above,  the length of L element should be this way. The K constant is the correcting part of the bottom formula, the sum of the tangents.

Is that right?

Thanks,
Y.

//EDIT: Sorry! A mistake! In the L length formula, there should be lambdaGL / 2pi not the other way round!

[Yansi]

Maybe I should make an example so we can better understand each other:

My design goal is a 0.5dB Chebyshev fc 1GHz, 7th order. 50ohm in, 50ohm out.

Using a 0.8mm (32mil) thick FR4 PCB (epsilon_r of 4.6). These impedances/TMLs were chosen.

Zo = 50ohm, 60mil wide, guided wavelength 162.5mm (effective epsilon_r 3.406)
Zc = 10ohm, 500mil wide, guided wavelength 146.8mm
Zl = 110ohm, 8mil wide, guided wavelength 175.5mm

The normalized filter coefficients are: 1.737, 1.258, 2.638, 1.344, 2.638, 1.258, 1.737
From the coefficients, I get this set of lumped element values: 5.5pF, 10nH, 8.4pF, 10.7nH, 8.4pF, 10nH, 5.5pF
So far so good. Now to calculate the uncompensated lengths:
L2 = L6 = 10nH = 17mm
L4 = 10.7nH = 18.4mm
C1 = C7 = 5.5pF = 8.3mm
C3=C5 = 8.4pF = 13mm

How should I compensate the lengths now? For each inductor (L2, L4, L6) should I use a sum of tangents of all capacitive elements from the filter?
Meaning the K in this case should be equal:  K = Zc * ( 2*tan(pi*8.3mm/10) +  2*tan(pi*13mm/10) )
Am I right?

//UPDATE:

The compensating coefficient K for all capacitor lengths in the filter is 9.3025 ohms or thereabout (hope I calculated those tangents right).
After trying to compensate L2(L6) - the 10nH inductor, the new length is 14.2mm instead of 17mm.  At least it seems a legit number, not some strange bullshit.

[uncle_bob]

Hi

Is this just a paper exercise or are you trying to actually build a filter?

Bob

[Yansi]

Doesn't really matter, so I don't understand such question.

PS: Will build the filter afterwards and measure the performance.

[uncle_bob]

Doesn't really matter, so I don't understand such question.

PS: Will build the filter afterwards and measure the performance.

Hi

It most emphatically matters !!!

If you are trying to actually build a working filter, there is a proper way to go about the task. If you simply want to play with a bunch of numbers for the fun of it .... that's a very different thing. Helping you with one is probably not going to help you with the other.

Bob

[Yansi]

So  tell us, what is the proper way? 


I don't see any other way than calculating the filter, simulating the result, if not good repeat steps 1 and 2, manufacture and test and if not good repeat from the beginning.

If you are going to suggest using some multi billion $ software for it, sorry, you don't have to.

[uncle_bob]

So  tell us, what is the proper way? 


I don't see any other way than calculating the filter, simulating the result, if not good repeat steps 1 and 2, manufacture and test and if not good repeat from the beginning.

If you are going to suggest using some multi billion $ software for it, sorry, you don't have to.

Hi

If the objective is to actually make a filter of higher than about third order ... the first step is to run some boards and model the parasitics that will always be present. Extracting them from a 7th order filter without a major test equipment budget ... not going to work. Even with microwave laminates there are things you need to model. If you are planning to do this with FR4 there are even more things to do.

Bob

[Yansi]

I have expected such answer.

"Don't do that, you don't have the equipment, you don't have a budget, you have to simulate that or that, fuck it"

Thanx for help and support. 





I have built the filter and made some first crude and cruel measurement. Upper trace being noise source directly, lower trace same through the filter. 0-3GHz sweep.  It does something. Now I should kill myself, probably?


EDIT: I hope that S53MV did know very good what he was doing with his 13th order lowpass on FR4 laminate.
http://lea.hamradio.si/~s53mv/spectana/sa/secondmixer.jpg

[rfeecs]

So this is the way I have understood how to calculate the lengths. Taking the formula from page 3 of the PDF above,  the length of L element should be this way. The K constant is the correcting part of the bottom formula, the sum of the tangents.

Is that right?

Thanks,
Y.

//EDIT: Sorry! A mistake! In the L length formula, there should be lambdaGL / 2pi not the other way round!

Doesn't look right.  He is saying that the low impedance elements are not just capacitors, but have some inductance.  And the high impedance inductive elements also have some capacitance.  So by "compensation" he means adjusting for this extra capacitance or inductance of the two elements that are on each side.  For example, for a high impedance inductive element, add (half of) the inductance of the two capacitive elements that are on each side of it.

Yes, in practice people would just use software to synthesize and simulate.  One free option for simulation is Sonnet Lite:
http://www.sonnetsoftware.com/products/lite/
which should be able to simulate a simple structure like this.

Even for EM simulation, getting the loss right can be tricky.  The loss can affect the shape of the filter roll off.  It may take some "calibration", comparing measured to simulated to improve simulation accuracy.

[Yansi]

Thank you for advice. That also was the second obvious, what the professor probably meant.

The filter I have already prototyped was calculated using what I have written above, ie. the compensation coefficient was the same for all elements, calculated from all components (which is probably wrong).
Too much shortened lengths of the elements could therefore explain why the filter cutoff is in reality not 1.00GHz, but somewhere between 1050 and 1100MHz. 

I don't have currently any microwave equipment other then the SA and a broadband noise source. I have also borrowed some chinese "USB RF something" ( https://sigrok.org/wiki/BG7TBL ) which claims being a 35-4400MHz spectrum analyzer and who knows what else, but trust me - it is a piece of barely useful shit. It's not even usable as a VCO, due to the 3rd harmonic being only about 12dB below the fundamental.    I was given the thing as unused kit bought from ebay and told, it might work also as a wobler - which would indeed be useful for sweeping such filters. Unfortunately, it can't work as a wobler, as it feeds the output exactly the same frequency, as the input mixer, resulting in DC IF, which is a nonsense (surprisingly, connecting OUT to IN of the device results in only some little more signal noise over the noisefloor).

Sonnet lite - yes! I have found this interesting tool, having one already installed. Will need to learn it first. It also seems to be very restricted, so dunno, what it could simulate and what not, in the Lite version.

Thanx,
Yan

[G0HZU]

If it's of any interest/use see below for a LPF design I did for 3200MHz.

I just entered this into Sonnet and it used about 100Mb of memory so this is above the 32Mb limit for Sonnet Lite. But you may find the techniques used to shrink up the filter to be interesting. This technique is old and well established and you can find stepped LPFs like this in many old school spectrum analysers for example.

I didn't calculate anything for this filter. I entered it all by hand from experience. You can see I didn't even make the end sections symmetrical. That was just sloppiness/laziness on my part. Note also that I originally drew this design in another SW program and I transferred it across to Sonnet today. I don't like using the Sonnet UI very much but I do like the performance/accuracy it offers

EDIT: I hope that S53MV did know very good what he was doing with his 13th order lowpass on FR4 laminate.
http://lea.hamradio.si/~s53mv/spectana/sa/secondmixer.jpg

If you do a design for a high order filter you will see that the middle sections are pretty much step and repeat. In my old simulation below the middle sections were the same on the first cut. I only had to slightly tweak the 'inductor' lines to get the response in the simulation.

[Yansi]

Thank you, that is an interesting idea, how to shrink the filter in size. I could probably at least make the inductive lines curled a little, to shrink its length. If you look at the mixer from S53MV, the output filter on the right side of the photo - just do it similar way.

Well...  I thought the 32MBytes were totally useless. So I need to find some errr... "medicine" to simulate even a simple filter . I really don't know, what the companies are thinking about us, hobbyists... But I know, they just don't care...

[G0HZU]

I had a quick go with the various memory saving options in Sonnet and I got the memory size down to just 13Mb for my filter. Presumably this would now be OK with Sonnet Lite? I have no way to verify this though...

It still seems to simulate the filter OK but it does complain about simulation issues with the test enclosure. You can simulate the filter in a box with/without a lid and sometimes you get warning messages to do with de embedding or resonances wrt the enclosure/box.

[G0HZU]

I also had a go at a quick and dirty 1000MHz LPF with low passband ripple. This filter uses the minimum cap topology so it starts and ends with a series inductance.  In the interests of speed, I cheated here and used a synthesis program to determine the dimensions but the idea is to show you that the circuit below just fits inside the 32Mb limit for Sonnet Lite without needing to resort to memory saving tricks.

You can see it is just starting to re enter at 3GHz and the filter will have poor stopband performance above 3GHz.

[uncle_bob]

I have expected such answer.

"Don't do that, you don't have the equipment, you don't have a budget, you have to simulate that or that, fuck it"

Thanx for help and support. 





I have built the filter and made some first crude and cruel measurement. Upper trace being noise source directly, lower trace same through the filter. 0-3GHz sweep.  It does something. Now I should kill myself, probably?


EDIT: I hope that S53MV did know very good what he was doing with his 13th order lowpass on FR4 laminate.
http://lea.hamradio.si/~s53mv/spectana/sa/secondmixer.jpg

Hi

Excuse me, but you are the one with a massive attitude here. Have you ever considered that *maybe* somebody else on the planet *might* matter other than yourself ?

The approach that works is pretty simple. Do some basic structures, do some easy measurements on them. Based on that data that can be done easily, move up to more complex structures.

Does that really sound like you can't possibly do it ??


Bob

[Yansi]

My friend made some simple simulation of my microstrip layout in CST suite, resulting in this. The filter seems to have a good rolloff and a correct cutoff, unfortunately for higher frequencies ( f > 3fc), there is a lot of nasty spurious responses.  The literature I have read suggests, that this type of filter (stepped impedance) is especially bad with those spurious responses. The question is, if such "crazy spurious garbagge" is often really that crazy.

I might also try to design and test another type of microstrip filter, like the one with a length of high impedance TML with various stubs along the length.

[G0HZU]

unfortunately for higher frequencies ( f > 3fc), there is a lot of nasty spurious responses.  The literature I have read suggests, that this type of filter (stepped impedance) is especially bad with those spurious responses.

Yes the filter will typically begin to show re entry modes at about 3F and upwards. Some printed filter types are even worse than this and they can only give a good stopband up to 2F.

One solution to this is to add a roofing LPF in series with your current filter. This will make a big difference but you still won't get good stopbands out at (say) 5F or 6F. However, in your case you could use a lumped filter if lumped components are allowed.

[Yansi]

Adding a second filter seems interesting idea, correlating probably with what I have seen in the Dave's teardown of the Siglent SA in episode #892. The input filter seems to be a two different types cascaded: First one being the high impedance TML with stubs and the second with some attenuation poles. ( https://youtu.be/-8fr_otW0q4?t=1363 )

Lumped components are not forbidden, but would you trust standard and common SMD LC stuff  having a usable Q at 1GHz or more, say 4GHz? I am sorry but have no experience with such high frequencies yet.

This whole work is meant as an exercise to gain some basic experience what is and what isn't possible to do at home. The overall motivation was to try some basic MW RF stuff for the upper amateur radio bands (mostly the 3.4GHz band) and also being tempted to try something like S53MV's diy spectrum analyser. However I would not like to build a copy of his work, I'd like to try something similar, but using more modern parts.
So the goal is not high, nor is it any kind of professional stuff, just me being (maybe sometimes too much) curious to try some new stuff. World would be boring without a challenge 

[nctnico]

The presentation in the first post is based on the book 'microstrip filters for rf/microwave applications' by Hong. I suggest to get that. It builds slowly towards building all kinds of microstrip filters and also has all the formulas to calculate the geometries. However you'll need to implement the formulas for calculating the widths of microstrips in an Excel sheet because you'll be needing those a lot.

[Yansi]

Thanks, will try to find the book.

I have already thought about making an excel sheet for it. But more probably I will make a simple application to do that, which would allow some features that excel does not (without learning the damn VB stuff).
Calculation them on a piece of paper might be not fast enough, but it's still doable.

By the way, how can I determine how much space is needed in between the TML element and other pieces of copper on the signal side of the PCB? Suppose I need to place the filter (or even only the 50ohm line) on a tight layout where space is sparse, how should I determine how close it can be to other (ground) element on the signal side of the PCB? Is there any rule of thumb?

[nctnico]

Thanks, will try to find the book.

I have already thought about making an excel sheet for it. But more probably I will make a simple application to do that, which would allow some features that excel does not (without learning the damn VB stuff).
Calculation them on a piece of paper might be not fast enough, but it's still doable.

By the way, how can I determine how much space is needed in between the TML element and other pieces of copper on the signal side of the PCB? Suppose I need to place the filter (or even only the 50ohm line) on a tight layout where space is sparse, how should I determine how close it can be to other (ground) element on the signal side of the PCB? Is there any rule of thumb?

Calculating a stepped impedance filter on paper is definitely doable especially if you start from a lumped element filter (look for a free program called 'svc filter'). I don't know any rule of thumb but I guess a few mm should do the trick. When messing with microstrip structures it is a good idea to learn how to use a tool like Sonnet lite although this will take some getting used to. With Sonnet you should be able to simulate your filter structure and you can play with effects of putting ground traces near microstrip objects.

[Yansi]

Yeah, I have already installed Sonnet, but I will need to get some courage to start using it :-) Currently not much spare time, maybe after a week or two.

I have already made up first legit use for such filter - as I've mentioned in my other thread about 9cm band transverter, I need a LO of 1627.5MHz. Yesterday, I have scored a VCO (MiniCircuits JTOS-1830-1) and a PLL (LMX2325) together with a stable 10MHz TCXO from an old and obsolete NORTEL wireless internet communication equipment.  I will  use the lowpass filter for the output of the LO, to get rid of the harmonics of the VCO (it has quite nasty output, but I think not as nasty, as the ADF4351 from the chinese junk "analyzer").

So my first "microwave" project will be a stable 1627.5MHz LO.

[nctnico]

The first thing you need to do in a Sonnet project is setup the dielectric layers. I think the standard material between ground and the first layer is air but ofcourse you want to change that to your circuit board material (likely FR4). You also need to set the height above the circuit because the simulation will assume a metal casing around the circuit.

[diyaudio]

I have expected such answer.

"Don't do that, you don't have the equipment, you don't have a budget, you have to simulate that or that, fuck it"

Thanx for help and support. 





I have built the filter and made some first crude and cruel measurement. Upper trace being noise source directly, lower trace same through the filter. 0-3GHz sweep.  It does something. Now I should kill myself, probably?


EDIT: I hope that S53MV did know very good what he was doing with his 13th order lowpass on FR4 laminate.
http://lea.hamradio.si/~s53mv/spectana/sa/secondmixer.jpg

thank you for submitting this I was patiently waiting for someone to post stuff about microstrip filters.
I cannot participate I have no equipment.

The book can be found here.
http://bbs.hwrf.com.cn/downebd/71081d1332166653-__microstrip_filters_for_rf_microwave_applications.pdf