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# Newbie: frequency relation with permitivity of substrate

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#### luckyali

##### Member level 5
hi every one,
I have designed a power divider for 20 Ghz, simulated results were S12=S13=-3dB, but the tested measured result deviates heavily from simulated results. out put powers are S12= -4 db and S13 = -4.9 db.
the substrate i have used was roger Er=3.35 and SMA connectors are used.

for the search of reason behind these losses. I read somewhere that it is preferable to use Alumina or any other material with higher Er e.g 9... so I have a very common question that what's the relation between dielectric constant of a material and operation frequency.

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A complete S-parameter measurement will tell if you are actually facing losses ór simply mismatch. According to substrate data, i would expect a few 0.1 dB true losses and mismatch for anything above it.

The difference between ports suggests that the problem is related to mechanical inaccuracies. A higher Er substrate will involve reduced dimensions respective less relative accuracy and most likely tighten the problem.

All in all it sounds like a problem of unrealistic assumptions.

What kind of simulation did you perform? A full EM simulation of the geometry including SMA connectors or just ideal transmission line segments?

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You can follow AWR examples, and your design is lack of a isolator resistor.
For 20G, you need a careful design for everything.

At 20GHz, I would think that the solder job on the SMA pins is critical. Look at the thickness of
your traces compared to the solder joints.

Take off about 30% of the solder of each SMA pin. One at a time, and re-measure. I would
expect significant changes.

Cheers

at 20GHz, your wavelength is 1.5cm in air, if you use substrate with Er=3, then wavelength is shrunk further to 5mm. What is the size of your design? Any unwanted thing that has a size of around mm level will become a defect.

At anything over 6GHz, it will be a struggle not to lose some at the coaxial - microstrip transition.
At 20Ghz, even the shape of the fillet into the the trace can lose 0.3dB.
SMB connectors interfaces might lose 0.3dB each - or more.
At 20Ghz, think about the substrate loss. It is not the dielectric constant that gives loss, it is the loss tangent.

Example: The insertion loss of 50 Ohm microstrip at 20Ghz on Rogers RO4350B laminate is about 0.5dB/inch!

Consider a Wilkinson style splitter. It might not be as sensitive to layout.

Easily the most awkward thing about the coax transition is the connection under the PCB to the box ground right next to the SMB connector. The transfomation of the TEM radial field in the coax onto microstrip makes a messy radiation problem right there.

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At 20Ghz, think about the substrate loss. It is not the dielectric constant that gives loss, it is the loss tangent.

that clicked me. I looked back into the laminate data sheet and found at f=18 GHz, the insertion losses of RO4003 are -0.3db /inch. since my design is around 20 Ghz I can assume that to be the reason of power losses.

Consider a Wilkinson style splitter. It might not be as sensitive to layout.

I tried to simulate one but was not successful, at such high frequency we use thin film resistors. i was afraid since i am having standart smt 0402 resistos the output lines are too much close to each other and may produce coupling...

I nearly replied - and then I had to think about it. This is more considered.

Wilkinsons are fine things, and have been used at extreme frequencies, in miniature form on high dielectric constant substrates. There are even multi-stage versions to increase bandwidth. They are loved because an amplifier can catastrophically fail in one branch while service continues 3dB down via the other. The highest frequency I have seen for one constructed on board is 10GHz.

I include some pictures before we say goodbye to them.

As you have pointed out, when the frequency is so high, a quarter wave size should not compete with the dimensions of a resistor, and you can see from the pictures the attempts to make the meeting at the resistor as isolated as possible.

Fortunately, one can come up with a structure that delivers the resistor effect while changing them into single terminated ports. This is a kind of half-way house between a rat-race hybrid and a Wilkinson. It is called a "Gysel" combiner. You use 5 ports to make a 2-way split. It has better bandwidth than a Wilkinson, indeed, the impedance of the cross branch can be used to tweak for bandwidth.

Here is a picture. and some temptation
The RLR looks better than 25dB over a useful range, getting down to 50dB at the design frequency.

If you make your terminations out of 100R resistors in parallel, sticking out sideways from the line each side, and landing on a radial stub with a via or two set at the centres, I think you might have a better chance at getting it to work than the splitter shown at the start of this discussion.

Take heed also all the earlier advice about mechanical inaccuracies, solder fillets (which when done right, can make a coax-to-microstrip transition quite good!). Good luck with it..

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