# Most precise patch input impedance formulas.

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#### Terminator3

I hope somebody can share experience on patch impedance formula gives correct result.

This calculator gives me 234 Ohm impedance:
http://www.emtalk.com/mpacalc.php
and it seems that it uses formula similar to Zin= 90*(Er^2)/(Er-1) * (L/W)^2
or to G=W/(120*lambda0)*(1-1/24*(k0*H)^2), Zin=1/(2*G), k0=2*Pi/lambda0

This calculator gives 467 Ohm impedance:
http://www-antenna.ee.titech.ac.jp/~hira/hobby/edu/em/antenna/patch/rect/index.html
and uses formula Zi=0.5*Rr=0.5*90*(lambda0/W)^2
as w<0.35lambda0
(or w<lambda0 according to patch antenna primer by J P Silver):
G=1/90*(W/lambda0)^2
Zin=1/(2*G)
and can give the result similar to emtalk only for W>2lambda0 formula

also author of second page states something about impedance is twice or half in his experience.

Also it is unclear how to obtain patch impedance from Sonnet lite. It is possible using S11 value. but we must put some feeding line to add port. I also moved reference plane to patch, but impedance based on S11 value gives less than 100 ohm zin, which is unrealistic. Incorrect setup with autognd port on patch gives Zin around 200 ohms, but from formulas above it must be more like 400 Ohms. Please explain me in which direction shoul i move to clarify imput impedance approx. value.

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#### Terminator3

still have this question. How to properly determine patch edge impedance?

#### volker@muehlhaus

Here we can see the same problem: http://www.gunthard-kraus.de/Tutorial_Sonnet/pdf_English/Tutorial_Sonnet_e.pdf
edge impedance calculated is 197.1 Ohm (by calculator on EMtalk and not very correct patch autognd port in sonnet lite)
As the Sonnet support specialist, I had discussed the appnote with Gunthard. What he did there - place a port across the entire with of the patch - is wrong by design. The width of circuit ports in Sonnet and other similar EM simulators must be small compared to the wavelength. He violated that rule and this gives funny results - no surprise.

I can't comment on the correct method, but this EM calculation was definitely wrong.

Terminator3

### Terminator3

points: 2

#### Terminator3

Thank for you reply. Can i get correct result using thin feeding line with autognd port and reference plane at patch edge? Or maybe using via port near edge. I am going to try it tommorow. Actually i want to see difference less than 50...100 ohm between formulas i found and simulation result.

#### volker@muehlhaus

Thank for you reply. Can i get correct result using thin feeding line with autognd port and reference plane at patch edge?
I haven't tried that, but it should work. There will be some extra inductance from the step in width between the line and the patch, but it should work.

Actually, I have difficulties to understand the meaning/definition of that edge impedance for wide patches. Looking at the current density plots, I would think that it is different at the different locations along the egde?

Or maybe using via port near edge. I am going to try it tommorow.
Via port will have the via inductance included in results, which should be OK because we are looking at rather high impedance levels. I will be interesting to learn about your results!

#### Terminator3

In Sonnet Lite s11 magnitude around 0.44 and R=50*(1+s11)/(1-s11) around 128 Ohms. I used different feeding line width and length and it seems that reference plane works right. With formula i still get around 400 Ohms (Zin=0.5*90*(lambda0/W)^2).

I was hoping to find the answer in real dessign. But here is the funny part. I measured patch dimensions of two X-band microstrip sensor antennas on 1.0mm FR4. Feeding lines is around 0.3mm (100Ohm). It is interesting to note that one of the designs use inset feed (1.5mm deep) with 100 Ohm feeding line, but the other design directly connects patch to 100 Ohm line. Performance of antennas is similar, but oscillators use different transistors. Both designs patch height is around 6.2mm, and identical quarterwave stub length. I guess one of the design still have better matching, not sure which. I think the only way is to make two antennas and compare them. Also one antenna design proves that Sonnet Line is right (128 Ohm ~ 100 Ohm 0.3 line), while another design is more like with formula with 400 Ohms (1/4 patch height inset feed lowers 400 Ohm impedance to around 200 Ohm, which connects to ~100 Ohm line).

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