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# Parallel microstrip transmission line impedance, wavelength

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#### Pow

##### Newbie level 3
Re: Parallel microstrip transmission line impedance, wavelen

I could not find formulae for calculating characteristic impedance and wavelength for transmission line consisting of 2 parallel strips separated by dielectric (PCB).

Can anyone help out?

Given parameters are:
trace width
trace thickness (I guess it shouldn't matter)
pcb height == spacing between two strips
dielectric constant of pcb
frequency

#### mr_ghz

##### Full Member level 5
Re: Parallel microstrip transmission line impedance, wavelen

Hi pow

Try the free AppCAD tool from Agilents' website. You can calculate microstrip and striplines.

Regards

#### sinatra

##### Full Member level 4
Re: Parallel microstrip transmission line impedance, wavelen

Hello Pow.
The approximate formulas to find characteristic impedance and effective epsylon can be found in:

"Transmission Line Design Handbook", Wadel, page 249

Those equations were published in the following paper (according to Wadels book):

"Computer-aided design models for broad-side coupled striplines and milimeter wave suspended substrate microstrip lines", Bhartia, Bracash and Pramanick, IEEE transaction on microwave theory and techniques, vol MTT-36, 11 november 1988,p.1476-1481

and correction on

MTT-37 , 10 october 1989, p.1658

If I'm not wrong that is the right paper to get those equations. I probably have already read it and implemented some of the equations in one of my personal codes....

Hope it helps.

S.

### Pow

Points: 2

#### jian

Re: Parallel microstrip transmission line impedance, wavelen

Please also try our free LineGauge Basic software from www.zeland.com. You can do the microstrip, stripline, coaxial line, rectangular waveguide etc. For parallel line, if you define the Substrate_Thickness_of_microstrip = 0.5 * Parallel_Strip_Separation, you will get Zc_of_Parallel_Strip = 2 * Zc_of_microstrip.

#### frannk

##### Member level 3
Re: Parallel microstrip transmission line impedance, wavelen

#### jian

Hi, Frannk:

I think POW is trying to find the Zc of the up and down case.

--------==strip1==----------
substrate
--------==strip2==----------

from his description. It is not for the parallel lines side by side in the follow:

----==strip1==------==strip2==-----
substrate
----------------------------------------

The up and down case should be almost identical to the microstrip case except there is a factor of 2 in the substrate height and the Zc.

#### Pow

##### Newbie level 3
Re: Parallel microstrip transmission line impedance, wavelen

mr_ghz said:
Try the free AppCAD tool from Agilents' website. You can calculate microstrip and striplines.
Unfortunately it does not support transmission line I'm looking for.

jian said:
Please also try our free LineGauge Basic software from www.zeland.com. You can do the microstrip, stripline, coaxial line, rectangular waveguide etc. For parallel line, if you define the Substrate_Thickness_of_microstrip = 0.5 * Parallel_Strip_Separation, you will get Zc_of_Parallel_Strip = 2 * Zc_of_microstrip.
I'm already using LineGauge, but unfortunately transmission line I'm looking for is not supported in LineGauge. Are you suggesting that Microstrip formulas can be used to calculate Zc for vertically spaced microstrip transmission line? This web page (**broken link removed**) suggests that solution for my case is much simpler than microstrip case, but I'm not sure it's correct though...

sinatra said:
Hello Pow.
The approximate formulas to find characteristic impedance and effective epsylon can be found in:

"Transmission Line Design Handbook", Wadel, page 249

Those equations were published in the following paper (according to Wadels book):

"Computer-aided design models for broad-side coupled striplines and milimeter wave suspended substrate microstrip lines", Bhartia, Bracash and Pramanick, IEEE transaction on microwave theory and techniques, vol MTT-36, 11 november 1988,p.1476-1481

and correction on

MTT-37 , 10 october 1989, p.1658

If I'm not wrong that is the right paper to get those equations. I probably have already read it and implemented some of the equations in one of my personal codes....

Hope it helps.

S.
Thanks. Are these papers available on the web somewhere? I don't have IEEE subscription.

#### tapa

##### Super Member
Re: Parallel microstrip transmission line impedance, wavelen

Hello

If you need a calc for diferential lines, it helps you with u-strip and striplines.

TaPa

#### Pow

##### Newbie level 3
Re: Parallel microstrip transmission line impedance, wavelen

tapa said:
If you need a calc for diferential lines, it helps you with u-strip and striplines.
No. As jian already pointed out, my transmission line is:
--------==strip1==----------
substrate
--------==strip2==----------

i.e. _vertically_ spaced strips, not horizontally.

#### biff44

Re: Parallel microstrip transmission line impedance, wavelen

The important thing that you should realize is that if there is air above and below then it does not have a wavelength, like a stripline coupler would. It has two different effective dielectric constants depending on how you excite the structure. In the even mode, the dielectric constant is almost the same as air. In the odd mode, the dielectric constant is almost the same as the dielectric material the two strips are printed on either side on.

#### jian

Hi, POW:

Yes. You can use the microstirp line's formula for the parallel plate structure. The only differences are:

Strip_separation = 2 * Microstrip_Substrate_Thickness
Zc_of_strips = 2 * Zs_microstrip.

Think about it, your case is just the microstrip plus its image with the ground plane removed.

Jian

#### sinatra

##### Full Member level 4
Re: Parallel microstrip transmission line impedance, wavelen

Hello jian.
I'm not sure that pow can use the calculataion you provided. Just looking at the aproximate formulas that describe this type of transmission lines you will see that the solution is not so simple.....

I propose again to take a look in the paper I described in my last post.

This transmission line is rarely used that 's why theres not so much information about it, but due to the higher coupling coeficients that can be obtained it can be attractive in some cases...... maybe in the case of narrow band couplers with high coupling coeficient, etc...

Sorry pow I searching in my stuff here but I couldn't find it, sorry again. Anyway I will keep trying to find it.

You can try also to take a look in the book I proposed. This is a good book but unfortunately there ae many typing errors in many of the equations described.....but anyway you should take a look on it.

S.

#### jian

Re: Parallel microstrip transmission line impedance, wavelen

Hi, Sinatra:

In my opinion, it is like what I said.

For a microstrip, we have the boundary as:

--------==strip==------ P = V
substrate h
=====ground====== p = 0

Fro a parallel line, the boundary is:

---------==strip==------ p = V/2

substrate H

---------==strip==-------- p = - V/2

You an see it as:

----------==strip==-------- P = V/2
substrate
-------symmetry plane with zero potential---
subsrate
----------==strip==-------- P = - V/2

Basically, you can consider the "symmetry plane with zero potential" as the ground of the microstrip case. The upper part of the coupled strip structure has the same field distribution as the microstrip case. If you make sure the H = 2 * h, you will get the Zc_coupled_strips = Zc_microstrip

Best regards,

#### rautio

##### Full Member level 5
Re: Parallel microstrip transmission line impedance, wavelen

Hi Folks.

If there is no third conductor (like a ground plane), only the odd mode works to DC. The even mode can not propagate at DC. At RF, the even mode would be similar to a surface wave.

Assuming all you want is the odd mode, notice that there is a virtual ground plane mid way between the two strips:

----------====Strip 1====-------------Voltage = +Vo, Current = +Io

---------------------------------------------Virtual ground plane, Voltage = 0

----------====Strip 2====-------------Voltage = -Vo, Current = -Io

This looks just like two microstrip lines sharing a single (virtual) ground plane!

Let's say you have one of the microstrip lines and you excite it with Vo volts connected between the virtual ground and Strip 1. This generates Current Io flowing on the micrstrip line.

The equivalent 2 strip line will have 2Vo connected between strip 1 and strip 2, but exactly the same Io flowing in both lines. The current flows into the top strip (positive current) and flows out of the bottom strip (negative current).

Thus the impedance of the two strip line is exactly twice the impedance of one of the microstrip lines. The impedance of one microstrip line (with substrate thickness set to half of your PCB thickness) is calculated by many many different programs. Just double it to get the impedance for your double strip line.

The velocity of propagation is the same for both the microstrip and the double strip line.

Post script -- I see Jian posted essentially the same description just a few minutes before I did. It seems we both agree completely.

#### jian

Re: Parallel microstrip transmission line impedance, wavelen

Hi:

Actually, my first posting is completely correct. I forgot a factor of 2 in my second posting.

Zc_coupled_strips = 2 * Zc_microstrip

Have a nice weekend!

Best regards,

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