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jabb
Post subject: Transmission line Matching network Posted: Wed Nov 01, 2006 1:12 am

Captain

Joined: Tue Apr 18, 2006 10:40 pm
Posts: 9
hi...i have couple of question on basic transmission line matching network design:

how do you choose what Zo (characteristic impedance) one might want for the matching series and stubs? since they are matching networks Zo doesn't have to be 50 Ohm then how do you go about selecting it? does higher Zo mean lower alpha (attenuation loss)? in other words, is Zo proportional to 1/alpha?

what exactly is dispersion and which has less dispersion: microstrip or coplanar? how is diespersion related to attenuation and Zo. thanks


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IR
Post subject: Posted: Thu Nov 02, 2006 2:41 pm

Site Admin


Joined: Mon Jun 27, 2005 2:02 pm
Posts: 373
Location: Germany
Hello jabb,

The 50-ohm characteristic impedance is a compromise between the need for minimum attenuation and the ability to deliver maximal power.
In a system of Zo=77 ohm, there is a minimal attenuation and in a system of Zo=33 ohm there is maximal power capability. Another consideration is the dimension (Width9 of the line depending on the substrate and frequency. So 50 ohm was chosen as the best trade-off to all of these constraints.

Dispersion is a different signal velocity versus the frequency - similar to the group delay in filters (After all a transmission line is a filter). The dispersion is much smaller in Coplanar and Stripline than in microstrip.

In the following line you can find more about the dispersion of different transmission lines:

http://www.microwaves101.com/encycloped ... ersion.cfm

_________________
Best regards,

- IR


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nubbage
Post subject: Posted: Fri Nov 03, 2006 4:38 am

General


Joined: Fri Feb 17, 2006 12:07 pm
Posts: 218
Location: London UK
In addition to the points IR has made, remember that the input impedance (and therefore the inductance or capacitance) of a short section of line depends on its intrinsic characteristic impedance, and the terminating impedance.

Zin = Z0 * (Zr + jZ0 * TAN(2pi*length/lambda))
___________________________________
(Z0 + jZr * TAN(2pi length/lambda))

Z0 is the intrinsic characteristic impedance, Zr is the terminating impedance, and lambda is the wavelength in the dielectric of the substrate. The transformer ratio is thus Z0/Zr

The intrinsic characteristic impedance is dependent on physical dimensions and the substrate permittivity.

So if a matching network calls for a particular L and C combination, then for a particular center frequency you have to find the right length, width and junction point for the series and shunt element traces.

Thank goodness we have software these days to do all this. But at least we need to know what the software is trying to do, in order to understand the answers and judge if they make sense.


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Augusto
Post subject: Posted: Wed Nov 29, 2006 8:12 pm

Lieutenant

Joined: Wed Nov 29, 2006 5:51 pm
Posts: 2
Quote:
how do you choose what Zo (characteristic impedance) one might want for the matching series and stubs?


It all depends mostly on what bandwidth you need.

In order to go from from a certain (usually) low impedance to a 50 ohm impedance you use matching techniques that will transform the impedance from the one you have at the device to a certain intermediate value from where you will use another element to move again. In most cases for today's higher frequency designs they are done using microstrip transmission lines and stubs that will rotate the impedance point in a smith chart around the transmission line's characteristic impedance and the degrees it rotates will be determined by the length of the transmission line.

There are infinity solutions to a matching network ranging from a one step to multiple steps using the transmission lines or capacitive stubs that you mentioned depending which way in the smith chart you want to rotate but they all have very different broadband responses.

The multiple step approach usually allows you to go from point A to point B keeping the broader bandwidth because the Q of the network will be lower.

Transformations with devices like baluns allow you to get your point B closer to the match requiring lower Q networks since you're starting from a closer point.

As a general rule of thumb broader bandwidth matches are better for temperature variations and for manufacturing because they allow for variations in device impedance with little or no degradation in performance.

Augusto.



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