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2nd December 2018, 18:28 #1
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[AWR Microwave Office ] Impedance of parallel connection of transmission lines
Hi All,
in last time, I'm confused due to some simulations in the AWR Environment. I've connected three TLs as a parrarel configuration, and I measured the total impedance of such circuit. According to circuit theory, and my knowledge  I should obserce impedance equal to Z0=Z_TL/3  so in case presented bellow  it should be Z0 = 2.481 ohms. Unfortunatelly, AWR is showing Z0=0.8428ohm... Proper value can be observed only when port impedance is divided by number of TLs (i.e. 3)  so then the port impedance is equal to 16.67 ohms, NOT to 50 ohms.
E.
Why is this hapen ? Must I consider changes of port impedance to measure "real" value of connection in this case ?
Best Regards,
E.

2nd December 2018, 22:02 #2
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
What do you mean with "total circuit impedance"? How do you measure it?
I think, your assumptions about the observed impedance are wrong. If the transmission lines are not terminated with their characteristic impedance, they transform the load impedance to a different value depending on the electrical length.

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2nd December 2018, 23:39 #3
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
By the term "total circuit impedance" I had in mind resultant resistance of presented configuration.
I understand your thoughts (I hope so...), that in such case TLs are working as impedance transformers. So maybe I'll ask about other thing  how should I measure the resultant impedance in AWR Office ? On this moment, I'm using ZIN measurement. Below I'm sending next schematic of circuit constructed under mentioned environment. The independent TL has characteristic impedance Z0=30 ohms. I'm assuming that, for resonant frequency (where electrical length is equal to 90 degrees), such element is working as a resistor. So parallel connection of three elements must give value of Z_All=10 ohms, and I notice this value only when impedance of ports is decresed by number of TLs (port impedance is equal to 50/3 ohms).
I'm confused about this fact, because I know that you are right with transforming, but I don't see straight the solution why I must divide port impedance to have proper value according to Ohm's law...

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3rd December 2018, 15:34 #4
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
Your independent TL Zo is not 30 ohms, but it is 39 ohms.
And I think that for your test you have to make the lines 180 degrees long, instead of 90 degrees.

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3rd December 2018, 15:54 #5
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
I get impedance of 30.5 ohm with simple and 38.6 with more trustworthy tools.
In any case you get maximal transformation with 90 degree electrical length. 50 ohm is transformed to about 3.4 ohm by 13 ohm (39/3) transmission line.

3rd December 2018, 16:52 #6
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
Circuit theory is not applicable in this case where you talk about waves and not signals. You should study on the concept of "characteristic impedance"
"By the term "total circuit impedance" I had in mind resultant resistance of presented configuration. "
You are trying to use Norton and Thevenin circuit models when dealing with waves. Circuit Theory, Wave Theory and Microwave Theory apply under different conditions. First step is, knowing which one to use in the right environment.

3rd December 2018, 19:32 #7
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
Thank You for all sugestions and answers.
I forgot about one important thing, that the ZIN measurement in AWR is measuring input impedance of lines (from port side)... so mentioned 30 ohms is input impedance, not characteristic one... (if I'm wrong  correct me). FvM you have absolutely right.
So a new question arises: how can we calculate mathemtically total input impedance of such configuration  I mean  how we can calculate impedance which is seen on port 1 or 2 ?
I used following conception:
1) Take ZIN values of TL1, TL2 and TL2
2) Calculate characteristic impedances of them (Z01=sqrt(ZIN1*50), and so on)
3) Calculate resultant impedance ZR according to the Ohm law (ktr  yes, I know that we shouldn't use this conception from circuit theory, so here I've first main issue)
4) Calculate output impedance by using impedance from 3) i.e. Zout = (ZR^2)/50  here we should have final value of such connection (and here is probably another issue)
Is there a simple explanation how to approach it?

3rd December 2018, 22:28 #8
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
so mentioned 30 ohms is input impedance, not characteristic one...
If the observed impedance is different from calculated 3.4 ohm value, the electrical length is probably not 90 degree.

4th December 2018, 19:17 #9
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
I see. FvM, vfone thank you for help.
I'm now wondering how it will be work, when lines will create a coupled structure. I know that the oddeven mode analysis can be used, but as I know such method is related only to circuits which have symmetry (so 2,4,6, etc. lines), so how discussed three line coupled structure can be considered ?

4th December 2018, 23:23 #10
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
I understand that the lines in the original example are uncoupled and have equal length. In this case, the impedance is simply divided.
I don't see coupled lines specified in the circuit example. However, if a structure has symmetrical coupling, it will only expose its common mode impedance and not behave different than the uncoupled.

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5th December 2018, 16:34 #11
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Re: [AWR Microwave Office ] Impedance of parallel connection of transmission lines
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