# Characteristic Impedance of Differential Transmission Line

1. ## Characteristic Impedance of Differential Transmission Line

Thanks to members here, I learned that for a 2-port single-ended transmission line, I can obtained its characteristic impedance using:
Z0_meas = sqrt(Zopen*Zshort)

where:
Zopen is input impedance with output port open
Zshort is input impedance with output port shorted

In SPICE, I built a single-ended transmission line model and performed AC sims to obtain Zopen and Zshort to obtain Z0_meas.
Knowing that if I model a transmission line with many "transmission line unit elements" with R,L,G,C parameters per unit length, I get:
Z0_calc = sqrt((R+jwL)/(G+jwC))

My simulations to determine Z0_meas is identical to Z0_calc from 1Hz to 100GHz proving Z0_meas=sqrt(Zopen*Zshort) works!

However, how do I obtain Z0 for a differential transmission line with 4-ports?

Below is my thinking and let me know if it works or not:

What I was thinking of doing was driving the two input ports differentially. Then I would treat the two ports as though they were independent of each other. So I would do the same thing as was done for the single-ended line with Zopen and Zshort. This would give me Z0_plus=Z0_minus.

Then is it fair to say that Z0_diff = 2*Z0_plus = 2*Z0_minus?

To properly terminate a differential transmission line, I am thinking that I can:
Connect the two output ports with two resistors in series with value Z0_plus=Z0_minus. Let's call the node between the two resistors, node C:
1. Do not connect node C to anything it just connects the two resistors together.
OR
2. Connect node C to the output reference node which is ground. Since Node C is an AC virtual ground anyway, it should work the same as (1).

Let me know if my thinking on differential transmission line is correct.

Thanks again!

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2. ## Re: Characteristic Impedance of Differential Transmission Line

To make a complete differential transmission line model, differential and common mode impedance must be modeled separately. In SPICE, you need three TL components or a respectively complex lumped circuit.

Notice that the propagation delay of common mode and differential part aren't necessarily equal, except for the trivial case that either common mode or differential line have infinite impedance and can be omitted (either differential line without ground or no coupling between two single ended lines).

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3. ## Re: Characteristic Impedance of Differential Transmission Line

Originally Posted by FvM
To make a complete differential transmission line model, differential and common mode impedance must be modeled separately. In SPICE, you need three TL components or a respectively complex lumped circuit.

Notice that the propagation delay of common mode and differential part aren't necessarily equal, except for the trivial case that either common mode or differential line have infinite impedance and can be omitted (either differential line without ground or no coupling between two single ended lines).

Since I am using this transmission line only in differential mode, I guess my question is how to simulate to determine its characteristic impedance and do impedance matching. I know in a single-ended transmission line you can obtain it as:
Z0 = sqrt(Zshort*Zopen)

Does that work in differential transmission line in differential mode somehow?

(I understand now that the mode of operation means it will have a different characteristic between common mode and differential mode so thanks for that.)

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4. ## Re: Characteristic Impedance of Differential Transmission Line

If you have access to spectre or any simulator which can measure S11, you can drive the line deferentially while varying the source impedance. The value of source impedance which minimizes S11 is your differential characteristic impedance. Same can be done for common mode.

5. ## Re: Characteristic Impedance of Differential Transmission Line

Originally Posted by deba_fire
If you have access to spectre or any simulator which can measure S11, you can drive the line deferentially while varying the source impedance. The value of source impedance which minimizes S11 is your differential characteristic impedance. Same can be done for common mode.
That is not strictly correct. While the characteristic impedance for any mode in the modal domain is decoupled from other modes (i.e., there is only one scalar value), in the terminal domain the characteristic impedance couples multiple conductors -- i.e., it is a matrix.

As such, the correct characteristic impedance (in the terminal domain) will manifest itself as an impedance connecting each conductor to the others.

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6. ## Re: Characteristic Impedance of Differential Transmission Line

Differential Transmission Lines have 2 impedances.Even mode and odd mode.The characteristic impedance of a differential lines is composed of these two mode dependent characteristic impedances.For more information, "RF and Microwave Coupled-Line Circuits", Inder Bahl, Prakash Bhartia,Rajesh Mongia.
Artech House

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