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Transmission Line Characteristic Impedance
This example will show users several ways of determining the characteristic impedance of a transmission line. This example will demonstrate with a CPW line, but the approach is general and can be applied to any transmission line structure, such as microstrip, stripline, coax, etc.
Overview
The AWR design environment has several ways you can calculate a line's characteristic impedance.
1. TXLINE is a free addition to AWR software that allows the user to enter geometry and calculate impedance or vice-versa. Please select Tools > TXLine to access this software. This approach will not work if you are only given s-parameters and have to determine the impedance only from the frequency response of the line.
2. Determine the impedance looking into one side of the line at the frequency where the line is quarter wavelength long. Then using the quarter wavelength transformer equation, calculate the characteristic impedance of the line.
3. Set the port impedances on either side of the line to be a variable and tune or optimize the impedance until the line is perfectly matched, the value of the port impedances is the characteristic impedance of your line.
Techniques 2 and 3 are discussed in more detail below.
Technique 2
In the project, please see the graphs Normalized and Input Impedance. The Normalized graph is showing the s-parameters of the line on a smith chart. The Input Impedance plot is looking at the impedance looking into port 1 of the schematic. The most important aspect of this approach is that we want to simulate either a long enough line or high enough in frequency such that the line is quarter wavelength a frequency simulated. Notice the marker on the Normalized plot is crossing the real axis at 11.6 GHz so in this example, we have met these criteria.
From impedance matching theory, you can calculate the characteristic impedance of a quarter wave transformer, by this equation:
Zc = sqrt(Zo*ZL)
Where Zc is the characteristic impedance of the quarter wavelength line, ZL is the load impedance and Zo is the impedance you are matching to. We know that ZL in this case is 50 ohms, due to the port impedance setting. Then we read what the impedance is at quarter wavelength. This impedance can be read from the smith chart where the response crosses the real axis or from the minimum or maximum of the Input Impedance graph. From either approaches, this value is 28 ohms. Using the equation above, the characteristic impedance of the line is 37.42 ohms.
Technique 3
In this project, please see the graphs Normalized and S11. We are plotting both S11 on a smith chart and a rectangular plot. Now notice that the impedance on each port of the line is set to a variable z which is set equal to 50 ohms. This variable can be tuned and/or optimized. Tune this value until S11 is at the center of the smith chart or is below -30 dB on the rectangular plot. At this point the characteristic impedance of the line is the value of this variable. By changing the port impedances, we are changing the system impedance until we have a perfectly matched system.
Note, one advantage of this approach is you can use the optimizer. The variable z has also set to be optimized. Please run any optimizer and watch the value of z approach the value of 34 ohms, very close to the value previously calculated.
Comments
If you run EM simulation or just have two port s-parameter data, the approach is the same. The only difference is that the model in your schematic would be a subcircuit of either the s-parameter data or the EM Simulation.
Exercises
Try determining the characteristic impedances of different width lines. Try a line with a characteristic impedance greater than 50 ohms (set W = 0.005mm).
Try the same exercises with an electrically short line (set L = 0.5 mm). Notice how you cannot determine the value accurately with a short line.
Try different transmission structures such as microstrip lines or coaxial lines.
Schematic - CPW_Line
Graph - Normalized
Graph - S11
Graph - Input Impedance