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Using atlc with coupled lines

Starting with version 4.0.0 of atlc, coupled lines can be analysed too. The support for coupled lines is not finished yet, and some bugs do remain. However, it is possible to calculate the properties of a pair of coupled lines in vacuum. Mixed dielectric, or any dielectric other than a vacuum is not currently supported.

Consider the transmission lines below, which has three metal conductors - a ground shown in green and the two inner conductors shown (shown red and blue) coupled together.

coupled lines

Such a structure has two characteristic impedances - an odd mode impedance Zodd and an even mode impedance Zeven. If the structure is drawn in red, blue and green, atlc will interpret this as a coupler and compute both impedances.

wren  % atlc -v  couplerxx.bmp

couplerxx.bmp Er= 1.0000 C= 55.1412 pF/m L= 201.7820 nH/m Zo= N/A Ohms Zodd= 60.4927 Ohms Zeven= N/A Ohms v= 2.9979 e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 54.1717 pF/m L= 205.3932 nH/m Zo= N/A Ohms Zodd= 61.5753 Ohms Zeven= N/A Ohms v= 2.9979 e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 54.0835 pF/m L= 205.7283 nH/m Zo= N/A Ohms Zodd= 61.6758 Ohms Zeven= N/A Ohms v= 2.9979 e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 54.0683 pF/m L= 205.7862 nH/m Zo= N/A Ohms Zodd= 61.6931 Ohms Zeven= N/A Ohms v= 2.9979 e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 54.0657 pF/m L= 205.7958 nH/m Zo= N/A Ohms Zodd= 61.6960 Ohms Zeven= N/A Ohms v= 2.99792e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 36.6079 pF/m L= 303.9368 nH/m Zo= 74.9774 Ohms Zodd= 61.6960 Ohms Zeven= 91.1180 Ohms v= 2.99792e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 35.5586 pF/m L= 312.9064 nH/m Zo= 76.0757 Ohms Zodd= 61.6960 Ohms Zeven= 93.8070 Ohms v= 2.99792e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 35.4672 pF/m L= 313.7124 nH/m Zo= 76.1736 Ohms Zodd= 61.6960 Ohms Zeven= 94.0486 Ohms v= 2.99792e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 35.4513 pF/m L= 313.8534 nH/m Zo= 76.1908 Ohms Zodd= 61.6960 Ohms Zeven= 94.0909 Ohms v= 2.99792e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 35.4486 pF/m L= 313.8773 nH/m Zo= 76.1937 Ohms Zodd= 61.6960 Ohms Zeven= 94.0980 Ohms v= 2.99792e+08 m/s v_f= 1.0000 VERSION= 4.0.0
couplerxx.bmp Er= 1.0000 C= 35.4486 pF/m L= 313.8773 nH/m Zo= 76.1937 Ohms Zodd= 61.6960 Ohms Zeven= 94.0980 Ohms v= 2.99792e+08 m/s v_f= 1.0000 VERSION= 4.0.0

Note that atlc first computes the odd mode impedance, then on a second run computes the even mode impedance. The characteristic impedance is Zo=sqrt(Zodd*Zeven), so this is also computed on the second run. The accuracy of the calculation of odd and even mode impedances in couplers is discussed in the accuracy section.

Later version of atlc will include some software to make use of the impedance values to calculate the properties of a directional coupler, although you should be able to use these in the free versions of spice or pspice. I have not tried that I must admit. There is also a cheapish ($10) programme called Puff available from http://www.its.caltech.edu/~mmic/puffindex/puffE/puffE.htm . That would certainly allow such calculations. There's a Unix verison too at http://wwwhome.cs.utwente.nl/~ptdeboer/ham/puff.html. Puff is very good. A combination of atlc to find the electrical properties (Zo, Zodd Zeven etc) of transmission lines and Puff to simulate the properties (coupling factor, directivity, frequency response etc) given those parameters, should be very useful.