atlc How to determine the properties of an arbitrary coupler
Description: Calculte Zodd and Zeven Using atlc
Keywords: Zodd odd even mode impedance coupler directional

# How to determine the properties of an arbitrary coupler, given its physical dimensions.

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

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 therefore computes 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, and 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

atlc is written and supported by Dr. David Kirkby (G8WRB) It it issued under the GNU General Public License

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