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Below is a Set of Algebraic Equations to result with an Equation, where one can enter ... the Input Impedance, Zin, measured at the Transmitter Side of the Transmission Line, and the Length and Velocity Factor of the Transmission Line; and, calculate the Impedance, Zl, at the Load (Antenna) Side. |
For those who prefer to enter the Length of the Transmission Line, in Meters ... |
For those who prefer to enter the Length of the Transmission Line, in Feet ... |
Using the 'Terminal' Application of an iMac 27" 2017 ... Example: Please Note: ------------------------------------------------------------------------------ Last login: Sat Oct 13 07:10:22 on console s@s.local:~:python import math as m # Importing the standard Math Module / Package. Instead of 'math.cos()', one only needs to enter 'm.cos(). ZO = complex(50, 0) # Enter the complex Values of the Transmission Line. Transmission Lines have 0 Reactance, only Resistance. lamda = 300 / 7.050 # lamda is the calculated Wavelength. 300 is 300000000 m/s - the Speed of Light. 7.050 is 7050000 Hz, a 40m Amateur Radio Frequency. beta = ( 2 * m.pi ) / lamda # beta is the Imaginary Part of the Propagation Constant; and, represents the rate at which the RF Waves oscillate as a function of Position on the Transmission Line. # Below we will make the Physical Length of the Transmission Line to 25 meters, or 82.021 feet. cLen = 25 / 0.66 # cLen is the Wavelength Length of the Transmission Line. This Length is always longer than the actual Physical Length. x = beta * cLen # # By letting x = beta * cLen, it is easier to handle the single Variable of the 'm.cos()' and 'm.sin()' Functions. cosx = m.cos(x) # Calculate the cosine of x. num01 = ZO*(complex((ZL*cosx),(ZO*sinx))) # Calculate the Numerator Value. Zin = num01/den01 # Finally, calculate the Input (or Transmitter) Impedance (complex) Values. # Let us now confirm the 2nd Equation: ZL = ZO (Zin cos(x) - jZO sin(x)) / (ZO cos(x) - jZin sin(s)). num02 = ZO*(complex((Zin*cosx),(-ZO*sinx))) # Calculate the Numerator Value. ZL02 = num02/den02 # Finally, calculate the Output (Ant) Impedance (complex) Values. ------------------------------------------------------------------------------ Yes, you can actually copy each and every Line of Code [with / without the # and Text after it], individually - and paste into 'Terminal' the Text (and then press <return>); and after the final <return> - you should the originally entered ZL, and the calculated ZL02. This therefore proves the ZL = (ZO (Zin cos(Bl) -j(ZO sin(Bl))) / (ZO cos(Bl) -j(Zin sin(Bl))) resultant Equation, generated above, is correct. |
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Created: 13.10.2018, Modified: 13.10.2018 ©2008 - 2099, Alle Rechte vorbehalten, SJWL |