characteristic impedance of a transmission line depends on frequency of transmission as can be seen by its expression.
What will be the characteristic impedance of TL if my signal has two frequency components? What will be its expression?
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2 Answers
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Above about 1MHz, normal cable characteristic impedance is fairly contant with frequency as per the equation: -
\$Z_0 = \sqrt{\dfrac{L}{C}}\$ where L and C are inductance and capacitance per unit distance.
The theoretically correct equation for all frequencies is: -
\$Z_0 = \sqrt{\dfrac{R+j\omega L}{G + j\omega C}}\$ where R and G are series resistance and shunt conductance per unit distance.
This tends to reduce to a complex value in the sub-1MHz area of: -
\$Z_0 = \sqrt{\dfrac{R}{j\omega C}}\$
If both frequencies are well above 1MHz then you can take Z0 to be a constant.
answered Nov 20, 2014 at 19:50
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1\$\begingroup\$ There is also a high-frequency limit where these equations become invalid --- The first one typically breaks when the skin effect becomes significant, and the second one because the transmission line becomes multimode. \$\endgroup\$ Commented Nov 20, 2014 at 20:17
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You will have two different impedances, one at each frequency. The impedances could be almost the same, depending on the frequencies. Generally these sort of systems are analyzed under the assumption of superposition, only considering one single frequency at a time. If you have a nonlinear transmission line, then the superposition principle does not apply, in which case the concept of 'impedance' does not really apply either.
answered Nov 20, 2014 at 19:46
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\$\begingroup\$ Like we derive the characteristic impedance value by solving telegraph equations, cant we derive the value of characteristic impedance for multi frequency case? \$\endgroup\$ Commented Nov 20, 2014 at 21:35