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Applying the transmission line model based on the telegrapher's equations as derived below, [1] [2] the general expression for the characteristic impedance of a transmission line is: = + + where R {\displaystyle R} is the resistance per unit length, considering the two conductors to be in series ,
The characteristic impedance or surge impedance (usually written Z 0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in the absence of reflections in the other direction. Alternatively and equivalently it can be defined ...
Impedance (Z) parameter may defines by applying a fixed current into one port (I1) of a transmission line with the other port open and measuring the resulting voltage on each port (V1, V2) [8] [9] and computing the impedance parameter Z11 is V1/I1, and the impedance parameter Z12 is V2/I1. Since transmission lines are electrically passive and ...
Equivalent circuit of an unbalanced transmission line (such as coaxial cable) where: 2/Z o is the trans-admittance of VCCS (Voltage Controlled Current Source), x is the length of transmission line, Z(s) ≡ Z o (s) is the characteristic impedance, T(s) is the propagation function, γ(s) is the propagation "constant", s ≡ j ω, and j 2 ≡ −1.
Fig.1 Transmission line. The distributed-element model applied to a transmission line. In electrical engineering, the distributed-element model or transmission-line model of electrical circuits assumes that the attributes of the circuit (resistance, capacitance, and inductance) are distributed continuously throughout the material of the circuit.
Using transmission-line theory, if a transmission line is terminated in an impedance which differs from its characteristic impedance (), a standing wave will be formed on the line comprising the resultant of both the incident or forward and the reflected or reversed waves.
This pulse will be partially reflected and transmitted according to the transmission-line theory. If we assume that each line has a characteristic impedance , then the incident pulse sees effectively three transmission lines in parallel with a total impedance of /. The reflection coefficient and the transmission coefficient are given by
To test for a match, the reference impedance of the bridge is set to the expected load impedance (for example, 50 Ohms), and the transmission line connected as the unknown impedance. RF power is applied to the circuit. The voltage at the line input represents the vector sum of the forward wave, and the wave reflected from the load.