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The characteristic impedance () of an infinite transmission line at a given angular frequency is the ratio of the voltage and current of a pure sinusoidal wave of the same frequency travelling along the line. This relation is also the case for finite transmission lines until the wave reaches the end of the line.
A transmission line is drawn as two black wires. At a distance x into the line, there is current I(x) travelling through each wire, and there is a voltage difference V(x) between the wires. If the current and voltage come from a single wave (with no reflection), then V(x) / I(x) = Z 0, where Z 0 is the characteristic impedance of the line.
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.
The ratio of the line input voltage to the voltage a distance further down the line (that is, after one section of the equivalent circuit) is given by a standard voltage divider calculation. The remainder of the line to the right, as in the characteristic impedance calculation, is replaced with Z 0 {\displaystyle \scriptstyle Z_{0}} , [ 19 ] [ 20 ]
The most widely used types of feed line are coaxial cable, twin-lead, ladder line, and at microwave frequencies, waveguide. Particularly with a transmitting antenna, the feed line is a critical component that must be adjusted to work correctly with the antenna and transmitter. Each type of transmission line has a specific characteristic impedance.
L networks for narrowband matching a source or load impedance Z to a transmission line with characteristic impedance Z 0. X and B may each be either positive (inductor) or negative (capacitor). If Z/Z 0 is inside the 1+jx circle on the Smith chart (i.e. if Re(Z/Z 0)>1), network (a) can be used; otherwise network (b) can be used. [2]
[2] [a] The calculation of the characteristic impedance of a transmission line composed of straight, parallel good conductors may be replaced by the calculation of the D.C. resistance between electrodes placed on a two-dimensional resistive surface. This equivalence can be used in reverse to calculate the resistance between two conductors on a ...
For many systems, the terminator is a resistor, with a value chosen to match the characteristic impedance of the transmission line and chosen to have acceptably low parasitic inductance and capacitance at the frequencies relevant to the system. Examples include 75-ohm resistors often used to terminate 75-ohm video transmission coaxial cables.
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