![]() If there were perfect matching at the load, we would have the transmission line reflection coefficient at the load being equal to zero the same applies at the source end. Input impedance for a transmission line section of length l in terms of the transmission line reflection coefficient at the load end. The input impedance of the transmission line is the value used for impedance matching at the source and is defined as: We generally consider the load impedance to be composed of the true input impedance and any termination specified at the load. In other words, it is the impedance seen by the source due to the presence of the load and the transmission line’s characteristic impedance. The input impedance is the impedance of the line looking into the source end. The input impedance of a transmission line section is a function of the transmission line reflection coefficient. Here, we need to understand the input impedance of the transmission line, which is also a function of the transmission line reflection coefficient as measured at the load. Normally, this equation is derived while assuming the electromagnetic wave is a plane wave, and most treatments only consider what happens between the transmission line and the load component.Īlthough there is a reflection coefficient at the load end of a transmission line, there is also a reflection between the source and the input impedance of the transmission line:ĭefinition of transmission line reflection coefficient at the source. This quantity describes the voltage reflected off the load of a transmission line due to an impedance mismatch. Here, Z L is the load impedance and Z 0 is the transmission line’s characteristic impedance. ![]() ![]() The general definition for the transmission line reflection coefficient is:ĭefinition of transmission line reflection coefficient at the load. Transmission line schematic with input, source, and load impedances.ĭeriving the reflection coefficient for a plane wave is a standard homework problem given in every electromagnetics class. The impedances involved in a transmission line connected to a load impedance Z in, source impedance Z S, and with input impedance Z in are shown below: In electronics, this is due to a mismatch in impedances (note that all of these quantities are related!). In electromagnetics, we say that this is due to a mismatch between the dielectric constants of the two media. In optics, we say this occurs due to refractive index contrast. It doesn’t matter whether we are dealing with digital pulses or harmonic AC waves, an incoming wavefront of an electromagnetic wave can reflect off of the interface between two materials. S-parameters and Input ImpedanceĪll transmission lines are media used to direct propagation of an electromagnetic pulse or wave. Transmission Line Reflection Coefficient vs. ![]() Instead, we need S-parameters and input impedance to properly describe signal behavior at an impedance discontinuity along a transmission line. In a channel with finite size and definite geometry, signals will not propagate as plane waves and their reflection cannot be described using the transmission line reflection coefficient. Unfortunately, most designers who are not versed in signal integrity analysis may not know that the reflection coefficient is not a complete metric for describing reflection from the load on a transmission line. New designers often refer to the reflection coefficient to describe reflections off the load end of a transmission line. Plane waves reflecting off of water are described with a reflection coefficient. The reflection of a plane wave can be perfectly described using a reflection coefficient, but this is not the whole story in a complex structure like a printed circuit board.ĭesigners need to use input impedance and S-parameters to describe reflections in transmission lines. All electromagnetic waves experience some reflection when they reach the interface between two media that have refractive index contrast.
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