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A digital rising or falling edge is a step function that can be modeled as a high-frequency wavefront. As the wavefront travels along the transmission line, it acts as a purely AC signal, encountering the characteristic impedance (Z0) of the transmission line. When the wavefront reaches the end of the path, if Z0 and the termination (Zt) do not match, portions of the wave are reflected. As the wave reflects back along the transmission line, it eventually reaches the original source impedance (Zs). If the transmission line characteristic impedance (Z0) and Zs do not match, then portions of the wave are re-reflected. The superposition of these reflected waves can cause significant signal degradation.
Reflection caused by an impedance mismatch at the end of a transmission line is quantified
by the reflection coefficient. Reflection coefficient Γ is given by the following formula:
Γ = Vr/Vi = (Zt - Z0)/(Zt + Z0)
where Vr is the reflected voltage, Vi is the incident voltage, Zt is the terminating impedance, and Z0 is the characteristic impedance of the transmission line.
For example, by applying this formula, you can calculate that when a 3.3 V wave, traveling down a 50 Ω characteristic medium hits a 1 kΩ load impedance, the reflection coefficient, Γt, is equal to (1 kΩ - 50 Ω)/(1 kΩ + 50 Ω), or .90, and Vr equals 0.9 x 3.3 V = 2.97 V.
Thus, the reflected wave Vr is almost the same magnitude as the incident wave. At the load, this condition only has the effect of giving an erroneous voltage—assuming that the circuit was originally calibrated with a 50 Ω load. While nearly the entire signal is reflected back, this reflection is eliminated at the source because the source and the transmission line are matched.
However, should the transmission line/cable be mismatched from the source and the load, the mismatch causes a scenario of multiple reflections resulting in aberrations at the load similar to what is shown in the improperly terminated signal in the Termination topic.
|Note NI strongly recommends that you take great care to ensure that the source impedance of the system is matched as closely as possible to the characteristic impedance of the transmission line. For generation operations, the source impedance is inside the NI device and is handled by the hardware architecture. For acquisition operations, however, you control the source impedance of the system. You should create a source impedance as close to the characteristic impedance of your device as possible.|