Impedance and Impedance Matching

NI High-Speed Digitizers Help (NI-SCOPE)

Edition Date: January 2017

Part Number: 370592AB-01

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When broadband signals are carried on transmission lines of any significant length, care must be taken that the transmission medium is matched to its terminations. The source and load impedances should equal the characteristic impedance of the transmission line, as this minimizes signal reflections. The presence of impedance discontinuities or mismatches degrades the amplitude and phase accuracy, as well as the temporal fidelity, of measurements made with a digitizer. The example below shows one of the most common mismatch errors encountered in such measurements.

Example

Selectable termination impedances are provided at the digitizer inputs to accommodate the most popular coaxial cable characteristic impedances: 50 Ω and 75 Ω. The diagram below illustrates what happens when a coaxial cable of the wrong characteristic impedance (50 Ω) is used with 75 Ω source and load impedances.

The pulse encounters impedance mismatches at each end of the cable, whereupon it is partially reflected. The reflected pulse traverses the cable back and forth numerous times, diminishing at each end by the reflection coefficient, .

where

vr = reflected voltage
vi = incident voltage
zt = termination impedance
z0 = characteristic impedance

The resulting voltage waveform recorded by the digitizer is distorted by the asymptotic decay of the reflected pulse as shown, exaggerated for visual effect. Impedance discontinuities of smaller magnitude and/or duration have correspondingly smaller effects. Also displayed is the waveform that results when a cable of matched impedance (75 Ω) is used.

Mismatch Uncertainty

Impedance matching is also important for preserving the absolute power measurement accuracy of a digitizer. The accuracy with which power can be measured is limited by mismatch error. The mismatch error in a system can be shown to be bounded by:

where

L = load reflection coefficient
G = generator reflection coefficient

The denominator term represents mismatch uncertainty, which is a fundamental limit to the power transfer accuracy that can be achieved across a mismatched junction.

Resistive Matching

Signal sources with low (high) source impedance can be matched with a resistor placed in series (shunt) such that the total source impedance (admittance) is matched to the cable characteristic impedance (admittance). Sources that are not capable of driving the cable impedance directly can be coupled through a matching L-pad, an example of which is shown in the following figure. In this case, the source sees a 500 Ω load, while the source impedance presented to the cable is 50 Ω. High-frequency components and layout techniques should be used throughout to minimize parasitic effects.

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