A signal source is characterized at a given output level. The same source, measured on a different bench with a different sensor and a short adapter in line, reads several tenths of a decibel lower. Both instruments hold current calibration certificates.
Neither reading is wrong in the sense of instrument error. The difference comes from reflections at the connection between source and sensor, and those reflections change with what is connected and at what frequency.
Mismatch uncertainty is frequently the largest single contributor to total measurement uncertainty in radio-frequency power measurement, and it is the one least affected by calibration.
Reflections Occur Wherever Impedance Changes
A transmission line carries energy toward a load, and the load absorbs it fully only when its impedance matches the line.
Any departure from that match reflects a portion of the incident energy back toward the source. The reflected fraction is described by the reflection coefficient, and its magnitude relates directly to voltage standing wave ratio.
A sensor is a load. Its input impedance is designed to approximate the system impedance, but the approximation degrades with frequency and no sensor is perfectly matched across its full range.
The source has its own reflection coefficient, and it is generally worse than the sensor’s, particularly for amplifiers and signal generators without output isolation.
Two Reflections Interact
With a reflection at both ends of the connection, energy travels back and forth between source and sensor.
The reflected wave from the sensor returns to the source, reflects again from the source’s own mismatch, and travels forward to the sensor a second time. That re-reflected component adds to the incident wave.
Whether it adds constructively or destructively depends on the phase relationship between the two, which depends on the electrical length between source and sensor and therefore on frequency.
The result is a measurement that reads high at some frequencies and low at others, oscillating as frequency changes. The envelope of that oscillation is set by the product of the two reflection coefficient magnitudes.
The Uncertainty Bound Is Calculable
Mismatch uncertainty is bounded rather than known, because the phase relationship is usually unknown.
The bound is determined from the magnitudes of the source and sensor reflection coefficients. The limits are asymmetric, with the positive and negative bounds differing slightly, and the interval widens as either reflection coefficient increases.
Sensor reflection coefficient is published, typically as a maximum against frequency. Source reflection coefficient is often not published, and where it is not, assumption can measure or bound it.
Where both are known in magnitude and phase, the correction can be calculated rather than treated as uncertainty, which reduces the interval substantially.
Adapters and Cables Add Their Own Discontinuities
Every connection in the path introduces a potential impedance discontinuity.
Adapters between connector series are a common contributor, since the transition between geometries is never perfectly matched. A between-series adapter can dominate the mismatch at higher frequencies.
Cables contribute loss, which attenuates reflections and can improve apparent match, but they also contribute their own discontinuities at each end.
Connector condition matters. Worn, dirty, or damaged interfaces present higher reflection than clean ones in good condition, and the degradation is not visible without inspection.
Torque affects the interface. Precision connectors specify a torque value, and connections tightened by hand or overtightened present different electrical characteristics.
Sensor Technology Affects the Match
Different detection methods present different input characteristics.
Thermistor-based sensors use a bridge circuit that holds resistance constant, which produces good match by design over their operating range.
Thermocouple sensors present a resistive load through a matching network, with match that varies across their frequency range.
A diode power sensor uses a diode detector with a matching resistor, and its match depends on the network design and on frequency, generally degrading toward the upper end of its specified range.
None of these is inherently correct or incorrect. What matters for uncertainty is the published reflection coefficient at the frequency of measurement, taken from the specification rather than assumed from the technology.
Attenuators Trade Level for Match
Inserting a fixed attenuator between source and sensor improves the effective match at both ports.
A reflection traveling back through the attenuator is attenuated twice, once on each pass, so a 10 dB attenuator reduces the reflected component by 20 dB.
The improvement applies to both the source and the sensor as seen through the attenuator, and it reduces the mismatch uncertainty bound considerably.
The cost is signal level. Ten decibels of attenuation moves the measurement 10 dB down the sensor’s dynamic range, which may push it toward the noise floor for low-level signals.
The attenuator’s own calibration factor and its uncertainty then enter the budget, replacing part of the mismatch uncertainty with a known and smaller quantity.
Isolators Provide One-Way Improvement
A ferrite isolator passes energy in one direction and absorbs it in the reverse direction.
Placed at the source output, it presents a well-matched load to reflections returning from the sensor, effectively removing the source mismatch from the interaction.
Isolators are frequency-band limited and introduce insertion loss, and their reverse isolation is finite. Within their band they are more effective than an equivalent attenuator because the forward loss is lower.
Documenting the Budget Makes Comparisons Possible
An uncertainty budget lists each contribution and combines them.
Calibration factor uncertainty, from the sensor’s calibration. Instrument uncertainty, from the meter. Linearity, across the dynamic range. Noise and drift, at low levels. Mismatch, from the reflection coefficients. Connector repeatability, from the interface.
Combining them in quadrature, where they are independent, produces a total that is smaller than their sum and represents the realistic figure.
Two measurements of the same signal agreeing within their stated uncertainties are consistent. Two measurements disagreeing by more than that indicate something unaccounted for, and mismatch is the usual candidate.
What the Assessment Requires?
The information is available from specifications and from the measurement setup.
Frequency of measurement. Sensor reflection coefficient at that frequency, from its specification. Source reflection coefficient, measured or bounded. Every adapter, cable, and connector in the path, and its contribution. Signal level relative to sensor range, to judge whether attenuation is affordable.
Calibration addresses the sensor. Mismatch addresses the connection, and it is a property of the setup rather than of the instrument. See more.