A detector is calibrated at a reference level and used to compare two signals ten decibels apart. The output voltage ratio implies a difference of eight decibels. Repeating the comparison at a lower level returns nearly ten.
The detector is functioning normally. What changed is the relationship between input power and output voltage, which is not the same at every level. Assuming one relationship across the full range produces errors that grow with level and that no calibration at a single point can correct.
Detector Output Follows Two Different Laws
A diode detector rectifies the incoming signal and produces a DC output proportional to some function of the input.
At low input levels the diode operates on the curved portion of its characteristic near zero bias, and the output voltage is proportional to input power. This is the square-law region, so named because power is proportional to the square of voltage, so output tracks the square of the input voltage amplitude.
At high input levels the diode conducts strongly on signal peaks, and the output voltage becomes proportional to the input voltage amplitude rather than to power. This is the linear region, sometimes called the peak-detecting region.
Between them lies a transition where the response follows neither law cleanly.
The Transition Is Gradual and Level Dependent
There is no sharp boundary between the two regions.
Departure from square law begins well before the response becomes recognizably linear. The output starts compressing relative to the square-law prediction, and the amount of compression grows with level.
The level at which departure becomes significant depends on the diode, the matching network, and the load resistance. It is a property of the detector as built rather than a universal figure.
Manufacturers specify a square-law range within which the response holds to a stated tolerance. Above that range the response continues but requires correction.
Errors Compound in Ratio Measurements
Comparing two levels through a detector uses the response curve twice.
If both measurements fall within the square-law region, the ratio is recovered correctly. If one falls in the transition and the other in square law, the two are read against different slopes and the computed ratio is wrong.
The direction is predictable. Compression at the higher level makes the measured difference smaller than the actual difference, so the reading understates the ratio.
This affects gain measurements, insertion loss measurements, and any comparison where the two levels differ substantially. The error appears as an instrument problem and is a range problem.
Correction Requires a Characterized Curve
The response above square law is repeatable, which means it can be corrected.
A calibration performed at multiple levels across the range produces a transfer curve rather than a single sensitivity figure. Measurements are then converted through that curve.
The correction is specific to the individual detector. Two units of the same model have similar but not identical curves, and using one unit’s data with another introduces error.
Where a system applies correction automatically, the stored curve has to correspond to the connected detector. Substituting a detector without updating the curve produces confident wrong answers.
Temperature Moves the Curve
Diode characteristics vary with temperature, and both sensitivity and the square-law limit shift with it.
Sensitivity in the square-law region changes measurably across an operating temperature range, which appears as a level offset if uncorrected.
The departure point also moves, so the range over which square law holds is not fixed across temperature.
Some detector designs include compensation, using a matched reference diode or a thermistor network to offset the drift. Where compensation is absent, temperature has to be controlled or its effect included in the uncertainty.
Warm-up matters. A detector reaching thermal equilibrium after connection reads differently during the first minutes than afterward, and measurements taken during that period drift.
Detector Technology Affects the Usable Range
Different device structures place the square-law limit at different levels and offer different sensitivity.
Schottky barrier diodes are widely used, with a square-law region extending over a defined range and sensitivity determined by the barrier characteristics.
Tunnel diode detectors operate on a different conduction mechanism and are specified with their own square-law range and sensitivity figures, with characteristics that suit particular sensitivity and frequency requirements.
Zero-bias devices avoid the need for a bias supply, at the cost of a different sensitivity and drift profile than biased designs.
The selection question is where the intended measurement levels sit relative to each device’s specified square-law range, taken from the specification rather than inferred from the technology.
Noise Sets the Lower Limit
Square law holds down to low levels, but detector output eventually falls below the noise of the following amplifier.
Tangential sensitivity describes the level at which the signal becomes distinguishable from noise, and it depends on both the detector and the video amplifier bandwidth.
Narrowing video bandwidth reduces noise and improves sensitivity, at the cost of slower response. For continuous-wave measurement this trade favors narrow bandwidth. For pulse measurement it does not.
Averaging improves the effective noise floor for stable signals, and the improvement follows the square root of the averaging count.
Pulse Measurement Adds Bandwidth Constraints
Detecting a modulated or pulsed signal requires the output to follow the envelope.
Video bandwidth determines how fast the output can change. A detector with insufficient video bandwidth rounds the edges of a pulse and, for short pulses, fails to reach full amplitude.
Rise time relates inversely to video bandwidth, and measuring a pulse accurately requires rise time substantially shorter than the pulse width.
Where the pulse amplitude falls in the transition region, both the level error and the bandwidth limitation apply, and the two are difficult to separate in the observed waveform.
What the Selection Requires
The parameters are specific and available.
Expected input levels, including the full range between minimum and maximum. The detector’s specified square-law range and its tolerance. Sensitivity, and whether it is adequate at the lowest expected level. Video bandwidth, against the fastest envelope change to be measured. Temperature range and whether compensation is included. Availability of multi-level calibration data for correction above square law.
A detector calibrated at one level and used across a wide range reports levels correct at one point and progressively wrong elsewhere. The correction is straightforward once the curve is known, and the error is invisible until someone checks.
