Hand-considered hypotheses, 1901–2000
Electronics and instrumentation: analogue front ends, converters, noise, grounding, shielding, timing, references, cabling
Written one at a time, not composed. The logical form is printed with each entry because the forms are what differ: several of these claim a quantity is misattributed, several assert a bound, several invert a standard practice, one or two are no-go statements that would remove a whole family of corrections if they held. The distribution is uneven and was not fixed in advance. None has been tested. Any number followed by “(estimate)” is an order-of-magnitude expectation, not a measurement; nothing here is a datum, and no citation is implied.
Analogue front ends
Hidden term
H1901. The input bias current of a CMOS front end carries a surface-leakage term that grows severalfold per ten points of relative humidity (estimate), and below a few picoamps that term, not the silicon, sets the offset. It runs across the package surface and the flux residue around the input pin. Washing half a batch and storing both halves at 80% relative humidity gives two bias-current populations at identical die temperature.
Misattribution
H1902. Settling tails that outlast a fast amplifier's specified settling time are commonly blamed on slew limiting, but they are the thermal tail of the input pair, whose junction temperature carries the step's history and relaxes with the die's thermal time constant. The tail's size follows the change in input-stage dissipation, which slew limiting does not. Driving equal steps from two different baseline levels changes the input stage's dissipation by different amounts while leaving the slew demand identical, so the tail's size separates the two.
Inversion of standard practice
H1903. A series resistor at a high-impedance input is fitted so the amplifier survives transients, yet inside the loop of a transimpedance stage it adds phase lag at exactly the frequency where the cable's own resonance sits, and the stage peaks instead of settling. The resistor and the cable capacitance make the pole; the loop's crossover decides whether it matters. Moving the resistor from the amplifier end to the far end of the cable, at the same value, changes the peaking if the cable is responsible.
Artefact mimicking effect
H1904. Much of the improved linearity claimed for a differential front end feeding a 24-bit converter belongs to the averaging rather than to the amplifier, because input dither and the anti-alias corner both smooth a transfer curve while leaving its local slope error intact. Measured distortion therefore falls as the record lengthens even when the amplifier is unchanged. Notching the fundamental ahead of the converter and measuring the residual at the same effective bandwidth shows whose number it is.
Threshold
H1905. Below a source resistance of a few hundred ohms (estimate), a bipolar front end's offset stops being the amplifier's and becomes the Seebeck voltage of its two input solder joints, a few microvolts per kelvin of difference between them. The joints sit at different temperatures whenever the board carries a gradient. Reversing the connector's orientation while the gradient is held fixed flips the sign only if the joint pair is the source.
Identity
H1906. Common-mode rejection and its variation with common-mode level are published as two specifications, but the second is the derivative of the first and cannot be improved separately: a part with flat rejection has no level dependence, and a part with level dependence is only as good as its rejection at one point. Any datasheet quoting both a rejection and a rejection linearity is quoting a number and its slope. Plotting offset against common-mode voltage on one part and differentiating reproduces the second number from the first.
Bound
H1907. The usable transimpedance of a photodiode front end is bounded by the diode's shunt resistance and the feedback resistor's stray capacitance, not by the amplifier's gain-bandwidth, and past the crossover those two buy nothing. Signal current is shunted away before it reaches the summing node, and the stray capacitance fixes the noise gain. Two diodes of equal capacitance but shunt resistances a decade apart should peak at feedback resistors a decade apart.
Selection effect
H1908. Datasheet typical curves are drawn from characterised parts that passed a screen, so a typical curve is a survivor's curve and the part in the drawer comes from the full distribution. The screen removes the slow and the noisy, which are precisely the tails a designer budgets for. Buying thirty units from a distributor and measuring the same curve costs an afternoon and redraws the plot.
Scale argument
H1909. Electrode polarisation decays as a power law rather than an exponential, so any high-pass corner that removes it also removes signal, and how much depends on how long the electrode soaked before recording began. A self-similar decay has no time constant for the filter to sit below. Recording the same electrode at two soak durations and filtering both identically tests whether the corner or the soak sets the loss.
Reversal
H1910. Adding capacitance at the input of a high-impedance amplifier usually lowers noise, but there is a source resistance above which the same capacitor raises it, because the capacitor forms a pole with the source and the amplifier's own voltage noise is amplified by the resulting noise gain before the signal is. Signal and noise see different transfer functions once the source impedance is large. Noise measured against source resistance for two capacitor values crosses at the resistance in question.
Converters and sampling
Hysteresis claim
H1911. The settling error that shows up as code-dependent distortion in a SAR converter's output contains a term that remembers the previous conversion, because the sampling switch's channel charge divides between source and capacitor according to the impedance present at turn-off. That split is set by the last code as much as by the present input. Holding the input fixed and walking the previous code through its range isolates the memory.
Misattribution
H1912. Aperture jitter inferred from a converter's signal-to-noise ratio with a high-frequency input is usually charged to the clock generator, but part of it is internal, since the sampling network's turn-off instant moves with the input's slope. The internal term grows faster with input frequency than the external clock's jitter does. One clock driving two converters of different architectures, compared at several input frequencies, separates the two slopes.
Derived quantity
H1913. Equivalent noise bandwidth is quoted in hertz and then used as if it were a power ratio, so a cascade is often assigned the bandwidth of one section; two identical single-pole sections actually have an equivalent noise bandwidth near 1.22 times their own −3 dB bandwidth, not 1.57 times (estimate). The product rule fails because the second section's corner is not the cascade's corner. Measuring integrated noise through one and through two sections against a calibrated white source reports which factor the firmware assumed.
Selection effect
H1914. Published effective-number-of-bits figures come from parts that passed a spectral-purity screen, so the survivors' distribution understates the risk of idle tones in a bought batch. Screening removes exactly the units a production line will meet. Testing every unit of a purchased lot with a DC input and a slow staircase counts the tone incidence without the screen.
Reversal
H1915. In a delta-sigma modulator, idle tones grow as the DC input approaches zero, so the converter is least well behaved at its smallest signals, which inverts the usual assumption that quiet inputs are benign. The quantiser's limit cycle lengthens as the input's fractional part nears a simple rational, and tone amplitude follows the cycle length. A slow staircase through zero with a long transform at each step plots tone amplitude against input and puts the peak at zero.
Count
H1916. A converter with N bits has at most 2^N − 1 independent code transitions, so an integral-nonlinearity curve fitted with more parameters than that is fitting the test's own noise. Beyond that count the fit has no degrees of freedom left to distinguish the parts. Raising the polynomial order on one dataset and watching the residual stop falling at the predicted order shows where the information ends.
Artefact mimicking effect
H1917. A spur in a digitised spectrum that moves when the record length changes is an alias beat between the sampling clock and a source that is not coherent with it, not a real tone in the input. A true spur holds its frequency and amplitude as the record lengthens; a beat does not. Two record lengths at one sample rate separate them in a single sitting.
Identity
H1918. Charge injection and sampling-network nonlinearity in a switched-capacitor input are one mechanism seen at two source impedances, since both are the signal-dependent division of the switch's charge between source and hold capacitor. Nothing else in the input path depends on the source that way. Sweeping source resistance at fixed input frequency should collapse the two measured curves onto one when plotted against the impedance ratio.
No-go claim
H1919. No anti-alias filter suppresses an interferer that sits exactly at a multiple of the sampling rate, because its alias lands at DC where the filter's stopband has no authority. What leaks there is the clock's own coupling into the input, not the signal path's response. Raising the filter order while injecting a tone at the sample rate leaves the DC shift unchanged, which is the proof.
Scale argument
H1920. Quantisation error is uniform only when the input crosses many codes inside the measurement window; for an input that occupies a handful of codes the error is a deterministic function of that input and the spectrum is a comb, not a floor. Window length and input amplitude together decide which regime applies. Stepping the amplitude down at fixed record length turns a flat spectrum into a line spectrum at a predictable amplitude.
Noise and its origins
Misattribution
H1921. Excess low-frequency noise in a biased sensor is usually assigned to the sensor, but part of it belongs to the bias resistor, which shows excess noise only while carrying current. At zero bias the same resistor is quiet, which is the tell. Swapping in a metal-foil resistor of the same value and repeating at two bias currents attributes the excess to the right component.
Unit trap
H1922. Noise figure is defined at a 50 Ω source, so a device whose optimum is 1 kΩ and whose datasheet says 0.5 dB is not 0.5 dB at the impedance actually presented to it. The number carries its reference impedance invisibly. Measuring the same device through a transformer at 50 Ω and at 1 kΩ, and comparing with the datasheet's noise contour, settles the question.
Scale argument
H1923. Excess noise in a film resistor scales inversely with the film's volume, so two resistors of identical value in different case sizes have different low-frequency excess noise, and the smaller one is the noisier at every current. Geometry rather than resistivity sets the volume that averages the fluctuations. Two case sizes of one value, measured at the same dissipated power, should differ by the volume ratio.
Bound
H1924. A guard ring can cut leakage by decades but cannot take it below the surface generation current of the guard's own junction, so there is a floor belonging to the guard rather than to the guarded node. The ring collects what the surface produces; it cannot produce less. Sweeping the guard's potential through the node's potential and finding where the difference current reverses locates that floor.
Reversal
H1925. Cooling a high-impedance front end lowers its thermal noise and raises its dielectric absorption time constant, because the relaxation processes in the board and cable slow down faster than the noise falls. Below some temperature the settling of a scanned measurement degrades more than the noise improves. Settling time and noise measured on one node from 300 K to 150 K cross at the temperature that matters.
Count
H1926. The number of independent excess-noise sources in a thin-film network equals the number of distinct current paths through it, so an N-link trimmed network shows at most N components, and a network showing more has a contact problem rather than a film problem. Each link's fluctuation is its own; the contacts add a different spectrum. Trimming links one at a time and counting the components that disappear attributes each peak.
Threshold
H1927. There is a photodiode bias below which the transimpedance amplifier's own current noise dominates and above which the diode's excess noise takes over, and the crossover moves with the diode's area, so a low-noise claim per unit area says nothing. Area buys signal and buys dark-current noise at the same time. Two diodes of different area at one bias, measured against a common amplifier, put the crossover where the areas predict.
Artefact mimicking effect
H1928. The apparent noise reduction from averaging repeated acquisitions stops at a level set by a coherent interferer locked to the trigger, not by the instrument's own limit, because a stationary component is identical in every record and survives the average while the random part falls. That residual's amplitude does not depend on the count. Randomising the trigger phase makes the interferer average away as well, which is how to tell the two apart.
Identity
H1929. Popcorn noise and low-frequency excess noise in a bipolar input stage come from the same defect population seen at two time scales, so a part screened for popcorn at room temperature will still show elevated excess noise at another. The defect's emission time constant moves with temperature and swings through the measurement band. Screening a batch for popcorn at 25 °C and measuring excess noise on the survivors at 85 °C tests the link.
Inversion of standard practice
H1930. Driving a guard from the amplifier's own output is the usual recipe, but at low frequency it returns the amplifier's noise to the guarded node through the guard capacitance, and a quiet node ends up carrying the buffer's noise. The guard is a second input as far as noise is concerned. Driving it from a separate, slower, lower-noise buffer and comparing the node's spectrum tests the practice.
Grounding and return paths
Misattribution
H1931. Low-frequency ground-loop interference is blamed on loop area, but at 50 or 60 Hz the shared-return voltage division usually dominates, because magnetic pick-up grows with area while the shared resistance grows with the return's resistance. The two scale differently with geometry. Two loops of equal area and different return resistance, in the same field, show which term is doing the work.
Hidden term
H1932. Every single-ended measurement includes the return conductor's inductance in its transfer function, so a reading taken through a long return is a filtered version of the truth even at a hertz. The corner sits at the return's L/R and is invisible in the schematic. Shortening the return and repeating a step response exposes the corner.
Bound
H1933. The rejection a differential front end achieves against a ground loop is bounded by the match of its two source impedances, not by the amplifier's rejection ratio, because mismatch converts common-mode voltage into a differential one ahead of the amplifier. A 0.1% mismatch caps rejection near 55 dB (estimate) regardless of the part. Deliberately trimming one source resistor by 0.1% and measuring the rejection confirms the bound.
Reversal
H1934. Star grounding suppresses low-frequency loop currents and worsens high-frequency behaviour, because the star's branches are inductances and the loop they form is large. Above a few hundred kilohertz a solid plane is the quieter topology. Building the same circuit both ways and measuring at 1 MHz decides which argument applies at the frequency of interest.
Count
H1935. A system with N chassis bonded at M points has at most N + M − 1 independent ground paths, and the number that actually carries current is smaller than the number drawn, which is why schematics overstate the loop count. Paths in parallel share current according to impedance, and the low-impedance ones dominate. Injecting current at each bond in turn and measuring the voltage at every other bond recovers the real count.
Threshold
H1936. A split in a ground plane stops isolating and starts coupling below a certain width, where the two edges' capacitance dominates the split's inductance and the plane behaves as one. Narrow splits are capacitors; wide ones are chokes. Sweeping the split from 0.2 mm to 5 mm and measuring coupling at 100 MHz finds the width where the trend reverses.
Artefact mimicking effect
H1937. Ground bounce seen on a digital output is often the probe's own return, because the ground lead's inductance sits in series with the measurement and the tip sees the difference between two grounds. The circuit may be quiet while the probe rings. Repeating with a coaxial tip-and-barrel connection, or with the ground lead shortened to a millimetre, makes the bounce disappear.
Symmetry claim
H1938. Galvanic isolation by transformer and by optocoupler is the same mechanism at the barrier: displacement current through the barrier capacitance, which sets the frequency at which isolation fails. The transformer's inter-winding capacitance and the optocoupler's package capacitance play identical roles. Driving each barrier with the same common-mode step and measuring the current through it gives one curve for both.
Scale argument
H1939. A ground loop of one square metre picks up microvolts at 50 Hz and millivolts at 50 kHz, but the scaling is not the frequency ratio unless the field is uniform: near a conductor the field falls as 1/r, so the loop's position changes the answer more than its area. Area sets the flux only in a uniform field. Moving the loop at constant area, toward and away from the conductor, separates the two dependences.
Inversion of standard practice
H1940. Bonding a cable shield at both ends is normally forbidden, yet for a low-level cable in a strong radio-frequency field it is the better choice, because the shield current is driven by the field and a single-ended shield is an antenna with a free end. The rule against both-end bonding applies to low-frequency magnetic coupling, not to radio-frequency electric coupling. Measuring the shield current and the centre conductor's noise with one end and then both ends, in the same field, decides which coupling dominates.
Shielding and coupling
Misattribution
H1941. Leakage into a shielded enclosure is blamed on the seams, but below the box's first resonance the dominant path is usually the cable penetration's pigtail, whose inductance is far larger than any seam's. Seams matter above the first cavity mode; below it the cable is the antenna. Replacing the pigtail with a 360° bond and repeating the sweep identifies the path.
Hidden term
H1942. A shielding-effectiveness figure includes the measurement antenna's own coupling to the enclosure, so a small box measured close in looks better than it is. The antenna samples the near field it helped create. Repeating the measurement at several distances at fixed frequency separates the box's response from the geometry's.
Bound
H1943. No braided shield exceeds a transfer impedance set by its optical coverage, and above the frequency where the braid's apertures dominate the shield behaves as a filter rather than a barrier. Coverage sets the floor; the braid's lay length sets where the floor is reached. Line-injection measurements on two coverage grades of the same diameter show the floor moving with coverage.
Threshold
H1944. An aperture in a shield stops leaking above a cutoff set by its longest dimension, and below that cutoff the leak falls steeply as the aperture becomes a waveguide beyond cutoff. A hole that ruins a 1 GHz measurement is irrelevant at 100 MHz. Sweeping one aperture's size at a fixed frequency locates the cutoff and shows the slope.
Reversal
H1945. A ferrite bead on a cable lowers high-frequency common-mode current and can worsen emission at one frequency, where the bead's inductance resonates with the cable's capacitance and the impedance meant to be resistive turns capacitive. The bead is a component, not an attenuator. Measuring emission with the bead at three positions along the cable, and with a bead of a different material, exposes the resonance.
Count
H1946. Mode density in a cavity grows as the cube of frequency, so an enclosure that is well behaved at 300 MHz has roughly a thousand times as many modes to control at 3 GHz (estimate). Mode density, not the box's worst resonance, sets the difficulty of a broadband shield. Counting resonances in a swept measurement of one box at two bands checks the exponent.
Scale argument
H1947. Shielding effectiveness measured in a small transverse-electromagnetic cell is not the free-space value, because the cell presents a wave impedance that differs from 377 Ω and the coupling to the box depends on that ratio. The ratio is computable and is the correction. Measuring one box in the cell and on an open-range site at the same frequency gives the factor.
Artefact mimicking effect
H1948. A resonance in a shield's effectiveness curve that shifts when the enclosure is rotated but not when the source is belongs to the test setup, not to the shield. Rotation changes the coupling to the room; the source's position changes the illumination. Doing both, one at a time, assigns the peak.
Identity
H1949. What is called electric-field shielding and what is called magnetic-field shielding differ at low frequency only in the shield's bonding and thickness, not in mechanism: a floating foil blocks the electric field and passes the magnetic one, and the same foil bonded at a single point blocks neither well. Eddy currents and charge redistribution are one response viewed through two boundary conditions. Testing a foil floating, bonded at one point, and bonded all round at 50 Hz and at 50 kHz gives the map.
Inversion of standard practice
H1950. A high-permeability magnetic shield works better with a deliberate gap than without one when the ambient field is strong, because the gap raises the saturation threshold and the material then diverts flux instead of saturating. The usual practice of closing the box completely fails exactly where the field is largest. Measuring the internal field against the applied field for a closed and a gapped shield traces the saturation knee.
Timing, clocks and jitter
Misattribution
H1951. Jitter read from an oscilloscope histogram is usually charged to the clock, but the instrument's trigger path contributes a term that depends on the edge's slew rate, so a slow edge from a good clock reads worse than a fast edge from the same clock. The trigger's own noise is divided by the slope. Two edges of different slew from one source, measured on the same channel, separate the instrument's term from the source's.
Hidden term
H1952. A phase-noise plot includes the analyser's reference, which is not drawn on the same axes, and cross-correlation removes it only when the two internal references are independent. Otherwise the reference's skirt is attributed to the device. Measuring a known-quiet source at two correlation counts shows how much of the floor belongs to the instrument.
Bound
H1953. The resolution of a time-to-digital converter is bounded by the uniformity of its bins, not by their number, so a 100 ps converter with 10% differential nonlinearity is worse than a 200 ps one with 1%. Bin width sets the scale; bin uniformity sets the information. Feeding both the same interval distribution from a calibrated delay line shows which one resolves the structure.
Threshold
H1954. Below some clock frequency a divider's jitter is its own flip-flop's and above it the input's, with the crossover where the divider's added jitter equals the source's. The divider's contribution is roughly constant in time; the source's is constant in phase. Measuring the same source through one and through ten divider stages at several frequencies locates the crossover.
Reversal
H1955. Raising a crystal's drive level lowers its phase noise up to a point and then raises it, because the larger amplitude improves the signal-to-noise ratio at the resonator while driving the quartz's own amplitude-to-phase conversion harder. The optimum is below the maximum rated drive. Sweeping drive level on one crystal and measuring both the close-in and the far-out phase noise shows the two trends crossing.
Count
H1956. A cable's phase drift with temperature has one coefficient per dielectric material in it, so a cable with a foam core and a solid jacket has two, and a specification giving one number is an average over a range where the two dominate in turn. Each material's expansion and permittivity slope contribute separately. Cycling one cable over a range and fitting two exponentials, then repeating with the jacket stripped, counts them.
Artefact mimicking effect
H1957. Cycle-to-cycle jitter reported by a digital oscilloscope contains a term from the instrument's interpolation, which grows with the sample spacing and appears as jitter on a signal that has none. The interpolator reconstructs between samples, and its error is not the signal's. The same source measured at two sample rates gives two jitter numbers whose difference is the interpolation term.
Unit trap
H1958. A one-picosecond timing specification means an absolute time at one frequency and a phase at another, and the two convert only through the period, so a part specified as a phase at 10 GHz and used at 1 GHz must hold ten times the absolute jitter to meet the same number. Absolute and phase specifications are not interchangeable. Measuring the same clock at both frequencies with one instrument reports which quantity the datasheet meant.
Identity
H1959. Reference jitter and voltage-controlled-oscillator jitter are the same quantity filtered by the loop, so an output measurement cannot separate them without changing the loop bandwidth. The loop's transfer function weights each by its own shape. Measuring the output at two loop bandwidths and solving the two equations recovers both contributions.
Scale argument
H1960. At long averaging times a clock's Allan deviation turns upward because of temperature, and at short times downward because of white phase; the two regions meet at a time constant set by the oven's thermal mass rather than by the quartz. The crystal sets the short-time slope, the package sets the long-time turn. Measuring one oscillator with and without its outer insulation moves the turn and identifies the mechanism.
References and stable sources
Misattribution
H1961. Noise seen on a voltage reference's output during conversion is often the reference's own, but part of it is load regulation responding to the converter's conversion current, which is synchronous with the conversions and absent when they stop. The reference is being asked for charge at the conversion rate. Freezing the converter's conversions and remeasuring the output spectrum separates the two.
Hidden term
H1962. A reference's output impedance forms a divider with the converter's sampling capacitor, so the reference noise seen by the converter includes the reference's settling after every charge transfer, which is a function of the impedance and not of the reference's noise. The datasheet's noise is measured unloaded. Loading the reference with a switched capacitor of known size and sweeping the impedance shows the added term.
Threshold
H1963. Below a minimum cathode current a shunt reference's noise rises not because regulation fails but because the avalanche becomes bursty, so the current for best noise is well above the current for adequate regulation. The two minima are different operating points. Sweeping bias current while measuring both the output voltage and its low-frequency spectrum shows them separating.
Bound
H1964. The thermal hysteresis of a reference after a temperature cycle is bounded by the package's stress rather than by the die's design, so a better die in the same package shows the same hysteresis. The package transmits the mismatch. Two references in different packages, cycled identically, separate the die's contribution from the package's.
Reversal
H1965. A large capacitor at a reference's output lowers its high-frequency impedance and worsens its response to a load step, because the capacitor's dielectric absorption releases charge slowly after the step and the reference's loop has to correct for it. The capacitance that quietens the noise also lengthens the recovery. Comparing two capacitors of the same value and different dielectric, with a repeated load step, shows the recovery tracking the absorption.
Count
H1966. A ratiometric measurement has one fewer independent error term than an absolute one, because the reference's error divides out, so a system budgeted for n terms and run ratiometrically has n − 1 to spend and is over-specified if it does not. The cancellation is exact only where one reference feeds both excitation and conversion. Running one measurement both ways with a deliberately drifted reference shows the term vanishing.
Artefact mimicking effect
H1967. Steps visible on a reference's output are often the probe's own thermocouple, formed at the junction of the probe's dissimilar metals, rather than the reference. The step appears when the probe's tip moves, not when the load changes. Reversing the probe's polarity or replacing it with a shorter, homogeneous pair moves the steps.
Unit trap
H1968. A reference's temperature coefficient is quoted in parts per million per degree, but its effect on a converter is in codes, so the conversion needs the reference's value, the input range and the bit count together; one part per million per degree in a 16-bit system costs about two-thirds of a code over ten degrees (estimate). The same coefficient costs sixteen times as much in a 20-bit system. Measuring one reference in two converters over one temperature sweep shows the code error scaling.
Identity
H1969. Long-term stability and thermal hysteresis are one parameter measured over different times, so a reference with excellent long-term stability and poor hysteresis is one that has been annealed, not one that is intrinsically stable. Both come from the same stress relaxation, sampled at different periods. Cycling a part and then measuring it for a month shows whether the hysteresis decays or persists.
Inversion of standard practice
H1970. Forcing air over a reference to flatten its temperature coefficient is standard, yet the turbulence adds a low-frequency temperature fluctuation that can be worse than the steady gradient it replaced, particularly for a part with a fast thermal response. Still air and thermal mass give a slower, smaller error. Measuring one part in still air, in laminar flow and in turbulent flow at the same mean temperature shows the noise added by the airflow.
Cabling, connectors and transmission
Misattribution
H1971. Noise produced when a cable is flexed is usually called triboelectric, but in cables with a semiconducting layer the dominant term is the layer's resistance modulation, which is why coating the dielectric does not remove it. The semiconductive layer is part of the signal path's shielding, not a separate screen. Flexing a coated and an uncoated cable of the same construction at the same rate separates the two.
Hidden term
H1972. A measured transfer impedance includes the connectors' inductance, so a shield characterised as a cable and installed with connectors is a different shield above the frequency where the connector dominates. The pigtail inside the connector is usually the largest single term. Measuring the same cable with its connectors and with a clamped bulkhead transition shows the difference.
Bound
H1973. The maximum length over which a cable carries a given bandwidth is bounded by its dielectric loss rather than its copper resistance, because the loss tangent's contribution grows with frequency while the skin-effect resistance grows only as its root. The two cross at a frequency that depends on the dielectric. Two cables of the same gauge and different dielectrics, measured to the same attenuation, differ in reach by the loss-tangent ratio.
Threshold
H1974. Below a certain cable length a reflection from an impedance mismatch arrives after the measurement has finished and is indistinguishable from the source's own settling, so a clean cable is often one that is short rather than one that is matched. Length sets the arrival time; the source sets the window. Extending the cable in steps while watching the settling tail shows the reflection emerge from the noise.
Reversal
H1975. Twisting a pair more tightly lowers magnetic pick-up and raises the pair's capacitance, so the tighter pair is worse above the frequency where the capacitance's loss dominates. The two effects scale in opposite directions with the lay length. Two pairs of the same gauge and different lay lengths, measured for both pick-up and attenuation, cross at a frequency set by the lay.
Scale argument
H1976. Shielding against electric fields scales with the shield's coverage, and against magnetic fields with its thickness relative to the skin depth, so a foil that is excellent at 1 MHz is poor at 50 Hz and the two specifications cannot be traded against each other. Coverage and thickness are different currencies. Measuring one foil against both kinds of field at both frequencies prices them separately.
Artefact mimicking effect
H1977. The notch in a long cable's response is the cable's quarter-wave mode, which moves with length and not with the termination, so a termination problem diagnosed from a fixed-frequency test is often a length problem. The mode's frequency is set by the propagation velocity and the length. Changing the length by ten per cent and watching the notch move identifies it.
Identity
H1978. A connector's contact resistance and its thermal electromotive force are the same contact-quality parameter seen through two probes, because both are set by the true contact area at the asperities. A corroded contact is both resistive and thermoelectric. Measuring both on the same set of aged connectors and plotting one against the other shows whether they track.
Unit trap
H1979. Cable loss is quoted in decibels per hundred metres, but a short sample's measured loss includes the connectors' fixed loss and the launch mismatch, so the extrapolated per-length figure comes out too high and the error grows as the sample shrinks. A slope and an offset are different quantities. Measuring 1 m, 10 m and 100 m of one cable at a single frequency separates the fixed term from the per-length one.
Inversion of standard practice
H1980. Keeping cables short is the usual rule, but a cable near a quarter wavelength of an interfering field is a better antenna than a longer one at a different length, so the worst length is a resonant one and not the longest. Resonance, not length, sets the pick-up. Sweeping one cable's length through a quarter wave in a fixed field maps the peak.
Calibration and measurement practice
Selection effect
H1981. Inter-laboratory comparisons select laboratories as well as measurements, so the claimed uncertainty of a comparison is a survivor's uncertainty and understates what a new entrant would find. Laboratories that did badly tend not to return. Comparing the reported uncertainty with the spread of the first round's results, before any withdrawal, shows the truncation.
Threshold
H1982. Below some input level a digital multimeter's reading is set by its own input bias current flowing through the source, not by its resolution, and the error is a resistance times a current rather than a count. Resolution is the wrong specification at that level. Reading one high-value resistor on two meters, one with a much lower bias current, shows the level where the reading changes.
Misattribution
H1983. Drift in a four-wire resistance measurement is often the sense leads' thermal electromotive force rather than the resistor, because the sense pair carries no current and therefore contributes only its junction voltages. Reversing the current reverses the resistor's contribution and leaves the junction's. A current-reversal measurement repeated as the room warms separates them.
Hidden term
H1984. A two-wire resistance measurement includes the lead resistance and its temperature coefficient, so the coefficient obtained is the sum of the resistor's and the copper's, and a low-value resistor measured this way has a coefficient dominated by the leads. Four-wire sensing removes the term but not the junction. Measuring one resistor with two lead lengths at the same temperature attributes the coefficient.
Bound
H1985. The accuracy of an alternating-current measurement is bounded by the thermal converter's own alternating-to-direct transfer difference, not by the meter's resolution, so extra digits do not buy accuracy at the top of the range. The converter is the standard. Comparing two converters against each other and against a direct-current standard gives the bound without a better reference.
Count
H1986. A calibration chain of n links carries at most n independent corrections, so a chain claiming more has counted the same correction twice or has invented one. Each link contributes one transfer and one uncertainty. Recomputing a chain's budget from the end backwards and seeing which corrections cancel exposes the double count.
Artefact mimicking effect
H1987. A rise in a measurement's Allan deviation at long averaging times is often the room's temperature cycling rather than the instrument, because the cycle period is long and its amplitude is small but coherent. The instrument's own drift is usually monotone. Comparing a run with the thermostat disabled and one with it enabled separates them.
Null claim
H1988. Increasing a converter's resolution does not increase the information in a measurement whose source noise exceeds one least-significant bit, because the extra bits resolve the noise more finely rather than the signal. Resolution and information are different quantities. Averaging the same source with two converters of different resolution and comparing the scatter of the means shows where the extra bits stop helping.
Unit trap
H1989. A specification in parts per million of reading and one in parts per million of range differ by the ratio of the range to the reading, so mixing them mis-budgets by that ratio and usually in the optimistic direction at the bottom of the range. One meter can be quoted either way. Applying both interpretations to one measurement near full scale and near one per cent of it shows where they diverge.
Identity
H1990. Settling time and dielectric absorption are the same property of an insulator viewed in the time and frequency domains, so a capacitor that settles slowly has a matching low-frequency loss, and one cannot be improved without the other. The absorption is the time-domain shadow of the loss tangent's slope. Measuring both on one capacitor and comparing the predicted settling with the measured one tests the identity.
System-level and cross-cutting
Misattribution
H1991. Interference that appears only when a second instrument is connected is usually a mains ground loop rather than radiation, because the second chassis completes a return path the first did not have. Radiation would not care about the second instrument's mains lead. Running both from one outlet, then through an isolation transformer, then with a common-mode choke around both mains leads, distinguishes the path.
Hidden term
H1992. A test's uncertainty includes the device's own impedance, which the instrument assumes equals its reference, so a source that is not 50 Ω is measured with an error that is a function of the mismatch and not of the instrument's accuracy. The assumption is invisible in the specification. Inserting a calibrated pad of known impedance and comparing the reading with and without it exposes the term.
Bound
H1993. The dynamic range of a receiving chain is bounded by the largest signal's intermodulation products rather than by its noise floor, because the products land in the band and cannot be averaged away. A chain can be quiet and still be unusable. Two tones at the top of the range, swept down in level, show where the products fall below the noise and set the real range.
Threshold
H1994. Below some load current a current-sense amplifier's reading is set by the thermal electromotive force of its own shunt, which depends on the load's duty cycle rather than on the current, so the zero moves when the duty cycle changes. The shunt is a thermocouple at low currents. Measuring the same average current at two duty cycles, with the same shunt, shows the offset moving.
Reversal
H1995. Attenuating a signal before an amplifier improves its large-signal distortion and degrades its noise figure, so there is an attenuation at which the two effects balance and the chain's overall fidelity is best, and it is neither zero nor maximum. The optimum moves with the signal's level. Sweeping a step attenuator ahead of the amplifier and measuring both distortion and noise at one output level locates it.
Count
H1996. Distinct ground-referenced error sources in a chain number as many as the places where a signal's return path differs from its forward path, which is not the number of ground symbols on the schematic. Symbols are conventions; returns are currents. Breaking each return in turn and measuring the change in the output attributes one error to each place, and the count of places is the count of terms.
Scale argument
H1997. Bits required by a measurement scale with the logarithm of the ratio of its largest to its smallest resolvable signal, so resolution and range are one specification, and a converter quoted at a microvolt resolves that only over the range it was quoted at. Range and resolution trade against each other linearly in codes. Measuring the same small signal on two ranges of one converter shows the code size changing.
Artefact mimicking effect
H1998. An improvement in measured emission after a shielding change is often the improvement from moving the cable, since the cable's position sets its coupling to the room more than the shield does at low frequency. The shield is a small perturbation on a large geometry. Repeating the measurement with the shield fitted but the cable returned to its original position, and the reverse, assigns the change.
Inversion of standard practice
H1999. Raising a digitizer's sample rate does not lower its noise density in a band, so a faster converter is not a quieter one, yet it does narrow the band a given number of samples averages over and so improves a slow measurement's resolution. Speed buys averaging, not silence. One source digitised at two rates and averaged over the same number of samples gives two resolutions whose ratio is the root of the rate ratio.
Selection effect
H2000. Requirements for a measurement system are usually written from one application's data, so the specification excludes the cases that would have changed it and the instrument is precise about the wrong thing. The data that shaped the requirement is the data the instrument was then validated on. Testing the finished system on an application deliberately outside the original set shows which requirements were general and which were local.
Status
One hundred entries, 1901 to 2000, contiguous. The forms were allowed to fall where the subject put them; a list with equal counts in each category would have been a grid wearing labels.
Three that could be settled with apparatus most electronics laboratories already own: H1902, that a fast amplifier's settling tail belongs to the input pair's thermal history and not to slew limiting; H1905, that a bipolar front end's offset becomes the Seebeck voltage of its own solder joints below a few hundred ohms of source; and H1941, that a shielded enclosure leaks through its cable penetration rather than its seams below the first cavity mode.
If one of these is worth an afternoon, it is H1902 — drive one amplifier with steps of the same amplitude from two baselines that hold the input stage's dissipation constant, and watch whether the tail follows the step or the dissipation. It needs a fast source, a scope and the amplifier already on the bench.
Incoprea Research · hand-considered hypotheses 1901–2000 · electronics, instrumentation and the signal chain · 3 November 2026 · ~/Desktop/Nov3/