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[+] What is a resistor?

A resistor is a passive electronic component consisting of a material that is characterized by high electrical resistivity,
with a low-resistivity terminal attached to each end for electrical connections. The resistor produces a voltage drop across its terminals which is
proportional to the electric current passing through it (see Ohm’s law). Resistors are used to limit electrical current, measure or establish voltage
levels, divide voltages, and attenuate signals. They may also act as heaters and fuses.

[+] What is Ohm’s law?

Ohm’s law states the proportionality between the electrical current through a resistor and the voltage measured across the resistor:

I = V/R

Where I is the current (amps), V is the voltage (volts), and R is the resistance (ohms).

Expression for electrical power:

P = VI

Power (P), in watts, may be transformed using Ohm’s law as follows:

P = V^{2}/R or P = I^{2}R

[+] Acceptable quality limit (AQL):

The maximum percent defective (or maximum number of defects per hundred units) that, for the purpose of sampling inspection, can be considered
satisfactory as a process average. Defects may be both major and minor, according to definition, and may have different AQLs. AQLs of 1% major
and 2.5% minor are common. A sampling plan should have a low Producer's Risk for quality which is equal to or better than the AQL.

[+] Accuracy:

The degree to which the measured value of resistance approximates the specified value of resistance. This is normally expressed in percent
deviation but in precision resistors the results are reported in parts per million (ppm), a more practical expression for very small deviations. For
example, a resistor of 5000Ω nominal value that actually measures 4999.75Ω has a minus 50ppm (-0.005%) deviation. Note that it takes a
minimum of seven significant figures to properly measure a precision resistor of 50ppm accuracy.

[+] Allowable spread:

The limits to which a given parameter can range.

[+] Backlash:

The amount of reverse rotation of an adjustment control (potentiometers or rheostats) required to cause an electrical change in the opposite direction.

[+] Bulk properties:

Bulk properties are the characteristics of the parent metal and/or alloy from which a resistive element is made. These bulk properties are degraded
by rolling, drawing, winding, evaporating, sputtering, heat treating and laminating. Various compensating techniques permit the finished devices to
display properties similar to the parent metal, but foil resistors provide the most faithful reproduction of bulk properties in commercially available
resistors.

[+] Contact resistance:

An unwanted resistance between the trimmer’s resistive element and its contact wiper. Since the wiper is connected to the wiper terminal, it
results in variation in the electrical output of a trimmer not representative of the electrical input. Contact resistance becomes evident when the
wiper traverses the resistive element. Its value is expressed in ohms or as a percentage of the total resistance of the trimmer.

[+] Contact resistance variation - CRV (noise):

The instantaneous change in contact resistance that may occur as a result of wiper movement. Typically its maximum value is given as a
percentage of total resistance of the trimmer or is expressed in ohms.

[+] Critical resistance:

Critical resistance is the resistance value at which the resistor dissipates rated power at rated voltage. Per transformations of Ohm’s law V = IR:

1. P = E^{2}/R &

2. E =

It is evident that as R decreases, P increases per equation 1. When P increases to the resistor’s maximum rating, then E must decrease along
with R or the resistor’s maximum power rating will be exceeded. Similarly, from equation 2, when R increases, E increases. When E increases
to its maximum rating, continued increasing of R would cause E to exceed its maximum rating. Therefore, to continue to increase R, P must be
decreased (by reducing current) or the resistor’s maximum voltage rating would be exceeded. Thus,

1. The resistor must be run at less than its maximum voltage rating for resistance values below the critical resistance, and

2. The resistor must be run at less than its maximum power rating for resistance values above the critical resistance.

[+] Cross talk:

A signal received in a nearby component caused by the signal in a transmitting component. This is primarily a result of RF radiation and may be
eliminated by shielding to ground.

[+] Current noise:

Spurious error voltages generated across a resistor when a current is passed through it. Current noise is usually expressed in RMS microvolts
per volt (µV/V) applied to the resistor. It may also be expressed in dB (noise index figures).

[+] Current rating:

The highest current that may pass through the device (usually continuously) over a long period of time without causing the component to fail or
causing a shift of the component’s principal parameters outside of allowable limits. Current ratings are considered in conjunction with voltage and
power ratings and must be monitored accordingly. See “Critical Resistance.”

[+] Derating:

The intentional restriction of power dissipation below the manufacturer’s stated power rating. Some military programs require derating of all
resistors to half power, but this is not necessary with foil resistors because they are rated for very predictable low long-term drift at full rated
power at maximum temperature.

[+] Dielectric withstanding voltage (DWV):

The DWV is the maximum voltage that can be applied without breakdown (arc-over) or other harm to the device. It is normally specified in DC volts for a specified period of time and with a maximum allowed leakage current.

[+] Electromagentic interference (EMI):

Radiation from an external source causing signal distortion.

[+] Electrostatic discharge (ESD):

A high voltage pulse induced into a device as a result of its coming in contact with or in proximity to an electrically charged object. In very dry climates, charges build up on any moving object including people. These charges may pass (discharge) to an electronic device when the charged body comes into proximity with it. A device is said to be ESD-sensitive if this passage of charge does harm to the device in any way.

[+] End resistance (ER):

In trimming potentiometers and rheostats, the resistance measured between the wiper terminal and an end terminal when the wiper is positioned against the stop at that particular end terminal.

[+] Equivalent noise resistance - ENR (Zero-Based CRV):

In trimming potentiometers and rheostats, the change in contact resistance made up of a DC offset plus CRV. The resistance measured between the wiper and the resistance element when one milliampere of current is passed through the wiper as it is adjusted.

[+] Established reliability (ER):

The demonstrated ability of an item to perform a required function under stated conditions for a stated period of time. As a practical matter it is not possible to demonstrate item reliability under all conditions so load-life testing is relied upon to represent other demands and a failure rate demonstration is concluded. Qualification and maintenance testing over an extended period of time demonstrate failure rates such as 0.1% failures per 1,000 hours of testing. This equates to a mean time between failures (MTBF) of 1 million hours.

[+] Frequency response:

The ability of a resistor to faithfully replicate a signal at specified frequency. In an AC circuit, the voltage drop and the current passed are a function of not just the DC resistance but also the reactance at a specified frequency. Foil resistors deliver good frequency response at frequencies into the megahertz range.

[+] Hermetic sealing:

The placement of a device in an enclosure impervious to gas transmission, generally for the purpose of protecting it from moisture. The degree of hermeticity is usually determined by exposure to pressurized helium and then measuring the rate at which the helium escapes. Acceptable leak rates normally are equal to or less than 1 x 10 -7 cc per second at normal atmospheric pressure. Helium is used because its small molecules pass through small openings while also being easy to handle and detect in production.

[+] Hop-off:

The resistance change measured between the wiper and an end terminal as the wiper moves off that end terminal and initially comes in contact with the resistance element.

[+] Humidity coating:

The application of various coating materials (glasses, polymers, etc.) for the purpose of retarding the ingress of moisture to components and circuitry.

[+] Impedance:

The vector sum of the resistance and reactances (inductive and capacitive) of a circuit or device.

[+] Improved performance testing (IPT):

A regimen of testing prior to shipment designed to exercise a resistor beyond normal application stresses in order to reduce in-service changes and add levels of confidence in actual application. Generally it is preferred to design the product for a given level of stability, but in precision applications where a few parts per million shift can be objectionable, conditioning of a part prior to shipment becomes a necessary alternative. Powertron has a specific IPT routine for this purpose as well as offering a variety of test plans.

[+] Insulation resistance (IR):

The resistance presented to a direct voltage applied between the trimmer terminals and electrically isolated external metallic parts such as shaft, housing, and mounting hardware.

[+] Limiting quality (LQ):

The lowest product quality that the consumer defines for the acceptance of the output of a specific test regimen, usually expressed as a maximum percent defective allowed.

[+] Load-life stability:

The measured change in resistance resulting from the application of specified power at specified temperature for a specified time interval. Commonly used time intervals are 1,000, 2,000, and 10,000 hours and commonly used temperatures are 60, 70, 85 and 125°C. Allowable changes depend on the resistor element technology. Foil elements are the most stable, exhibiting the least change under comparable conditions.

[+] Lot average:

The arithmetic mean of test results of a lot of devices, each having an individual value.

[+] Match or matching:

Two or more resistors grouped into narrower limits within the total tolerance span.

[+] Maximum working voltage:

The highest voltage that may be applied across the resistor terminals (usually continuously) over a long period of time without causing the component to fail or shift outside of allowable limits of principal parameters. Maximum working voltage is commonly applicable to high-ohmic value resistors particularly because in low-ohmic resistors the voltage is limited by the power rating of the resistor.

[+] Mechanical stops:

Physical limits to wiper motion at each end of the wiper travel.

[+] Microhenry (µH):

1 µH = 10^{-6} Henry. (The Henry is the unit of inductance.)

[+] Moisture resistance:

The ability to retain initial characteristics through specified moisture and voltage application. Unless hermetically sealed, all resistors experience some change in value due to moisture. Because of their bulk properties, foil resistors experience the least amount of change in commercially available precision resistors.

[+] Noise:

An unwanted signal inserted by the flow of electrical current in a resistor (see Current noise, above), by thermal movement of electrons and by discrete nature of electrical current.

[+] Nominal:

The specified value of resistor parameter (resistance, TCR or other) to which a tolerance or spread is applied.

[+] Parts per million (ppm):

Relative unit equal to 1/1,000,000. (Conversion of % to ppm)

[+] Operating temperature range:

The lowest to the highest ambient temperature range within which a device is expected to operate for a prescribed period of time while its parameters remain within prescribed limits.

[+] Percent defective allowable (PDA):

The limiting number of defects in one inspection lot that will permit acceptance of the lot. For example, if more than 3% of the lot fails, reject the entire lot. Tightened inspection may be permitted with a larger PDA and additional samples in the inspection plan.

[+] Phase shift:

The result of capacitive and/or inductive reactance causing the resistor output signal to lead or lag the input signal.

[+] Picofarad (pF):

1 pF = 10^{-12} Farads. (The Farad is the unit of capacitance).

[+] Power rating:

The maximum power that can be applied, under specified conditions of environment and duration, which will not produce a permanent change of resistor parameters in excess of specified limits. Foil resistors are capable of considerable overload for short periods of time and exhibit the least amount of long-term drift for any commercially available resistors subjected to rated power. Further drift reduction is obtainable through derating, power conditioning and/or IPT.

[+] Precision:

Precision of a lot of resistors is the measure of dispersion of resistance values in relation to the *lot average*. It is quantified by *standard deviation*.

[+] Qualified Product List (QPL):

A government listing of products and suppliers currently qualified to a military specification.

[+] Reactance:

Reactance of resistor is its opposition to an alternating current, caused by the build up of electric or magnetic fields due to the current. A positive reactance implies that the resistor is inductive, where phase of the voltage leads the phase of the current; while a negative reactance implies that the resistor is capacitive, where phase of the voltage lags the phase of the current. The vector sum of resistance and reactance gives impedance of the resistor at a given frequency. Powertron foil resistors have extremely low reactances and thus have fast rise times and good frequency response.

[+] Reliability:

The ability of an item to perform a required function under stated conditions for a stated period of time. In practice, the mean time between failures (MTBF) is a more precise mathematical way of defining reliability.

[+] Resistance range:

The spectrum of resistance values that can be manufactured within a particular product style and still comply with a common set of specifications.

[+] Rise and decay time:

The length of time between the initial imposition of a voltage across a resistor and the time that the resistor is passing a constant current. It is measured between the points in time when the current reaches 10% and 90% of its final steady-state value.

[+] Root mean square (RMS):

The effective value of an alternating current (voltage) is numerically equal to the value of DC current (voltage) producing the same heating in a given resistor as the given alternating current (voltage). The root mean square calculation of periodic waveform f(t) is performed according to the formula:

where T1 and T2 are beginning and end moments of a period of periodic waveform f(t). The RMS value of a sine wave is equal to its peak value multiplied by 0.707.

[+] Rotational life:

In a trimmer, the number of traverses (back and forth) of the wiper across the entire resistive element before the trimmer exceeds allowable resistance change or fails to meet prescribed performance criteria.

[+] Self heating:

The heat generation within the resistive element caused by the application of electrical voltage. Self heating raises the device temperature above the ambient temperature. The internal hot spot temperature is kept within safe limits by adherence to the power rating and derating curves.

[+] Settability:

The degree of accuracy to which a trimmer can be adjusted to a previously determined point in 20 seconds. This point can be either an output voltage ratio or some specific value of resistance expressed as a percentage of the trimmer’s total resistance.

[+] Setting stability:

The ability of a trimmer’s wiper contact to remain stationary when the trimmer is subjected to various environmental stress.

Expressed as:

Where: E1 = voltage across one end terminal and the wiper terminal, and E2 = voltage across the end terminals. The difference between the initial measurement made before the environmental test and the measurement made after the test indicates the setting stability in %.

[+] Shelf-life stability:

The change in resistance value when an item is stored under standard conditions, such as +25°C, ±15°C and 10% to 75% relative humidity for a stated period of time. Foil resistors undergo no significant permanent change due to shelf conditions but may see some small change due to humidity fluctuation. This humidity effect is completely reversible by drying.

[+] Short time overload (STOL):

The application of a specified extra power for a short period of time. Usually used as a screen test or qualifying test. Foil resistors can sustain considerable overload without damage and routinely receive 6.25 times rated power for five seconds during final inspection.

[+] Source control drawing (SCD):

A user-generated specification, usually created in the absence of a military specification but embracing much of the discipline of a military specification. May require non-standard parts approval before proceeding.

[+] Speed or speed of response:

The time interval necessary for the current to pass from 10% to 95% of full current following a voltage application. Foil resistors are the fastest of any precision resistors and require less than 1 nanosecond rise time

[+] Spread:

The total range of values within a lot.

[+] Stability:

The ability of any device to retain its initial characteristics through one or more imposed stresses. Foil resistors are uniquely stable through all environments.

[+] Standard Deviation (σ):

The standard deviation (root mean square deviation) is used to measure the dispersion of a group of quantities about their mean value ( x ). When the quantities have normal (Gaussian) distribution, approximately 68% of the quantities in the group will be within x ± σ interval as shown in the graph below. The formula for finding the standard deviation is

The normal distribution curve is a pictorial representative of the distribution of readings about their mean value. Pictured is a representation of the TCR values of Vishay Foil Resistor style S102C foil resistors in temperature range from +25°C to +125°C.

[+] Normal distribution curve:

[+] Temperature coefficient of resistance (TCR):

This coefficient relates the change in resistance to any change related to a given range of temperatures. The general equation is:

Negative TCRs are possible when R2 is less than R1. TCR is generally expressed as parts per million per degree Celsius (ppm/°C). Foil resistors have the lowest and most consistent TCR and the least spread of TCR of any commercially available resistor.

[+] TCR – end-to-end:

The temperature coefficient relating a change in the trimmer end-to-end resistance (pin 1 to pin 3 with the wiper on an end pad) to the difference in temperature producing the change.

[+] TCR – through the wiper:

The temperature coefficient relating a change in the trimmer wiper to end resistance (pin 2 to pin 1 or 3 with the wiper at 40% to 60% of mid-range) to the difference in temperature producing the change.

[+] Thermal electromotive force (Thermal EMF):

The temperature-dependent electrical potential produced continuously between two junctions of two dissimilar metals or alloys. Various metals and their alloys have different thermal EMFs in combination with other metals and alloys. Since resistors commonly have copper terminals, the various metals employed in making resistors are characterized by their thermal EMF expressed in µV/°C versus copper. Foil resistors have very low thermal EMF because the foil alloy has a low EMF versus copper. In addition to having very low absolute thermal EMF, foil resistors posses extremely good thermal efficiency, which keeps a near-zero thermal difference across the terminations, thereby further reducing the effective thermal EMF across the resistor.

[+] Thermal shock:

A major temperature change with specified rate of change imposed on the device. Foil resistors can sustain considerable thermal shock including the sudden shock from immersion in liquid nitrogen to hot oil. Many other constructions require a ramp up and dwell to avoid destruction of internal connections.

[+] Tolerance:

The permissible deviation of actual resistance from nominal resistance expressed in percent; e.g. ±0.005%. Note that the tolerance normally permits deviation either side of nominal but circumstances could call for deviation on one side. For example, the allowable spread could be 0% + 0.01%/-0.0% to indicate that the allowable resistance tolerance is on the plus side only.

[+] Track or tracking:

Two or more resistors exhibiting similar responses to temperature within specified limits or "track." While tracking with temperature is the most frequent use of the term, there may be occasions when tracking with load, environmental and time are required. Foil resistors offer the best available tracking with all stresses in addition to temperature.

[+] Typical:

A designer’s reference which represents that 85% of the units supplied, over a long period of time, will be at least the figure shown or better.

[+] Voltage coefficient:

Expresses the non-linearity of resistance versus voltage when a change in voltage produces a change in resistance other than predicted by Ohm’s law, E = IR. The voltage coefficient of foil resistors is so low that it is largely ignored in practice. Some other resistor technologies significantly deviate from Ohm’s law and exhibit different resistance values when measured under different voltages.