Resistor
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Resistor

Resistor
Electronic-Axial-Lead-Resistors-Array.png
An array of axial-lead resistors
TypePassive
Working principleElectric resistance
Electronic symbol
IEEE 315-1975 (1993).2.1.1.a.svg IEEE 315-1975 (1993) 2.1.1.b.svg
IEEE schematic symbols
Various resistor types of different shapes and sizes

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, light, humidity, force, or chemical activity.

Resistors are common elements of electrical networks and electronic circuits and are ubiquitous in electronic equipment. Practical resistors as discrete components can be composed of various compounds and forms. Resistors are also implemented within integrated circuits.

The electrical function of a resistor is specified by its resistance: common commercial resistors are manufactured over a range of more than nine orders of magnitude. The nominal value of the resistance falls within the manufacturing tolerance, indicated on the component.

Electronic symbols and notation

Two typical schematic diagram symbols are as follows:

The notation to state a resistor's value in a circuit diagram varies.

One common scheme is the RKM code following IEC 60062. Rather than using a decimal separator, this notation uses a letter loosely associated with SI prefixes corresponding with the part's resistance. For example, 8K2 as part marking code, in a circuit diagram or in a bill of materials (BOM) indicates a resistor value of 8.2 k?. Additional zeros imply a tighter tolerance, for example 15M0 for three significant digits. When the value can be expressed without the need for a prefix (that is, multiplicator 1), an "R" is used instead of the decimal separator. For example, 1R2 indicates 1.2 ?, and 18R indicates 18 ?.

Theory of operation

The hydraulic analogy compares electric current flowing through circuits to water flowing through pipes. When a pipe (left) is clogged with hair (right), it takes a larger pressure to achieve the same flow of water. Pushing electric current through a large resistance is like pushing water through a pipe clogged with hair: It requires a larger push (voltage) to drive the same flow (electric current).[1]

Ohm's law

The behaviour of an ideal resistor is described by Ohm's law:

Ohm's law states that the voltage () across a resistor is proportional to the current () passing through it, where the constant of proportionality is the resistance (). For example, if a 300-ohm resistor is attached across the terminals of a 12-volt battery, then a current of 12 / 300 = 0.04 amperes flows through that resistor.

The ohm (symbol: ?) is the SI unit of electrical resistance, named after Georg Simon Ohm. An ohm is equivalent to a volt per ampere. Since resistors are specified and manufactured over a very large range of values, the derived units of milliohm (1 m? = 10-3 ?), kilohm (1 k? = 103 ?), and megohm (1 M? = 106 ?) are also in common usage.[2][3]

Series and parallel resistors

The total resistance of resistors connected in series is the sum of their individual resistance values.

Circuit diagram of several resistors, labelled R1, R2 ... Rn, connected end to end

The total resistance of resistors connected in parallel is the reciprocal of the sum of the reciprocals of the individual resistors.[3]

Circuit diagram of several resistors, labelled R1, R2 ... Rn, side by side, both leads of each connected to the same wires

For example, a 10 ohm resistor connected in parallel with a 5 ohm resistor and a 15 ohm resistor produces 1/1/10 + 1/5 + 1/15 ohms of resistance, or 30/11 = 2.727 ohms.

A resistor network that is a combination of parallel and series connections can be broken up into smaller parts that are either one or the other. Some complex networks of resistors cannot be resolved in this manner, requiring more sophisticated circuit analysis. Generally, the Y-? transform, or matrix methods can be used to solve such problems.[4][5][6]

Power dissipation

At any instant, the power P (watts) consumed by a resistor of resistance R (ohms) is calculated as:

where V (volts) is the voltage across the resistor and I (amps) is the current flowing through it. Using Ohm's law, the two other forms can be derived. This power is converted into heat which must be dissipated by the resistor's package before its temperature rises excessively.[3]

Resistors are rated according to their maximum power dissipation. Discrete resistors in solid-state electronic systems are typically rated as 110, 18, or 14 watt. They usually absorb much less than a watt of electrical power and require little attention to their power rating.

An aluminium-encased power resistor rated for dissipation of 50 W when mounted on a heat-sink

Power resistors are required to dissipate substantial amounts of power and are typically used in power supplies, power conversion circuits, and power amplifiers; this designation is loosely applied to resistors with power ratings of 1 watt or greater. Power resistors are physically larger and may not use the preferred values, color codes, and external packages described below.

If the average power dissipated by a resistor is more than its power rating, damage to the resistor may occur, permanently altering its resistance; this is distinct from the reversible change in resistance due to its temperature coefficient when it warms. Excessive power dissipation may raise the temperature of the resistor to a point where it can burn the circuit board or adjacent components, or even cause a fire. There are flameproof resistors that will not produce flames with any overload of any duration.

Resistors may be specified with higher rated dissipation than is experienced in service to account for poor air circulation, high altitude, or high operating temperature.

All resistors have a maximum voltage rating; this may limit the power dissipation for higher resistance values.[7] For instance, among 14 watt resistors (a very common sort of leaded resistor) one is listed with a resistance of 100 M?[8] and a maximum rated voltage of 750 V. However even placing 750 V across a 100 M? resistor continuously would only result in a power dissipation of less than 6 mW, making the nominal 14 watt rating meaningless.

VZR power resistor 1.5 k? 12 W, manufactured in 1963 in the Soviet Union

Nonideal properties

Practical resistors have a series inductance and a small parallel capacitance; these specifications can be important in high-frequency applications. In a low-noise amplifier or pre-amp, the noise characteristics of a resistor may be an issue.

In some precision applications, the temperature coefficient of the resistance may also be of concern.

The unwanted inductance, excess noise, and temperature coefficient are mainly dependent on the technology used in manufacturing the resistor. They are not normally specified individually for a particular family of resistors manufactured using a particular technology.[9] A family of discrete resistors may also be characterized according to its form factor, that is, the size of the device and the position of its leads (or terminals). This is relevant in the practical manufacturing of circuits that may use them.

Practical resistors are also specified as having a maximum power rating which must exceed the anticipated power dissipation of that resistor in a particular circuit: this is mainly of concern in power electronics applications. Resistors with higher power ratings are physically larger and may require heat sinks. In a high-voltage circuit, attention must sometimes be paid to the rated maximum working voltage of the resistor. While there is no minimum working voltage for a given resistor, failure to account for a resistor's maximum rating may cause the resistor to incinerate when current is run through it.

Fixed resistors

A single in line (SIL) resistor package with 8 individual 47 ohm resistors. This package is also known as a SIP-9. One end of each resistor is connected to a separate pin and the other ends are all connected together to the remaining (common) pin - pin 1, at the end identified by the white dot.

Lead arrangements

Axial resistors with wire leads for through-hole mounting

Through-hole components typically have "leads" (pronounced ) leaving the body "axially", that is, on a line parallel with the part's longest axis. Others have leads coming off their body "radially" instead. Other components may be SMT (surface mount technology), while high power resistors may have one of their leads designed into the heat sink.

Carbon composition

Old style "dog bone" resistors with "body, tip, dot" color code marking
Three carbon composition resistors in a 1960s valve (vacuum tube) radio

Carbon composition resistors (CCR) consist of a solid cylindrical resistive element with embedded wire leads or metal end caps to which the lead wires are attached. The body of the resistor is protected with paint or plastic. Early 20th-century carbon composition resistors had uninsulated bodies; the lead wires were wrapped around the ends of the resistance element rod and soldered. The completed resistor was painted for color-coding of its value.

The resistive element in carbon composition resistors is made from a mixture of finely powdered carbon and an insulating material, usually ceramic. A resin holds the mixture together. The resistance is determined by the ratio of the fill material (the powdered ceramic) to the carbon. Higher concentrations of carbon, which is a good conductor, result in lower resistances. Carbon composition resistors were commonly used in the 1960s and earlier, but are not popular for general use now as other types have better specifications, such as tolerance, voltage dependence, and stress. Carbon composition resistors change value when stressed with over-voltages. Moreover, if internal moisture content, such as from exposure for some length of time to a humid environment, is significant, soldering heat creates a non-reversible change in resistance value. Carbon composition resistors have poor stability with time and were consequently factory sorted to, at best, only 5% tolerance.[10] These resistors are non-inductive, which provides benefits when used in voltage pulse reduction and surge protection applications.[11] Carbon composition resistors have higher capability to withstand overload relative to the component's size.[12]

Carbon composition resistors are still available, but relatively expensive. Values ranged from fractions of an ohm to 22 megohms. Due to their high price, these resistors are no longer used in most applications. However, they are used in power supplies and welding controls.[12] They are also in demand for repair of vintage electronic equipment where authenticity is a factor.

Carbon pile

A carbon pile resistor is made of a stack of carbon disks compressed between two metal contact plates. Adjusting the clamping pressure changes the resistance between the plates. These resistors are used when an adjustable load is required, such as in testing automotive batteries or radio transmitters. A carbon pile resistor can also be used as a speed control for small motors in household appliances (sewing machines, hand-held mixers) with ratings up to a few hundred watts.[13] A carbon pile resistor can be incorporated in automatic voltage regulators for generators, where the carbon pile controls the field current to maintain relatively constant voltage.[14] This principle is also applied in the carbon microphone.

Carbon film

Carbon film resistor with exposed carbon spiral (Tesla TR-212 1 k?)

In manufacturing carbon film resistors, a carbon film is deposited on an insulating substrate, and a helix is cut in it to create a long, narrow resistive path. Varying shapes, coupled with the resistivity of amorphous carbon (ranging from 500 to 800  m), can provide a wide range of resistance values. Carbon film resistors feature lower noise compared to carbon composition resistors because of the precise distribution of the pure graphite without binding.[15] Carbon film resistors feature a power rating range of 0.125 W to 5 W at 70 °C. Resistances available range from 1 ohm to 10 megaohm. The carbon film resistor has an operating temperature range of -55 °C to 155 °C. It has 200 to 600 volts maximum working voltage range. Special carbon film resistors are used in applications requiring high pulse stability.[12]

Printed carbon resistors

Carbon resistors (black rectangles) printed directly onto the SMD pads on the PCB of a Psion Organiser II from 1989

Carbon composition resistors can be printed directly onto printed circuit board (PCB) substrates as part of the PCB manufacturing process. Although this technique is more common on hybrid PCB modules, it can also be used on standard fibreglass PCBs. Tolerances are typically quite large and can be in the order of 30%. A typical application would be non-critical pull-up resistors.

Thick and thin film

Laser Trimmed Precision Thin Film Resistor Network from Fluke, used in the Keithley DMM7510 multimeter. Ceramic backed with glass hermetic seal cover.

Thick film resistors became popular during the 1970s, and most SMD (surface mount device) resistors today are of this type. The resistive element of thick films is 1000 times thicker than thin films,[16] but the principal difference is how the film is applied to the cylinder (axial resistors) or the surface (SMD resistors).

Thin film resistors are made by sputtering (a method of vacuum deposition) the resistive material onto an insulating substrate. The film is then etched in a similar manner to the old (subtractive) process for making printed circuit boards; that is, the surface is coated with a photo-sensitive material, covered by a pattern film, irradiated with ultraviolet light, and then the exposed photo-sensitive coating is developed, and underlying thin film is etched away.

Thick film resistors are manufactured using screen and stencil printing processes.[12]

Because the time during which the sputtering is performed can be controlled, the thickness of the thin film can be accurately controlled. The type of material also varies, consisting of one or more ceramic (cermet) conductors such as tantalum nitride (TaN), ruthenium oxide , lead oxide (PbO), bismuth ruthenate , nickel chromium (NiCr), or bismuth iridate .

The resistance of both thin and thick film resistors after manufacture is not highly accurate; they are usually trimmed to an accurate value by abrasive or laser trimming. Thin film resistors are usually specified with tolerances of 1% and 5%, and with temperature coefficients of 5 to 50 ppm/K. They also have much lower noise levels, on the level of 10-100 times less than thick film resistors.[17] Thick film resistors may use the same conductive ceramics, but they are mixed with sintered (powdered) glass and a carrier liquid so that the composite can be screen-printed. This composite of glass and conductive ceramic (cermet) material is then fused (baked) in an oven at about 850 °C.

When first manufactured, thick film resistors had tolerances of 5%, but standard tolerances have improved to 2% or 1% in the last few decades.[timeframe?] Temperature coefficients of thick film resistors are typically ±200 or ±250 ppm/K; a 40-kelvin (70 °F) temperature change can change the resistance by 1%.

Thin film resistors are usually far more expensive than thick film resistors. For example, SMD thin film resistors, with 0.5% tolerances and with 25 ppm/K temperature coefficients, when bought in full size reel quantities, are about twice the cost of 1%, 250 ppm/K thick film resistors.

Metal film

A common type of axial-leaded resistor today is the metal-film resistor. Metal Electrode Leadless Face (MELF) resistors often use the same technology.

Metal film resistors are usually coated with nickel chromium (NiCr), but might be coated with any of the cermet materials listed above for thin film resistors. Unlike thin film resistors, the material may be applied using different techniques than sputtering (though this is one technique used). The resistance value is determined by cutting a helix through the coating rather than by etching, similar to the way carbon resistors are made. The result is a reasonable tolerance (0.5%, 1%, or 2%) and a temperature coefficient that is generally between 50 and 100 ppm/K.[18] Metal film resistors possess good noise characteristics and low non-linearity due to a low voltage coefficient. They are also beneficial due to long-term stability.[12]

Metal oxide film

Metal-oxide film resistors are made of metal oxides which results in a higher operating temperature and greater stability and reliability than metal film. They are used in applications with high endurance demands.

Wire wound

High-power wire wound resistors used for dynamic braking on an electric railway car. Such resistors may dissipate many kilowatts for an extended length of time.
Types of windings in wire resistors:
  1. common
  2. bifilar
  3. common on a thin former
  4. Ayrton-Perry

Wirewound resistors are commonly made by winding a metal wire, usually nichrome, around a ceramic, plastic, or fiberglass core. The ends of the wire are soldered or welded to two caps or rings, attached to the ends of the core. The assembly is protected with a layer of paint, molded plastic, or an enamel coating baked at high temperature. These resistors are designed to withstand unusually high temperatures of up to 450 °C.[12] Wire leads in low power wirewound resistors are usually between 0.6 and 0.8 mm in diameter and tinned for ease of soldering. For higher power wirewound resistors, either a ceramic outer case or an aluminum outer case on top of an insulating layer is used. If the outer case is ceramic, such resistors are sometimes described as "cement" resistors, though they do not actually contain any traditional cement. The aluminum-cased types are designed to be attached to a heat sink to dissipate the heat; the rated power is dependent on being used with a suitable heat sink, e.g., a 50 W power rated resistor overheats at a fraction of the power dissipation if not used with a heat sink. Large wirewound resistors may be rated for 1,000 watts or more.

Because wirewound resistors are coils they have more undesirable inductance than other types of resistor. However, winding the wire in sections with alternately reversed direction can minimize inductance. Other techniques employ bifilar winding, or a flat thin former (to reduce cross-section area of the coil). For the most demanding circuits, resistors with Ayrton-Perry winding are used.

Applications of wirewound resistors are similar to those of composition resistors with the exception of high frequency applications. The high frequency response of wirewound resistors is substantially worse than that of a composition resistor.[12]

Metal foil resistor

Metal foil resistor

In 1960, Felix Zandman and Sidney J. Stein[19] presented a development of resistor film of very high stability.

The primary resistance element of a foil resistor is a chromium nickel alloy foil several micrometers thick. Chromium nickel alloys are characterized by having a large electrical resistance (about 58 times that of copper), a small temperature coefficient and high resistance to oxidation. Examples are Chromel A and Nichrome V, whose typical composition is 80 Ni and 20 Cr, with a melting point of 1420 °C. When iron is added, the chromium nickel alloy becomes more ductile. The Nichrome and Chromel C are examples of an alloy containing iron. The composition typical of Nichrome is 60 Ni, 12 Cr, 26 Fe, 2 Mn and Chromel C, 64 Ni, 11 Cr, Fe 25. The melting temperature of these alloys are 1350 °C and 1390 °C, respectively.[20][full ]

Since their introduction in the 1960s, foil resistors have had the best precision and stability of any resistor available. One of the important parameters of stability is the temperature coefficient of resistance (TCR). The TCR of foil resistors is extremely low, and has been further improved over the years. One range of ultra-precision foil resistors offers a TCR of 0.14 ppm/°C, tolerance ±0.005%, long-term stability (1 year) 25 ppm, (3 years) 50 ppm (further improved 5-fold by hermetic sealing), stability under load (2000 hours) 0.03%, thermal EMF 0.1 ?V/°C, noise -42 dB, voltage coefficient 0.1 ppm/V, inductance 0.08 ?H, capacitance 0.5 pF.[21]

The thermal stability of this type of resistor also has to do with the opposing effects of the metal's electrical resistance increasing with temperature, and being reduced by thermal expansion leading to an increase in thickness of the foil, whose other dimensions are constrained by a ceramic substrate.[]

Ammeter shunts

An ammeter shunt is a special type of current-sensing resistor, having four terminals and a value in milliohms or even micro-ohms. Current-measuring instruments, by themselves, can usually accept only limited currents. To measure high currents, the current passes through the shunt across which the voltage drop is measured and interpreted as current. A typical shunt consists of two solid metal blocks, sometimes brass, mounted on an insulating base. Between the blocks, and soldered or brazed to them, are one or more strips of low temperature coefficient of resistance (TCR) manganin alloy. Large bolts threaded into the blocks make the current connections, while much smaller screws provide volt meter connections. Shunts are rated by full-scale current, and often have a voltage drop of 50 mV at rated current. Such meters are adapted to the shunt full current rating by using an appropriately marked dial face; no change need to be made to the other parts of the meter.

Grid resistor

In heavy-duty industrial high-current applications, a grid resistor is a large convection-cooled lattice of stamped metal alloy strips connected in rows between two electrodes. Such industrial grade resistors can be as large as a refrigerator; some designs can handle over 500 amperes of current, with a range of resistances extending lower than 0.04 ohms. They are used in applications such as dynamic braking and load banking for locomotives and trams, neutral grounding for industrial AC distribution, control loads for cranes and heavy equipment, load testing of generators and harmonic filtering for electric substations.[22]

The term grid resistor is sometimes used to describe a resistor of any type connected to the control grid of a vacuum tube. This is not a resistor technology; it is an electronic circuit topology.

Special varieties

Variable resistors

Adjustable resistors

A resistor may have one or more fixed tapping points so that the resistance can be changed by moving the connecting wires to different terminals. Some wirewound power resistors have a tapping point that can slide along the resistance element, allowing a larger or smaller part of the resistance to be used.

Where continuous adjustment of the resistance value during operation of equipment is required, the sliding resistance tap can be connected to a knob accessible to an operator. Such a device is called a rheostat and has two terminals.

Potentiometers

Typical panel mount potentiometer
Drawing of potentiometer with case cut away, showing parts: (A) shaft, (B) stationary carbon composition resistance element, (C) phosphor bronze wiper, (D) shaft attached to wiper, (E, G) terminals connected to ends of resistance element, (F) terminal connected to wiper.
An assortment of small through-hole potentiometers designed for mounting on printed circuit boards.

A potentiometer (colloquially, pot) is a three-terminal resistor with a continuously adjustable tapping point controlled by rotation of a shaft or knob or by a linear slider.[23] The name potentiometer comes from its function as an adjustable voltage divider to provide a variable potential at the terminal connected to the tapping point. Volume control in an audio device is a common application of a potentiometer. A typical low power potentiometer (see drawing) is constructed of a flat resistance element (B) of carbon composition, metal film, or conductive plastic, with a springy phosphor bronze wiper contact (C) which moves along the surface. An alternate construction is resistance wire wound on a form, with the wiper sliding axially along the coil.[23] These have lower resolution, since as the wiper moves the resistance changes in steps equal to the resistance of a single turn.[23]

High-resolution multiturn potentiometers are used in precision applications. These have wire-wound resistance elements typically wound on a helical mandrel, with the wiper moving on a helical track as the control is turned, making continuous contact with the wire. Some include a conductive-plastic resistance coating over the wire to improve resolution. These typically offer ten turns of their shafts to cover their full range. They are usually set with dials that include a simple turns counter and a graduated dial, and can typically achieve three-digit resolution. Electronic analog computers used them in quantity for setting coefficients and delayed-sweep oscilloscopes of recent decades included one on their panels.

Resistance decade boxes

Resistance decade box, made in former East Germany.

A resistance decade box or resistor substitution box is a unit containing resistors of many values, with one or more mechanical switches which allow any one of various discrete resistances offered by the box to be dialed in. Usually the resistance is accurate to high precision, ranging from laboratory/calibration grade accuracy of 20 parts per million, to field grade at 1%. Inexpensive boxes with lesser accuracy are also available. All types offer a convenient way of selecting and quickly changing a resistance in laboratory, experimental and development work without needing to attach resistors one by one, or even stock each value. The range of resistance provided, the maximum resolution, and the accuracy characterize the box. For example, one box offers resistances from 0 to 100 megohms, maximum resolution 0.1 ohm, accuracy 0.1%.[24]

Special devices

There are various devices whose resistance changes with various quantities. The resistance of NTC thermistors exhibit a strong negative temperature coefficient, making them useful for measuring temperatures. Since their resistance can be large until they are allowed to heat up due to the passage of current, they are also commonly used to prevent excessive current surges when equipment is powered on. Similarly, the resistance of a humistor varies with humidity. One sort of photodetector, the photoresistor, has a resistance which varies with illumination.

The strain gauge, invented by Edward E. Simmons and Arthur C. Ruge in 1938, is a type of resistor that changes value with applied strain. A single resistor may be used, or a pair (half bridge), or four resistors connected in a Wheatstone bridge configuration. The strain resistor is bonded with adhesive to an object that is subjected to mechanical strain. With the strain gauge and a filter, amplifier, and analog/digital converter, the strain on an object can be measured.

A related but more recent invention uses a Quantum Tunnelling Composite to sense mechanical stress. It passes a current whose magnitude can vary by a factor of 1012 in response to changes in applied pressure.

Measurement

The value of a resistor can be measured with an ohmmeter, which may be one function of a multimeter. Usually, probes on the ends of test leads connect to the resistor. A simple ohmmeter may apply a voltage from a battery across the unknown resistor (with an internal resistor of a known value in series) producing a current which drives a meter movement. The current, in accordance with Ohm's law, is inversely proportional to the sum of the internal resistance and the resistor being tested, resulting in an analog meter scale which is very non-linear, calibrated from infinity to 0 ohms. A digital multimeter, using active electronics, may instead pass a specified current through the test resistance. The voltage generated across the test resistance in that case is linearly proportional to its resistance, which is measured and displayed. In either case the low-resistance ranges of the meter pass much more current through the test leads than do high-resistance ranges. This allows for the voltages present to be at reasonable levels (generally below 10 volts) but still measurable.

Measuring low-value resistors, such as fractional-ohm resistors, with acceptable accuracy requires four-terminal connections. One pair of terminals applies a known, calibrated current to the resistor, while the other pair senses the voltage drop across the resistor. Some laboratory quality ohmmeters, milliohmmeters, and even some of the better digital multimeters sense using four input terminals for this purpose, which may be used with special test leads called Kelvin clips. Each of the two clips has a pair of jaws insulated from each other. One side of each clip applies the measuring current, while the other connections are only to sense the voltage drop. The resistance is again calculated using Ohm's Law as the measured voltage divided by the applied current.

Standards

Production resistors

Resistor characteristics are quantified and reported using various national standards. In the US, MIL-STD-202[25] contains the relevant test methods to which other standards refer.

There are various standards specifying properties of resistors for use in equipment:

There are other United States military procurement MIL-R- standards.

Resistance standards

The primary standard for resistance, the "mercury ohm" was initially defined in 1884 in as a column of mercury 106.3 cm long and in cross-section, at . Difficulties in precisely measuring the physical constants to replicate this standard result in variations of as much as 30 ppm. From 1900 the mercury ohm was replaced with a precision machined plate of manganin.[27] Since 1990 the international resistance standard has been based on the quantized Hall effect discovered by Klaus von Klitzing, for which he won the Nobel Prize in Physics in 1985.[28]

Resistors of extremely high precision are manufactured for calibration and laboratory use. They may have four terminals, using one pair to carry an operating current and the other pair to measure the voltage drop; this eliminates errors caused by voltage drops across the lead resistances, because no charge flows through voltage sensing leads. It is important in small value resistors (100-0.0001 ohm) where lead resistance is significant or even comparable with respect to resistance standard value.[29]

Resistor marking

Wheel-based RMA Resistor Color Code guide. Circa 1945-1950.

Axial resistors' cases are usually tan, brown, blue, or green (though other colors are occasionally found as well, such as dark red or dark gray), and display 3-6 colored stripes that indicate resistance (and by extension tolerance), and may include bands to indicate the temperature coefficient and reliability class. In four-striped resistors, the first two stripes represent the first two digits of the resistance in ohms, the third represents a multiplier, and the fourth the tolerance (which if absent, denotes ±20%). For five- and six- striped resistors the third band is the third digit, the fourth is the multiplier and the fifth is the tolerance; a sixth stripe represents the temperature coefficient. The power rating of the resistor is usually not marked and is deduced from its size.

Surface-mount resistors are marked numerically.

Early 20th century resistors, essentially uninsulated, were dipped in paint to cover their entire body for color-coding. This base color represented the first digit. A second color of paint was applied to one end of the element to represent a second digit, and a color dot (or band) in the middle provided the third digit. The rule was "body, tip, dot", providing two significant digits for value and the decimal multiplier, in that sequence. Default tolerance was ±20%. Closer-tolerance resistors had silver (±10%) or gold-colored (±5%) paint on the other end.

Preferred values

Early resistors were made in more or less arbitrary round numbers; a series might have 100, 125, 150, 200, 300, etc.[30] Early power wirewound resistors, such as brown vitreous-enameled types, were made with a system of preferred values like some of those mentioned here. Resistors as manufactured are subject to a certain percentage tolerance, and it makes sense to manufacture values that correlate with the tolerance, so that the actual value of a resistor overlaps slightly with its neighbors. Wider spacing leaves gaps; narrower spacing increases manufacturing and inventory costs to provide resistors that are more or less interchangeable.

A logical scheme is to produce resistors in a range of values which increase in a geometric progression, so that each value is greater than its predecessor by a fixed multiplier or percentage, chosen to match the tolerance of the range. For example, for a tolerance of ±20% it makes sense to have each resistor about 1.5 times its predecessor, covering a decade in 6 values. More precisely, the factor used is 1.4678 ? , giving values of 1.47, 2.15, 3.16, 4.64, 6.81, 10 for the 1-10-decade (a decade is a range increasing by a factor of 10; 0.1-1 and 10-100 are other examples); these are rounded in practice to 1.5, 2.2, 3.3, 4.7, 6.8, 10; followed by 15, 22, 33, ... and preceded by ... 0.47, 0.68, 1. This scheme has been adopted as the E6 series of the IEC 60063 preferred number values. There are also E12, E24, E48, E96 and E192 series for components of progressively finer resolution, with 12, 24, 48, 96, and 192 different values within each decade. The actual values used are in the IEC 60063 lists of preferred numbers.

A resistor of 100 ohms ±20% would be expected to have a value between 80 and 120 ohms; its E6 neighbors are 68 (54-82) and 150 (120-180) ohms. A sensible spacing, E6 is used for ±20% components; E12 for ±10%; E24 for ±5%; E48 for ±2%, E96 for ±1%; E192 for ±0.5% or better. Resistors are manufactured in values from a few milliohms to about a gigaohm in IEC60063 ranges appropriate for their tolerance. Manufacturers may sort resistors into tolerance-classes based on measurement. Accordingly, a selection of 100 ohms resistors with a tolerance of ±10%, might not lie just around 100 ohm (but no more than 10% off) as one would expect (a bell-curve), but rather be in two groups - either between 5 and 10% too high or 5 to 10% too low (but not closer to 100 ohm than that) because any resistors the factory had measured as being less than 5% off would have been marked and sold as resistors with only ±5% tolerance or better. When designing a circuit, this may become a consideration. This process of sorting parts based on post-production measurement is known as "binning", and can be applied to other components than resistors (such as speed grades for CPUs).

SMT resistors

This image shows four surface-mount resistors (the component at the upper left is a capacitor) including two zero-ohm resistors. Zero-ohm links are often used instead of wire links, so that they can be inserted by a resistor-inserting machine. Their resistance is negligible.

Surface mounted resistors of larger sizes (metric 1608 and above) are printed with numerical values in a code related to that used on axial resistors. Standard-tolerance surface-mount technology (SMT) resistors are marked with a three-digit code, in which the first two digits are the first two significant digits of the value and the third digit is the power of ten (the number of zeroes). For example:

  • 334 = 33 × 104 ? = 330 k?
  • 222 = 22 × 102 ? = 2.2 k?
  • 473 = 47 × 103 ? = 47 k?
  • 105 = 10 × 105 ? = 1 M?

Resistances less than 100 ? are written: 100, 220, 470. The final zero represents ten to the power zero, which is 1. For example:

  • 100 = 10 × 100 ? = 10 ?
  • 220 = 22 × 100 ? = 22 ?

Sometimes these values are marked as 10 or 22 to prevent a mistake.

Resistances less than 10 ? have 'R' to indicate the position of the decimal point (radix point). For example:

  • 4R7 = 4.7 ?
  • R300 = 0.30 ?
  • 0R22 = 0.22 ?
  • 0R01 = 0.01 ?

000 and 0000 sometimes appear as values on surface-mount zero-ohm links, since these have (approximately) zero resistance.

More recent surface-mount resistors are too small, physically, to permit practical markings to be applied.

Precision resistor markings

Many precision resistors, including surface mount and axial-lead types, are marked with a four-digit code. The first three digits are the significant figures and the fourth is the power of ten. For example:

  • 1001 = 100 × 101 ? = 1.00 k?
  • 4992 = 499 × 102 ? = 49.9 k?
  • 1000 = 100 × 100 ? = 100 ?

Axial-lead precision resistors often use color code bands to represent this four-digit code.

EIA-96 marking

The former EIA-96 marking system now included in IEC 60062:2016 is a more compact marking system intended for physically small high-precision resistors. It uses a two-digit code plus a letter (a total of three alphanumeric characters) to indicate 1% resistance values to three significant digits.[31] The two digits (from "01" to "96") are a code that indicates one of the 96 "positions" in the standard E96 series of 1% resistor values. The uppercase letter is a code that indicates a power of ten multiplier. For example, the marking "01C" represents 10 kOhm; "10C" represents 12.4 kOhm; "96C" represents 97.6 kOhm.[32][33][34][35][36]

Code Series Letter
Digits E96 Y / S X / R A B / H C D E
01 1.00 1R00 10R0 100R 1K00 10K0 100K 1M00
02 1.02 1R02 10R2 102R 1K02 10K2 102K 1M02
03 1.05 1R05 10R5 105R 1K05 10K5 105K 1M05
04 1.07 1R07 10R7 107R 1K07 10K7 107K 1M07
05 1.10 1R10 11R0 110R 1K10 11K0 110K 1M10
06 1.13 1R13 11R3 113R 1K13 11K3 113K 1M13
07 1.15 1R15 11R5 115R 1K15 11K5 115K 1M15
08 1.18 1R18 11R8 118R 1K18 11K8 118K 1M18
09 1.21 1R21 12R1 121R 1K21 12K1 121K 1M21
10 1.24 1R24 12R4 124R 1K24 12K4 124K 1M24
11 1.27 1R27 12R7 127R 1K27 12K7 127K 1M27
12 1.30 1R30 13R0 130R 1K30 13K0 130K 1M30
13 1.33 1R33 13R3 133R 1K33 13K3 133K 1M33
14 1.37 1R37 13R7 137R 1K37 13K7 137K 1M37
15 1.40 1R40 14R0 140R 1K40 14K0 140K 1M40
16 1.43 1R43 14R3 143R 1K43 14K3 143K 1M43
17 1.47 1R47 14R7 147R 1K47 14K7 147K 1M47
18 1.50 1R50 15R0 150R 1K50 15K0 150K 1M50
19 1.54 1R54 15R4 154R 1K54 15K4 154K 1M54
20 1.58 1R58 15R8 158R 1K58 15K8 158K 1M58
21 1.62 1R62 16R2 162R 1K62 16K2 162K 1M62
22 1.65 1R65 16R5 165R 1K65 16K5 165K 1M65
23 1.69 1R69 16R9 169R 1K69 16K9 169K 1M69
24 1.74 1R74 17R4 174R 1K74 17K4 174K 1M74
25 1.78 1R78 17R8 178R 1K78 17K8 178K 1M78
26 1.82 1R82 18R2 182R 1K82 18K2 182K 1M82
27 1.87 1R87 18R7 187R 1K87 18K7 187K 1M87
28 1.91 1R91 19R1 191R 1K91 19K1 191K 1M91
29 1.96 1R96 19R6 196R 1K96 19K6 196K 1M96
30 2.00 2R00 20R0 200R 2K00 20K0 200K 2M00
31 2.05 2R05 20R5 205R 2K05 20K5 205K 2M05
32 2.10 2R10 21R0 210R 2K10 21K0 210K 2M10
33 2.15 2R15 21R5 215R 2K15 21K5 215K 2M15
34 2.21 2R21 22R1 221R 2K21 22K1 221K 2M21
35 2.26 2R26 22R6 226R 2K26 22K6 226K 2M26
36 2.32 2R32 23R2 232R 2K32 23K2 232K 2M32
37 2.37 2R37 23R7 237R 2K37 23K7 237K 2M37
38 2.43 2R43 24R3 243R 2K43 24K3 243K 2M43
39 2.49 2R49 24R9 249R 2K49 24K9 249K 2M49
40 2.55 2R55 25R5 255R 2K55 25K5 255K 2M55
41 2.61 2R61 26R1 261R 2K61 26K1 261K 2M61
42 2.67 2R67 26R7 267R 2K67 26K7 267K 2M67
43 2.74 2R74 27R4 274R 2K74 27K4 274K 2M74
44 2.80 2R80 28R0 280R 2K80 28K0 280K 2M80
45 2.87 2R87 28R7 287R 2K87 28K7 287K 2M87
46 2.94 2R94 29R4 294R 2K94 29K4 294K 2M94
47 3.01 3R01 30R1 301R 3K01 30K1 301K 3M01
48 3.09 3R09 30R9 309R 3K09 30K9 309K 3M09
Code Series Letter
Digits E96 Y / S X / R A B / H C D E
49 3.16 3R16 31R6 316R 3K16 31K6 316K 3M16
50 3.24 3R24 32R4 324R 3K24 32K4 324K 3M24
51 3.32 3R32 33R2 332R 3K32 33K2 332K 3M32
52 3.40 3R40 34R0 340R 3K40 34K0 340K 3M40
53 3.48 3R48 34R8 348R 3K48 34K8 348K 3M48
54 3.57 3R57 35R7 357R 3K57 35K7 357K 3M57
55 3.65 3R65 36R5 365R 3K65 36K5 365K 3M65
56 3.74 3R74 37R4 374R 3K74 37K4 374K 3M74
57 3.83 3R83 38R3 383R 3K83 38K3 383K 3M83
58 3.92 3R92 39R2 392R 3K92 39K2 392K 3M92
59 4.02 4R02 40R2 402R 4K02 40K2 402K 4M02
60 4.12 4R12 41R2 412R 4K12 41K2 412K 4M12
61 4.22 4R22 42R2 422R 4K22 42K2 422K 4M22
62 4.32 4R32 43R2 432R 4K32 43K2 432K 4M32
63 4.42 4R42 44R2 442R 4K42 44K2 442K 4M42
64 4.53 4R53 45R3 453R 4K53 45K3 453K 4M53
65 4.64 4R64 46R4 464R 4K64 46K4 464K 4M64
66 4.75 4R75 47R5 475R 4K75 47K5 475K 4M75
67 4.87 4R87 48R7 487R 4K87 48K7 487K 4M87
68 4.99 4R99 49R9 499R 4K99 49K9 499K 4M99
69 5.11 5R11 51R1 511R 5K11 51K1 511K 5M11
70 5.23 5R23 52R3 523R 5K23 52K3 523K 5M23
71 5.36 5R36 53R6 536R 5K36 53K6 536K 5M36
72 5.49 5R49 54R9 549R 5K49 54K9 549K 5M49
73 5.62 5R62 56R2 562R 5K62 56K2 562K 5M62
74 5.76 5R76 57R6 576R 5K76 57K6 576K 5M76
75 5.90 5R90 59R0 590R 5K90 59K0 590K 5M90
76 6.04 6R04 60R4 604R 6K04 60K4 604K 6M04
77 6.19 6R19 61R9 619R 6K19 61K9 619K 6M19
78 6.34 6R34 63R4 634R 6K34 63K4 634K 6M34
79 6.49 6R49 64R9 649R 6K49 64K9 649K 6M49
80 6.65 6R65 66R5 665R 6K65 66K5 665K 6M65
81 6.81 6R81 68R1 681R 6K81 68K1 681K 6M81
82 6.98 6R98 69R8 698R 6K98 69K8 698K 6M98
83 7.15 7R15 71R5 715R 7K15 71K5 715K 7M15
84 7.32 7R32 73R2 732R 7K32 73K2 732K 7M32
85 7.50 7R50 75R0 750R 7K50 75K0 750K 7M50
86 7.68 7R68 76R8 768R 7K68 76K8 768K 7M68
87 7.87 7R87 78R7 787R 7K87 78K7 787K 7M87
88 8.06 8R06 80R6 806R 8K06 80K6 806K 8M06
89 8.25 8R25 82R5 825R 8K25 82K5 825K 8M25
90 8.45 8R45 84R5 845R 8K45 84K5 845K 8M45
91 8.66 8R66 86R6 866R 8K66 86K6 866K 8M66
92 8.87 8R87 88R7 887R 8K87 88K7 887K 8M87
93 9.09 9R09 90R9 909R 9K09 90K9 909K 9M09
94 9.31 9R31 93R1 931R 9K31 93K1 931K 9M31
95 9.53 9R53 95R3 953R 9K53 95K3 953K 9M53
96 9.76 9R76 97R6 976R 9K76 97K6 976K 9M76

Industrial type designation

Power Rating at 70 °C
Type no. Power
rating
(watts)
MIL-R-11
style
MIL-R-39008
style
BB 18 RC05 RCR05
CB 14 RC07 RCR07
EB 12 RC20 RCR20
GB 1 RC32 RCR32
HB 2 RC42 RCR42
GM 3 - -
HM 4 - -
Tolerance code
Industrial type designation Tolerance MIL designation
5 ±5% J
2 ±20% M
1 ±10% K
- ±2% G
- ±1% F
- ±0.5% D
- ±0.25% C
- ±0.1% B

Steps to find out the resistance or capacitance values:[37]

  1. First two letters gives the power dissipation capacity.
  2. Next three digits gives the resistance value.
    1. First two digits are the significant values
    2. Third digit is the multiplier.
  3. Final digit gives the tolerance.

If a resistor is coded:

  • EB1041: power dissipation capacity = 1/2 watts, resistance value = ±10% = between ohms and ohms.
  • CB3932: power dissipation capacity = 1/4 watts, resistance value = ±20% = between and ohms.

Electrical and thermal noise

In amplifying faint signals, it is often necessary to minimize electronic noise, particularly in the first stage of amplification. As a dissipative element, even an ideal resistor naturally produces a randomly fluctuating voltage, or noise, across its terminals. This Johnson-Nyquist noise is a fundamental noise source which depends only upon the temperature and resistance of the resistor, and is predicted by the fluctuation-dissipation theorem. Using a larger value of resistance produces a larger voltage noise, whereas a smaller value of resistance generates more current noise, at a given temperature.

The thermal noise of a practical resistor may also be larger than the theoretical prediction and that increase is typically frequency-dependent. Excess noise of a practical resistor is observed only when current flows through it. This is specified in unit of ?V/V/decade - ?V of noise per volt applied across the resistor per decade of frequency. The ?V/V/decade value is frequently given in dB so that a resistor with a noise index of 0 dB exhibits 1 ?V (rms) of excess noise for each volt across the resistor in each frequency decade. Excess noise is thus an example of 1/f noise. Thick-film and carbon composition resistors generate more excess noise than other types at low frequencies. Wire-wound and thin-film resistors are often used for their better noise characteristics. Carbon composition resistors can exhibit a noise index of 0 dB while bulk metal foil resistors may have a noise index of -40 dB, usually making the excess noise of metal foil resistors insignificant.[38] Thin film surface mount resistors typically have lower noise and better thermal stability than thick film surface mount resistors. Excess noise is also size-dependent: in general, excess noise is reduced as the physical size of a resistor is increased (or multiple resistors are used in parallel), as the independently fluctuating resistances of smaller components tend to average out.

While not an example of "noise" per se, a resistor may act as a thermocouple, producing a small DC voltage differential across it due to the thermoelectric effect if its ends are at different temperatures. This induced DC voltage can degrade the precision of instrumentation amplifiers in particular. Such voltages appear in the junctions of the resistor leads with the circuit board and with the resistor body. Common metal film resistors show such an effect at a magnitude of about 20 ?V/°C. Some carbon composition resistors can exhibit thermoelectric offsets as high as 400 ?V/°C, whereas specially constructed resistors can reduce this number to 0.05 ?V/°C. In applications where the thermoelectric effect may become important, care has to be taken to mount the resistors horizontally to avoid temperature gradients and to mind the air flow over the board.[39]

Failure modes

The failure rate of resistors in a properly designed circuit is low compared to other electronic components such as semiconductors and electrolytic capacitors. Damage to resistors most often occurs due to overheating when the average power delivered to it greatly exceeds its ability to dissipate heat (specified by the resistor's power rating). This may be due to a fault external to the circuit but is frequently caused by the failure of another component (such as a transistor that shorts out) in the circuit connected to the resistor. Operating a resistor too close to its power rating can limit the resistor's lifespan or cause a significant change in its resistance. A safe design generally uses overrated resistors in power applications to avoid this danger.

Low-power thin-film resistors can be damaged by long-term high-voltage stress, even below maximum specified voltage and below maximum power rating. This is often the case for the startup resistors feeding a switched-mode power supply integrated circuit.[]

When overheated, carbon-film resistors may decrease or increase in resistance.[40] Carbon film and composition resistors can fail (open circuit) if running close to their maximum dissipation. This is also possible but less likely with metal film and wirewound resistors.

There can also be failure of resistors due to mechanical stress and adverse environmental factors including humidity. If not enclosed, wirewound resistors can corrode.

Surface mount resistors have been known to fail due to the ingress of sulfur into the internal makeup of the resistor. This sulfur chemically reacts with the silver layer to produce non-conductive silver sulfide. The resistor's impedance goes to infinity. Sulfur resistant and anti-corrosive resistors are sold into automotive, industrial, and military applications. ASTM B809 is an industry standard that tests a part's susceptibility to sulfur.

An alternative failure mode can be encountered where large value resistors are used (hundreds of kilohms and higher). Resistors are not only specified with a maximum power dissipation, but also for a maximum voltage drop. Exceeding this voltage causes the resistor to degrade slowly reducing in resistance. The voltage dropped across large value resistors can be exceeded before the power dissipation reaches its limiting value. Since the maximum voltage specified for commonly encountered resistors is a few hundred volts, this is a problem only in applications where these voltages are encountered.

Variable resistors can also degrade in a different manner, typically involving poor contact between the wiper and the body of the resistance. This may be due to dirt or corrosion and is typically perceived as "crackling" as the contact resistance fluctuates; this is especially noticed as the device is adjusted. This is similar to crackling caused by poor contact in switches, and like switches, potentiometers are to some extent self-cleaning: running the wiper across the resistance may improve the contact. Potentiometers which are seldom adjusted, especially in dirty or harsh environments, are most likely to develop this problem. When self-cleaning of the contact is insufficient, improvement can usually be obtained through the use of contact cleaner (also known as "tuner cleaner") spray. The crackling noise associated with turning the shaft of a dirty potentiometer in an audio circuit (such as the volume control) is greatly accentuated when an undesired DC voltage is present, often indicating the failure of a DC blocking capacitor in the circuit.

See also

References

  1. ^ Harder, Douglas Wilhelm. "Resistors: A Motor with a Constant Force (Force Source)". Department of Electrical and Computer Engineering, University of Waterloo. Retrieved 2014.
  2. ^ American Radio Relay League (ARRL) (2021). "Fundamental Theory--Circuits and Components". ARRL Handbook for Radio Communications (98 ed.). American Radio Relay League. ISBN 978-1-62595-139-7.
  3. ^ a b c Doug DeMaw, ed. (1968). "Electrical Laws and Circuits --Resistance". Radio Amateurs Handbook (45 ed.). American Radio Relay League.
  4. ^ Farago, P.S. (1961) An Introduction to Linear Network Analysis, pp. 18-21, The English Universities Press Ltd.
  5. ^ Wu, F. Y. (2004). "Theory of resistor networks: The two-point resistance". Journal of Physics A: Mathematical and General. 37 (26): 6653-6673. arXiv:math-ph/0402038. Bibcode:2004JPhA...37.6653W. doi:10.1088/0305-4470/37/26/004. S2CID 119611570.
  6. ^ Wu, Fa Yueh; Yang, Chen Ning (2009). Exactly Solved Models: A Journey in Statistical Mechanics : Selected Papers with Commentaries (1963-2008). World Scientific. pp. 489-. ISBN 978-981-281-388-6.
  7. ^ "Specifications and How to Interpret Them" (PDF). Stackpole Electronics. Retrieved 2021.
  8. ^ https://nl.farnell.com/te-connectivity/rgp0207chj100m/res-100m-5-250mw-axial-thick-film/dp/2805251[bare URL]
  9. ^ A family of resistors may also be characterized according to its critical resistance. Applying a constant voltage across resistors in that family below the critical resistance will exceed the maximum power rating first; resistances larger than the critical resistance fail first from exceeding the maximum voltage rating. See Middleton, Wendy; Van Valkenburg, Mac E. (2002). Reference data for engineers: radio, electronics, computer, and communications (9 ed.). Newnes. pp. 5-10. ISBN 0-7506-7291-9.
  10. ^ Harter, James H. and Lin, Paul Y. (1982) Essentials of electric circuits. Reston Publishing Company. pp. 96-97. ISBN 0-8359-1767-3.
  11. ^ HVR International (ed.). "SR Series: Surge Resistors for PCB Mounting". (PDF; 252 kB), 26 May 2005, retrieved 24 January 2017.
  12. ^ a b c d e f g Beyschlag, Vishay (2008). "Basics of Linear Fixed Resistors Application Note", Document Number 28771.
  13. ^ Morris, C. G. (ed.) (1992). Academic Press Dictionary of Science and Technology. Gulf Professional Publishing. p. 360. ISBN 0122004000.
  14. ^ Principles of automotive vehicles. United States Department of the Army (1985). p. 13
  15. ^ "Carbon Film Resistor". The Resistorguide. Retrieved 2013.
  16. ^ "Thick Film and Thin Film" (PDF). Digi-Key (SEI). Archived from the original (PDF) on 27 September 2011. Retrieved 2011.
  17. ^ "Thin and Thick film". resisitorguide.com. resistor guide. Retrieved 2017.
  18. ^ Kuhn, Kenneth A. "Measuring the Temperature Coefficient of a Resistor" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved .
  19. ^ Zandman, F.; Stein, S. (1964). "A New Precision Film Resistor Exhibiting Bulk Properties". IEEE Transactions on Component Parts. 11 (2): 107-119. doi:10.1109/TCP.1964.1135008.
  20. ^ Procedures in Experimental Physics, John Strong, p. 546.
  21. ^ "Alpha Electronics Corp. Metal Foil Resistors". Alpha-elec.co.jp. Retrieved .
  22. ^ "Grid Resistors: High Power/High Current". Milwaukee Resistor Corporation. Retrieved 14 May 2012.
  23. ^ a b c Mazda, F. F. (1981). Discrete Electronic Components. CUP Archive. pp. 57-61. ISBN 0521234700.
  24. ^ "Decade Box - Resistance Decade Boxes". Ietlabs.com. Retrieved .
  25. ^ "Test method standard: electronic and electrical component parts" (PDF). Department of Defense. Archived from the original (PDF) on 2015-02-09.
  26. ^ Fusing Resistors and Temperature-Limited Resistors for Radio- and Television- Type Appliances UL 1412. ulstandardsinfonet.ul.com
  27. ^ Stability of Double-Walled Manganin Resistors Archived 2006-10-06 at the Wayback Machine. NIST.gov
  28. ^ Klaus von Klitzing The Quantized Hall Effect. Nobel lecture, December 9, 1985. nobelprize.org
  29. ^ "Standard Resistance Unit Type 4737B". Tinsley.co.uk. Archived from the original on 2008-08-21. Retrieved .
  30. ^ "1940 Catalog - page 60 - Resistors". RadioShack. Archived from the original on 11 July 2017. Retrieved 2017.
  31. ^ "Chapter 2 - Resistor standards and codes".
  32. ^ "CRP0603 Series - Precision Chip Resistors". p. 3.
  33. ^ "Online calculator - EIA-96 SMD resistor".
  34. ^ "SMD Resistor Codes: How to Find the Value of SMD Resistors".
  35. ^ "Marking Codes used on Welwyn Chip Resistors". p. 2.
  36. ^ "Surface Mount Resistor: codes & markings".
  37. ^ Maini, A. K. (2008), Electronics and Communications Simplified, 9th ed., Khanna Publications. ISBN 817409217X
  38. ^ Audio Noise Reduction Through the Use of Bulk Metal Foil Resistors - "Hear the Difference" (PDF). Archived from the original (PDF) on 2013-01-19. Retrieved ., Application note AN0003, Vishay Intertechnology Inc, 12 July 2005.
  39. ^ Jung, Walt (2005). "Chapter 7 - Hardware and Housekeeping Techniques" (PDF). Op Amp Applications Handbook. p. 7.11. ISBN 0-7506-7844-5.
  40. ^ "Electronic components - resistors". Inspector's Technical Guide. US Food and Drug Administration. 1978-01-16. Archived from the original on 2008-04-03. Retrieved .

External links


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