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1. Resistors

1.1 Resistivity

While resistance is an electrical quantity, resistivity is a physical property of materials, which is used to produce resistance.

1.1.1 Resistance of materials

Resistance or conductance depend entirely on a conductor's physical parameters:

The resistance depends on the number of valency electrons available in the material. This property of the material is called "resistivity", (or specific resistance) with the symbol "rho"(rho).

The resistivity rho has the unit ohms*mm2/m.

Definition of resistivity for different conductor materials
The condition under which the resistivity rho(rho) is defined for different conductor materials:

1m long
1mm2 area
20 C temperature

The resistance increases (proportional) with increasing length and decrease (inverse proportional) with the area.

This is expressed by the formula:


The reciprocal of the resistivity rho is the conductivity kappa (Kappa).

The unit of the conductivity is m/(ohms*mm2)

Using kappa, the resistance can be calculated by the formula:


For materials with very high resistivity (insulators), the resistivity may have different units,
for instance ohms*cm2/cm = ohms*cm or ohms*m2/m = ohms*m.

Conditions for specifying the resistivity of insulators.
Conditions for specifying the resistivity of insulators.
length = 1cm, csa = 1cm2
length = 1m, csa = 1m2

1.1.2 Conductors, Insulators, Semiconductors

The resistivity of a material depends on

  1. the number of carriers of electrical charges per unit of volume
  2. the mobility of such carriers within the material.

In conductor materials the valency electrons can move freely, thus the resistivity is low.

Most metals are good conductors. Commonly used metal for conductors is copper (Cu).
Other conductor materials:
Aluminium, silver, tin, lead, nickel, platinum, tantalum, tungsten.
Also alloys (e.g. brass or solder) are used.

Conduction of electrical current is also possible in electrolytes.
These are liquids like acids, alkaline solutions and solutions of salts.

In non-conductors or insulators the electrons of the outer shell are tightly bound into the material structure and cannot move, if no extreme outer force breaks them out of this structure. This may occur under high voltage or high temperatures.
We say insulators "break through".

Some common insulator materials are:
Plastics, rubber, glass, ceramics, but also air, oil or vacuum.

Both, conductors and insulators are important materials in electrical engineering.

Some materials can not be considered as insulators nor as conductors. They behave as insulators when cold, but become conductive when heated. They form the group of the semiconductors. The most common ones are germanium and silicon.

These materials play an important role in electronics and will be dealt with thoroughly later.

1.1.3 Tables of resistivities of Materials

Pure Metals    
  Symbol resistivity
Aluminium Al ca. 0.0290
Arsenic As 0.2600
Beryllium Be 0.0750
Lead Pb 0.2200
Chromium Cr ca. 0.0260
Iron Fe 0.0960
Gold Au 0.0240
Indium In 0.0900
Iridium Ir 0.0490
Cadmium Cd 0.0680
Potassium K 0.0700
Calcium Ca 0.0470
Cobalt Co 0.0570
Copper Cu ca. 0.0175
Lithium Li 0.0940
Magnesium Mg 0.0440
Molybdenum Mo 0.0560
Sodium Na 0.0480
Nickel Ni 0.0700
Palladium Pd 0.1070
Platinum Pt 0.1080
Mercury Hg 0.9580
Rhodium Rh 0.0470
Silver Ag ca. 0.0163
Strontium Sr 0.3300
Tantalum Ta 0.1300
Titanium Ti 0.4800
Uranium U 0.3200
Vanadium V 0.2000
Bismuth Bi 1.1000
Tungsten(Wolfram) W 0.0550
Caesium Cs 0.2090
Zinc Zn 0.0600
Tin Sn 0.1100
  resistivity (ohmsmm2/m)
Aluminium bronze 0.13...0.29
Bronze 0.021...0.028
Nickel chromium 0.9...1.1
Chromic iron 0.6
Duraluminium 0.05
Invar 0.75
Constantan 0.49
Manganin 0.43
Brass 0.07...0.08
Nickel silver, alpaca 0.35...0.41
Nickeline 0.33...0.4
Platinum iridium 0.18...0.31
Platinum silver 0.25
Silicon steel 0.50
  Symbol resistivity
Germanium Ge ca. 890.0
Silicon(Silicium) Si ca. 1000.0
Carbon C 30 ... 100
  resistivity (ohmscm)
Amber 1018
Mica 1016
Ceramic 108.... 1012
Micanite 1014
Pertinax ca. 1011
Polystyrene >1017
Ceramic 108....1012
Quartz >1018
Silicon elastomer 1014...1016
Teflon >1015

1.1.5 Temperature and resistance

Most materials change their resistivity with temperature.
The rate by which the resistance changes per degree of temperature is called temperature coefficient, the symbol is TC or alpha (alpha).

The unit of the temperature coefficient is 1/K or 1/C.
(1K is the change in temperature by 1 degree Kelvin which is equal to a change of 1C.)

Depending, whether the resistivity increases or decreases with increasing temperature, the temperature coefficient may be positive or negative.

In most metals the resistivity increases with increasing temperature. They have a positive TC.
When the temperature of metals approaches the absolute zero temperature of 0K (=-273C), their resistivity becomes 0.
This state is called superconduction.

The resistivity of most electrolytes, insulators and semiconductors decreases with increasing temperature, they have a negative TC.
At 0K these materials have infinite resistivity, they are pure insulators.

The resistivity of conductors is normally quoted for a temperature of 20C.

Temperature coefficient of copper is alphaCu = 0.0039 1/K = 0.0039 K-1 = 0.39 %/K

Certain alloys can be made to have very low TC, e.g. -0.001 %/K to 0.005 %/K. These are used for precision wire wound resistors.

The resistance of a material after a change of temperature can be calculated by the formula

1.2 Fixed Resistors

Fixed resistors are the most common circuit elements in electronics. Although their technology is relatively simple and they are considered reliable elements, their big number and their different applications require to consider their construction carefully.

1.2.1 Standard Values and Tolerances

Any device produced in mass production will have a certain variations of its characteristics, the manufacturing tolerance. Generally devices with low tolerances (= high precision) will be more expensive than those with larger tolerance.

The electrical circuits will be designed to accept these tolerances.

The nominal value and the tolerances will result in a certain range of possible values of the resistor. Therefore it would make no sense to provide an infinite number of different values or resistors. It is sufficient to distinguish different values, which lay out of the tolerance range of the neighbouring values.

The industry established and standardized a system whereby the nominal values and the manufacturing tolerances are related: The E-series.

The E-series standardizes the values available for each decade of values. The number of values per decade give the name of the E-series, e.g. E24 means a system with 24 different values between 1 and 10.

In electronics often no very precise values for resistors are required. Therefore in many cases the resistance of the E12 series which requires 10% tolerance are used. It is useful to memorize these values:

The tolerance ranges of the E12-series with 10% tolerance.
The tolerance ranges of the E12-series with 10% tolerance. Note that the whole range of one decade is covered by the 12 values.

For resistors with different tolerance therefore different series are used:

Tolerance: 20% 10% 5% 2% 1%
Series: E6 E12 E24 E48 E96
Base values: 1,0 1,0 1,0  
  1,2 1,2  
  1,5 1,5 1,5  
  1,8 1,8  
  2,2 2,2 2,2  
  2,7 2,7  
  3,3 3,3 3,3  
  3,9 3,9  
  4,7 4,7 4,7  
  5,6 5,6  
  6,8 6,8 6,8  
  8,2 8,2  
  10 10 10  

The values of other decades can be found by multiplying the base values by powers of ten. (e.g. 82kohms = 8.2*104ohms)

For general electronic applications 10% or 5% tolerance resistors are sufficient. For precision applications 2% and 1% types may be used.

For measuring applications resistors with tolerances down to 0.01% are available. Their values will be according to the application and will not follow an E-series.

1.2.2 The Colour Code

In former times all resistors were labelled with figures indicating their values. These figures were substituted by colour rings which indicate the value and the tolerance. The reasons were:

The international colour code defines the corresponding values of each colour.

colour Value: Multiplier Tolerance:
black 0 100 = 1  
brown 1 101 = 10 1%
red 2 102 = 100 2%
orange 3 103 = 1k  
yellow 4 104 = 10k  
green 5 105 = 100k  
blue 6 106 = 1M  
violet 7    
grey 8    
white 9    
gold   10-1 = 0.1 5%
silver   10-2 = 0.01 10%
none     20%

Values with a tolerances between 20% and 5% can be specified by 2 significant numbers. Therefore such resistors will have

Values with smaller tolerances (2% and 1%) require three significant numbers. Therefore such resistor will have

4 colour rings for
5% and 10% tolerance resistors:
              5 colour rings for
1% and 2% tolerance resistors:
Resistor with 4 colour rings for 5% and 10% tolerance resistors               Resistor with 5 colour rings for 1% and 2% tolerance resistors

1.2.3 Power rating

Resistors transform electrical energy into heat. This heat has to be transferred to the environment by any form of cooling. Cooling will be discussed in detail in chapter 7.

Different types of resistors will be able to transform different amount of electrical energy to heat without being damaged. This will depend on the construction of the resistor:

The power rating of a resistor will give the maximum power that can be permanently applied to the resistor under normal operation conditions without causing any damage to the resistor.

The power rating given in the data sheets will only apply for normal environment temperatures. For higher temperatures the power handling capacity of the resistor will be reduced.

Typical power characteristic of a resistor versus the ambient temperature.
Typical power characteristic of a resistor versus the ambient temperature. The power handling capacity reduces at higher ambient temperatures.

Exceeding the rated power may cause damage to a resistor, mainly:

Overloaded resistors will "burn". Their conductor will evaporate or oxidize and normally their resistance goes to infinite.

The power resistors can handle for short moments may be considerably higher (10 to 1000 times) than the power rating. This is because in such short moments the temperature of the resistor will not rise to excessive values.

Different types of resistors will have different pulse power ratings.

1.2.4 Cases and constructions

Theoretically a resistor is constructed of a resistive wire. In practice the following parts will be required in addition:

Depending on the application such resistors can be constructed in many different way. The construction will depend on the application of the resistor.

Low power axial resistors

This is the largest group of resistors in electronics. They are used for powers up to a few watts in printed circuits and open wiring.

- insulating body: ceramic cylinder
- contacting: metal caps with welded axial wires
- insulating coating: lacquer coating
Construction of a standard type low power resistor with axial connectors.
Construction of a standard type low power resistor with axial connectors.

These resistors are available in standardized dimensions.
Some of the ones commonly used in electronics today are:

Type: length: diameter: appr. power rating:
0204 3.6mm 1.8mm 0.125W
0207 6.3mm 2.5mm 0.25W
0411 10.5mm 3.7mm 0.5W

High power axial resistors

The construction of these types differ from the previous types basically by their dimensions and there coating.

The dimensions of the resistor will be somehow proportional to the power rating.
Higher power dissipations requires more surface to transfer the heat. Furthermore the higher currents and voltages of such resistor require more volume for the conductors.

Generally high power resistors have to withstand higher temperature (up to 150C). All materials used have to be suitable for such temperatures.
Therefore coating materials on ceramic basis will be used in practice:

Special types of power resistors are available with metal cases which can be mounted on heat sinks for better cooling.

Power resistor in metal case to be mounted on a heat sink to increase the power handling.
Example of a power resistor in metal case to be mounted on a heat sink to increase the power handling.

Surface Mounted Device Resistors (SMD)

For the new technology of surface mounted devices special resistors are available. They have no connector wires and will be soldered directly to the surface of the PCB. These resistors have extremely small dimensions to allow high package densities on the PCB. Normally they are of block shape rather than cylindric. The mounting and soldering can only be done with special automatic machines, as these elements are too small for manual handling.

Due to the fact that the resistive layer is on a ceramic chip, they are also called chip resistors.

Construction of a SMD resistor.
Construction of a SMD resistor.

Resistor Arrays

In digital circuits often many resistors of similar values are required, e.g. for bus termination or as pull-up resistors. For these purposes several resistors can be integrated in one standard single-in-line (SIL) or dual-in-line (DIL) package. In many applications all of the resistors will be connected to one potential, e.g. ground. Therefore such resistor arrays will be available with one end of all resistors connected to one point. This reduces the number of required terminals and will therefore reduce the size of the package.

Packages and resistor arrangements of different resistor arrays.
Packages and resistor arrangements of different resistor arrays.

All resistors of an array normally have the same values. All values of the E12 series are available from 22ohms to 1Mohms.

High precision voltage divider resistors for voltmeters are available in one package. Typically these are 1kohms, 9kohms, 90kohms and 900kohms.

1.2.5 Fixed Resistor's Technologies

Fixed resistors are cheap circuit elements which normally do not produce problems. But they represent the largest group of circuit elements in electronic circuits and therefore deserve some consideration. To understand the particular properties of different types of resistors it is necessary to have a look at their construction. Wire wound resistors

The oldest technology of resistors is based upon the resistivity of metals and certain alloy. The principle of production is still the same today. Alloy wires having a defined resistivity are coiled upon a carrier, which is equipped with suitable terminals.

The essential electric properties of a resistor are determined by the coiled wire. The performance and reliability depend on the kind of contact between resistance wire and terminals. The resistance wire will be coiled with a pre-calculated number of turns around the ceramic body. Terminal caps with welded terminal wires are pressed to the ends of the ceramic body. The ends of the resistance wire are welded to the terminal caps. This gives very reliable connections.

Wire wound resistors are either used for high power applications or as precision resistors.

Precision wire wound resistors, which can be produced with temperature coefficients of 1 ppm/K and tolerances of +/-0.01%, must have a welding or soldering contact. Normally power dissipation is not a problem for these applications.

Not so with power resistors. Here heat conversion is an important factor in relation to acceptable size of the element, while on the other hand the tolerance of the resistance is not so important. Changes in values of up to 3% of the nominal value are acceptable in most applications. In the power field mainly wire resistors with cases with relatively large surfaces are applied.

Except for the above mentioned properties of precision and power rating, one should take a look at the resistors' impulse chargeability. Depending on duration and the energy of the impulse, wire resistors can handle impulses of their 200- to 50,000-fold nominal chargeability without risk of damage.

A disadvantage of wire wound resistors may be their relatively high inductance for steep flanks of impulse and high frequency applications. For these applications bifilar coiled resistor should be selected. (See 1.3) Composite carbon resistors

In the history of resistors, the second to be produced were pure carbon resistors. They were, however, the first resistors to be manufactured in mass production. Essential for the development of this technology was the discovery that resistors with a large range of values up to the Megohms can be manufactured relatively easily by mixing carbon powder with resins, e.g. phenyl resin.

Also here, production technology is nearly still the same today: the carbon-resin mixture, whose resistivity is determined by the resin content, is pressed into strings under heat, then being cut into resistor elements. Terminal contacts are pressed into the elements. A plastic case protects the construction.

Today these resistors do not fulfil the requirements of modern electronics any more because of their instability and their dependence on temperature and voltage.

They do, however, have two properties that keep them worth mentioning:

Composite carbon resistors may today be seen as special elements which may be compulsory for some applications. Carbon film resistors

The negative properties of composite carbon resistors arise mainly from the use of the composite material, the resin.

Pure carbon, on the contrary, has significantly better properties. The technology to deposit carbon from carbohydrates on ceramic carriers by pyrolysis laid the foundation for industrial manufacturing of carbon film resistors. The maximum values of resistivity of carbon film ceramic cylinders are limited by the feasible thickness of the layer. The obtainable surface resistance is smaller than 5Kohms.

An essential structural feature of all film resistors is their helix structure. The resistance surface between the contact caps is cut by helical groove to a helical resistive track. The path of the current is comparable to the windings of a wire resistor. Due to the increased length and the reduced c.s.a. of the helical track the value of the plane resistor is increased. The helix factor - the relation between the final value at the end of the grooving process and the surface resistance - is about 5...2,000 for carbon layer resistors. The grooving is done by grinding or by laser cutting and is controlled simultaneously by resistance measurement.

The construction of the resistors is simple. After cutting the helix, terminal wires are welded to the caps and the resistor is coated with several layers of varnish.

Carbon layer resistors of this sort are applied in nearly all fields of electronics and are the most commonly used resistors. The values ranges from 1ohms to 10Mohms. For most applications the tolerances of +/-5% is sufficient.

The temperature coefficient is dependent on the film's thickness and ranges between -200 and -1,200 ppm/K. Carbon film resistors have current noise which is by far less than of composite carbon resistors. They are relatively insensitive to high impulse loading. Metal Film Resistors

Structurally metal film resistors are practically the same as carbon film resistors. The essential difference is the film itself: it consists of chemically pure chromium-nickel alloys, which are brought on a ceramic body by vapouring in vacuum or by a sputtering process. The metallic film on the carrier has a thickness of 10nm to 100nm and a surface resistance of up to 3kohms.

Reliability and quality of terminal contact are important factors for the reliability of the resistors. Neither the contact caps nor the ceramic cylinders are exactly circular - the contact area between cap and metal film is therefore punctual. There is also the danger that the thin metal film is damaged when fixing the caps. To improve the reliability and the contact at the terminal caps, some manufacturers apply an additional film of gold. This makes the product more expensive, but it reduces the risk of defects.

The resistor's protection by the coating is of great importance. Thin films which are under voltage and are exposed to humidity are prone to electrolytic processes. The handling of the resistors has to be in a way that a damage of the coating is avoided.

The electrical data of the metal film resistors make them destined for demands of highest precision. The metal surface shows only minimal changes in values caused by time and load effects. Therefore it makes sense to produce resistors with small tolerances. Together with the temperature coefficient which can be controlled down to almost zero one can produce near to perfect precision resistors; the degree of precision determines the price.

Tolerances of resistance of +/-0.005% and temperature coefficients of +/-2ppm/K are obtainable; the stability ranges between 20 and 2,000 ppm - depending on the electrical loading. Metal Oxide Film Resistors

Resistors with a metal oxide film are produced by hydrolysis: with hydrolysis of tin chloride, a film of about 1microm tin oxide is deposited on the ceramic body. This film is a relatively stable resistance material, even with temperatures up to 300C and it has clearly a higher over-loading capacity than metal film resistors of the same structure.

There are no differences in structure compared to the other above mentioned film technologies, the resistors have a helix structure, caps and are mainly lacquer coated.

The electrical data however, differ significantly from those of the CrNi-metal film resistors. The value stability under load is 2...4%, so that only relatively large tolerances make sense, predominantly +/-5%. The temperature coefficient is high with values of 200...400 ppm/K. This excludes the application of metal oxide resistors in the precision field.

The wide resistance range is an advantage. The power ratings range from 0.25W to more than 6W. Metal oxide resistors are therefore used as power resistors for the higher value range where wire wound resistors can not be economically produced. Metal oxide resistors also practically replaced carbon film resistors for power ratings higher than 1W. Metal Glaze Film Resistors

Metal glaze film resistors are occasionally grouped under the "mass resistors" - which can be explained by the relatively high thickness of the resistive film of about 20-30microm. But technologically they are film resistors. The actual resistor film consists of a mixture of several metals, metal oxides, metal nitrates and glass. At temperatures of around 1,000C these components are melted to form a resistive film on the ceramic body. The composition of the ingredients determines the surface resistance, which is widely variable. By cutting a helix, high resistances can be obtained.

Metal glaze films are stable and insensitive in such a way that the terminal wires with upset ends can be soldered directly to the nickel-plated ends of the ceramic body. If this highly reliable contact is even equipped with a coating against external mechanical and electrical damages, you have an absolutely robust resistor which satisfies high demands of precision and reliability.

The resistors' electrical properties are, however limited due to the inhomogenous film. The ageing stability under heat and load range between 0.2 and 0.5%.

With the introduction of SMD technology , metal glaze film technology has increased in importance. Today the main part of SMD resistors are produced in this technology, for this guarantees a reasonable relation of price and performance. Summary of characteristics

Roughly the mentioned resistor types can be associated with the following basic applications:

Wire wound resistors   power applications
Composite carbon resistor   high frequency applications
Carbon film resistors   general applications
Metal film resistors   precession applications
Metal oxide film resistors   power applications
Metal glaze film resistors   high reliability applications

The following table compares some of the important parameters for the different resistor technologies:

resistor type wire wound carbon film metal film metal oxide film metal glaze film
0.01ohms ... 10kohms 1ohms ... 10Mohms 1ohms ... 10Mohms 1ohms ... 5Mohms 0.1ohms ... 100Mohms
tolerance 0.001% ... 5% 2% ... 5% 0.005% ... 2% 2% ... 5% 0.5% ... 5%
stability 0.1% ... 1% 1% ... 3% 0.1% ... 0.3% 1% ... 4% 0.2% ... 1%
1 ... 100 -200 ... -1200 2 ... 100 200 ... 400 25 ... 200
failure rate
0.1 ... 5 0.3 ... 30 1 ... 10 1 ... 10 0.1 ... 1
power rating 1W ... 1kW 0.1W ... 2W 0.1W ... 2W 0.5W ... 10W 0.1 ... 3W
impulse loading
very high high low high very high
current noise
low low very low low high
max. operation
150C ... 300C 125C ... 155C 150C ... 175C 175C ... 250C 175C ... 200C

1.3 Reactance of Resistors

In practice it will turn out that resistors behave like real resistors only at d.c. and at low frequencies. Due to their physical construction resistors always have a certain amount of inductance and capacitance. Although these reactive components are small, they may become important at high frequencies.

The inductive component of resistors obviously results from their helical construction. Therefore wire wound resistors and high resistance resistors with many helical turns will have relatively high inductances. In practice inductances in the range of nH to microH are found.

The construction of normal resistors, showing the coil shaped resistive path.
Fig. 1.3.1:
The construction of normal resistors, showing the coil shaped resistive path.

The inductance can be reduced by special constructions:

Bifilar winding:
A wire wound resistor is not wound from the beginning to the end in one direction around the body, but half of the wire is wound in one direction and the second half in the opposite direction. By this the magnetic field of the winding cancels and the inductance is minimized.

In a bifilar wound resistor the magnetic fields of the turns cancel.
Fig. 1.3.2:
In a bifilar wound resistor the magnetic fields of the turns cancel.

Meander resistive track:
For film resistors the resistive path is not produced by cutting a helical groove into the film, but the length of the path is increased by cutting radial cuts which form a zick-zack shaped path. By this the current will always flow to and fro and the magnetic fields will cancel and the inductances is minimized.

Principle of the meander path of a low reactance film resistor.
Fig. 1.3.3:
Principle of the meander path of a low reactance film resistor.

Both types of constructions are available on demand as special low reactance resistors. But due to the more complex production and the low production numbers these types are more expensive.

Composite carbon resistors will have very low inductances, because their resistive path has minimum length. They are preferred for high frequency applications.

SMD resistors also have minimum inductance because of the small dimensions and because they always have a meander structure of the resistive track.

SMD chip resistors always have meander resistive paths.
Fig. 1.3.4:
SMD chip resistors always have meander resistive paths.

The capacitance of resistors occurs between areas (plates) of different potential. These are mainly the contact caps, but also small capacitors are formed by any point of different potential. The capacitance spreads over the entire resistor. Also the capacitance between the PCB and the resistor has to be considered. Altogether these capacitances lie in the range of less than 1pF.

In practice there is little possibility to further reduce the capacitances of resistors.

The capacitance of a resistor has to be considered to be spread between any areas of different potential.
Fig. 1.3.5:
The capacitance of a resistor has to be considered to be spread between any areas of different potential.

The inductance and the capacitance of resistors can be considered in parallel and form a parallel tuned circuit. Therefore a resistor will have a resonant frequency at which the impedance will have a maximum.

The frequency limit of a resistor is considered where the impedance exceeds the tolerance for the resistor.

1.4 Variable Resistors

Manually variable resistors are used whenever resistance value are to be changed during operation or alignment of equipment. The resistance is varied by changing the length of the resistive path between 0 and maximum. Variable resistors are always denominated by their maximum resistance. They normally have three terminals (beginning, end, slider), so they can be used as resistor or voltage divider.

The majority of the variable resistors are rotating types with circular (approximately 270) resistive tracks. For special applications linear variable resistors are available.

Potentiometer or faders we call the variable resistors which are manipulated during operation.

Trim potentiometer or trim resistors are variable resistors which are manipulated during alignment procedures. Often they are screw driver operated.

Circuit symbols of different types of variable resistors.
Fig. 1.4.1:
Circuit symbols of different types of variable resistors.

Variable resistors are produced using the same technologies as for fixed resistors. But their construction always requires some more or less complex mechanics and therefore is subject to wear.

1.4.1 Wire Wound Resistors

As for fixed resistors wire wound resistors are mainly used for high power applications and for low resistance values. In all constructions the wire is wound around a ceramic body. The wiper makes contact to the windings along a line across the windings. Wire wound variable resistor will vary their resistance in steps as the wiper moves along the windings.

Wire wound variable resistors are available as rotating and as linear types. Linear types are mainly used as trim resistors.

Construction of wire wound variable resistors.
Construction of wire wound variable resistors.

1.4.2 Carbon Track Resistors

Carbon track trim resistors and potentiometer form the largest group of variable resistors in electronics. They are cheap and suitable for low power applications.

The resistive layer is made of hard carbon on a hard paper or ceramic insulating base. The wiper is of bronze, often equipped with a carbon brush. Due to the wear of the wiper and the carbon track these variable resistors have a limited life time. The reliability may be increased by equipping the slider with a double brush.

Carbon track variable resistors are mainly built as rotating types, either open or with case for dust protection and shielding.

Different types of carbon track variable resistors.
Different types of carbon track variable resistors.

1.4.3 Metal Glaze Track Resistors

This technology is also called "CERMET" (ceramic metal) and is used for high reliability variable resistors. The resistive track is extremely hard and resists wear very well. The base for these variable resistors is always ceramic. Generally this type of variable resistors is more expensive than carbon track types.

Metal glaze track variable resistors are produced in the same types and constructions as the carbon track types.

For fine adjustment trim potentiometers with multi-turn drive are available. The slider is moved by a spindle along a linear or a circular track.

Constructions of a cermet spindle potentiometer.  Constructions of a cermet spindle potentiometer.
Constructions of a cermet spindle potentiometer.

1.4.4 Potentiometer Characteristics

Generally the resistance of a variable resistor changes linearly with the angle or distance of movement. This is achieved by a homogeneous resistive layer along the track. Such variable resistors are called linear variable resistors.

For certain applications (e.g. volume controls) a non-linear or specially a logarithmic relationship between movement and resistance is required. This can be achieved by changing the resistance of the layer along the track.

Different characteristics of variable resistors.
Different characteristics of variable resistors.
The logarithmic characteristic of a variable resistor can be approximated by different sections with constant resistance.
The logarithmic characteristic of a variable resistor can be approximated by different sections with constant resistance.

To achieve a true logarithmic characteristic it is necessary to increase the resistance of the layer permanently along the track. This is difficult to manufacture. In practice the resistance will be increased in three or four steps, approaching an logarithmic characteristic.

For special applications (e.g. professional faders) special characteristics of the resistive track can be manufactured. Such special constructions normally result in a very high price for the circuit elements.

When variable resistors are used as voltage dividers (potentiometers), they will have their ideal characteristic only when they are not loaded. Any loading of the potentiometer will distort the characteristic.

The characteristic of a potentiometer will change, if it is loaded with a fixed resistor.
The characteristic of a potentiometer will change, if it is loaded with a fixed resistor.

It can be seen that the characteristic of a heavily loaded linear potentiometer approaches the logarithmic characteristic. This can be used to substitute a logarithmic potentiometer, if only a linear type is available.

1.5 Temperature Dependent Resistors

Also called thermistors.

These are circuit elements made of poly-cristaline ceramic mixtures with a resistance with very high temperature coefficient. They are used whenever temperatures have to be sensed by or in electronic circuits. We distinguish thermistors with positive temperature coefficients (PTC) and with negative temperature coefficient (NTC).

NTC resistors are easier and cheaper to produce and therefore present the majority of the thermistors.

1.5.1 Negative Temperature Coefficient (NTC)

NTC resistors can be used in a temperature range from -50C to +500C. In this range they can change their resistance over three to four decades. The nominal resistance is given for a temperature of 25C. NTC resistors with nominal values from ohms to mega-ohms are available.

Practical NTC are denominated by the

The B-value has the unit of K and describes the temperature characteristic of the NTC. As the formulas are relatively complex, it is more common to use graphs.

The temperature coefficients (alpha) of NTC resistors lie between -2.5% and -4.5%.
The graphical and the mathematical representation of the characteristic of a NTC resistor.
The graphical and the mathematical representation of the characteristic of a NTC resistor.

symbols used in the formulas:

NTC resistors are used in the ambient heated mode and in the self heated mode.

Ambient heated mode

When used in this mode, the temperature of the NTC and thus the resistance depend on the ambient temperature. This requires that the power dissipation in the NTC is negligible and does not influence the temperature of the NTC. In this mode NTC resistors are used for

Self Heated Mode

In this mode the temperature of the NTC resistor depends basically on its own power dissipation. As the NTC resistor reduces its resistance with increasing temperature it tends to increase it current when getting hot. This is called "thermal run-away". If the NTC resistor is operated on a constant voltage the power dissipation will increase to very high values, finally destroying the element. Therefore NTCs in the self-heating mode will always require some measures to limit the current to safe values.

Voltage current characteristic of the NTC in self-heating mode.
Voltage current characteristic of the NTC in self-heating mode.

There are different applications for the self-heating mode:

- Starter NTC-resistor:
The NTC resistor is in series with a load (e.g. a motor). When the load is off no current flows. The NTC is cold and has a high resistance. When the voltage is switched on the high resistance of the NTC will allow only little current and the major part of the power is dissipated in the NTC. The NTC will heat up, reducing its resistance, allowing more current to the load. Finally a stable state will be reached, when the NTC reaches its final temperature with low resistance and the current being mainly limited by the load.
Such circuits are used for "soft start" of motors and lamps.
Arrangement of a motor with NTC resistor in series to limit the heavy starting current of the motor.
Arrangement of a motor with NTC resistor in series to limit the heavy starting current of the motor.

- Cooling sense:
The current is adjusted through the NTC so that it heats well over ambient temperature (e.g. 100C). The NTC is mounted in the air stream of a cooling fan to be supervised. The air cooling will also cool the NTC, increasing its resistance. In case the cooling fan fails, the NTC will increase its temperature, reducing its resistance, which will be detected by a suitable electronic circuit giving an indication.

- Media sense:
A NTC in self heating mode will change its temperature and thus its resistance, if it comes into another media with different thermal conduction.
E.g. a NTC can be mounted in a water reservoir to sense the water level. When the water reaches the self heated NTC it will cool the NTC, increasing its resistance, which can be used to give an indication.

1.5.2 Positive Temperature Coefficient (PTC)

In fact all metal conductors can be considered as PTC resistor. But their temperature coefficient is relatively small compared to the special PTC elements.

PTC resistor are made of sintered barium-carbonite, strontium-oxide, titanum-oxide and other powdered materials. They are available in pill, disk and bar shapes and are built in different cases for the various applications.

PTC resistors are more difficult to produce and are therefore more expensive than NTC resistors. As a result NTC resistors will be used whenever possible, while PTC resistors will only be selected when their special features are required.

The resistance characteristic of a PTC resistor can not be described by a mathematical function, but will be given by a graph. Note that the curve has sections with positive and with negative temperature coefficients. A PTC will only be operated in the range of positive temperature coefficient.

Circuit symbol and typical characteristic of a PTC resistor.
Circuit symbol and typical characteristic of a PTC resistor.

The curve has the following characteristic points:

 Rmin Minimum resistance.
Lowest possible resistance of the PTC. At this point the temperature coefficient changes from negative to positive.
 Rn Nominal resistance.
Rn is defined as 2*Rmin.
 Rmax End resistance.
Above this value the temperature coefficient will decrease significantly.
 alphaR Temperature coefficient at the working point.
This is the slope of the curve at the selected working point.
 Tmin Start temerature.
Temperature of Rmin.
 Tn Nominal temperature.
Temperature at Rn. The PTC resistor will normally be operated above this temperature.
 Tmax End temperature.
A PTC resistor will normally be operated below this temperature.

In data sheets the curves for the resistance characteristic is often given for the useful range from Rn to Rmax only.

When a PTC resistor is used in the self-heating mode also the voltage-current characteristic is important.

Voltage-current characteristic of a PTC resistor.
Voltage-current characteristic of a PTC resistor.

Note that the curve will not exceed the maximum power curve and therefore the PTC resistor shows no thermal run-away.

Comparing the PTC with NTC resistors, the following features can be named:

Positive temperature coefficient:
Steep slope of characteristic:
Complex characteristic:
No thermal run-away:
Voltage dependent characteristic:
High capacitance:

PTC resistors will be used for the following applications:

Ambient Heated Mode:

- Temperature sensing:
Whenever high sensitivity is required for a temperature sense a PTC resistor will be used because of its high temperature coefficient.

Self-Heated Mode:

- Current stabilization:
If a suitable PTC resistor is connected in series with a load, the current through the load can be maintained constant over a wide range of supply voltage.
Load line for a load resistor in the voltage-current characteristic of a PTC.
The load line for a load resistor in the voltage-current characteristic of a PTC.
Note that the current across the resistor will reduce, although the supply voltage is increased. Also the reduction in load resistance will not increase the current.

- Circuit protection:
In this application a PTC resistor is connected in series with some device or circuit to protect it from excessive currents. The normal working point of the PTC resistor is in the ambient mode with low temperature and resistance, producing little voltage drop. In case of excessive voltage or a short circuit within the device the working point of the PTC moves into the self heating range, reducing the current to safe values. Note that the original working point can only be achieved after switching of the supply.

Due to the thermal delay of the PTC this circuit is not able to protect against short voltage surges.
Load line for a load resistor in the voltage-current characteristic of a PTC.
The load line for a load resistor in the voltage-current characteristic of a PTC.
Note the normal working point A in the ambient range of the PTC. Any increase in supply voltage or any reduction in load resistance will bring the PTC into the self-heated mode resulting in working point B.

- Coil or motor protection:
A PTC resistor is mounted directly in the coil to be protected and connected in series with it. When the coil becomes hot due to overheating, the PTC will increase its resistance, reducing the current through the coil.

- Amplitude stabilization:
In oscillator circuits the PTC resistor can be used to stabilize the output amplitude. The PTC resistor will be connected in the positive feed back path of the oscillator. When the amplitude increases the PTC will increase it temperature and thus its resistance, so the positive feed back will be reduced.
Principle circuit of an oscillator with PTC resistor in the feed back path for amplitude stabilization.
Principle circuit of an oscillator with PTC resistor in the feed back path for amplitude stabilization.

- Media Sense:
This application is similar to the one with the NTC resistor. When a PTC resistor is used for this application no additional series resistor is required to stabilize the working point, because the PTC is self stabilizing. Due to the safe working mode such device may even be used for inflammable liquids.

1.6 Light Dependent Resistors (LDR)

There are a number of light dependent electronic components, most of which belong to the group of semiconductors. These will be discussed thoroughly in an own subject.

All LDR reduce their resistance as the light intensity increases.

In photo optics the Cadmium-Sulfide (CdS) photo resistor plays a certain roll, because its light sensitivity is similar to the human eye. The CdS photo resistor has a resistance characteristic which is proportional to the light intensity over a wide range.

Because of its linear characteristic it is widely used as photometers in cameras.

Typical characteristic of a CdS photo resistor and the standardized circuit symbol.
Fig. 1.6.1:
Typical characteristic of a CdS photo resistor and the standardized circuit symbol.

LDR change their resistance relatively slow with the light intensity. Therefore they can not be used for applications higher than 10Hz.

For many applications LDR were substituted by photo diodes, because they are cheaper, faster and more sensitive.

1.7 Voltage Dependent Resistors (VDR)

VDR or varistors have a symmetrical voltage-current characteristic. The resistance decreases as the voltage increases. Modern VDR have a similar characteristic as Zener diodes, but they are symmetrical devices, this means they can handle a.c. as well as d.c..

VDR are mainly used to protect electronic equipment from excessive voltages caused by lightning and other interference. They are widely used in telecommunication system for the protection of incoming lines.

Formerly VDR were using a silicon-carbide element, today mainly metal-oxide (MO)(mainly zinc-oxide) VDR are used, because they have the following advantages:

The function of the MO-VDR is based on its crystal structure. Each MO crystal produces a break-through voltage of app. 3.8V. By cascading many crystal in series and in parallel in one element high voltages and high currents can be reached.

Construction and principle of function of the MO VDR.
Fig. 1.7.1:
Construction and principle of function of the MO VDR.

MO VDR of different size.
Fig. 1.7.2:
MO VDR of different size.

The U/I characteristic or VDR follow the expression


Due to the exponential function of the characteristic the graphical representation will use logarithmic scales.

U/I characteristic of a MO VDR.
Fig. 1.7.3:
U/I characteristic of a MO VDR.

Normally the characteristics of VDR are described by the following parameters:

maximum operational voltage (Umax):

voltage for a current of 1mA (U1mA):
maximum power rating (Pmax):
maximum surge current (Imax):
maximum surge energy (Emax):

In order to be able to protect a circuit or an element from excessive voltages, the VDR is connected in parallel. The surge energy will then be dissipated by the line and the VDR. In case the energy of the excessive voltage would be sufficient to destroy the VDR, a fuse may be connected in series with the supply or signal line.

VDR used to protect a circuit from voltage surges.
Fig. 1.7.4:
The VDR is used to protect a circuit from voltage surges. The surge energy will be dissipated by the line resistance and the VDR. A fuse may be used as additional protection.

1.8 Magnetic Dependent Resistors

The function of the magnetic dependent resistor (MDR) is based on the so-called Hall effect. This effect can best be explained by the Hall element.

1.8.1 Hall Element

The hall element is a four pole which can be considered as magnetic flux density dependent voltage source. It is based on the Hall effect.

The Hall effect uses the well known law of induction, which states that electrons will be deflected, if they move through a magnetic field. In the hall element electrons moving from one electrode to the other are deflected by an external magnetic field so that they move their path towards a second pair of electrodes. Between these electrons a voltage can be measured which depends on the magnetic field density B.

In normal conductor materials the speed of movement of the electrons is so slow, that no significant deflection of the electron's path will be experienced. Therefore hall elements use semiconductor materials with only few valency electrons which will have to move very fast. With this voltages up to 2V can be achieved across the hall element.

Principle and characteristic of a hall element.
Principle and characteristic of a hall element.

Hall elements are used whenever magnetic fields have to be sensed and measured. They are also widely used to detect the position of the electric motor's magnetic fields for electronic commutation in brushless d.c. motors.

1.8.2 Magnetoresistor

The magnetoresistors are magnetic dependent resistors (MDR). They apply the same principle as hall elements and are made of the same materials, but they are two poles. When an MDR is exposed to a magnetic field, the path of the electrones will be deflected. This leads to an increase in the length of the path and therefore to an increase in resistance.

The principle construction of the MDR.
The principle construction of the MDR.

MDRs are used to detect magnetic fields. It is also possible to build variable resistors, which are controlled by moving a perment magnet. The advantage of such variable resistor is that it works without friction.

1.9 Wire Strain Gauges

Wire strain gauges (WSG) are extension dependent resistors. They are used to convert mechanical quantities like force, torque or movement into electrical quantities for further signal processing. This is required in many modern electronically controlled machines.

WSGs basically convert variation of length into variation of resistance. Their principle is based on the change of resistance of a conductor with length.

Principle of the construction of the wire strain gauge.
Fig. 1.9.1:
The principle of the construction of the wire strain gauge. When it is stressed, the length of the path increases while the c.s.a. decreases. This results in an increase of resistance.

As the variation of length are normally small, the sensitivity of the WSG is increased by giving the conductor a meander-shapped path to multiply the effective length.

To increase the sensitivity and to reduce the influence of temperature two crosswise coupled elements can be used in a bridge configuration.

Two WSG in crosswise configuration.
Fig. 1.9.2:
Two WSG in crosswise configuration. They can be connected in a bridge circuit to increase the sensitivity and for temperature compensation.


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