Resistance and Examples of Resistors

Background

To describe different types of resistors requires a comprehension of what is meant by resistance. In turn understanding resistance requires a basic understanding of electricity and its components. An atom is made of three major particles: electrons, protons, and neutrons, each with a different electrical charge. The electron is negatively charged; the proton is positively charged; and the neutron has no charge, neutral. If two bodies have opposite electrical charges (positive and negative), they attract each other; if they have like charges (both positive or negative), they repel each other. This is similar to magnets, which have a north and south pole (opposite charges); the north and south poles of two magnets attract each other. On the other hand, two north or two south poles repel each other. For electricity to flow there must be opposite charges between two particles or objects. The attraction between electrons and protons causes the electrons to flow to the protons; this flow is electricity. Electricity has two main measurements: voltage (pressure of the electricity) and current (the amount of electrons flowing during a given time). An analogy can be made to water flowing through a hose and the measurement of electricity. The water pressure in the hose would be the voltage (i.e. pounds per square inch), while the amount of water flowing past a point (i.e. gallons per hour), would be the current.

If the only constraint on whether electricity flowed were a difference of charge, then electricity would flow as soon as it was created and the electrons and protons would immediately recombine and electricity would have no use; however, here, resistance enters the picture. Every substance has a resistance associated with it. Wire, water, rubber, and air all have a measurable resistance, though their resistances vary greatly. The way the electrons arrange in shells around the atom’s nucleus determines the amount of resistance that each material has. The outer most shell, called the valence shell, is the factor that controls the amount of resistance. The maximum number of electrons in the valence shell is eight and the fuller the shell, the higher the resistance of the material. The elements of the periodic table and materials, in general, are in three groups, based on their conductivity (conductivity is the opposite of resistance, higher conductivity equals less opposition to electron flow). The three groups are: conductors, semiconductors, and insulators, with conductors having the least resistance and insulators the most. The breakdown for the classification of an atom’s conductivity is as follows:

 Electrons in Valence Shell Classification Three or less Conductor Four Semiconductor Five or more Insulator

To see how resistance works, it is easiest to see how conductance works. An atom seeks to fill its valence shell to the maximum number of electrons, so if there is an electron available, it adds the electron to its valence shell. In a conductor, valence electrons are not held in place, but are free floating, as if in a sea of electrons, creating virtual shells. An electric current adds electrons; the conductor takes in the electrons filling in the vacancies in the valence shells. The electrons do not stay in a given valence shell, because the attraction of the electrons to the protons of the nucleus is less than the attraction to the protons of the current source, so the electrons continue to flow through the conductor. Other electrons from the source of electricity immediately fill the places vacated by these electrons. Resistance occurs when the source electrons "bump" into the electrons that were all ready in the valence shell. The bumping takes the energy from the electrons’ motion and turns it into heat. In a conductor, there are few valence electrons (one, two, or three, with room for eight), so there is little resistance. This allows many electrons to flow, which, by the definition of current, means a high current. With all these electrons flowing, at a high speed, when the collisions occur there is a lot of motion energy turned into heat. One can literally see this in a light bulb, which converts such a high degree of electrical energy into heat energy, that it causes the metal filament (a conductor) to glow, producing light.

When people think of resistance, they usually have in mind a material with the properties of a semiconductor. It has four valence electrons, giving it properties of an insulator and a conductor. Like a conductor, it accepts electrons from an electric current, but unlike a conductor, the nucleus of the atom holds the electrons, in the valence shell, much more firmly. This makes it more difficult for the electrons to pass through a semiconductor. The electric current’s electrons must dodge and bump into the electrons of the atoms, as opposed to a conductor where they float together. It seems as though a semiconductor would convert more electrical energy into heat than a conductor would, but this is not the case. First, since a semiconductor only needs four electrons to fill the valence shell as opposed to a conductor that can have five to eight electrons filling its shell, this limits the amount of current that will flow. A lower current means fewer electrons to bump into other electrons. Second, the current moves more slowly in a semiconductor, than a conductor. With the electrons firmly attached to the nucleus, the electrons from the current source have to move around them, much like a rock in a stream, where the water flows around the rock, slowing down the water. This slow down means less energy when the electrons do bump into each other, creating less heat.

The last category is the insulators, which have the highest amount of resistance. The situation in an insulator is similar to that of the semiconductor, except greatly amplified. Insulators have most or all of their valence shell filled, leaving little or no room for electrons from an electric current. The insulator atoms hold very tightly on to their electrons, creating a sort of roadblock for the few electrons that do try flow through the insulator. It is difficult for any current to flow at all. It takes an electric source with very high voltage, to overcome an insulator’s resistance. It does this by overcoming the force of the nucleus on its electrons and making the electrons flow; there is an extreme amount of heat given off when this occurs. In the water hose analogy voltage is compared to the pressure of the water. If the pressure of the voltage becomes high enough it can force the electrons through a conductor. One of the best and most important insulators is air; it totally halts all current flow, but even air’s ability to insulate breaks down when exposed to enough electrical energy, for instance lightning. Regardless of the substance size plays a role in resistance. The longer a wire (or substance, in general) is, the higher its resistance. This is caused by electrons, in the current-flow, traveling further, which makes them have more collisions, with other electrons. Conversely, the wider the wire or substance is, the lower resistance the wire of substance is. The added width gives the electrons more paths so they are less crowded and less likely to hit other electrons.

Definition of Resistance

In the above atomic simplification of resistance, the flow of electricity was described in terms of voltage and current; these two measurements are related. An electrically charged particle exerts a pressure or force; the quantity of this force is called electric potential. If the amount of this force was measured at one point and then another, the difference in the two measurements or electric potentials would be the potential difference, this is the voltage. The force that creates the potential difference is called an electric field (E); it is a vector force, meaning it has magnitude and a direction.

Current is the number of electrons that flow in a given time period. If the current in a given area is considered, this is also a vector quantity current density (J), having magnitude and direction,

.

A current density and an electric field are established any time a potential difference is maintained across conductors. If the two vectors, J and E, are related to each other through a proportionality constant sigma (), giving:

then the substance is said to be ohmic, following Ohm’s law (see below). Sigma is called the conductivity of the conductor, the larger the constant the more easily the substance conducts. Resistivity () is the inverse of sigma, that is:

An ideal conductor would have zero resistivity (as goes to infinity) and an ideal resistor would have infinite resistance (as goes to zero). To define resistance and Ohm’s law, if a straight wire has a potential difference applied to both ends and the wire has a length of l, assuming a uniform electric field, then combining:

and with

,

then

Resistance is defined then as

,

Resistance is in effect a proportionality constant between voltage and current (this is Ohm’s law). Having defined resistance the different types of resistors can now be discussed. (Serway, 749-847)

Examples of Resistors

Resistors can be divided and subdivided into many groups, but the major division is between active and passive resistors.

Active Resistors

In general, active resistors are field-effect transistors (FET); operated in a particular region. An MOSFET (the most common type of FET) has three regions of operation: cutoff, triode, and saturation. The region the MOSFET is operation in depends on the voltages applied and the intrinsic characteristics of the transistor. An MOSFET has three terminals, a gate (G), a drain (D) and a source (S). For the transistor to operate (i.e. not in the cutoff region), the voltage applied between the gate and the source must be higher than a built in characteristic of the transistor called the threshold voltage (Vt). When the threshold voltage is overcome the transistor (vGS>Vt ) induces a "channel" for the current to flow through. Now if the voltage between the drain and the source is less than vGS-Vt, the transistor is in the triode region and the channel is small, which restricts the flow of current acting as a resistor. This resistance is variable, depending on the voltage between the drain and source; the larger the voltage the larger the channel, allowing more current can flow. When vds> vGS-Vt , the channel reaches its maximum the transistor leaves the triode region and is now in the saturation

MOSFET with vGS>Vt (Sedra/Smith, 358)

region, no longer operating as a variable resistor.

MOSFET Transistor Operating Regions (Sedra/Smith, 367)

The main advantage of using the MOSFET resistor is in integrated circuits (IC). To implement a large resistor on an IC, it takes up a large amount of area. The more resistance needed the larger the required space on the chip. Using a FET can solve this problem, since a FET has a small footprint when implemented on an IC. Another advantage to is it can act as a variable resistor and the conditions in the circuit can set the parameters for the resistance. That is the circuit can be made such that the vds changes as the conditions in the circuit change, thus changing the resistance of the FET. Disadvantages of the FET as a resistor include some high frequency problems and more complicated to implement in a circuit than a two terminal resistor (Sedra/Smith, 353-464). Note: for more detail on MOSFETs see Sedra/Smith

Passive Resistors

The largest category of resistors is the passive types; this encompasses most familiar resistors, which are main discrete components, but some technologies can be use either as discrete or on ICs.

Carbon Resistors

The resistor, most commonly identified as a resistor, is the carbon resistor. The carbon resistor, as it name implies, is made carbon, an element, which is classified as a semiconductor. Its resistance is derived from the natural properties of a semiconductor to impede the flow of current. The simplest are a carbon cylinders molded around two electrodes. To control the resistance, the length of the carbon is increased, raising the resistance. To decrease the resistance the width of the carbon is increased, this also increases the wattage of the resistor. These resistors are typically made in accuracy tolerance ranges of 5, 10 and 20%. Carbon resistors are generally discrete devices, though can be used in some circuit board designs. The advantages of the carbon resistor is its low cost and availability. Disadvantages include low power handling capability (1-2 watt maximum) and poor heat dissipation, causing non-linear response. Carbon resistors have good frequency response until about 1MHz. The frequency limitation is caused in any resistor by its make-up and it cross-section to length ration. This ratio causes parasitic capacitance and inductance effects (Analog Devices).

Metal Film Resistors (Thin Film)

A metal film resistor takes a ceramic core and coats a thin film of resistance material on the core. The resistance material is generally composed of Nichrome, tin oxide or tantalum nitride. A helical groove is cut in the film; by changing the angle of the spiral cut, the length and width of the groove can be changed, changing the resistance. Metal end caps are fitted on and then the assembly is covered with an insulator such as ceramic. Metal film resistors can be manufactured directly onto circuit boards. The advantages of metal film

Metal Film Resistor (Bigelow)

resistors include high accuracy with values being within 1% of their rating, excellent high frequency response, up to 100MHz, because of their low cross-section to length ratio, excellent linear response with an increase in temperature and a higher power handling capability than carbon resistors. Disadvantages of metal film resistors, with higher accuracy comes an increase in cost.

Wire Wound Resistors

Wire wound resistors take a length of wire (a conductor) and winding it around a ceramic; the resistance is adjusted by the length and width of the wire. The main advantages of the wire wound resistors are can be made to tight tolerances (at low frequencies), high power handling capabilities and heat dissipation. The wire wound resistors have several disadvantages that become even more of a problem with modern circuits. The first is space; wire wound resistors are large; higher resistances take more wire, meaning more space. In addition, wire wound resistors have inductance, caused by the winding of the wire. Since impedance of an inductor is directly proportional to the frequency (Z = 2pfL), this typically causes problems when frequencies increase above 50kHz (Analog Devices).

Conclusion

The concept of resistance, an opposition to current flow, is a simple idea, but the actual mechanics of resistance needs to be studied on a sub-atomic scale to be fully understood. It is on this sub-atomic scale that different principles electric fields, current flow and resistance are manipulated to make the different types of resistors. As these concepts are better understood at the atomic level, devices that can overcome the shortcomings of the present day components can be designed.

Sources

Sedra, Adel S.and Kenneth C. Smith. Microelectronic Circuits 4e. New York: Oxford U P, 1998

Serway, Raymond A., Robert J Beichner. Physics for Scientists and Engineers. Fort Worth. Saunders C P, 2000

Bigelow, Ken. "Circuit Components: the Resistor". 15 Mar 2003

http://www.play-hookey.com/dc_theory/components_resistors.html

Analog Devices. "Analog Devices: Analog Dialogue: Ask The Applications Engineer – 24." 18 Mar 2003. http://www.analog.com/library/analogDialogue/archives/31-1/Ask_Engineer.html