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The most common type of three phase induction motor is the squirrel cage type. This electric motor has its name derived from the fact that the rotor resembles the wheel of a squirrel's cage. It has a very simple and durable design so its very universal. Not to mention, it is used in most commercial and industrial applications.

Construction of the Squirrel Cage Motor

A squirrel-cage motor consists essentially of two units, namely

1. Rotor

2. Stator

The rotor (or secondary) is also constructed of steel laminations, but the windings consist of conductor bars placed approximately parallel to the shaft and close to the rotor surface. These windings are connected at each end of the rotor, by a solid ring. The rotors of large motors have bars and rings of copper connected at each end by a conducting end ring made of copper or brass. The joints between the bars and end rings are usually electrically welded into one unit, with blowers mounted on each end of the rotor. In small squirrel-cage rotors, the bars, end rings, and blowers are of aluminum cast in one piece instead of welded together.

The stator (or primary) consists of a laminated sheet-steel core with slots where the insulated coils are placed. The coils are grouped and connected to form a definite polar area and to produce a ROTATING MAGNETIC FIELD when connected to a polyphase alternating current.

The air gap between the rotor and stator must be very small in order for the best power factor to be obtained. The shaft must, therefore, be very rigid and furnished with quality bearings of the sleeve or ball-bearing type.

Principles of Operation

In a squirrel-cage motor, the secondary winding takes the place of the field winding in a synchronous motor. As in a synchronous motor, the currents in the stator set up a rotating magnetic field. This field is produced by the increasing and decreasing currents in the windings. When the current increases in the first phase, only the first winding produces a magnetic field. As the current decreases in this winding and increases in the second, the magnetic field shifts slightly, until it is all produced by the second winding. When the third winding has maximum current flowing in it, the field is shifted a little more. The windings are so distributed that this shifting is uniform and continuous. It is this action that produces a rotating magnetic field.

As this field rotates, it cuts the squirrel-cage conductors, and voltages are set up in these just as though the conductors were cutting the field in a DC generator. These voltages cause currents to flow in the squirrel-cage circuit – through the bars under the adjacent south poles into the other end ring, and back to the original bars under the north poles to complete the circuit.

The current flowing in the squirrel-cage, down one group of bars and back in the adjacent group, makes a loop that establishes magnetic fields in the rotor core with north and south poles. This loop consists of one turn, but there are several conductors in parallel and the currents may be large. The poles in the rotor are attracted by the poles of the rotating field set up by the currents in the armature winding and follow them around in a manner similar to the way in which the field poles follow the armature poles in a synchronous motor.

There is, however, one interesting and important difference between the synchronous and the induction motor: the rotor of the latter does not rotate as fast as the rotating field in the armature. If the squirrel cage were to go as fast as the rotating field, the conductors in it would be standing still with respect to the rotating field, rather than cutting across the field. Then there would be no voltage induced in the squirrel cage, no currents in it, no magnetic poles set up in the rotor, and no attraction between it and the rotating field in the stator.


The three-phase AC induction motor has a squirrel cage rotor in which aluminum conductors or bars are shorted together at both ends of the rotor by cast aluminum end rings. When three currents flow through the three symmetrically placed windings, a sinusoidally distributed air gap flux generating the rotor current is produced. The interaction of the sinusoidally distributed air gap flux and induced rotor currents produces a torque on the rotor. The mechanical angular velocity of the rotor is lower then the angular velocity of the flux wave by so called slip velocity.

In adjustable speed applications, AC motors are powered by inverters. The inverter converts DC power to AC power at the required frequency and amplitude. The inverter consists of three half-bridge units where the upper and lower switches are controlled complimentarily. As the power device's turn-off time is longer than its turn-on time, some dead-time must be inserted between the turn-off of one transistor of the half-bridge and turn-on of its complementary device. The output voltage is mostly created by a pulse width modulation (PWM) technique.The three-phase voltage waves are shifted 120° to one another and thus a three-phase motor can be supplied.

The stator windings of an AC induction motor are distributed around the stator to produce a roughly sinusoidal distribution. When three-phase AC voltages are applied to the stator windings, a rotating magnetic field is produced.

The rotor of an induction motor also consists of windings or more often a copper squirrel cage embedded within iron laminates. Only the iron laminates are shown. An electric current is induced in the rotor bars which also produce a magnetic field.

The rotating magnetic field of the stator drags the rotor around. The rotor does not quite keep up with the rotating magnetic field of the stator. It falls behind or slips as the field rotates.

In this animation, for every time the magnetic field rotates, the rotor only makes three-fourths of a turn. If you follow one of the bright green or red rotor teeth with the mouse, you will notice it change color as it falls behind the rotating field. The slip has been greatly exaggerated to enable visualization of this concept. A real induction motor only slips a few percent.


Three phase transformers are very commonly used throughout commercial and inudstrial projects in North America to change voltgae and current. Three phase power is produced, transmitted and distributed on a regular basis by the utility companies so its essential to understand how to utilize it with three phase transformers.

Three phase transformers differ from single phase transformers by the way the connections are made. SINGLE PHASE TRANSFORMERS have two phases on the primary and two phases on the secondary. But three phase transformers have a variety of connections, most notably the Delta-to-Wye connection.

A delta-wye transformer has its primary winding connected in delta and its secondary winding connected in wye.

A very common usage of this application is in 480v 3ø to 208v 3ø systems:

The diagram above demonstrates that the incoming voltage is 480v 3ø and the outgoing voltage is 208v 3ø. This very common type of transformer is typically used in commercial buildings over 30,000 s.f. and in most industrial applications. The reason is that by utilizing a higher voltage electrical service, the amperage of the electrical service will be much less than if it were 208v 3ø. The lower the amperage, the more economical the service will be. In the typical scenario of this system, the lighting and hvac equipment is supplied on the 480v panelboards and the power receptacles and other 120v power is served by the 208v 3ø panelboard. The diagram below illustrates the exact details of this system.


Single phase synchronous motors are available in small sizes for applications requiring precise timing such as time keeping, (clocks) and tape players. Though battery powered quartz regulated clocks are widely available, the AC line operated variety has better long term accuracy-- over a period of months. This is due to power plant operators purposely maintaining the long term accuracy of the frequency of the AC distribution system. If it falls behind by a few cycles, they will make up the lost cycles of AC so that clocks lose no time.

Above 10 Horsepower (10 kW) the higher efficiency and leading powerfactor make large synchronous motors useful in industry. Large synchronous motors are a few percent more efficient than the more common induction motors. Though, the synchronous motor is more complex.

Since motors and generators are similar in construction, it should be possible to use a generator as a motor, conversely, use a motor as a generator. A synchronous motor is similar to an alternator with a rotating field. The figure below shows small alternators with a permanent magnet rotating field. This figure below could either be two paralleled and synchronized alternators driven by a mechanical energy sources, or an alternator driving a synchronous motor. Or, it could be two motors, if an external power source were connected. The point is that in either case the rotors must run at the same nominal frequency, and be in phase with each other. That is, they must be synchronized. The procedure for synchronizing two alternators is to (1) open the switch, (2) drive both alternators at the same rotational rate, (3) advance or retard the phase of one unit until both AC outputs are in phase, (4) close the switch before they drift out of phase. Once synchronized, the alternators will be locked to each other, requiring considerable torque to break one unit loose (out of synchronization) from the other.

Synchronous motor running in step with alternator.

If more torque in the direction of rotation is applied to the rotor of one of the above rotating alternators, the angle of the rotor will advance (opposite of (3)) with respect to the magnetic field in the stator coils while still synchronized and the rotor will deliver energy to the AC line like an alternator. The rotor will also be advanced with respect to the rotor in the other alternator. If a load such as a brake is applied to one of the above units, the angle of the rotor will lag the stator field as at (3), extracting energy from the AC line, like a motor. If excessive torque or drag is applied, the rotor will exceed the maximum torque angle advancing or lagging so much that synchronization is lost. Torque is developed only when synchronization of the motor is maintained.

In the case of a small synchronous motor in place of the alternator Figure above right, it is not necessary to go through the elaborate synchronization procedure for alternators. However, the synchronous motor is not self starting and must still be brought up to the approximate alternator electrical speed before it will lock (synchronize) to the generator rotational rate. Once up to speed, the synchronous motor will maintain synchronism with the AC power source and develop torque.

Sinewave drives synchronous motor.

Assuming that the motor is up to synchronous speed, as the sine wave changes to positive in Figure above (1), the lower north coil pushes the north rotor pole, while the upper south coil attracts that rotor north pole. In a similar manner the rotor south pole is repelled by the upper south coil and attracted to the lower north coil. By the time that the sine wave reaches a peak at (2), the torque holding the north pole of the rotor up is at a maximum. This torque decreases as the sine wave decreases to 0 VDC at (3) with the torque at a minimum.

As the sine wave changes to negative between (3&4), the lower south coil pushes the south rotor pole, while attracting rotor north rotor pole. In a similar manner the rotor north pole is repelled by the upper north coil and attracted to the lower south coil. At (4) the sinewave reaches a negative peak with holding torque again at a maximum. As the sine wave changes from negative to 0 VDC to positive, The process repeats for a new cycle of sine wave.

Note, the above figure illustrates the rotor position for a no-load condition (α=0o). In actual practice, loading the rotor will cause the rotor to lag the positions shown by angle α. This angle increases with loading until the maximum motor torque is reached at α=90o electrical. Synchronization and torque are lost beyond this angle.

The current in the coils of a single phase synchronous motor pulsates while alternating polarity. If the permanent magnet rotor speed is close to the frequency of this alternation, it synchronizes to this alternation. Since the coil field pulsates and does not rotate, it is necessary to bring the permanent magnet rotor up to speed with an auxiliary motor. This is a small induction motor similar to those in the next section.

Addition of field poles decreases speed.

A 2-pole (pair of N-S poles) alternator will generate a 60 Hz sine wave when rotated at 3600 rpm (revolutions per minute). The 3600 rpm corresponds to 60 revolutions per second. A similar 2-pole permanent magnet synchronous motor will also rotate at 3600 rpm. A lower speedmotor may be constructed by adding more pole pairs. A 4-pole motor would rotate at 1800 rpm, a 12-pole motor at 600 rpm. The style of construction shown (Figure above)) is for illustration. Higher efficiency higher torque multi-pole stator synchronous motors actually have multiple poles in the rotor.

One-winding 12-pole synchronous motor.

Rather than wind 12-coils for a 12-pole motor, wind a single coil with twelve interdigitated steel poles pieces as shown in Figure above. Though the polarity of the coil alternates due to the appplied AC, assume that the top is temporarily north, the bottom south. Pole pieces route the south flux from the bottom and outside of the coil to the top. These 6-souths are interleaved with 6-north tabs bent up from the top of the steel pole piece of the coil. Thus, a permanent magnet rotor bar will encounter 6-pole pairs corresponding to 6-cycles of AC in one physical rotation of the bar magnet. The rotation speed will be 1/6 of the electrical speed of the AC. Rotor speed will be 1/6 of that experienced with a 2-pole synchronous motor. Example: 60 Hz would rotate a 2-pole motor at 3600 rpm, or 600 rpm for a 12-pole motor.

Reprinted by permission of Westclox History at

The stator (Figure above) shows a 12-pole Westclox synchronous clock motor. Construction is similar to the previous figure with a single coil. The one coil style of construction is economical for low torque motors. This 600 rpm motor drives reduction gears moving clock hands.

If the Westclox motor were to run at 600 rpm from a 50 Hz power source, how many poles would be required? A 10-pole motor would have 5-pairs of N-S poles. It would rotate at 50/5 = 10 rotations per second or 600 rpm (10 s-1 x 60 s/minute.)

Reprinted by permission of Westclox History at

The rotor (Figure above) consists of a permanent magnet bar and a steel induction motor cup. The synchronous motor bar rotating within the pole tabs keeps accurate time. The induction motor cup outside of the bar magnet fits outside and over the tabs for self starting. At one time non-self-starting motors without the induction motor cup were manufactured.

A 3-phase synchronous motor as shown in Figure below generates an electrically rotating field in the stator. Such motors are not self starting if started from a fixed frequency power source such as 50 or 60 Hz as found in an industrial setting. Furthermore, the rotor is not a permanent magnet as shown below for the multi-horsepower (multi-kilowatt) motors used in industry, but an electromagnet. Large industrial synchronous motors are more efficient than induction motors. They are used when constant speed is required. Having a leading power factor, they can correct the AC line for a lagging power factor.

The three phases of stator excitation add vectorially to produce a single resultant magnetic field which rotates f/2n times per second, where f is the power line frequency, 50 or 60 Hz for industrial power line operated motors. The number of poles is n. For rotor speed in rpm, multiply by 60.

                    S = f120/n
                    where:  S = rotor speed in rpm
                            f = AC line frequency
                            n = number of poles per phase

The 3-phase 4-pole (per phase) synchronous motor (Figure below) will rotate at 1800 rpm with 60 Hz power or 1500 rpm with 50 Hz power. If the coils are energized one at a time in the sequence φ-1, φ-2, φ-3, the rotor should point to the corresponding poles in turn. Since the sine waves actually overlap, the resultant field will rotate, not in steps, but smoothly. For example, when the φ-1 and φ-2 sinewaves coincide, the field will be at a peak pointing between these poles. The bar magnet rotor shown is only appropriate for small motors. The rotor with multiple magnet poles (below right) is used in any efficient motor driving a substantial load. These will be slip ring fed electromagnets in large industrial motors. Large industrial synchronous motors are self started by embedded squirrel cage conductors in the armature, acting like an inductionmotor. The electromagnetic armature is only energized after the rotor is brought up to near synchronous speed.

Three phase, 4-pole synchronous motor

Small multi-phase synchronous motors (Figure above) may be started by ramping the drive frequency from zero to the final running frequency. The multi-phase drive signals are generated by electronic circuits, and will be square waves in all but the most demanding applications. Such motors are known as brushless DC motors. True synchronous motors are driven by sine waveforms. Two or three phase drive may be used by supplying the appropriate number of windings in the stator. Only 3-phase is shown above.

Electronic synchronous motor

The block diagram (Figure above) shows the drive electronics associated with a low voltage (12 VDC) synchronous motor. These motors have aposition sensor integrated within the motor, which provides a low level signal with a frequency proportional to the speed of rotation of themotor. The position sensor could be as simple as as solid state magnetic field sensors such as Hall effect devices providing commutation (armature current direction) timing to the drive electronics The position sensor could be a high resolution angular sensor such as a resolver, an inductosyn (magnetic encoder), or an optical encoder.

If constant and accurate speed of rotation is required, (as for a disk drive) a tachometer and phase locked loop may be included. (Figure below) This tachometer signal, a pulse train proportional to motor speed, is fed back to a phase locked loop, which compares the tachometer frequency and phase to a stable reference frequency source such as a crystal oscillator.

Phase locked loop controls synchronous motor speed.

A motor driven by square waves of current, as provided by simple hall effect sensors, is known as a brushless DC motor. This type of motor has higher ripple torque torque variation through a shaft revolution than a sine wave driven motor. This is not a problem for many applications. Though, we are primarily interested in synchronous motors in this section.

Motor ripple torque and mechanical analog.

Ripple torque, or cogging is caused by magnetic attraction of the rotor poles to the stator pole pieces. (Figure above) Note that there are no stator coils, not even a motor. The PM rotor may be rotated by hand but will encounter attraction to the pole pieces when near them. This is analogous to the mechanical situation. Would ripple torque be a problem for a motor used in a tape player? Yes, we do not want the motor to alternately speed and slow as it moves audio tape past a tape playback head. Would ripple torque be a problem for a fan motor? No.

Windings distributed in a belt produce a more sinusoidal field.

If a motor is driven by sinewaves of current synchronous with the motor back emf, it is classified as a synchronous AC motor, regardless of whether the drive waveforms are generated by electronic means. A synchronous motor will generate a sinusoidal back emf if the stator magnetic field has a sinusoidal distribution. It will be more sinusoidal if pole windings are distributed in a belt (Figure above) across many slots instead of concentrated on one large pole (as drawn in most of our simplified illustrations). This arrangement cancels many of the stator field odd harmonics. Slots having fewer windings at the edge of the phase winding may share the space with other phases. Winding belts may take on an alternate concentric form as shown in Figure below.

Concentric belts.

For a 2-phase motor, driven by a sinewave, the torque is constant throughout a revolution by the trigonometric identity:

           sin2θ + cos2θ = 1

The generation and synchronization of the drive waveform requires a more precise rotor position indication than provided by the hall effect sensors used in brushless DC motors. A resolver, or optical or magnetic encoder provides resolution of hundreds to thousands of parts (pulses) per revolution. A resolver provides analog angular position signals in the form of signals proportional to the sine and cosine of shaft angle. Encoders provide a digital angular position indication in either serial or parallel format. The sine wave drive may actually be from a PWM, Pulse Width Modulator, a high efficiency method of approximating a sinewave with a digital waveform. (Figure below) Each phase requires drive electronics for this wave form phase-shifted by the appropriate amount per phase.

PWM approximates a sinewave.

Synchronous motor efficiency is higher than that of induction motors. The synchronous motor can also be smaller, especially if high energy permanent magnets are used in the rotor. The advent of modern solid state electronics makes it possible to drive these motors at variable speed. Induction motors are mostly used in railway traction. However, a small synchronous motor, which mounts inside a drive wheel, makes it attractive for such applications. The high temperature superconducting version of this motor is one fifth to one third the weight of a copper wound motor.[1] The largest experimental superconducting synchronous motor is capable of driving a naval destroyer class ship. In all these applications the electronic variable speed drive is essential.

The variable speed drive must also reduce the drive voltage at low speed due to decreased inductive reactance at lower frequency. To develop maximum torque, the rotor needs to lag the stator field direction by 90o. Any more, it loses synchronization. Much less results in reduced torque. Thus, the position of the rotor needs to be known accurately. And the position of the rotor with respect to the stator field needs to be calculated, and controlled. This type of control is known as vector phase control. It is implemented with a fast microprocessor driving a pulse width modulator for the stator phases.

The stator of a synchronous motor is the same as that of the more popular induction motor. As a result the industrial grade electronic speed control used with induction motors is also applicable to large industrial synchronous motors.

If the rotor and stator of a conventional rotary synchronous motor are unrolled, a synchronous linear motor results. This type of motor is applied to precise high speed linear positioning.

A larger version of the linear synchronous motor with a movable carriage containing high energy NdBFe permanent magnets is being developed to launch aircraft from naval aricraft carriers.


Solid-state electronic devices are part of our everyday lives. The transistor, invented in 1947 by Bell Labs, was the first solid-state device to come into commercial use in the 1960s. Solid-state electronic devices have replacedvacuum tubes in just about all electronics devices. Vacuum tubes are still used in the transmitters of radio stations you listen to, many guitar amplifiers and some audiophile equipment. Vacuum tubes are the opposite of "solid-state" because tubes burnout, break, etc.

One of the first solid-state devices was a crystal radio. In a crystal radio, a piece of wire positioned on a crystal's surface is able to separate the lower-frequency audio from the higher-frequency transmitted radio carrier wave. This form of signal detection is due to the crystal's ability to pass a current in only one direction. For more details, see How Radio Works.

Solid-state gets its name from the path that electrical signals take through solid pieces of semi-conductor material. Prior to the use of solid-state devices, such as the common transistor, electricity passed through the various elements inside of a heated vacuum tube. Solid-state devices, such as a transistor, use conductors to control the flow of signals through a circuit.

  • In a transistor amplifier, a small change on the input signal's amplitude is immediately reflected in larger amplitude in the output within a transistor.
  • In a vacuum tube amplifier, after the tube warms up, a signal is applied to the "grid" of a tube and the resultant output of the same frequency is at a much higher amplitude.

In the sandwich-like construction of a transistor, the emitter, base, and collector do a similar task at much lower DC voltages, with no "warm-up" time! In digital circuits, an integrated circuit chip is nothing more that a collection of transistors and wires that hook them together.

Solid state devices called diodes have a replaced rectifier vacuum tubes, used to transform alternating current (AC) to direct current (DC). Cool-running light-emitting diodes (LEDs), another solid-state device used for indicators on the front panel of your computer and monitor, have replaced the earlier incandescent bulbs. Multiple bright LEDs are also used for the third stoplight on many U.S. vehicles and for traffic signals.

Solid-state miniature electronic components are in many places:

  • Mounted on flexible thin film printed circuits in cameras and disk drives.
  • The beeping sound made by a cell phone, page or auto dashboard alarm.
  • The voice chip in an answering machine.
  • TV remote control.
  • Laser pointer.
  • The inside of an MP3 player.
  • A quartz watch.
  • The image sensor in a digital camera and a camcorder.
  • The computer monitor you are viewing.
  • The mouse you will click to the next HSW screen!


A diode is an electrical device allowing current to move through it in one direction with far greater ease than in the other. The most common kind of diode in modern circuit design is the semiconductor diode, although other diode technologies exist. Semiconductor diodes are symbolized in schematic diagrams such as Figure below. The term “diode” is customarily reserved for small signal devices, I ≤ 1 A. The term rectifier is used for power devices, I > 1 A.

Semiconductor diode schematic symbol: Arrows indicate the direction of electron current flow.

When placed in a simple battery-lamp circuit, the diode will either allow or prevent current through the lamp, depending on the polarity of the applied voltage. (Figure below)

Diode operation: (a) Current flow is permitted; the diode is forward biased. (b) Current flow is prohibited; the diode is reversed biased.

When the polarity of the battery is such that electrons are allowed to flow through the diode, the diode is said to be forward-biased. Conversely, when the battery is “backward” and the diode blocks current, the diode is said to be reverse-biased. A diode may be thought of as like a switch: “closed” when forward-biased and “open” when reverse-biased.

Oddly enough, the direction of the diode symbol's “arrowhead” points against the direction of electron flow. This is because the diode symbol was invented by engineers, who predominantly use conventional flow notation in their schematics, showing current as a flow of charge from the positive (+) side of the voltage source to the negative (-). This convention holds true for all semiconductor symbols possessing “arrowheads:” the arrow points in the permitted direction of conventional flow, and against the permitted direction of electron flow.

Diode behavior is analogous to the behavior of a hydraulic device called a check valve. A check valve allows fluid flow through it in only one direction as in Figure below.

Hydraulic check valve analogy: (a) Electron current flow permitted. (b) Current flow prohibited.

Check valves are essentially pressure-operated devices: they open and allow flow if the pressure across them is of the correct “polarity” to open the gate (in the analogy shown, greater fluid pressure on the right than on the left). If the pressure is of the opposite “polarity,” the pressure difference across the check valve will close and hold the gate so that no flow occurs.

Like check valves, diodes are essentially “pressure-” operated (voltage-operated) devices. The essential difference between forward-bias and reverse-bias is the polarity of the voltage dropped across the diode. Let's take a closer look at the simple battery-diode-lamp circuit shown earlier, this time investigating voltage drops across the various components in Figure below.

Diode circuit voltage measurements: (a) Forward biased. (b) Reverse biased.

A forward-biased diode conducts current and drops a small voltage across it, leaving most of the battery voltage dropped across the lamp. If the battery's polarity is reversed, the diode becomes reverse-biased, and drops all of the battery's voltage leaving none for the lamp. If we consider the diode to be a self-actuating switch (closed in the forward-bias mode and open in the reverse-bias mode), this behavior makes sense. The most substantial difference is that the diode drops a lot more voltage when conducting than the average mechanical switch (0.7 volts versus tens of millivolts).

This forward-bias voltage drop exhibited by the diode is due to the action of the depletion region formed by the P-N junction under the influence of an applied voltage. If no voltage applied is across a semiconductor diode, a thin depletion region exists around the region of the P-N junction, preventing current flow. (Figure below (a)) The depletion region is almost devoid of available charge carriers, and acts as an insulator:

Diode representations: PN-junction model, schematic symbol, physical part.

The schematic symbol of the diode is shown in Figure above (b) such that the anode (pointing end) corresponds to the P-type semiconductor at (a). The cathode bar, non-pointing end, at (b) corresponds to the N-type material at (a). Also note that the cathode stripe on the physical part (c) corresponds to the cathode on the symbol.

If a reverse-biasing voltage is applied across the P-N junction, this depletion region expands, further resisting any current through it. (Figurebelow)

Depletion region expands with reverse bias.

Conversely, if a forward-biasing voltage is applied across the P-N junction, the depletion region collapses becoming thinner. The diode becomes less resistive to current through it. In order for a sustained current to go through the diode; though, the depletion region must be fully collapsed by the applied voltage. This takes a certain minimum voltage to accomplish, called the forward voltage as illustrated in Figure below.

Inceasing forward bias from (a) to (b) decreases depletion region thickness.

For silicon diodes, the typical forward voltage is 0.7 volts, nominal. For germanium diodes, the forward voltage is only 0.3 volts. The chemical constituency of the P-N junction comprising the diode accounts for its nominal forward voltage figure, which is why silicon and germanium diodeshave such different forward voltages. Forward voltage drop remains approximately constant for a wide range of diode currents, meaning that diode voltage drop is not like that of a resistor or even a normal (closed) switch. For most simplified circuit analysis, the voltage drop across a conducting diode may be considered constant at the nominal figure and not related to the amount of current.

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Actually, forward voltage drop is more complex. An equation describes the exact current through a diode, given the voltage dropped across the junction, the temperature of the junction, and several physical constants. It is commonly known as the diode equation:

The term kT/q describes the voltage produced within the P-N junction due to the action of temperature, and is called the thermal voltage, or Vtof the junction. At room temperature, this is about 26 millivolts. Knowing this, and assuming a “nonideality” coefficient of 1, we may simplify the diode equation and re-write it as such:

You need not be familiar with the “diode equation” to analyze simple diode circuits. Just understand that the voltage dropped across a current-conducting diode does change with the amount of current going through it, but that this change is fairly small over a wide range of currents. This is why many textbooks simply say the voltage drop across a conducting, semiconductor diode remains constant at 0.7 volts for silicon and 0.3 volts for germanium. However, some circuits intentionally make use of the P-N junction's inherent exponential current/voltage relationship and thus can only be understood in the context of this equation. Also, since temperature is a factor in the diode equation, a forward-biased P-N junction may also be used as a temperature-sensing device, and thus can only be understood if one has a conceptual grasp on this mathematical relationship.

A reverse-biased diode prevents current from going through it, due to the expanded depletion region. In actuality, a very small amount of current can and does go through a reverse-biased diode, called the leakage current, but it can be ignored for most purposes. The ability of a diode to withstand reverse-bias voltages is limited, as it is for any insulator. If the applied reverse-bias voltage becomes too great, the diode will experience a condition known as breakdown (Figure below), which is usually destructive. A diode's maximum reverse-bias voltage rating is known as the Peak Inverse Voltage, or PIV, and may be obtained from the manufacturer. Like forward voltage, the PIV rating of a diode varies with temperature, except that PIV increases with increased temperature and decreases as the diode becomes cooler -- exactly opposite that of forward voltage.

Diode curve: showing knee at 0.7 V forward bias for Si, and reverse breakdown.

Typically, the PIV rating of a generic “rectifier” diode is at least 50 volts at room temperature. Diodes with PIV ratings in the many thousands of volts are available for modest prices.


In addition to voltage and current, there is another measure of free electron activity in a circuit: power. First, we need to understand just what power is before we analyze it in any circuits.

Power is a measure of how much work can be performed in a given amount of time. Work is generally defined in terms of the lifting of a weight against the pull of gravity. The heavier the weight and/or the higher it is lifted, the more work has been done. Power is a measure of how rapidly a standard amount of work is done.

For American automobiles, engine power is rated in a unit called "horsepower," invented initially as a way for steam engine manufacturers to quantify the working ability of their machines in terms of the most common power source of their day: horses. One horsepower is defined in British units as 550 ft-lbs of work per second of time. The power of a car's engine won't indicate how tall of a hill it can climb or how much weight it can tow, but it will indicate how fast it can climb a specific hill or tow a specific weight.

The power of a mechanical engine is a function of both the engine's speed and its torque provided at the output shaft. Speed of an engine's output shaft is measured in revolutions per minute, or RPM. Torque is the amount of twisting force produced by the engine, and it is usually measured in pound-feet, or lb-ft (not to be confused with foot-pounds or ft-lbs, which is the unit for work). Neither speed nor torque alone is a measure of an engine's power.

A 100 horsepower diesel tractor engine will turn relatively slowly, but provide great amounts of torque. A 100 horsepower motorcycle engine will turn very fast, but provide relatively little torque. Both will produce 100 horsepower, but at different speeds and different torques. The equation for shaft horsepower is simple:

Notice how there are only two variable terms on the right-hand side of the equation, S and T. All the other terms on that side are constant: 2, pi, and 33,000 are all constants (they do not change in value). The horsepower varies only with changes in speed and torque, nothing else. We can re-write the equation to show this relationship:

Because the unit of the "horsepower" doesn't coincide exactly with speed in revolutions per minute multiplied by torque in pound-feet, we can't say that horsepower equals ST. However, they are proportional to one another. As the mathematical product of ST changes, the value for horsepower will change by the same proportion.

In electric circuits, power is a function of both voltage and current. Not surprisingly, this relationship bears striking resemblance to the "proportional" horsepower formula above:

In this case, however, power (P) is exactly equal to current (I) multiplied by voltage (E), rather than merely being proportional to IE. When using this formula, the unit of measurement for power is the watt, abbreviated with the letter "W."

It must be understood that neither voltage nor current by themselves constitute power. Rather, power is the combination of both voltage and current in a circuit. Remember that voltage is the specific work (or potential energy) per unit charge, while current is the rate at which electric charges move through a conductor. Voltage (specific work) is analogous to the work done in lifting a weight against the pull of gravity. Current (rate) is analogous to the speed at which that weight is lifted. Together as a product (multiplication), voltage (work) and current (rate) constitute power.

Just as in the case of the diesel tractor engine and the motorcycle engine, a circuit with high voltage and low current may be dissipating the same amount of power as a circuit with low voltage and high current. Neither the amount of voltage alone nor the amount of current alone indicates the amount of power in an electric circuit.

In an open circuit, where voltage is present between the terminals of the source and there is zero current, there is zero power dissipated, no matter how great that voltage may be. Since P=IE and I=0 and anything multiplied by zero is zero, the power dissipated in any open circuit must be zero. Likewise, if we were to have a short circuit constructed of a loop of superconducting wire (absolutely zero resistance), we could have a condition of current in the loop with zero voltage, and likewise no power would be dissipated. Since P=IE and E=0 and anything multiplied by zero is zero, the power dissipated in a superconducting loop must be zero. (We'll be exploring the topic of superconductivity in a later chapter).

Whether we measure power in the unit of "horsepower" or the unit of "watt," we're still talking about the same thing: how much work can be done in a given amount of time. The two units are not numerically equal, but they express the same kind of thing. In fact, European automobile manufacturers typically advertise their engine power in terms of kilowatts (kW), or thousands of watts, instead of horsepower! These two units of power are related to each other by a simple conversion formula:

So, our 100 horsepower diesel and motorcycle engines could also be rated as "74570 watt" engines, or more properly, as "74.57 kilowatt" engines. In European engineering specifications, this rating would be the norm rather than the exception.


Long before the advent of digital electronic technology, computers were built to electronically perform calculations by employing voltages and currents to represent numerical quantities. This was especially useful for the simulation of physical processes. A variable voltage, for instance, might represent velocity or force in a physical system. Through the use of resistive voltage dividers and voltage amplifiers, the mathematical operations of division and multiplication could be easily performed on these signals.

The reactive properties of capacitors and inductors lend themselves well to the simulation of variables related by calculus functions. Remember how the current through a capacitor was a function of the voltage's rate of change, and how that rate of change was designated in calculus as the derivative? Well, if voltage across a capacitor were made to represent the velocity of an object, the current through the capacitor would represent the force required to accelerate or decelerate that object, the capacitor's capacitance representing the object's mass:

This analog electronic computation of the calculus derivative function is technically known as differentiation, and it is a natural function of a capacitor's current in relation to the voltage applied across it. Note that this circuit requires no "programming" to perform this relatively advanced mathematical function as a digital computer would.

Electronic circuits are very easy and inexpensive to create compared to complex physical systems, so this kind of analog electronic simulation was widely used in the research and development of mechanical systems. For realistic simulation, though, amplifier circuits of high accuracy and easy configurability were needed in these early computers.

It was found in the course of analog computer design that differential amplifiers with extremely high voltage gains met these requirements of accuracy and configurability better than single-ended amplifiers with custom-designed gains. Using simple components connected to the inputs and output of the high-gain differential amplifier, virtually any gain and any function could be obtained from the circuit, overall, without adjusting or modifying the internal circuitry of the amplifier itself. These high-gain differential amplifiers came to be known as operational amplifiers, or op-amps, because of their application in analog computers' mathematical operations.

Modern op-amps, like the popular model 741, are high-performance, inexpensive integrated circuits. Their input impedances are quite high, the inputs drawing currents in the range of half a microamp (maximum) for the 741, and far less for op-amps utilizing field-effect input transistors. Output impedance is typically quite low, about 75 Ω for the model 741, and many models have built-in output short circuit protection, meaning that their outputs can be directly shorted to ground without causing harm to the internal circuitry. With direct coupling between op-amps' internal transistor stages, they can amplify DC signals just as well as AC (up to certain maximum voltage-risetime limits). It would cost far more in money and time to design a comparable discrete-transistor amplifier circuit to match that kind of performance, unless high power capability was required. For these reasons, op-amps have all but obsoleted discrete-transistor signal amplifiers in many applications.

The following diagram shows the pin connections for single op-amps (741 included) when housed in an 8-pin DIP (Dual Inline Package) integrated circuit:

Some models of op-amp come two to a package, including the popular models TL082 and 1458. These are called "dual" units, and are typically housed in an 8-pin DIP package as well, with the following pin connections:

Operational amplifiers are also available four to a package, usually in 14-pin DIP arrangements. Unfortunately, pin assignments aren't as standard for these "quad" op-amps as they are for the "dual" or single units. Consult the manufacturer datasheet(s) for details.

Practical operational amplifier voltage gains are in the range of 200,000 or more, which makes them almost useless as an analog differential amplifier by themselves. For an op-amp with a voltage gain (AV) of 200,000 and a maximum output voltage swing of +15V/-15V, all it would take is a differential input voltage of 75 µV (microvolts) to drive it to saturation or cutoff! Before we take a look at how external components are used to bring the gain down to a reasonable level, let's investigate applications for the "bare" op-amp by itself.

One application is called the comparator. For all practical purposes, we can say that the output of an op-amp will be saturated fully positive if the (+) input is more positive than the (-) input, and saturated fully negative if the (+) input is less positive than the (-) input. In other words, an op-amp's extremely high voltage gain makes it useful as a device to compare two voltages and change output voltage states when one input exceeds the other in magnitude.

In the above circuit, we have an op-amp connected as a comparator, comparing the input voltage with a reference voltage set by the potentiometer (R1). If Vin drops below the voltage set by R1, the op-amp's output will saturate to +V, thereby lighting up the LED. Otherwise, if Vin is above the reference voltage, the LED will remain off. If Vin is a voltage signal produced by a measuring instrument, this comparator circuit could function as a "low" alarm, with the trip-point set by R1. Instead of an LED, the op-amp output could drive a relay, a transistor, an SCR, or any other device capable of switching power to a load such as a solenoid valve, to take action in the event of a low alarm.

Another application for the comparator circuit shown is a square-wave converter. Suppose that the input voltage applied to the inverting (-) input was an AC sine wave rather than a stable DC voltage. In that case, the output voltage would transition between opposing states of saturation whenever the input voltage was equal to the reference voltage produced by the potentiometer. The result would be a square wave:

Adjustments to the potentiometer setting would change the reference voltage applied to the noninverting (+) input, which would change the points at which the sine wave would cross, changing the on/off times, or duty cycle of the square wave:

It should be evident that the AC input voltage would not have to be a sine wave in particular for this circuit to perform the same function. The input voltage could be a triangle wave, sawtooth wave, or any other sort of wave that ramped smoothly from positive to negative to positive again. This sort of comparator circuit is very useful for creating square waves of varying duty cycle. This technique is sometimes referred to aspulse-width modulation, or PWM (varying, or modulating a waveform according to a controlling signal, in this case the signal produced by the potentiometer).

Another comparator application is that of the bargraph driver. If we had several op-amps connected as comparators, each with its own reference voltage connected to the inverting input, but each one monitoring the same voltage signal on their noninverting inputs, we could build a bargraph-style meter such as what is commonly seen on the face of stereo tuners and graphic equalizers. As the signal voltage (representing radio signal strength or audio sound level) increased, each comparator would "turn on" in sequence and send power to its respective LED. With each comparator switching "on" at a different level of audio sound, the number of LED's illuminated would indicate how strong the signal was.

In the circuit shown above, LED1 would be the first to light up as the input voltage increased in a positive direction. As the input voltage continued to increase, the other LED's would illuminate in succession, until all were lit.

This very same technology is used in some analog-to-digital signal converters, namely the flash converter, to translate an analog signal quantity into a series of on/off voltages representing a digital number.


The insulated-gate field-effect transistor (IGFET), also known as the metal oxide field effect transistor (MOSFET), is a derivative of the field effect transistor (FET). Today, most transistors are of the MOSFET type as components of digital integrated circuits. Though discrete BJT's are more numerous than discrete MOSFET's. The MOSFET transistor count within an integrated circuit may approach hundreds of a million. The dimensions of individual MOSFET devices are under a micron, decreasing every 18 months. Much larger MOSFET's are capable of switching nearly 100 amperes of current at low voltages; some handle nearly 1000 V at lower currents. These devices occupy a good fraction of a square centimeter of silicon. MOSFET's find much wider application than JFET's. However, MOSFET power devices are not as widely used as bipolar junction transistors at this time.

The MOSFET has source, gate, and drain terminals like the FET. However, the gate lead does not make a direct connection to the silicon compared with the case for the FET. The MOSFET gate is a metallic or polysilicon layer atop a silicon dioxide insulator. The gate bears a resemblance to a metal oxide semiconductor (MOS) capacitor in Figure below. When charged, the plates of the capacitor take on the charge polarity of the respective battery terminals. The lower plate is P-type silicon from which electrons are repelled by the negative (-) battery terminal toward the oxide, and attracted by the positive (+) top plate. This excess of electrons near the oxide creates an inverted (excess of electrons) channel under the oxide. This channel is also accompanied by a depletion region isolating the channel from the bulk silicon substrate.

N-channel MOS capacitor: (a) no charge, (b) charged.

In Figure below (a) the MOS capacitor is placed between a pair of N-type diffusions in a P-type substrate. With no charge on the capacitor, no bias on the gate, the N-type diffusions, the source and drain, remain electrically isolated.


N-channel MOSFET (enhancement type): (a) 0 V gate bias, (b) positive gate bias.

A positive bias applied to the gate, charges the capacitor (the gate). The gate atop the oxide takes on a positive charge from the gate bias battery. The P-type substrate below the gate takes on a negative charge. An inversion region with an excess of electrons forms below the gate oxide. This region now connects the source and drain N-type regions, forming a continuous N-region from source to drain. Thus, the MOSFET, like the FET is a unipolar device. One type of charge carrier is responsible for conduction. This example is an N-channel MOSFET. Conduction of a large current from source to drain is possible with a voltage applied between these connections. A practical circuit would have a load in series with the drain battery in Figure above (b).

The MOSFET described above in Figure above is known as an enhancement mode MOSFET. The non-conducting, off, channel is turned on by enhancing the channel below the gate by application of a bias. This is the most common kind of device. The other kind of MOSFET will not be described here. See the Insulated-gate field-effect transistor chapter for the depletion mode device.

The MOSFET, like the FET, is a voltage controlled device. A voltage input to the gate controls the flow of current from source to drain. The gate does not draw a continuous current. Though, the gate draws a surge of current to charge the gate capacitance.

The cross-section of an N-channel discrete MOSFET is shown in Figure below (a). Discrete devices are usually optimized for high power switching. The N+ indicates that the source and drain are heavily N-type doped. This minimizes resistive losses in the high current path from source to drain. The N- indicates light doping. The P-region under the gate, between source and drain can be inverted by application of a positive bias voltage. The doping profile is a cross-section, which may be laid out in a serpentine pattern on the silicon die. This greatly increases the area, and consequently, the current handling ability.

N-channel MOSFET (enhancement type): (a) Cross-section, (b) schematic symbol.

The MOSFET schematic symbol in Figure above (b) shows a “floating” gate, indicating no direct connection to the silicon substrate. The broken line from source to drain indicates that this device is off, not conducting, with zero bias on the gate. A normally “off” MOSFET is an enhancement mode device. The channel must be enhanced by application of a bias to the gate for conduction. The “pointing” end of the substrate arrow corresponds to P-type material, which points toward an N-type channel, the “non-pointing” end. This is the symbol for an N-channel MOSFET. The arrow points in the opposite direction for a P-channel device (not shown). MOSFET's are four terminal devices: source, gate, drain, and substrate. The substrate is connected to the source in discrete MOSFET's, making the packaged part a three terminal device.MOSFET's, that are part of an integrated circuit, have the substrate common to all devices, unless purposely isolated. This common connection may be bonded out of the die for connection to a ground or power supply bias voltage.

N-channel “V-MOS” transistor: (a) Cross-section, (b) schematic symbol.

The V-MOS device in (Figure above) is an improved power MOSFET with the doping profile arranged for lower on-state source to drain resistance. VMOS takes its name from the V-shaped gate region, which increases the cross-sectional area of the source-drain path. This minimizes losses and allows switching of higher levels of power. UMOS, a variation using a U-shaped grove, is more reproducible in manufactur

Integrated circuits

Digital circuits are circuits dealing with signals restricted to the extreme limits of zero and some full amount. This stands in contrast to analogcircuits, in which signals are free to vary continuously between the limits imposed by power supply voltage and circuit resistances. These circuitsfind use in "true/false" logical operations and digital computation.

The circuits in this chapter make use of IC, or integrated circuit, components. Such components are actually networks of interconnected components manufactured on a single wafer of semiconducting material. Integrated circuits providing a multitude of pre-engineered functions are available at very low cost, benefitting students, hobbyists and professional circuit designers alike. Most integrated circuits provide the same functionality as "discrete" semiconductor circuits at higher levels of reliability and at a fraction of the cost.

Circuits in this chapter will primarily use CMOS technology, as this form of IC design allows for a broad range of power supply voltage while maintaining generally low power consumption levels. Though CMOS circuitry is susceptible to damage from static electricity (high voltages will puncture the insulating barriers in the MOSFET transistors), modern CMOS ICs are far more tolerant of electrostatic discharge than the CMOS ICs of the past, reducing the risk of chip failure by mishandling. Proper handling of CMOS involves the use of anti-static foam for storage and transport of IC's, and measures to prevent static charge from building up on your body (use of a grounding wrist strap, or frequently touching a grounded object).

Circuits using TTL technology require a regulated power supply voltage of 5 volts, and will not tolerate any substantial deviation from this voltage level. Any TTL circuits in this chapter will be adequately labeled as such, and it will be expected that you realize its unique power supply requirements.

When building digital circuits using integrated circuit "chips," it is highly recommended that you use a breadboard with power supply "rail" connections along the length. These are sets of holes in the breadboard that are electrically common along the entire length of the board. Connect one to the positive terminal of a battery, and the other to the negative terminal, and DC power will be available to any area of the breadboard via connection through short jumper wires:

With so many of these integrated circuits having "reset," "enable," and "disable" terminals needing to be maintained in a "high" or "low" state, not to mention the VDD (or VCC) and ground power terminals which require connection to the power supply, having both terminals of the power supply readily available for connection at any point along the board's length is very useful.

Most breadboards that I have seen have these power supply "rail" holes, but some do not. Up until this point, I've been illustrating circuits using a breadboard lacking this feature, just to show how it isn't absolutely necessary. However, digital circuits seem to require more connections to the power supply than other types of breadboard circuits, making this feature more than just a convenience.

Induction motor

The three-phase AC induction motor has a squirrel cage rotor in which aluminum conductors or bars are shorted together at both ends of the rotor by cast aluminum end rings. When three currents flow through the three symmetrically placed windings, a sinusoidally distributed air gap flux generating the rotor current is produced. The interaction of the sinusoidally distributed air gap flux and induced rotor currents produces a torque on the rotor. The mechanical angular velocity of the rotor is lower then the angular velocity of the flux wave by so called slip velocity.

In adjustable speed applications, AC motors are powered by inverters. The inverter converts DC power to AC power at the required frequency and amplitude. The inverter consists of three half-bridge units where the upper and lower switches are controlled complimentarily. As the power device's turn-off time is longer than its turn-on time, some dead-time must be inserted between the turn-off of one transistor of the half-bridge and turn-on of its complementary device. The output voltage is mostly created by a pulse width modulation (PWM) technique.The three-phase voltage waves are shifted 120° to one another and thus a three-phase motor can be supplied.

The stator windings of an AC induction motor are distributed around the stator to produce a roughly sinusoidal distribution. When three-phase AC voltages are applied to the stator windings, a rotating magnetic field is produced.

The rotor of an induction motor also consists of windings or more often a copper squirrel cage embedded within iron laminates. Only the iron laminates are shown. An electric current is induced in the rotor bars which also produce a magnetic field.

The rotating magnetic field of the stator drags the rotor around. The rotor does not quite keep up with the rotating magnetic field of the stator. It falls behind or slips as the field rotates.

In this animation, for every time the magnetic field rotates, the rotor only makes three-fourths of a turn. If you follow one of the bright green or red rotor teeth with the mouse, you will notice it change color as it falls behind the rotating field. The slip has been greatly exaggerated to enable visualization of this concept. A real induction motor only slips a few percent.

The field effect transistor was proposed by Julius Lilienfeld in US patents in 1926 and 1933 (1,900,018). Moreover, Shockley, Brattain, and Bardeen were investigating the field effect transistor in 1947. Though, the extreme difficulties sidetracked them into inventing the bipolar transistor instead. Shockley's field effect transistor theory was published in 1952. However, the materials processing technology was not mature enough until 1960 when John Atalla produced a working device.

A field effect transistor (FET) is a unipolar device, conducting a current using only one kind of charge carrier. If based on an N-type slab of semiconductor, the carriers are electrons. Conversely, a P-type based device uses only holes.

At the circuit level, field effect transistor operation is simple. A voltage applied to the gate, input element, controls the resistance of thechannel, the unipolar region between the gate regions. (Figure below) In an N-channel device, this is a lightly doped N-type slab of silicon with terminals at the ends. The source and drain terminals are analogous to the emitter and collector, respectively, of a BJT. In an N-channel device, a heavy P-type region on both sides of the center of the slab serves as a control electrode, the gate. The gate is analogous to the base of a BJT.

“Cleanliness is next to godliness” applies to the manufacture of field effect transistors. Though it is possible to make bipolar transistors outside of a clean room, it is a necessity for field effect transistors. Even in such an environment, manufacture is tricky because of contamination control issues. The unipolar field effect transistor is conceptually simple, but difficult to manufacture. Most transistors today are a metal oxide semiconductor variety (later section) of the field effect transistor contained within integrated circuits. However, discrete JFET devices are available.

Junction field effect transistor cross-section.

A properly biased N-channel junction field effect transistor (JFET) is shown in Figure above. The gate constitutes a diode junction to the source to drain semiconductor slab. The gate is reverse biased. If a voltage (or an ohmmeter) were applied between the source and drain, the N-type bar would conduct in either direction because of the doping. Neither gate nor gate bias is required for conduction. If a gate junction is formed as shown, conduction can be controlled by the degree of reverse bias.

Figure below(a) shows the depletion region at the gate junction. This is due to diffusion of holes from the P-type gate region into the N-type channel, giving the charge separation about the junction, with a non-conductive depletion region at the junction. The depletion region extends more deeply into the channel side due to the heavy gate doping and light channel doping.

N-channel JFET: (a) Depletion at gate diode. (b) Reverse biased gate diode increases depletion region. (c) Increasing reverse bias enlarges depletion region. (d) Increasing reverse bias pinches-off the S-D channel.

The thickness of the depletion region can be increased Figure above (b) by applying moderate reverse bias. This increases the resistance of the source to drain channel by narrowing the channel. Increasing the reverse bias at (c) increases the depletion region, decreases the channel width, and increases the channel resistance. Increasing the reverse bias VGS at (d) will pinch-off the channel current. The channel resistance will be very high. This VGS at which pinch-off occurs is VP, the pinch-off voltage. It is typically a few volts. In summation, the channel resistance can be controlled by the degree of reverse biasing on the gate.

The source and drain are interchangeable, and the source to drain current may flow in either direction for low level drain battery voltage (< 0.6 V). That is, the drain battery may be replaced by a low voltage AC source. For a high drain power supply voltage, to 10's of volts for small signal devices, the polarity must be as indicated in Figure below(a). This drain power supply, not shown in previous figures, distorts the depletion region, enlarging it on the drain side of the gate. This is a more correct representation for common DC drain supply voltages, from a few to tens of volts. As drain voltage VDS is increased,the gate depletion region expands toward the drain. This increases the length of the narrow channel, increasing its resistance a little. We say "a little" because large resistance changes are due to changing gate bias. Figure below(b) shows the schematic symbol for an N-channel field effect transistor compared to the silicon cross-section at (a). The gate arrow points in the same direction as a junction diode. The “pointing” arrow and “non-pointing” bar correspond to P and N-type semiconductors, respectively.

N-channel JFET electron current flow from source to drain in (a) cross-section, (b) schematic symbol.

Figure above shows a large electron current flow from (-) battery terminal, to FET source, out the drain, returning to the (+) battery terminal. This current flow may be controlled by varying the gate voltage. A load in series with the battery sees an amplified version of the changing gate voltage.

P-channel field effect transistors are also available. The channel is made of P-type material. The gate is a heavily dopped N-type region. All the voltage sources are reversed in the P-channel circuit (Figure below) as compared with the more popular N-channel device. Also note, the arrow points out of the gate of the schematic symbol (b) of the P-channel field effect transistor.

P-channel JFET: (a) N-type gate, P-type channel, reversed voltage sources compared with N-channel device. (b) Note reversed gate arrow and voltage sources on schematic.

As the positive gate bias voltage is increased, the resistance of the P-channel increases, decreasing the current flow in the drain circuit.

Discrete devices are manufactured with the cross-section shown in Figure below. The cross-section, oriented so that it corresponds to the schematic symbol, is upside down with respect to a semiconductor wafer. That is, the gate connections are on the top of the wafer. The gate is heavily doped, P+, to diffuse holes well into the channel for a large depletion region. The source and drain connections in this N-channel device are heavily doped, N+ to lower connection resistance. However, the channel surrounding the gate is lightly doped to allow holes from the gate to diffuse deeply into the channel. That is the N- region.

Junction field effect transistor: (a) Discrete device cross-section, (b) schematic symbol, (c) integrated circuit device cross-section.

All three FET terminals are available on the top of the die for the integrated circuit version so that a metalization layer (not shown) can interconnect multiple components. (Figure above(c) ) Integrated circuit FET's are used in analog circuits for the high gate input resistance.. The N-channel region under the gate must be very thin so that the intrinsic region about the gate can control and pinch-off the channel. Thus, gate regions on both sides of the channel are not necessary.

Junction field effect transistor (static induction type): (a) Cross-section, (b) schematic symbol.

The static induction field effect transistor (SIT) is a short channel device with a buried gate. (Figure above) It is a power device, as opposed to a small signal device. The low gate resistance and low gate to source capacitance make for a fast switching device. The SIT is capable of hundreds of amps and thousands of volts. And, is said to be capable of an incredible frequency of 10 gHz.[YYT]

Metal semiconductor field effect transistor (MESFET): (a) schematic symbol, (b) cross-section.

The Metal semiconductor field effect transistor (MESFET) is similar to a JFET except the gate is a schottky diode instead of a junction diode. Aschottky diode is a metal rectifying contact to a semiconductor compared with a more common ohmic contact. In Figure above the source and drain are heavily doped (N+). The channel is lightly doped (N-). MESFET's are higher speed than JFET's. The MESET is a depletion mode device, normally on, like a JFET. They are used as microwave power amplifiers to 30 gHz. MESFET's can be fabricated from silicon, gallium arsenide, indium phosphide, silicon carbide, and the diamond allotrope of carbon.

Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism.

Electrical and Electronic Engineering is an exciting and dynamic field. Electrical engineers are responsible for the generation, transfer and conversion of electrical power, while electronic engineers are concerned with the transfer of information using radio waves, the design of electronic circuits, the design of computer systems and the development of control systems such as aircraft autopilots.

Electrical energy systems - The study and design of electrical transmission systems, electrical machines and variable speed drives; high power electronic converters and high voltage engineering.

Electronics - the study of components and circuits used to construct items such as audio amplifiers, radio transmitters and computer circuits. This includes elementary electrical components, transistors, integrated circuits, computer circuitry and power electronics; and specializes in areas such as microwave electronics, superconducting electronics.

Electromagnetic systems - are diverse and complex, ranging from the study of the electromagnetic effects of motors and electrical insulators to radio and radar antennas, radio waves and visible light (fiber optics).

Computer systems - This field also covers the design and construction of microcomputers built to control almost every electrical appliance, from automatic irrigation systems to autopilots for aircraft. Computer programming for embedded systems and reconfigurable logic circuits to address a variety of engineering problems, are also of key importance.

Control systems - From the temperature control in air conditioning systems to the sophisticated automatic landing systems that allow aircraft to land autonomously in thick fog or to point camera systems accurately from satellites to target areas on the ground. Techniques to design control systems for both electronic (analog) and computer (digital) implementations are key in this field.

Signal processing - Speech, radio waves and television images are all examples of signals. The behaviour of these signals is studied and applied to computers usefully to process them (e.g. speech, speaker and image recognition, software defined radios and protocols). Mathematical aids are created to analyze and understand these signals.

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