STUDY MATERIAL -MODULE-03 (B1.1 & B2)
1 Electron Theory
1.1 Electron Theory
1.2 The Atomic Structure
All substances, whether solid, liquid, or gas, are made up of atoms, which are grouped together in various
ways. In the center is the nucleus, made up of protons (with a positive charge) and neutrons (with no charge).
The electrons (with a negative charge) move around the nucleus in orbits, rather like the planets around the
sun, with each orbit (called a shell) having a certain number of electrons. The maximum number of orbits
around a nucleus is seven. These are located at defined distances from the nucleus, and are designated by the
letters K, L, M, N, O, P, and Ǫ, starting from the shell nearest the nucleus.
The mass of an electron is estimated to be about 9.1 x 10-31 kilograms (kg) and the charge it carries is about
1.6 x 10-19 Coulomb (C). These are extremely small quantities, but it is the electron on which the science of
electrics and electronics depends.
The charge on each proton is positive (+ve) and the charge on each electron is negative (-ve). There are the
same number of protons in an atom as electrons, so the total charge of an atom is neutral (unless we decide to
interfere and change it). The proton, however, is about 1,840 times larger than an electron, so that a quick
calculation gives its mass as 1.67 x 10-27 kg. The revolving electrons are pictured as moving in elliptical orbits
around the nucleus, held in their respective shells by the attractive force of the nucleus. The mass of the
neutron is similar to that of the proton.
1.3 Elements
When the same type of atoms are present in a substance, it is called an element. Ninety four elements have
been found in nature so far and others have been created artificially bringing the total (to date) to 118. For any
element, each shell contains a fixed number of electrons. There is a maximum number for each shell, relating
to the orbit’s distance from the nucleus, e.g., level K can contain up to 2 electrons, level L up to 8, level M up to
18 and so on. In the table below, the digits enclosed within parentheses denote the limit up to which each shell
can contain electrons.
The maximum theoretical number in each shell can be found from the formula 2n2 where n is the number of the
shell. For example, in the N (fourth) shell, the number of electrons equals 2n2 = 2 x 42 = 32.
However, in practice many atoms do not reach this theoretical number (2n2), and no atom can contain more
than eight electrons in its outer shell anyway.
1.4 Compound
A compound is a chemical combination of two or more elements. Carbon dioxide (CO2) is one of the common
compounds and is made up of one carbon atom and two oxygen atoms.
1.5 Molecule
The molecule of an element or compound is the smallest particle of it, which can normally exist separately
while retaining its identity. It consists of one or more atoms, of the same or different types joined together.
Familiar molecules include breathing oxygen (O2), water, consisting of two hydrogen atoms and one oxygen
atom (H2O), and sulfuric acid, consisting of two hydrogen atoms, one sulfur atom, and four oxygen atoms
(H2SO4).
1.6 Valence Electrons
The electrons (or electron) making up the outermost shell are called valence electrons. These are furthest from
the attractive force of the nucleus and are least tightly bound in the atom. It is the valence electrons that play
the active part in electrical conduction.
The hydrogen atom is comprised of 1 electron and 1 proton. Being a light gas, it contains a single shell called K
shell. The helium atom is comprised of 2 electrons and 2 protons. Being a light gas like hydrogen, it too
contains a single shell called K shell.
Silicon is a very important element in the manufacture of transistors. A silicon atom has 3 shells. The K, and L
shells hold 2 and 8 electrons respectively. There are 4 electrons in the M shell. Germanium atom is also a very
important element in the manufacture of transistors. Its K, L, M, and N take 2, 8, 18, and 4 electrons,
respectively. It also has 4 valence electrons.
1.7 Ions
Normally atoms are electrically neutral, as far as charge is concerned, because electrons and protons are
present in equal numbers. However, an atom can become positively or negatively charged if it has electrons
taken away or added.
When an atom gives up an electron, it becomes positively charged (it has more protons than electrons), and
this is called a positive ion. When it takes in an extra electron, it becomes negatively charged and it is called a
negative ion. An ion is therefore an atom which has lost or gained an electron.
1.8 Metals and Current
When a positive charge is placed across the conductor the negative electrons flow towards the positive end.
On the other hand, the conventional current flow occurs towards the negative end in the opposite direction.
When the electrons move in only one direction, then the current is known as Direct Current (DC), as when a
battery is used to provide the electrical force (DC voltage). When the electrons move backwards and forwards
(as when an alternator/AC generator is used [AC voltage]), the current is called Alternating Current (AC).
AC usually has a frequency on aircraft of 400 Hz (400 cycles per second).
1.9 Conductors, Insulators and Semiconductors
The orderly movement of electrons is called current (more correctly, electron flow) and metals which easily
permit current to flow are called conductors, e.g., copper, aluminium, silver, platinum, bronze, gold, most iron
metals, etc.
In other materials, the electrons are held more firmly in their outer shells and current flow is difficult to obtain.
In these materials, it is almost impossible to induce an orderly movement of electrons and they are classified
as non-conductors, or insulators, e.g., glass, rubber, plastic, air, wood, mica, etc.
There is a family of elements called semiconductors. Sometimes they behave like conductors, and sometimes
they behave like insulators. Typical semiconductor materials are silicon and germanium.
These materials have four valence electrons and each atom shares its electrons with adjacent atoms to form a
strongly bonded structure called a crystal lattice. The freedom of movement of electrons is poor, and in their
pure state these semiconductors act as insulators.
However, electron movement in a pure semiconductor can be achieved by heating. As the temperature rises,
the electrons become more agitated and will leave their orbits. In this condition, if a voltage is placed across
the material, electron movement occurs.
This is known as ‘intrinsic’ conduction which can cause problems. When current is switched-on, heat is
created. This will cause more conduction and more heat to occur, thus increasing the conduction even further
and so on. This cycle will continue until breakdown occurs, and is known as ‘thermal runaway’. This is a form of
positive feedback in the system which can be dangerous.
Another way to improve the conductivity of a semiconductor is by ‘doping’ the material with a tiny amount of
another element. This doping material is introduced into the crystal lattice structure which improves its
conductivity. More detail of this is available in Module 4.
Arsenic doping produces a free electron and it is this doping that allows the material to behave as a conductor.
The arsenic atom has 5 valance electrons and the silicon atom has 4, so a free electron is created. Almost any
atom can be a donor atom in this way provided it has one more electron in its valance shell than the material to
be doped.
An acceptor atom is opposite to a donor atom in that it has one less electron in its valance shell than the
material that it is doped into. This produces a ‘hole’, which will attract an electron from another atom: e.g., a 3valent atom doped into a material made up of 4-valent atoms will produce a ‘hole’.
Free electrons and free holes make the semi-conductor into a conductor. Without the free electrons and free
holes, it would be an insulator.
2 Static Electricity and Conduction
2.1 Static Electricity
Static electricity is where an object picks up a static charge without, necessarily, having a dynamic electron
flow such as an AC or DC current. Static electricity is usually caused when non-conductive materials, such as
rubber, plastic, or glass, are rubbed together causing a transfer of electrons, which results in an imbalance of
charges between the two materials.
2.2 Attractive and Repulsive Forces
When the atoms of an object lose electrons, the object is filled with a surplus of positive charge. This renders
the object positively-charged. Conversely, when an object gains electrons, it teems with negative charge.
One of the most fundamental laws of static electricity, as well as magnetics, deals with attraction and
repulsion. Like charges repel each other and unlike charges attract each other. All electrons possess a negative
charge and as such repel each other. Similarly, all protons possess a positive charge and as such repel each
other. Electrons (negative) and protons (positive) are opposite in their charge and attract each other. The basic
laws of electrostatics are; like charges repel and unlike charges attract.
2.3 Unit of Charge
The size of the charge is measured in Coulombs (C) which is defined as the amount of electrical charge which
passes a point in a conductor when a current of 1 ampere flows for 1 second.
2.4 Coulomb’s Law
The force which two charged bodies exert on each other can be calculated using Coulomb’s law, which states
that the force between two electric charges is inversely proportional to the square of the distance between
them.
2.5 Distribution of Electrostatic Charges
An electric charge sets up an electric field in the space surrounding it and an electric force is exerted on any
charged body placed in the field.
An electric line of force is a line drawn in an electric field such that its direction at any point gives the direction
of the electric field at that point.
These lines of force, sometimes known as magnetic lines of force or flux lines, have the following properties:
a) They begin and end in equal and opposite quantities of charge.
b) They are in a state of tension, which causes them to try to shorten, similar to a piece of elastic or a
rubber band.
c) They repel each other sideways.
d) They are invisible.
e) They can be ‘seen’ using such things as iron fillings or magnetic ink.
f) They will pass through non-magnetic substances but are diverted (concentrated) by magnetic
substances.
Thus the repulsion of two like charges is explained by the sideways repulsion between the lines of force and the
attraction of two unlike charges by the tension of lines of force joining them. The distribution of the charge on
an irregularly-shaped object differs from that on a regularly-shaped object. The charge on such objects is not
evenly distributed. The greatest charge is at the points, or areas of the sharpest curvature, of the objects.
2.6 Conduction
A conductor containing free electrons moving at random among positive ions. If a battery is connected across
the conductor, the free electrons near to the positive plate will be attracted to it (unlike charges attract) and the
free electrons near the negative plate will be repelled from it. This will cause a steady drift of electrons to take
place through the material from the negative battery terminal to the positive battery terminal. For each electron
entering the positive terminal one will be ejected from the negative terminal, so the number of electrons in the
material remains constant.
Since the atoms that have become positive ions are unable to move in a solid, they do not drift but remain
stationary. The drift of electrons is the electric current. The flow of electrons is from the negative side of the
battery to the positive side. This is known as electron flow. This is called conventional current flow. Conduction
can also occur through an evacuated tube containing two electrodes called an anode (+) and a cathode (-). The
cathode is a special material that, when heated, emits electrons from its surface. If the anode is now made
positive, then it will attract these electrons. This is the basis of the conduction through a Cathode Ray Tube
(CRT).
Another form of conduction takes place when the tube is filled with gas such as argon, helium, neon, or
mercury vapour, at a low pressure. The positive at the anode attracts electrons from the heated cathode with
sufficient velocity as to detach outer electrons from the gas atoms when they collide. These detached
electrons leave the gas atoms positively charged (positive ions).
This forming of positive ions is called ionisation. The free electrons join the cathode electrons and move
towards the anode. More collisions occur causing more positive ions. This ionisation causes a visible glow in
the tube.
3 Electrical Terminology
3.1 Electrical Terms
3.1.1 Electromotive-force (emf)
This is the driving influence that causes current to flow. Its unit is the Volt. A battery, cell, or generator can
produce an emf.
3.1.2 Potential Difference (pd)
This is the voltage difference between two parts of a circuit or between two circuits.
3.1.3 Voltage
Voltage (V) is the unit of emf and potential difference (pd). It can be compared to pressure in hydraulic or
fluid terms and is the force required to push electrons around a circuit. It is voltage that will produce
current.
3.1.4 Current (I)
The unit of electron flow measured in Amperes (A). It is defined as a flow of 1 Coulomb per second 6.3 x
1018. A Coulomb is about 6.3 x 1018 electrons (there is no need to remember this). Current can be
compared to flow in fluids.
3.1.5 Resistance (R)
Electrons flow more easily through some materials than others. This opposition to current flow is called
Resistance and is measured in ohms (Ω). There is not such a direct comparison with hydraulics here
though there is resistance to fluid flow due to viscosity, etc.
3.1.6 Conductance (G)
This is the reciprocal of resistance: G=1/R. The unit is the Siemen (S).
3.1.7
3.1.8
3.1.9
Charge (Ǫ)
The quantity of electricity passing a given point in a circuit when a current of 1 A is maintained for 1 second.
Ǫ = I (amps) x t (secs) COULOMBS (C).
Conventional Current Flow
The notation assigned to the electric charges was positive (+) for the abundance of charge and negative (-)
for a lack of charge. It then seemed natural to visualize the flow of current as being from the positive (+) to
the negative (-).
Electron Flow
Electron flow is what actually happens when an abundance of electrons flow out of the negative (-) source
to an area that lacks electrons or the positive (+) source. Both conventional flow and electron flow are used
in the industry.
4 Generation of Electricity
4.1 Friction
Electricity by friction is the production of static electricity as a result of rubbing non-conductive materials
together. Static electricity is a build-up of an electrical charge on the surface of an object. It is considered
“static” due to the fact that there is no current flowing as in Alternate Current (AC) or Direct Current (DC)
electricity.
4.2 Thermocouple
Electricity can also be produced by joining 2 dissimilar metals together and applying heat to the joint. If the
joint or junction is connected as part of a closed electrical circuit, then current will flow. This is called a
thermocouple.
The heated joint is called the hot junction and the joint at the other end is called the cold junction. When
heated, the hot junction will produce a small voltage known as an electro-motive force (emf). This is known as
the Seebeck effect. This emf (voltage) drives a current round the circuit. The emf generated is proportional to
the difference in temperature between the hot and cold junctions.
Typical metals used would be copper and constantan (40% nickel, 60% copper), used for engine cylinder head
temperature measurement with a maximum continuous temperature of 400° C. Iron or constantan is used for
maximum continuous temperatures of 850° C. A typical material combination for jet engine exhaust gas
temperature measurement is alumel (90% nickel, 2% aluminium, silicon, and manganese) and chromel (nickel
90%, chrome 10%) used with maximum continuous temperatures of 1,100° C.
4.3 Cathode
Another method, previously mentioned, is the heating of a material to emit electrons. The surface barrier of
clean metals is strong and few electrons leave the surface. However, if the metal is made very hot and the
metal (cathode) is coated at the tips with an oxide (barium and strontium mixture), the surface barrier becomes
weak and many electrons are emitted at red heat. These are caused to discharge to an anode. Heated
cathodes are used in CRTs and fluorescent lighting.
4.4 Photo-electric effect
Light is another source of energy which can create electron flow - typically in photo-electric cells (1 photon of
light will produce 1 electron of electrical flow). One such device is known as a photo-conductive cell or light
dependent resistor. It consists of metal electrodes on a surface made of cadmium sulphide. When light falls on
a photo-voltaic cell, a small voltage is produced. It breaks down the depletion layer of the p-n junction and
creates electron flow. Electrons flow from the p layer to the n layer to leave ‘holes’ in the p layer. It is considered
that these holes migrate from the n layer.
4.5 Piezoelectric Effect
Another method of generating electricity is by applying force or pressure to a crystal. This method uses
piezoelectric crystals such as quartz or barium titanate. When subjected to mechanical stress (a force on the
crystal), it produces a strain (a change in shape of the crystal – which is very small), causing an electrical
charge. Piezoelectric transducers are used on vibration monitoring systems on engines and helicopters, for
example.
4.6 Chemical
Chemical energy can be converted into electricity; the most common form of this is the battery. A primary
battery produces electricity using two different metals in a chemical solution like alkaline electrolyte, where a
chemical reaction between the metals and the chemicals frees more electrons in one metal than in the other.
One terminal of the battery is attached to one of the metals, such as zinc; the other terminal is attached to the
other metal, such as manganese oxide. The end that frees more electrons develops a positive charge and the
other end develops a negative charge. If a wire is attached from one end of the battery to the other, electrons
flow through the wire to balance the electrical charge. The two most common types of battery used in an
aircraft are lead-acid and Ni-Cd batteries.
5 Sources of Electricity
5.1 Cells or Batteries
A ‘cell’ is a device for ‘storing’, usually in chemical form, an electrical charge. They are commonly called
batteries and are divided into two main groups - primary cells and secondary cells.
A primary cell is one in which, when the voltage of the cell falls it cannot be recharged as the chemicals are
used up and the process cannot be reversed.
A secondary cell can be recharged (the chemical process reversed) once it has been discharged with the
process being capable of being repeated time and time again. Included in this category are aircraft batteries,
car batteries, etc.
A) The Voltaic Cell
The basis of most modern batteries, the Voltaic cell may take several forms but the principle of operation is
the same for all of them. Forms include:
 Two electrodes in a single container filled with an electrolyte.
 Two electrodes each in its own electrolyte filled container with a salt bridge connecting the two
electrolytes.
 Two electrodes in a container with two electrolytes separated by a porous membrane.
The below figure shows a Voltaic cell using a single electrolyte and two electrodes or plates connected by
an external circuit with an open circuit voltage of about 0.8 V. When the switch is closed as shown,
electrons flow through the external circuit from the zinc electrode to the copper electrode via the bulb (zinc
will readily give up electrons to copper). This will result in electrons being removed from the zinc electrode
and being deposited onto the copper electrode. As a zinc atom provides the electrons (2), it becomes a
positive ion and goes into the aqueous solution reducing the mass of the zinc electrode.
The 2 electrons received by the copper electrode allow for the conversion of a copper ion from the solution
into an uncharged copper atom. This atom is deposited on the electrode increasing its mass.
This leaves the zinc plate with a surplus of positive charge and the copper plate with a surplus of negative
charge, so negative sulphate ions (SO4 2-) in the electrolyte move to the zinc electrode to balance the
external electron flow. As oxidation (the loss of electrons) occurs at the zinc electrode, it is called the
anode and as reduction occurs at the copper electrode, it is called the cathode. Polarization can be
reduced by introducing a depolarizing agent to combine with the hydrogen, e.g., manganese dioxide as in
the Leclanché cell.
B) The Daniel Cell
This cell is used in some laboratories as a reference voltage as it produces a very accurate voltage. It
consists of a copper container filled with the saturated copper sulphate solution. Within the container
stands a porous earthenware pot containing a zinc rod immersed in a zinc sulphide solution (The Daniell
Cell Figure). When the poles are connected together with an external circuit, the electrons flow from the
zinc -ve pole to the copper +ve pole.
The porous pot prevents the copper ions (from the copper sulphate solution) from reaching the zinc
sulphate solution. Polarization does not occur because the copper, and not the hydrogen, is deposited on
the copper container pole. The advantage of the Daniell cell is that it keeps a very steady emf of 1.1 V and
so is used as a standard voltage for testing instruments, etc. Its disadvantage is that if it is not used for a
short period of time, then the copper sulphate solution will diffuse through the porous pot and deposit
copper on the zinc rod, which spoils its action. So, each time the cell is used it has to be made up afresh.
The more common type of cell is the ‘dry cell’ known as the Leclanché cell.
C) The Leclanchaė cell
This cell has evolved into the modern alkaline battery. The Leclanché cell consists of a carbon rod
surrounded by manganese dioxide and a powdered carbon compound. Around this, separated by a linen
liner, is an electrolytic paste of aqueous ammonium chloride. The positive plate is a brass capped carbon
rod and the negative plate is the battery case itself (made of zinc).
The cell voltage is typically 1.5 V and, again, electron flow is carbon rod (+ve cathode) to zinc case (-ve
anode) internally and zinc case to carbon rod through an external circuit (or load). Conventional current
flow, of course, is opposite.
D) Mercury Cell
Also called a Mercury Oxide battery, it is a non-rechargeable primary cell. Due to its mercury content, there
are legal restrictions in place in some countries as to its use. The outer case is the positive terminal and the
insert cap at the top is the negative terminal. Its open circuit voltage is held constant at about 1.35 V and it
will hold this for about 95% of its life. Replacements for this battery (in countries where they are banned)
include Zinc Air, Alkaline, and Silver Oxide batteries.
5.1.1
The Secondary Cell or Battery
The secondary cell is one in which the chemical action is reversible. It can be recharged by passing a
current through the cell after it has discharged and it can be used again. There are several types of
secondary cells, for example, lead acid, nickel cadmium, and ion lithium (sometimes called lithium ion).
5.1.1.1 The Lead Acid Cell
The lead acid cell has a positive plate of a lead antimony grid into which lead peroxide paste (PbO2) is
forced under pressure. The negative plate is a lead antimony grid into which pure spongy lead (Pb) is forced.
The electrolyte is a solution of sulphuric acid (H2SO4) and distilled water mixed to an SG (Specific Gravity)
of approximately 1.25 to 1.27.
The above figure shows an exploded view of the cell with a number of positive and negative plates. These
are interleaved together and each positive and negative plate is prevented from touching each other by
separators, which are typically made of micro-porous plastic.
Observe that the plates are arranged so that there is one more negative plate than positive so that the
negative plates are on the outside. This is because the positive plates tend to distort when there is
chemical action on one side only, so the battery is designed so that there is chemical action on both sides.
The plates are placed in an acid proof container and the container is filled with an electrolyte. At the top of
the container is a vent plug to allow gases to escape during the chemical action. The nominal voltage of
each cell is 2 V. Fully charged, the voltage will be 2.2 V, fully discharged 1.8 V.
Assume the cell is fully charged and connected to an external circuit (a load). The electrons will flow from
the spongy lead plate (-ve) to the lead peroxide plate (+ve) through the circuit.
A chemical reaction in the electrolyte causes lead sulphate to be deposited on both plates and they start to
become sulphated. Water is also released, which dilutes the electrolyte, i.e., the SG falls. When the voltage
falls to 1.8 V, the cell is said to be discharged.
By connecting a DC power source across the cell (+ve to +ve and -ve to -ve), it can be recharged. Electrons
are forced into the cell at the negative terminal which, by chemical action, changes the plates back to
spongy lead and lead peroxide. The water is changed back to sulphuric acid, and the SG of the electrolyte
rises, as does the cell voltage. When it reaches 2.2 V, the cell is now considered recharged.
5.1.1.2 The Nickle Cadmium Cell
One type of alkaline cell is the Nickel Cadmium (Ni-Cad) cell [a similar cell is the Nickel Metal Hydride (NiMH) cell]. In the Ni-Cad cell, the plates are a woven wire screen into which the active materials are sintered
(a form of powder technology) heat treated into the plates. The materials are nickel hydroxide [Ni(OH) 2] for
the positive plates and cadmium hydroxide [Cd(OH)2] for the negative plates.
The plates are housed in a polymer container fitted with a vent plug (to allow gases to escape) and positive
and negative connectors. The electrolyte is a solution of distilled water and potassium hydroxide (KOH)
with an SG of 1.24 to 1.3.
During discharge, oxygen is driven from the positive plate and recovered by the negative plate. No gassing
takes place, and the electrolyte is absorbed into the plates and the level drops.
During charging, the negative plates lose oxygen to the positive plates and become metallic cadmium. The
nickel hydroxide on the positive plates accepts this oxygen and becomes more highly oxidised Ni(OH)2 →
Ni(OH)3 and the positive plates give up hydrogen to the negative plates.
As the cell becomes fully charged and when being overcharged, it emits gas caused by the water in the
electrolyte being decomposed by electrolysis.
When the cell is fully charged (typically 1.5 V), there will be a small amount of gassing and electrolyte is
driven from the plates and it will be at its highest level within the cell. The electrolyte plays no part in the
chemical reaction; it is only used to provide a path for current flow so the SG does not change between
charge and discharge.
The nominal voltage of a Ni-Cad cell is 1.2 V. This voltage is maintained throughout the discharge period
until 80% capacity has been removed from the cell. This provides a constant voltage over a long period,
unlike the lead-acid battery where the voltage level drops steadily over the period of discharge.
This is why it is not possible to check the state of charge of a Ni-Cad battery by checking the voltage or the
SG of the electrolyte, unlike a lead acid battery where these values give a good indication of state of charge.
The complete battery is made up of a number of individual cells connected together in series to make up
the required total voltage output.
5.1.1.3 Lithium Ion Battery
The Lithium Ion (Li-ion or LIB) cell relies on the transfer of lithium ions from the negative electrode to the
positive electrode during discharge with the reverse happening during charging. The advantages include a
high open circuit voltage (volts per cell = 3.6 V); a good power to weight ratio (high power density), holds
charge well and does not suffer from the memory effect.
The disadvantages include: can catch fire and explode if overheated; can suffer from Thermal Runaway (a
serious problem with some aircraft); will damage if discharged below a certain value (has circuitry fitted to
prevent this); expensive and electrolyte inflammable. Used extensively in portable electronic equipment;
lap-top computers, cameras, mobile phones, etc.
5.1.2
Battery Symbol
The symbol for a conventional cell/battery is as shown in
the figure, with the longer vertical line being the positive
connection and the shorter one the negative connection.
5.1.3
Battery Connections
The majority of modern (metal) aircraft are wired on a single pole system, i.e., one terminal (usually the
negative) of every consumer component in the system is connected to earth (the metal of the airframe)
with the positive connection connected to the supply. The battery is connected with its positive terminal
connected to the positive supply line to the consumables (those requiring DC) and its negative terminal
connected to earth.
These type of batteries are fitted to older aircraft and when fitting the battery the positive lead is connected
first with the negative lead last. When disconnecting, remove the negative lead first and the positive lead
last. For all modern aircraft, both leads are connected via a single screw-in plug which is handed so the
connections cannot be reversed.
For composite aircraft, the airframe cannot be used (composites are normally non-conductive) as the
return path, so a single pole system cannot be used. In this case, the wiring system is a double pole system
with a positive and a negative wire going to each component (similar to domestic wiring - though that does
also have an earth wire). In some cases, the return line may go to return buses and from there back to the
negative side of the battery.
5.1.4
Current Flow
Conventional current flows out of the battery from the positive terminal, through the aircraft wiring circuits
to the components and back to the negative terminal of the battery via the (metal) airframe. If it is a
composite airframe, then the return path will be provided by a return harness or provided for in the normal
aircraft wiring. Within the battery, conventional flow is from the negative end to the positive end.
Electron flow of course, is opposite, with the electrons flowing through the external circuit from the
battery’s negative terminal to the battery’s positive terminal. Within the battery, the electrons flow from
positive to negative.
5.1.5
Battery Capacity
The capacity of a cell/battery is the maximum current it can deliver for a set period of time. If a cell is rated
10 Ah (Ampere Hours) at the one-hour rate and 100% efficient, then it should be capable of delivering 10 A
for 1 hour. For an aircraft battery to be considered serviceable, it must be at 80% efficiency.
5.1.6
Series and Parallel connections
If two cells are connected in series, then the total voltage output is the sum of the individual cells but the
total capacity remains the same. If each cell is rated at 2 V 10 AH. Connecting two in series gives a total
output of 4 V, 10 AH.
If the same two cells are connected in parallel, then the overall voltage output remains the same (2 V) but
the capacity doubles and would be 2 V 20 AH. If an aircraft has more than one battery connected to the DC
bus, then the batteries are normally connected in parallel.
6 DC Circuits
6.1 DC Circuits
Every aircraft has DC circuits as part of its electrical system.
6.2 Ohm’s Law
Ohm’s law states “The current through a conductor is directly proportional to the voltage across it if the
temperature and other physical conditions do not change”. This is a fundamental law of electricity and must be
remembered. Given two of the properties, you must be able to find the third.
6.2.1
Series Circuits
Where several components are connected end to end in such a way that there is only one path for the
current to flow and the same current flows through each component, then we have a series circuit.
There are three points to note about a series circuit:
1) The current is the same for all components in the circuit.
2) The voltage drop across each component when added together equals the total supply voltage (VS
= V1 + V2 + V3).
3) The total resistance of the circuit is the sum of the individual resistors (RT = R1 + R2 + R3).
6.2.2
Voltage Division
Because a voltage drop occurs across a resistor when current flows through it, several resistors can be
used in series across an applied voltage to give a division of voltage in a circuit. When resistors are
connected in this way, it is called a potential divider. Potential dividers are used to provide different
voltages for various circuits from a single supply voltage.
6.2.3
Parallel Circuits
Components connected in such a way that they provide alternative paths for current flow are parallel
connected and the circuit is a parallel circuit.
There are three points to note about parallel circuits:
1) The voltage is common across all the components.
2) The current (IT) divides between the components depending on the value of each resistance. If they
all have the same resistance value, then they will all have the same current irrespective of the
voltage. For those resistors having a low resistance, the current in that resistor will be high and for
high value resistors the current will be low. In any event the total current (IT) will be the sum of all
the individual resistor currents.
3) The total resistance of the circuit can be found by the formula
6.2.4
Series/ Parallel Circuits
This means that the voltage drop across the parallel resistors (VP) is the same for each of these resistors.
The voltage drop across the series resistor is VS and the total for the whole circuit is the addition of VP and
VS which will equal 12 V.
6.3 Kirchoff’s Law
6.3.1 First Law
Sometimes called the Current Law, it states that the total current flowing towards a junction in a circuit is
equal to the total current flowing away from that junction, that is, the algebraic sum of the currents flowing
towards the junction is zero.
6.3.2 Second Law
Sometimes known as the Voltage Law, it states that in any closed circuit, the algebraic sum of the potential
drops is equal to the algebraic sum of the emf’s acting in the loop.
7 Resistor/ Resistance
7.1 Resistance
Resistance is a property that relates two other fundamental properties, namely, current and voltage. It denotes
a substance's property to oppose electricity flow through the substance.
The factors which affect resistance are:
 Material: This value is found by measuring the resistance between the opposite faces of a unit cube of
the material and this is usually expressed in ohm-metres (Ωm) and is called the resistivity or specific
resistance of the material.
 Length of conductor: Resistance is therefore directly proportional to length.
 Cross sectional area of conductor: The greater the cross-section of the conductor, the smaller the
resistance.
 Temperature: The resistance of all pure metals (conductors) increases with an increase in temperature
and they are said to have a positive temperature coefficient. The resistance of insulators,
semiconductors, and thermistors decreases with an increase in temperature and are said to have a
negative temperature coefficient. Some alloys such as constantan, eureka, and manganin show very
little resistance change over their working temperature range.
7.2 Fixed Resistors
These are resistors the value of which cannot usually be changed. All resistors have a power rating (in watts),
which indicates the maximum power that can be dissipated without any temperature rise to prevent any
damage from occurring to the resistor. If the current through the resistor is exceeded, the resistor will overheat
and burn out. The greater the physical size, the greater its rating. The stability of a resistor is its ability to
maintain its resistance value over a period of time within a working circuit. This can be an important factor in
some electronic circuits.
7.2.1 Types of Fixed Resistors
In the carbon film type, a film of carbon is deposited on a ceramic rod and protected by an insulating
coating. Typical tolerance is ±5% with a range from just a few ohms to 10 MΩ. Ratings are from 0.125 W to 1
W with very good stability.
The metal film type is manufactured by a metal oxide being deposited on a ceramic rod and protected by an
insulating coating. The ratings are typically 0.5 W with a tolerance of ±1% and offer high stability.
Wire wound resistors have low tolerance and high stability, and any resistor over 1 W will be of the wire
wound type.
The wire is either nichrome, constantan, or manganin wound on a former and given a protective coating.
They have resistance values from 1 Ω to 25 kΩ and can operate up to 10 to 20 W.
If a very large power rating resistor is required, then the resistor may be metal bars within a cage to allow air
circulation for cooling.
7.2.2
Resistor Coding
One method employed for coding is shown in figure below. The resistor has four bands as shown. The first
band is the first digit, the second band gives the second digit and the third band gives the multiplier. The
fourth band gives the tolerance - typically ±5% or ±10%. If no fourth band is present, then the tolerance is
±20%.
Some resistors with a tolerance of ±1% are marked with a brown band and those with a tolerance of ±2%
are marked with a red band.
Some resistors have a fifth band, which indicates a reliability factor, which is a percentage of failure per
1000 hours of use. Tolerances are indicated by adding a letter at the end.
7.3 Variable Resistors
These are resistors where the value can be changed either manually or automatically whilst the system is
running. In their most basic form, they consist of a circular or straight track of carbon or a wire wound resistor
with a moveable wiper arm. The movement of the wiper arm may be circular around a pivot or hinge or it may
move linearly along a track.
There are two ways of using a variable resistor: as a rheostat or as a potentiometer. When used as a rheostat it
controls the current in a circuit, e.g., current to a lamp – the lamp can be made to burn brighter by increasing
the current to it or dimmer by reducing the current. So, the variable resistor changes the resistance in the
circuit and hence the current. When used as a potentiometer, it is used to provide a variable voltage from a
fixed supply.
7.4 Thermistors
These are ‘thermally sensitive resistors’ which are made of materials whose resistance changes considerably
with a small temperature change.
Most thermistors decrease their resistance with an increase in temperature, i.e., they have a negative
temperature coefficient. They are made in either rod, disc or bead form, and are made of oxides of nickel,
manganese, copper, cobalt and other materials. They are used extensively on aircraft as temperature sensors
in heating, air conditioning, and battery systems. There are some thermistors that have a positive temperature
coefficient. The material used for their construction is barium titanate and they may be used in circuits to limit
current due to excessive temperature rise.
7.5 Voltage Dependent Resistors
Sometimes known as varistors, these are devices whose resistance reduces as the applied voltage increases.
They are manufactured from silicon carbide. Applications include transient voltage suppression, voltage
stabilisation and switch contact protection. For example, it is connected across the component to be
protected and draws only a small current at its normal operating voltage. However, should the voltage increase,
(i.e., a surge), its resistance reduces, and it absorbs some of the energy in the surge by diverting current through
itself and away from other circuits.
7.6 The Wheatstone Bridge
The arrangement of resistors shown in the figure is called a Wheatstone Bridge. It is used in many systems to
include:
 Temperature measurement – acting as a
temperature control device for heated
windscreens, for example.
 Measuring strain – fitted to the landing gear of
some aircraft for the accurate measurement
of aircraft weight and the C of G position
calculation, for example.
 Measuring electrical values. Used in
measuring instruments.
Note that the bridge usually consists of four resistors
with a voltage supply across them and a connection
between them.
The Wheatstone bridge may be used to measure
unknown resistances. R1/R3 = R2 /R4
8 Power
8.1 Introduction
8.1.1 Energy and Work
Energy is the capacity to do work. A suspended weight has Potential Energy, and has potential to do work
when it falls under the influence of gravity. A moving object has Kinetic Energy because it can do work when
it impacts with something. All energy is measured in Joules (J) including electrical energy. One joule of
electrical energy is when one Coulomb passes through a component and the voltage across the
component is one volt, i.e.:
Joules (J) = Coulomb (C) x Volts (V) (equation 1)
As one Coulomb is one amp (I) maintained in a circuit for one second (t), then C = I x t. Substituting this into
equation (1) gives:
Joules = V x I x t
∴ energy = VIt joules
8.1.2
Power
This is the rate at which work is done and is measured in Watts (W). It is the power (P) developed in a circuit
when an applied voltage of one volt causes a current of one ampere to flow. So: P = V x I
So, the three formulas for power are:
P=VxI
P = I2 R, and P=V2/R Watts
So, Watts = Joules/seconds (Joules per second), and can be expressed as Watt seconds.
8.1.3
Power rating of Components
When current passes through a resistor, the resistor becomes hot, and if it gets too hot it could be
damaged. The heat developed by a current in a resistor is I2R Watts. Thus the rate at which heat is
produced is proportional to the square of the current. Therefore, if the current is doubled, then the rate at
which heat is produced goes up four times. The same consideration would apply to voltage across a
resistor. Power is equal to, V2/R so if V is doubled. Then power goes up four times.
Electrical components can only withstand a certain amount of heat without damage and it is normal to give
a wattage rating on the identification plate of the component. If this rating is exceeded, the component will
overheat.
8.2 Internal Resistance
All electrical components have internal resistance. V = E – Ir. Where V = Terminal voltage, E = emf,
I = Current, R = Internal resistance. The internal voltage drop cannot be measured directly.
8.3 Maximum Power Transfer Theorem
This states that, maximum power is developed in a load when the load resistance is equal to the internal
resistance of the supply. When the load resistance and supply internal resistance are equal, the load and
supply are said to be ‘matched’. The transference of maximum power from a supply to a load is often required
in electronic circuits, and a typical example being the matching of an audio amplifier to a loudspeaker.
9 Capacitance/ Capacitor
9.1 Capacitance
In general terms, it is the ability of two conductors positioned close to each other to store a charge (pd)
between them. When the voltage across the capacitor equals the battery voltage, electron flow stops. The
capacitor stores an electric charge and in its simplest form described so far consists of two parallel plates
separated by an insulator known as a dielectric - air in this case. The property of a capacitor to store an electric
charge when its plates are at different potentials is known as capacitance. The capacitor effectively blocks DC
current (except for the small initial current) but allows AC to pass. The unit of capacitance is the Farad (F)
which is defined as ‘the capacitance of a capacitor which has a potential difference of one volt across its
plates when it is charged by 1 Coulomb of electricity. C = Ǫ/V and Ǫ = CV Coulombs. The farad is a large unit
and typically the microfarad. The energy stored in a capacitor is given by the formula: ½CV2 joules.
The electric field strength (E) experienced by the dielectric is given by the formula: E = V/d volts per metre,
where V = voltage and d = distance between the plates. Factors which affect capacitance include:
 Area of plates: If the area of the plates is increased, a greater charge is allowed to be held and therefore
the plate area is directly proportional to capacitance.
 Their distance apart: By changing the distance between the plates, the capacitance will change. As
capacitance depends on the strength of the electric field, if the plates are moved further apart (weaker
field) capacitance decreases.
 The type of dielectric: The capacitance also depends on the dielectric material and its relative
permittivity (εr) or dielectric constant (k).
C = KA/d
Where C = capacitance, k = dielectric constant, A = area of plates opposite each other, d = distance the plates
are apart
9.1.1
Capacitors in Parallel
When capacitors are connected in parallel, the voltage is the same across each one, but their
charges may be different. For capacitors in parallel, we add their values, for capacitors in series,
we carry out a calculation similar to the one for resistors in parallel.
9.1.2
Capacitors in Series
The charge on each capacitor will be the same, but the voltage for each one will be less than the supply
voltage (VT).
9.1.3
Working Voltage
The insulating materials forming the dielectric have very few free electrons available to form a current
under normal conditions, but if they are subjected to an intense electric field, electrons may be torn from
their atoms and current will flow, and ‘dielectric breakdown’ will have taken place. The working voltage is
the largest voltage (DC or peak AC), which can be applied across a capacitor without the dielectric breaking
down and is often marked on the capacitor, e.g., 50 V WKG. If it is exceeded, dielectric breakdown will
occur and current will flow.
9.1.4
Leakage Current
No dielectric is perfect, so each dielectric has a few free electrons. Therefore, when the capacitor is
charged, a small leakage current will pass between the plates and for most practical purposes this can be
ignored.
9.1.5
Capacitor Coding
Usually only ‘preferred’ values are manufactured, similar to resistors.
9.2 Charging and Discharge of a Capacitor
9.2.1
Charging a Capacitor Through a Resistor (CR Circuit)
The capacitor continues to charge with the current falling steadily. This will continue until capacitor voltage
(VC) equals battery voltage (V).
9.2.2
Time Constant
The time constant (T) is the time taken for the capacitor to reach 63.2% of the applied voltage, where T =
CR seconds. Where T is in seconds, C is in Farads, and R is in ohms. The capacitor is fully charged in 5 CR
seconds.
9.2.3
Discharge of a Capacitor Through a Resistor
With the capacitor at V volts when the switch is closed, the capacitor will start to (rapidly) discharge into
the circuit, and voltage and current fall. The immediate current is V/R amperes. In CR seconds, the
capacitor has discharged to 36.8% of the pd across the plates. The capacitor is fully discharged in 5 CR
seconds and once again the curve is an exponential curve.
9.3 Types of Capacitors
Capacitors come in all shapes and sizes and are usually marked with their value in farads. They may also be
divided into two groups: fixed and variable. Polyester, mica, ceramic, and electrolytic capacitors are fixed type
capacitors.
9.4 Testing of Capacitors
An analogue multimeter or digital multimeter set to the high resistance range can be used to test a capacitor.
9.4.1
Non-polarised Types
If the resistance is less than about 1 MΩ, it will allow current from the battery in the multimeter to ‘pass’.
This indicates that the capacitor is leaking and faulty.
9.4.2
Polarised Types
For the dielectric to form in these types, a positive voltage must be applied to the positive side of the
capacitor (marked + or a groove). In most analogue multimeters the terminal marked - (black) is the
positive of the internal battery when selected to the ohms setting. For digital meters, the manufacturers’
instructions will have to be consulted. When the capacitor is first connected to the multimeter, its
resistance is low but rises as the dielectric forms. If it does not, the capacitor is faulty.
10 Magnetism
10.1 The Earth as a Magnet
The earth behaves as if it were a bar magnet. In fact, it is an enormous electro-magnet with the field being
generated by the moving molten core of the earth. Note that the poles of the magnet are south at the top
(near the earth’s north pole) and north at the bottom (near the earth’s south pole).
10.1.1 The Angle of Dip
The earth’s magnetic lines of force effectively go from north to south with the lines vertical at the poles and
horizontal at the equator. The angle of dip at the poles is vertical (90°) and at the equator near the earth’s
surface, it is horizontal (0°). The angle of dip is the angle between the direction of the earth’s magnetic flux
lines and the horizontal. The angle of dip is greatest at the poles and least at the magnetic equator. The dip
angle is 0° at the equator and 90° at the poles.
10.1.2 Declination or Variation
Where declination is zero, these points can be marked and joined up by a line on a map - this line is called
an agonic line. Along this line, the compass needle will point north. Where the declination is plus or minus
from zero, isogonic lines can be drawn on the map. These are lines drawn on the map that connect points
with the same declination.
10.2 Magnets
Magnets may be made in any shape but the two most common are the bar magnet and the horse-shoe
magnet. The horse-shoe magnet is shaped like a horse-shoe with the two ends being the poles - used in some
electric motors.
10.2.1 Properties of a Magnet
When a bar magnet is freely suspended at its middle by a piece of string, it may rotate clockwise or
anticlockwise for a short period of time but then comes to rest orientated in an approximate north-south
direction in-line with the Earth’s magnetic field. The magnet will have one end pointing to the Earth’s north
magnetic pole and is called the north-seeking pole or north (N) pole of the magnet. The other end is the
south seeking or south (S) pole. If the north pole of a magnet is moved close to the north pole of another
magnet, the two poles will repel each other. If either one or both of the magnets are free to move, then
they move away from each other.
10.3 Electromagnets
When a conductor carries a current, a magnetic field is produced around that conductor. When viewing a
conductor end-on, assume conventional current flow is from positive (+) to negative (–). With the current
flowing into the conductor (away from the reader into the page), the current is represented by a cross (⊗).
With current flowing out of the conductor (out of the page towards the reader), the symbol is a dot in the
middle of the conductor (⨀).
Once we know the direction of the current, we can determine the direction of the magnetic field. To determine
this, the Corkscrew Rule is used. To operate a corkscrew, it is rotated clockwise and it will move forward into
the cork. So, with the current going forward (into the page), the flux lines will rotate clockwise. With the
current coming out of the page (towards you), the field will be anti-clockwise.
10.3.1 The Solenoid
To obtain a stronger magnetic field from a conductor, it can be wound into a coil with many turns. This will
increase the magnetic effect as this provides the addition of each winding to increase the field in the coil.
When a DC current is passed through the coil, the flux pattern is similar to that of a bar magnet.
10.3.2 The Right Hand Grasp Rule
“If the solenoid is grasped in the right hand with the fingers in the direction of the current in the coils, then
the extended thumb points in the direction of the north pole”.
The rule is also applied to a conductor where the hand is held around the conductor with the fingers
pointing in the direction of the flux lines. The extended thumb will indicate the direction of the current
flow. This rule is not to be confused with Fleming’s right hand rule, which is used for generators.
10.3.3 More Magnetic Terms
Flux is measured in Webers (wb) (pronounced Vayber) and has the symbol F (phi). It is the total flux emitted
from the poles of a magnet. The flux density (T) is the flux per unit area Φ/A and is measured in Tesla (T).
The magneto motive force (mmf) is the force that establishes the flux around a coil due to current flow
through the turns of the coil. It is measured in Ampere turns (At). The magnetic field strength of the
solenoid can be increased significantly by putting a metal core within the coil - typically made of soft iron.
This is the principle of the electromagnet, which is used in relays, contactors, motors and generators.
10.3.3.1
Permeability (µ)
This is the ability of a material to accept lines of flux and increase their density. It is the ratio of magnetic
flux density (T) or magnetic flux induction produced by the magnetising force (H) producing it. If current is
passed through a coil which has an air core, then the flux produced is directly proportional to the magnetic
field strength. The ratio of T (flux induced into the metal) to H (magnetising force) is a constant for free
space and is called the permeability of free space. The ratio of the flux produced with a soft iron core to the
flux produced with an air core is called Relative Permeability and has the symbol μr.
10.4 Magnetic Materials
Ferromagnetic: The relative permeability of these materials is very high, which include iron, steel, nickel, cobalt
as well as a number of alloys. These materials may be further classified as ‘HARD’ or ‘SOFT’. These terms refer,
not to their physical hardness, but to their magnetic hardness. Magnetically soft materials have high
permeability and include soft iron, steel silicon alloys (up to 4.5% silicon), metals such as Permalloy (78.5%
nickel) and Mumetal (75% nickel).
Paramagnetic: These materials have a relative permeability whose value is slightly greater than unity and
become weakly magnetised in the direction of the magnetising field, for example, aluminium, chromium,
manganese and platinum.
Diamagnetic: These materials have a relative permeability of less than unity. They become weakly magnetised
but in the opposite direction to that of the magnetising field, for example, antimony, copper, gold, silver, zinc
and glass.
10.5
Magnetisation
10.5.1 The Domain Theory
The theory is that the electrons spinning around the atom’s nucleus of a ferromagnetic material also spin
on their own axis, each having a small magnetic field. A number of these atoms group together to form
domains. To magnetise a ferromagnetic bar, it is placed in a DC current carrying solenoid and the current
switched on for a period of time. The polarity of the bar can be found by using the Right Hand Grasp rule.
10.6 Demagnetisation
Sometimes an aircraft can become magnetised and also some components. In these cases, the
aircraft/component will have to be de-magnetised. Magnetised components will affect components that
require magnetism for their operation - magnetic compasses, for example.
10.6.1 The Coil Method
This uses a coil supplied with an AC supply via a step-down transformer. This is sometimes called deGaussing. For some de-Gaussing operations, the item is kept still and it is the coil that is moved.
For whole aircraft, large de-Gaussing coils are used.
10.6.2 Tapping
Light continuous tapping with a hammer while the part is held in an E-W direction can reduce the part’s
magnetic strength.
10.7 Care of Magnets
Magnets are used in motors, generators, transducers and other equipment in aircraft. Any vibration or rough
treatment such as dropping or hammering will cause weakening of the magnetism. Also, excessive heat can
destroy the magnetism.
10.8 Magnetic Shielding (Screening)
It is sometimes necessary to isolate equipment from the effects of magnetic fields. There are no known
insulators for magnetic lines of flux, so another technique is required. Typically the piece of equipment might
be surrounded with soft iron.
10.8.1 Hysteresis Cycle
If a magnetic material is taken through a complete cycle of magnetisation and demagnetisation and a graph
plotted of flux density (T) against magnetic field strength (H), then the given graph will result.
Points on the graph:
 O to P - Initial magnetisation curve from start (O) to saturation at P.
 P to Q - The magnetisation force is reduced to zero. The length of line O-Q represents the
remanence or residual magnetism (Retentivity).
 Q to R - To reduce the flux density to zero, the magnetising force is reversed and the length O-R
represents the coercive force.
 R to S - Increasing the reversed magnetising force causes the magnetic material to reach saturation
in the reverse direction.
 S to P - Reversal of the magnetising force through T and U again makes the material saturated in the
original direction.
10.8.1.1
Hysteresis Loss
Energy is required to magnetise and demagnetise a piece of magnetic material and this energy is dissipated
in the form of heat. The area bounded by the hysteresis curve represents the energy loss for each cycle of
magnetisation and demagnetisation. A large area (J, K, L, M, N, O) indicates a large energy loss, whereas the
curve Q, R, S, T, U, V represents a small energy loss.10.8.1.1 Remanence
10.8.1.2
Remanence
After initial magnetisation, most metals will retain some magnetic properties. The amount of residual
magnetism is called remanence and is measured in Tesla (T). The amount of reverse magnetisation required
to drive the magnetic field back to zero is called coercivity – also measured in T.
11 Inductance/ Inductor
11.1 Inductance
When a conductor is in a changing magnetic field, an emf is induced into it. The three essentials required for
inductance are:
 A conductor (a coil or a piece of wire connected to a circuit); a magnetic field.
 A magnet or a component causing a magnetic field.
 A changing flux field over the conductor.
When magnetic lines of flux cut or are cut by a coil, an emf is induced into the coil. This is the law of
electromagnetic induction known as Faraday’s law.
Faraday’s law states: ‘When a conductor cuts or is cut by a magnetic field, an emf will be induced into the
conductor. The magnitude of the emf is proportional to the rate of change of flux’. The rate of flux cutting can
be increased if the number of turns on the coil is increased – which will increase the emf. If the strength of the
magnetic field is increased (a stronger magnet), then once again the emf will increase.
So the induced voltage depends on the:
1. Rate of change of flux. The faster it changes, the better.
2. Number of turns of the coil. More the number of turns, the better.
3. Magnetic field strength. The higher, the better.
11.1.1 Mutual Inductance
The rate of change of flux through a coil can be achieved without any physical movement by varying the
current through the coil. In other words, using an AC supply. The effect of changing current in one coil and
the resultant change of flux inducing an emf into a coil close to the first coil is called mutual induction and
the two coils are said to have mutual inductance (M). If the circuits are close to each other, then they can
suffer inductive coupling. This is where the changing flux in one circuit can affect the other. For DC circuits,
this happens on switch-on and switch-off only, but for AC circuits this would be constant when the circuits
are on.
The unit of inductance is the henry (H). The mutual inductance of two circuits is one henry when a current
changing at the rate of one ampere per second in one circuit produces a mutually induced voltage of one
volt in the other circuit.
If the first coil (called the primary coil) is connected to an AC supply where there is a continual rate of
change of current, then a steady (AC) voltage would be induced in the second coil (called the secondary).
This is the basis of the transformer.
If the secondary coil is placed at right angles to the primary coil, then very little of the primary coil’s flux is
cutting the secondary, the flux being parallel to the turns of the coil. Therefore the emf induced and mutual
inductance are both low. If the coils are parallel to each other, then there will be more flux lines cutting.
11.1.2 The Coupling Coefficient
When two coils are placed together, most of the flux produced by one coil passes to the other and the coils
are said to be ‘tightly coupled’. If the coils are placed well apart, then only a small amount of the flux of one
is linked with the other and they are said to be ‘loosely coupled’. When there is linkage, the mutual
inductance (M) can be found from the formula:
11.1.3 Lenz’s law
Lenz's law states that: ‘The direction of an induced emf is always such as to oppose the effect producing it’.
This law is a fundamental law of the electrical theory.
11.1.4 Self Inductance
When a voltage is self-induced due to change of current in the coil itself, a phenomenon called selfinduction occurs. By Lenz’s law, this self-induced voltage will oppose what produced it, so this voltage will
oppose the fall in current and try to keep the current flowing. Any circuit (AC or DC) that has a voltage
induced in it by a change of current through the circuit itself has self-inductance. The effect of selfinductance is to oppose any change of current by virtue of the back emf. This is an additional continuous
resistance in an AC circuit where coils are concerned.
The unit of self-inductance (symbol L) is the henry (H). One henry is produced when a self-induced voltage
of one volt is produced by a current changing at the rate of one ampere per second. The self-induced
voltage can be increased by:
1. Increasing the number of turns on the coil.
2. Putting the coil on an iron core (increasing the permeability).
3. Increasing the rate at which current changes through the coil.
The ability of a coil to produce a back emf when there is a current change is a design factor and depends on
the:
 Number of turns (N)
 Cross-sectional area (a) in m2
 Length (l) in m
 Permeability of the core material
11.1.5 Energy stored in a Magnetic Field
The total amount of energy used during the time that the current changes from zero to its maximum value
is given by the formula:
Where L = inductance in henrys; I = current
11.1.6 Inductors
When a coil is used specifically to provide inductance and thus oppose any change of current in a circuit, it
is called an inductor or choke. When used in an AC circuit, where current and the magnetic field are both
changing all the time, there is always an induced voltage in the coil and a permanent opposition to the
current.
11.1.7 Types of Inductors
1. Iron cored: These are generally used where a large inductance is required. When used on AC
circuits, the flux is continually changing and by Faraday’s law an emf will be induced into the iron
giving rise to small circulating currents known as eddy currents. This causes the core to become
hot, which produces an energy loss known as eddy current loss.
2. Air cored: These inductors are used in high frequency circuits such as radio tuning circuits and have
a small inductance.
3. Iron dust and Ferrite cored: The iron based cores can be used at high frequencies if the material is
made into a powder form which is then coated with an insulator and pressed together. Used in
radio frequency tuned circuits. Ferrite cores are also used at high frequencies. They are made up of
ferric oxide combined with other oxides such as nickel oxide. These types of cores increase the
inductance considerably over the air-cored coil and their eddy current losses are also much
reduced.
11.2
Inductors in a DC (LR) Circuit
11.2.1 Effect of Inductance (L) and Resistance (R)
Almost every item of electrical equipment possesses resistance and inductance. When a voltage is applied
to a circuit containing resistance and inductance, the current does not rise to maximum immediately
because there is a self-induced emf (Lenz’s law) which opposes the build-up of current.
With no inductance, the current would rise to maximum (I = V/R ) immediately but with inductance the
current rises exponentially.
11.2.2 Time Constant
The time constant of the circuit is the time taken to reach 63.2% of its maximum value.
11.2.3 Decay of Current in an LR Circuit
The decay of current shows a similar pattern to the growth of current except that the induced emf tries to
keep the current flowing. The initial rate of decay is steep but the graph soon flattens out to take about 5
L/R time intervals to fall to zero. The value of one time constant is 36.8% of the maximum value.
11.2.4 Inductors in Series and Parallel
For a series circuit, the total inductance is LT = L1 + L2 + L3
For a parallel circuit, the equation for total inductance is
12 DC Motor/ Generator Theory
12.1 Introduction
12.1.1 Generator Theory
The direction of the induced emf can be found using Fleming’s right hand rule. The magnitude of the emf
generated in our simple generator depends on:
B = The flux density of the magnetic field in Tesla.
L = The length of the conductor in the magnetic field in metres.
V = The velocity (speed) of the conductor moving through the magnetic field in metres per second.
To generate a smoother output and enough power to supply aircraft systems, the practical generator has
many coils rotating in a strong magnetic field. As the number of loops increases, the output voltage
increases and the ripple effect becomes smaller.
12.1.2 Components of a DC Generator
The stationary part of the generator consists of a housing (yoke), mounting brackets - usually on the drive
end for attachment to the engine gearbox, pole pieces, field coils, brushes, brush holders, wiring and an
external connecting box complete with terminals.
The rotating part of a generator is driven by the aircraft engine via the accessory gearbox and consists of a
support shaft, an iron armature, output windings (rotating loops or coils), the commutator and support
bearings at each end of the shaft.
12.1.2.1
The Armature
This rotates within the yoke of the generator and has a laminated iron armature cut into slots into which
wires are laid to provide output windings. The output voltage and maximum current that may be taken from
a generator will depend to some extent on the method in which the coils of the armature are connected to
one another. There are two types in use: lap and wave windings. In a wave wound generator, there are two
paths in parallel irrespective of the number of poles, each supplying half the total current output. In a lap
wound generator, there are as many paths in parallel as there are poles.
12.1.2.2
Commutator
This is located at the non-drive end of the armature. It consists of a number of copper segments mounted
on, but insulated from, the shaft. They are also insulated from one another by strips of mica, which are
usually ‘undercut’ to make their top surface slightly below the level of the commutator segments.
12.1.2.3
Bushes and Brush Holders
Brushes must be made of a material which has a low contact resistance, low specific electrical resistance,
low coefficient of friction and good self-lubricating properties. The brush holders are in effect metal boxes
into which the brush is a good sliding fit. A force is applied to the top of the brush by a spring to maintain
good contact between the brush and the commutator. Each brush holder is secured to a support ring
sometimes called a brush rocker.
12.1.2.4
Magnetic Field System
The field windings are pre-formed coils mounted on the pole pieces and, when current passes through,
their polarity is changed with the polarity of the main poles alternating between north and south.
12.1.2.5
Bearings
The rotating armature is supported in ball or roller bearings. Normally a ball bearing (ball-race) is fitted at
the drive end with a roller race at the ‘tail’ end. This permits longitudinal expansion of the shaft (when it
gets warm). Bearings are lubricated with high melting point grease or lubricating oil. The cooling air may be
ram air from the aircraft forward movement via an external air duct and ducting to the generator, or by an
integral electrically operated fan or a combination of both methods.
The generator drive system must have some method of disconnecting the generator in the event of seizure
of the generator armature, so between the generator and the gearbox, a Quill drive resides.
12.1.3 Generator Load
If a generator is connected to a load, then a load current IL will flow. This will be equal to the armature
current IA. This armature current flows through the armature windings and brushes which have some
resistance (RA). Therefore, there must be an internal voltage drop (IARA) within the generator when it is
supplying a load. This voltage drop will cause the terminal voltage to fall.
12.1.4 Commutation
Reactive sparking occurs at each point of commutation for every coil. This will cause brushwear,
commutator wear and interference to radio systems. One method of overcoming this problem is to use
interpoles.
12.1.5 Interpoles and Compensation Windings
Interpoles are small poles located midway between the main poles. The interpole windings are connected in
series with the armature and the interpole has the same polarity as the next main pole ahead in the
direction of rotation. The poles are at the point of commutation and carry exactly the same current as the
armature winding. As the armature coils approach the point of commutation, they come under the
influence of the interpole which attempts to induce an emf into them. This is in opposition to the emf
already across the coil. The two opposite fluxes cancel, leaving no flux to collapse and no reactance voltage
and therefore no reactive sparking.
So, at high speeds, strong interpoles are required to ensure adequate compensation for the high reactance
emf. When the generator is driven at a lower speed with a heavy load, the main field will be strong and the
reactance emf is fairly small. At high speeds when the field is weak, little opposition to the interpole
strength is provided by the auxiliary windings.
12.1.6 Losses in a DC Generator
a) Copper Losses: Any current passing through armature windings, field windings and through the
brushes produce a power loss due to I2R losses as each of these has some resistance. This varies
with load.
b) Iron Losses: Independent of the load and mainly involve eddy current losses in the armature and
pole pieces and the hysteresis loss in the armature.
c) Friction Losses: These include brush friction, bearing friction and air resistance (windage) against
moving parts.
12.1.7 Classification of Generators
12.1.7.1
Permanent Magnet Generator
The simplest form of a DC generator is where the field is provided by high grade permanent magnets and
the armature is an iron core carrying a single coil whose ends are connected to the two segments of a
commutator. Typically used in small generators and in the older type insulation tester (the Meggar). The
volts/load characteristic graph shows a slight drop-off in voltage as more load is applied. This is due to the
armature reaction and resistance losses.
12.1.7.2
Separately Excited Generator
The main field winding is connected to an independent source of DC supply. The field winding is of fairly
high resistance and regulation of field current is by a variable resistor.
When connected to a load, the field current is unaffected and remains constant. The characteristic graph
shows a slight drop in voltage as the load current increases due to resistance losses (IR drop). This has no
practical application on aircraft.
12.1.7.3
Self-Excited Generators
These are further classified by the way the field winding is connected to the armature. Connection can be:
a) Series
b) Shunt
c) Compound
12.1.7.3.1 Self-Excited Series Wound Generator
The field coils are wound in series with the armature. There are a few turns of heavy wire or copper
strip of a large cross-sectional area and of low resistance. This type of generator has no practical use on
aircraft.
12.1.7.3.2 Self-Excited Shunt Wound Generator
Again the armature is the source of supply for the field, but in this generator the field windings are of
many turns of fine wire of high resistance connected in parallel (shunt) with the armature. If the load is
increased above the full load condition then the voltage drops to near zero. This feature on the
volts/load characteristic graph is known as ‘tuck-under’ or ‘turn-under’.
Shunt generators should be allowed to build up to their correct voltage before any load is applied. Else,
turn-under could occur and the generator will fail to excite. This type of generator is the one most used
on aircraft with DC as its main power source.
12.1.7.3.3 Self-Excited Compound Wound Generator
This uses a combination of series windings and shunt windings around the pole pieces. If they are
wound to assist one another, it is known as a cumulative compound generator.
If the number of series turns is arranged so that the output voltage at no-load and full-load is the same,
the generator is said to be level compounded. If the number of series turns is increased so that the
voltage increases with load, the generator is said to be over compounded. If the two fields are wound to
oppose each other, then this is a differential compound generator which has a steeply falling volts/load
characteristic curve. Neither of these has practical application on aircraft, although a compound
machine is used as a starter generator.
12.1.8 Interference Suppression
There is always some sparking at the brushes of the generator. This results in electromagnetic radiation
which interferes with radio wave transmission and reception. Typically, suppressors are fitted internally
within the generator and consist of capacitors connected between the generator casing (earth) and the
main terminals, i.e., across the output.
12.2
DC Motors
12.2.1 Theory
The flux lines under the conductor oppose each other and tend to cancel each other out and thus produce a
weaker field. All magnetic flux lines tend to behave elastically and will try to straighten, and at the same
time try to produce an even flux density. The magnetic flux lines above the conductor (being in tension) try
to straighten and repel each other sideways so a force is created forcing the conductor out of the magnetic
field, in this case down.
Using Fleming’s left hand rule it is possible to determine the direction of the current, force or field knowing
any two of them. The thumb, first finger and second finger of the left hand are placed mutually at right
angles to each other. The first finger gives the field direction (north to south), the second finger gives the
current direction and the thumb gives the direction of motion of the conductor as a result of the force.
12.2.2 The Basic Electric Motor
This is very similar to a basic DC generator. It has a coil rotating within two bar magnets connected to an
external circuit via a commutator.
12.2.3 A Practical DC Motor
The construction of a DC motor is identical to that of a DC generator. However, the motor converts electrical
energy into mechanical energy, but with a generator it is the other way round. When a current flows
through the large number of coils on the armature, their fields interact with the main field system to give a
turning motion, with the commutator switching the supply at the point of commutation.
12.2.3.1
Back emf
As the armature conductors of the motor rotate in the magnetic field, they cut this field and by Faraday’s
law an emf is induced. By Lenz’s law this induced emf opposes the applied voltage and is called back emf.
This back emf (EB) pushes one way and the applied voltage (V) pushes the other, so it is the difference
between these two which actually drives current through the armature circuit and this difference is known
as the effective voltage or armature voltage.
It is important to realise how back emf controls the current in a DC motor. When the motor is running. the
back emf is close to the value of the applied voltage.
12.2.3.2
Torque
It can be shown that the force on each armature conductor and therefore the total armature torque (T) is
directly proportional to (𝛼𝛼) the magnetic field strength (F) and armature current (IA). Torque is measured in
Newton metres (Nm). Torque losses vary with speed.
12.2.3.3
Power
The output power (P) of a motor has two variables in its formula, torque (T) and speed (N) so that P 𝑎𝑎 T x
N. Therefore, for a given power any increase in speed can only be attained at the expense of torque and vice
versa.
12.2.3.4
Reactive Sparking and Armature reaction
An armature reaction takes place in a motor for the same reasons as in a generator, i.e., the main field is
distorted by the armature field. Since back emf reduces armature current to a fairly small value, the
armature reaction is usually fairly small and many DC motors do not have any means of counteracting it.
Reactive sparking also occurs in motors.
12.2.3.5
Motor speed control
The effect of the back emf is to make the DC motor a self-regulating machine in which speed and armature
current adjust themselves to changing load conditions. When a motor is running on-load, the effect of
altering the load is as follows:
 Load reduced: The armature torque is greater than the load torque and the motor speeds up. The
armature conductors are now cutting the field flux faster and back emf increases.
 Load increased: The armature torque is less than load torque and the motor slows down. Less back
emf is generated, so armature current and torque both increase until torque balance is restored and
speed stabilised again.
12.2.4 Types of DC Motors
Like generators, motors are classified according to the way the field system is connected to the armature,
i.e.:
 Series wound motors.
 Shunt wound motors.
 Compound wound motors.
Two characteristics are used to show the properties of a motor: the speed/load characteristic and the
torque/load characteristic.
12.2.4.1
Series Motor
The motor must be connected to a load permanently as the off-load speed would get too high. As the field
and armature interactions increase when speed increases, the back emf rises and opposes armature
current. This causes the field to be weakened which reduces the back emf disproportionately and it cannot
build up sufficiently to control the rise in speed. Therefore, speed increases and the sequence continues
causing excessive speed of the armature.
12.2.4.2
Shunt Motor
The field winding of a shunt motor is connected in parallel with the armature and is of reasonably high
resistance. This connection, produces different properties. The speed characteristic shows that from no-load
to full-load the speed reduction is small and so it can be considered to be a constant speed machine. It is a
self-regulating machine in that when a new load is placed on the motor the motor automatically adjusts its
own effective voltage.
As the field is directly across the supply the field strength is practically constant. This means that the torque
of a shunt wound motor is proportional to armature current until approaching full load condition. The
starting torque is small, due to slow build-up of the field strength and the restricted armature current.
Shunt motors should therefore be started on light-load or under no-load conditions.
12.2.4.3
Compound Wound Motor
This motor has two windings wound on the pole pieces and the characteristics depend on whether the
shunt or series predominates and whether they are wound to assist one another (cumulative) or to oppose
one another (differential).

Cumulative Compound Motor
The most common application of the compound motor on aircraft is the cumulative compound machine
with a predominant shunt field winding. The series winding enables a fairly high starting torque to be
developed, allowing the motor to be started on a reasonable load.
This is an ideal characteristic for a motor supplying a load where the load torque is proportional to
speed, since the motor is virtually a constant torque machine.
This form of cumulative compound motor may be called a normal compound motor, and would be used
on DC systems for inverter drives, and on DC aircraft for fuel pumps as well as heavy duty actuators.

Differential Compound Motor
This is where the shunt and series field windings are wound to oppose each other. These motors are
mainly shunt wound machines with a minor series winding. This gives a speed/load characteristic graph
which is fairly constant but speed increases when the load becomes too great. The torque on light loads
is similar to a shunt wound motor as the characteristic graph shows but, if overloaded, the series
winding field strength will at some point cancel the shunt winding. There will be no torque and the
motor will stop, even though taking a high current.
12.2.5 Reversal of Rotation of a Motor
To reverse the direction of a motor, the direction of current through the armature or through the field must
be reversed. If the current through armature and field are both reversed, the motor continues in the same
direction.
To reverse the direction of rotation in a compound motor, the same principle applies. That is, reverse the
direction of current through the armature or the field. On aircraft it is normal to reverse the direction of
current through the armature by means of reversing relays. An alternative method used to reverse the
direction of a motor is to use two fields both wound on the same pole piece but with one giving opposite
polarity to the other. The split field series actuator is a special adaptation of the series motor and is used
extensively on aircraft.
12.2.6 Losses in a DC Motor
These are the same as those in a generator, i.e., copper losses, iron losses and friction losses.
12.3 Starter Generators
These are used on aircraft and offer a weight saving over the system which has a starter motor and a generator.
For starting purposes, the starter generator is supplied with a DC current and it performs as a motor. Once the
engine has started, the motor becomes a generator and supplies current to the operating systems, battery
charging systems, etc. via bus bars. Typically it is a self-excited compound wound machine which has
compensating windings and interpole windings with an integral cooling fan on the drive shaft. It is also cooled
by ram air when the aircraft is airborne.
12.4 Long Shunt and Short Shunt machines
For compound machines, generators or motors, there are two possible methods of connection, i.e., short shunt
and long shunt. The reasons for the arrangements is to obtain specific operating characteristics. The series and
shunt windings can be connected together in two ways. If the shunt winding is connected between the motor
and the series winding, then this is called a short shunt motor. If it is connected above the series winding, then
it is called a long shunt motor. The current will vary depending on demand. If there is a high demand (many
services switched on), then the current will be high. If there are no services switched on, then the current will
effectively be zero.
13 AC Theory
13.1 Alternating Voltage and Current
The alternating system is one in which if the circuit is switched on, the voltage, and current periodically reverse
in direction in a regular recurring manner. The complete sequence A to B is called a cycle and the waveform is
called a sine wave. A graph of voltage against time would be of a similar shape. There can be other waveforms,
like a square wave or a triangular wave or saw-tooth wave. The number of cycles occurring in one second is
called the frequency. This has the symbol f and the unit hertz (Hz). The frequency of most aircraft AC constant
frequency systems is 400 Hz (400 cycles per second). In aircraft radio and radar systems, many other
frequencies are used ranging from 3 kHz (kilo Hertz) to 30 GHz (Giga Hertz). The time taken to complete one
cycle is known as the periodic time or period denoted by the symbol T. T = 1/f
13.2 Sinusoidal Waveform
The mechanism to generate an AC waveform, It consists of a conducting loop rotating within a magnetic field
from a permanent magnet where the loop is connected to slip rings and then via brushes to an external circuit.
The loop (normally many coils of wire) is rotated in a magnetic field by a motor (the aircraft engine in the case
of aircraft generators). The magnetic field can be two magnets or coils carrying a DC supply and the rotating
loop cutting the flux lines will set-up an alternating voltage within the loop. If the loop and slip rings are
connected to a circuit (load) then an alternating current flows in the circuit. The production of a voltage (emf)
by a conductor cutting a magnetic field was first stated by Michael Faraday.
Faraday's law states that when a conductor cuts a magnetic field an emf (electromotive force) is induced into
the conductor.
13.2.1 AC Values
a) Instantaneous Value: An instantaneous value of voltage or current as mentioned previously is the
induced voltage or current flowing at any instant during a cycle. The sine wave represents a series of
these values. The instantaneous value of the voltage varies from zero at 0° to maximum at 90°, back
to zero at 180°, to maximum in the opposite direction at 270°, and to zero again at 360°.
b) Peak Value: The peak value of an alternating current or voltage is the maximum value reached
(either positive or negative) during a cycle. The peak or maximum value is sometimes called the
amplitude. The difference between the peak positive value and the peak negative value is called the
peak to peak value and is twice the peak value.
c) Average Value: The average value of an AC waveform over a full cycle is zero as the positive and
negative values are equal. It is usual therefore to use the average value of half a cycle. For a sine
wave, this average value will be: 0.637 x peak value.
d) Effective or Root Mean Square (RMS) Value: The RMS value of AC is that value of current which has
the same heating effect as its equivalent DC value. Power in a DC circuit is proportional to the
square of the current (I2R). This also applies to AC circuits.
RMS = 0.707 * peak value = peak value/ 1.414.
The form factor is therefore an indication of the shape of the waveform. The higher its value, the more
‘peaky’ is the waveform. For a pure sinusoidal waveform the form factor will always be equal to 1.11.
13.2.2 Phase Difference
When two or more alternating quantities with the same frequency pass through corresponding points in a
cycle at the same instant in time, then they are said to be in-phase with one another.
13.3 Three-phase Systems
It is possible for an AC system to consist of one phase, two phases or indeed as many phases as the designer
wishes. However, for AC generation on aircraft a three-phase system is used. In two-phase supplies, there are
two coils on the same armature wound at 90° to each other and there would be two cables going to the
consumer units (bus bars), and two earth cables. The graph will have two AC waveforms each 90° or π/2 out of
phase from each other. In the three-phase AC supply, there are three coils on the same armature wound at 120°
to each other producing three outputs at a 120° phase difference. Three supply cables would be used – one for
each phase, each going to its own bus on the aircraft.
13.3.1 Star Connected Generators
A simplified circuit for a star wound three-phase (blue, red and yellow) generator is shown in the below
figure. In this system, the end of each winding within the generator is connected to a common point called
the neutral or star point and a line is taken from the start and the other end of each phase winding. The line
current and phase current are the same. Line voltage = √3 * Phase Voltage.
Phase voltage (VPh) is measured between any line and the neutral line. Line voltage (VL) is measured
between any two lines.
13.3.2 Delta Connected Generators
Delta connected generators consist of three windings, which are connected in series. At each of the three
nodes, a line is taken to supply consumer circuits connected between phases. Note that line voltage (VL) and
phase voltage (VPh) are the same (VL = Vph). IL = √3 * Iph
13.3.3 Three-phase Voltages
As the output windings of the generator are identical, their outputs will be of equal amplitude.
13.3.3.1
Symmetrical Three-phase System
This system is the one in which the phase voltages are of the same magnitude and of the same phase
displacement.
13.3.3.2
Balanced Three-phase System
This is one in which the phase loads are equal and, therefore, the phase currents are equal in magnitude
and are operating at the same phase angle. As with the voltages on the previous discussion, the sum of the
instantaneous currents in a balanced system always equals zero.
13.3.3.2.1 Relationship between Line and Phase voltages
If the instantaneous values of two phases are added together, the result will be a third waveform.
13.4 Square Waves
A perfect square wave has vertical sides and a flat top. Such a theoretically perfect wave has an infinite number
of odd harmonics and no even harmonics. Such a waveform is not possible to achieve in electronic circuits.
However, by using the fundamental and the lowest nine odd harmonics (3rd to 19th) a good resemblance can
be obtained. Limiting the number of harmonics causes a sloping of the sides of the wave.
A voltage with a square waveform is often used as a test signal applied to the input of a system. If the system
does not respond well to higher frequencies, then the sides will slope. If it does not respond well to lower
frequencies, then the flat portions will become curved.
13.4.1 Properties of Square Wave
The square wave or derivatives of it is used in electronic circuits (multi-vibrators), digital systems and radar
systems. If a fundamental sine wave (frequency, say 1 Hz) and a number of its odd harmonics (3 Hz, 5 Hz, 7
Hz etc.) are added together, then a waveform is produced, which tends to be square in shape. A
symmetrical square wave is one with its positive and negative portions equal in time, whereas with an
asymmetrical wave, the portions are unequal. Asymmetrical square shaped waveforms are sometimes
called rectangular waveforms or pulses, which may be achieved by varying the mark-space ratio of the
square wave.
13.5 Triangular Waveforms
Triangular waveforms are generally bi-directional non-sinusoidal waveforms that oscillate between a positive
and a negative peak value. Although called a triangular waveform, the triangular wave is actually more of a
symmetrical linear ramp waveform because it is simply a slow rising and falling voltage signal at a constant
frequency or rate. The rate at which the voltage changes between each ramp direction is equal during both
halves of the cycle. Generally, for triangular waveforms the positive-going ramp or slope (rise), is of the same
time duration as the negative-going ramp (decay) giving the triangular waveform a 50% duty cycle.
13.6 Sawtooth Waveforms
Sawtoothed waveforms can have a mirror image of themselves, by having either a slow-rising but extremely
steep decay, or an extremely steep almost vertical rise and a slow-decay. The positive ramp sawtooth waveform
is the more common of the two waveform types with the ramp portion of the wave being almost perfectly
linear. The sawtooth waveform is commonly available from most function generators and consists of a
fundamental frequency (ƒ) and all its integer ratios of even harmonics only, 1/2, 1/4, 1/6 1/8 … 1/n, etc.
14 Resistive (R), Capacitive (C) and Inductive (L) circuits
14.1 Series AC Circuits
There is no such thing as a ‘pure’ resistance, a ‘pure’ inductance or a ‘pure’ capacitance. A wire wound resistor,
for instance, since it is wound in the form of a coil, has inductance as well as resistance. Similarly, a capacitor
has resistance as well as capacitance.
14.1.1 Pure Resistance in AC Circuits
Ohm's law and the use of RMS values apply at all times to a purely resistive circuit.
14.1.1.1
Power
The power is the average value of all the instantaneous values of power for a complete cycle. To find the
instantaneous power at any moment, the instantaneous values of voltage and current at that moment are
multiplied together. The power is always positive because current and voltage are in-phase. The average
power over a complete cycle is the average value of the power curve and this is represented by a line
halfway between maximum and minimum values of the curve. The power waveform has twice the
frequency of the supply. The power will fluctuates between zero and 12 watts (12 W), but over a complete
cycle, the average power is 6 W. The average power from now on will be referred to as ‘power’. It is half the
peak power in a resistive circuit, and this peak value is the maximum voltage multiplied by the maximum
current. The average power from now on will be referred to as ‘power’. It is half the peak power in a
resistive circuit, and this peak value is the maximum voltage multiplied by the maximum current.
To sum up, in a resistive circuit:
1) V and I are in-phase.
2) Normal Ohm's law calculations apply.
3) DC calculations apply for power.
4) Power is produced.
14.1.2 Pure Inductance in AC Circuits
When an AC supply is connected to an inductance (a coil), a back emf is induced into the circuit. This is
caused by the continuously varying current causing lines of flux to cut the turns of the coil. The inductance
value is dependent on the value of the inductor in henrys (H) and the rate of change of current.
The back emf in the circuit provides the opposition to current flow. It, therefore, acts in a similar manner to
a resistance in the circuit. It is a form of AC resistance but is called reactance. It is measured in ohms and
has the symbol XL to identify it as reactance in an inductive circuit.
14.1.2.1
Power
This is similar to the process carried out in a pure resistive circuit where V and I are multiplied at each point
to give a power curve. As the voltage and current are 90° out of phase, positive power and negative power
are produced. In the purely inductive circuit, the total power is zero, since positive power and negative
power cancel. Positive power is given to the circuit from the power supply in the one half cycle and negative
power is returned to the supply source in the other half of the power cycle. Over a complete cycle, the net
power is zero. It is important to note that current flows in the circuit but no work is being done when the
current is 90° out of phase with the voltage.
In an inductive circuit:
1. I lags V by 90˚or V leads I by 90˚.
2. Opposition to current flow is inductive reactance (XL).
XL = 2πfL ohms, XL = V/I ohms
3. No power is produced in a purely inductive circuit.
14.1.3 Pure Capacitance in AC Circuits
When a capacitor (C) in a circuit is supplied with an AC supply. Voltage exists across the plates of the
capacitor only after the current has flowed to charge the plates. And when looking to the graph, it can be
seen that the current leads the voltage and, in a pure capacitive circuit, by 90°. A capacitor opposes any
change in the value of voltage applied to it and so presents an opposition to current at all times. This
opposition is called capacitive reactance (XC) and is measured in ohms.
14.1.3.1
Power
To sum up, in a capacitive circuit:
1. I leads V by 90˚or V lags I by 90˚.
2. Opposition to current flow is capacitive reactance.
3.
4.
5. No power is produced in a purely capacitive circuit.
14.1.4 Inductance and Resistance in Series
The voltage (VR) and current are in phase for the resistance. However, for the inductance, the current lags
the voltage (VL) by 90°. This inductance causes the current to lag the overall voltage (V) by less than 90°.
14.1.4.1
Impedance
The opposition to current flow in this circuit is provided by the resistance of the resistor and the reactance
of the inductor and when there is a combination like this, the opposition to current flow is called impedance
(Z) in ohms. The opposition to current flow is therefore: Z=V/I ohms.
14.1.5 Capacitance and Resistance in Series
The opposition to current flow provided by the capacitive reactance (Xc) and resistance (R) is called
impedance (Z) and measured in ohms. The waveform diagram in the below figure shows the voltage and
current are out of phase by less than 90˚with current leading the voltage. The word CIVIL can be used as a
convenient way to remember the relative position of the phases between current and voltage in capacitive
and inductive circuits.
14.1.6 Resistance, Inductance and Capacitance in Series
14.1.6.1
Series Resonance
If we have a series circuit consisting of R, L, and C, and we can vary the frequency supply to the circuit, then
we can vary its properties. As the frequency rises, the inductive reactance XL rises, but the capacitive
reactance XC falls. At one particular frequency XL = XC, resonance occurs. The frequency at which this
happens is called the resonant frequency (fo). If XL = XC, they are 180˚apart (anti-phase), so they will cancel
leaving just the resistance of the circuit, so Z = R. If Z = R, then the impedance is at a minimum and
therefore the current will be at a maximum.
Also as VL and VC are anti-phase, they also cancel each other so the applied voltage will equal the voltage
across the resistor VR = V. Current will be in-phase with the supply voltage and the power factor is 1.
At resonance (f0), the current is high and voltages across L and C are equal and opposite so that their
resultant is zero.
14.1.6.2
Selectivity (Q)
The ability to respond to only a small range of frequencies over a wide range of frequencies near resonance
gives an indication of the selectivity of the circuit. Selectivity is the property of a tuned circuit which enables
it to respond to a particular signal and disregard others at different but close frequencies.
The selectivity of the series circuit depends on:
1. Resistance (high R).
As I = V/R at resonance, if R is doubled, then the current is halved and the curve ‘flattens’, thus out reducing
selectivity.
2. The ratio of L to C (L/C)
As 𝑓0 =
1
2𝜋√𝐿𝐶
𝑄0 =
1 𝐿
√
𝑅 𝐶
14.1.6.3
Q and Bandwidth
Series tuned circuits are used in radio receivers/transmitters to accept inputs at the resonant frequency and
in the immediate neighbourhood of resonance. In order to present a high impedance to inputs far removed
from resonance, the circuit must have a high Q value or a narrow bandwidth. The bandwidth of a circuit is
the separation between two frequencies either side of resonance at which the output current has fallen to
0.707 (1/√2 ) of the maximum value. So, for good selectivity, we require:
a) Low R.
b) High L C ratio.
c) High Qo
d) Narrow bandwidth.
14.2
Parallel AC Circuits
14.2.1 Resistance/ Inductance and Capacitance in Parallel
The current in the capacitor (IC) leads voltage by 90° and the current in the inductive circuit lags by some
angle less than 90° due to the resistance. The total current from the supply is the phasor addition of IC and
IL. If the frequency to this circuit was varied, then at one particular frequency (XL = XC) the current taken
from the supply is in-phase with the voltage.
14.2.1.1
Parallel Resonance
What is happening in the circuit is that the capacitor is charging up and then discharging through the
inductor. The emf induced in the inductor will then charge up the capacitor in the reverse direction and this
will continue to circulate a current between the two components. The circuit is said to be at resonance, so
we are now looking at a parallel resonant circuit. At resonance, the current drawn from the supply is small
and therefore the impedance is high. It should be noted that the actual current circulating between the
inductor and capacitor is high.
14.2.1.2
So:
Q Factor


In a parallel resonant circuit, current magnification takes place.
Selectivity in a series resonant circuit is the ability of the circuit to respond strongly to the required
signal at the resonant frequency and give a poor response to other signals. The steepness of the
slope of the resonance curves for the parallel circuit indicates the degree of selectivity.
14.3 Use of Resonant Circuits
Used in radio circuits and one of the main factors determining its use is the internal impedance of the supply.
Selectivity is best for a series circuit when the supply source internal impedance is the same as or lower than
the impedance at resonance. Similarly the parallel circuit has better selectivity when the supply source is the
same as or higher than its impedance (ZD) at resonance. So, if a source has a high internal impedance, a parallel
resonant circuit is used and if the source has a low internal impedance, a series resonant circuit is used. The first
tuned circuit is normally a series tuned circuit because it is fed from a low impedance source (the aerial).
Voltage magnification takes place where it is fed to an amplifier. The ‘load’ for the amplifier stages would be a
parallel tuned circuit because it is being fed from a high impedance source (transistor). Resonant circuits are
also used for control of rotary invertor outputs and some older aircraft generator frequency control circuits.
14.4 Power in AC Circuits
The component in-phase with the voltage is known as the active or real component and the component at 90˚to
the voltage is known as the quadrature or reactive component. The power in a purely resistive AC circuit is
found by multiplying together the RMS voltage and current. The component of the current that does no work in
the system still flows through the system and produces power which as we know cancels over one cycle, so no
net power is produced. The unit of reactive power is volt amps reactive (VAR). If the supply voltage is multiplied
by the current (I), then this will give us the apparent power being dissipated.
14.4.1 Power Factor
The ratio of True Power to Apparent Power is called the Power Factor.
15 Transformer
15.1 Introduction
A transformer can be defined as an electrical device by means of which electric power in one circuit is
transformed into electric power of the same frequency in another circuit. It can either raise or lower the voltage
while transforming. This however, is accompanied by a corresponding decrease or increase in current.
A transformer consists of two coils adjacent to each other and an AC supply is applied to one coil known as the
primary. The other coil is known as the secondary. The changing AC current in the primary creates a fluctuating
magnetic field that cuts the coils of the secondary coil and induces a voltage in it. This is called mutual
inductance. If the secondary is connected to a load, a secondary (AC) current flows and power is developed in
the load. A transformer does not generate power, it merely transfers power from the primary circuit to the
secondary and increases or reduces the voltage.
15.1.1 Turns Ratio
If the number of primary and secondary coils are identical, assuming no losses, and the secondary coil is an
open circuit, the emf induced in the secondary coil will be almost equal to, but opposite in phase, to the
applied voltage in the primary coil. This secondary coil will produce a mutually induced voltage which is
exactly the same as the primary back emf. If the number of turns on the secondary is increased, its
inductance increases, and hence the induced emf (voltage) increases. Secondary voltage (VS) is T times the
primary voltage (VP) where T is the turns ratio: VS = T x VP
15.1.2 Transformation Ratio
The ratio of Vs to Vp (or Ns to Np) is known as the transformation ratio. If Vs is smaller than Vp, then the
output will be less than the input and the transformer is called a step-down transformer. A step-up
transformer is one in which Vs is greater than Vp. A transformation ratio of 4:1 means that the output
voltage will be four times the input voltage (step-up) and a transformation ratio of 1:3 means that the
output voltage will be one-third the input voltage (step-down).
15.1.3 Transformer Losses
Losses may be due to iron losses and copper losses. Iron losses are due to two causes, eddy currents and
hysteresis. The resistive losses in the wires are called copper losses. If all the primary flux does not link with
the secondary, then flux leakage occurs. This may be reduced by the design of the core.
15.1.4 Transformer on No-Load
The primary (P) has a 100 V AC supply and it’s secondary is open-circuited (no load) with a turns ratio of 2:1.
The current that flows in the primary will cause an alternating flux in the core which will induce a voltage of
200 V AC in the secondary winding. The primary alternating flux will also induce a back emf into the primary
winding in opposition to the applied emf. The effective emf acting on the primary is therefore very small
and only a very small current will flow into the primary winding.
15.1.5 Transformer On-Load
If the secondary is now carrying current, then it is important to note that this current provides a flux in the
core which opposes the primary flux and so reduces the total flux in the core. This means that the primary
back emf is reduced, with a consequent increase in effective emf in the primary and hence an increase in
primary current.
15.1.6 Transformer Connections
A transformer with three secondary windings each having a different number of turns and each producing a
different output voltage depending on the turns ratio.
15.1.7 Phasing Dots
A transformer with three secondary windings. The dots at the ends of the windings are called phasing dots.
They show that the polarity at those points will be the same at the same moment in time. The centre
winding is therefore of opposite polarity to the other two secondary windings.
15.2
Transformer Efficiency
Iron losses are reasonably constant, but copper losses vary as the square of the currents flowing. Efficiency is
greatest when copper losses are equal to iron losses.
15.2.1 Regulation
As more current is drawn from the secondary of a transformer, the terminal voltage falls as copper losses
increase. The difference between the secondary voltage at no load and the secondary voltage at full load is
expressed as a percentage and is known as the regulation of the transformer. Typically, this is 1 to 2%.
15.3 Transformer Types
May be classified as single phase or multi-phase.
15.3.1 Single-Phase Transformers
15.3.1.1
Low Frequency Transformers
These are usually used within the AF (audio frequency) range. The core or former of a transformer on which
the coils are wound is invariably one of two types, the core type, or the shell type. The coils forming the
primary winding and the secondary winding(s) are wound so as to be in the closest proximity to each other
in order to achieve the maximum flux linkage (low flux leakage). It should be noted, that AF transformers
can be used as ‘matching’ impedances. They may also be used as isolation transformers, isolating
electrically one circuit from another without altering the AC parameters.
15.3.1.2
High Frequency Transformers
Radio frequency (RF) transformers are used in radio transmitters and receivers and are designed to work at
frequencies from 100 kHz to 100 MHz. RF transformers do not have iron cores because iron losses would be
high at such high frequencies. They are inefficient for power transfer and secondary voltage is not equal to T
(turns ratio) times the primary voltage. RF transformers often have iron dust (ferrite) cores which are used
to adjust the coil inductance or modify the coupling effect between the two coils.
15.3.1.3
Auto Transformers
This is a special type of transformer that has only a single winding which serves as both the primary and the
secondary. It may be used either as a step-up or step-down transformer. Auto transformers are found in
aircraft lighting circuits.
15.3.1.4
Quadrature Transformer or Mutual Reactor
A device was required that gave a phase angle of 90° between the current in one circuit and a signal being
put into another circuit. The angle between the primary current in a quadrature transformer and its
secondary voltage is 90°.
15.3.1.5
Current Transformer
The current transformer is designed to enable circuit currents to be measured without breaking into the
circuit, as is necessary with an ammeter or its shunt. The output of the current transformer may be applied
directly to a moving coil instrument, transduced into a digital signal for use in a computer or may be used to
control other circuits. It works on the principle of mutual inductance but its construction and mode of
operation are different to that of the voltage transformer. It has a step-up turns-ratio with the primary being
the load’s supply cable. The secondary winding (many turns of fine wire) is wound on a non-laminated
toroidal core of silicon iron.
15.3.1.5.1 Operation
When the load passes through the supply cable, it creates a magnetic field along its whole length which
is constantly building-up, collapsing, reversing, building up, etc. The varying flux thus creates and
induces emfs into the coils of the secondary winding. The primary, which depends on the load, may
therefore be regarded as a constant current/constant flux supply. The voltage in the secondary winding
causes a current to flow through its load and through the secondary winding. This produces a secondary
flux, which opposes the primary flux and so keeps the core flux to a very low level.
15.3.1.6
Impedance Matching Transformers
In any circuit impedance Z = V/I. Therefore, in a transformer, the impedance ZS of the secondary is the ratio
of secondary voltage to secondary current and the impedance ZP of the primary is the ratio of the primary
voltage to the primary current. The primary and secondary voltages and currents are related to each other
by the turn’s ratio of the transformer. Maximum power is transferred from a source of supply to a load
circuit only when the load impedance is equal to the internal impedance of the source of supply.
15.3.2 Three-phase Transformers
A three-phase transformer is effectively three interconnected single phase transformers with their windings
combined on a single magnetic circuit. The most common method of construction is the core type.
There are four combinations for three-phase transformers:
 Star-star
 Delta-delta
 Delta-star
 Star-delta
Calculations for star-star transformers are the same as for single-phase transformers except for power.
There is no phase shift between input and output. For delta-delta transformers single-phase calculations
apply except for power. Again there is no phase shift between input and output.
The star-delta transformer has a √3:1 step-down ratio in addition to the effect of the turns ratio. The deltastar transformer has a 1: √3 step-up ratio of line voltage in addition to the effect of the turn’s ratio.
16 Filters
16.1 Introduction
A component which is designed to block certain frequencies and pass others is called a filter. Filters can include:
 Low-pass filters
 High-pass filters
 Band-pass filters, and
 Band-stop filters
16.2 Low-Pass filters
A filter which passes all frequencies from zero up to some value and blocks all those above this value is known
as a low-pass filter. The simple form of the filter is made up of inductors and capacitors.
16.3 High-pass filters
This is the opposite to the low-pass filter and attenuates all frequencies up to the cut-off frequency and passes
all frequencies above this value. It is called a high-pass filter. This filter requires components that allows current
flow at high frequencies but also act as an open circuit at low frequencies. This can be achieved by a capacitor
in series with an inductor.
16.4 Band-pass filters
A filter that passes all frequency components between some low cut-off frequency fC1, and some high cut-off
frequency fC2 and blocks all frequencies below fC1 and above fC2. This is called a band-pass filter. It acts like a
capacitance at low frequencies and inductance at high frequencies.
16.5 Band-stop filters
This is a filter that stops the transmission of frequencies between fC1 and fC2. At lower frequencies, the series
resonant circuit impedance is high and the parallel resonant circuit impedance is low. Around the resonant
frequencies, the parallel circuit impedance is high and the series is low. Therefore frequencies are blocked in
this range. As the frequency increases, the parallel circuit impedance falls and the series circuit increases, so
frequencies are passed again.
16.6 Applications
Applications of filters in aircraft include:
 Communication transceivers.
 Radio, marker beacon, and instrument landing system (ILS) receivers.
 Engine vibration monitoring systems.
 Automatic flight control systems (AFCS).
 Flight director systems (FDS).
 Voice recorders.
16.7 Differentiators
These consist of a resistor and an inductor, and/or a capacitor arranged so that the circuit output waveform
represents the rate of change of the input waveform. They are used to:
 Detect sudden changes in an otherwise steady waveform.
 Provide feed-back signals in servo-mechanisms and in
 Autopilot and flight path computation systems.
 Modify waveforms in pulse circuitry.
The output is therefore proportional to how fast the input voltage changes, i.e. it is sensitive to the rate of
change of the input voltage.
16.8 Integrators
These produce a voltage output which is proportional to the product of input voltage (V) and time (T). In
general terms, VO = VI x T. Also used in autopilot and flight path computation systems.
17 AC Generators
17.1 Introduction
In AC generators, the rotating part of the generator is called the rotor and the stationary part is called the stator.
There are three basic types of AC generators:
 Permanent magnet generators.
 Rotating armature generators.
 Rotating field generators.
17.1.1 Permanent magnet type
The rotor of permanent magnet type AC generator is a permanent magnet and as the magnet is rotated, its
magnetic field cuts the stationary output windings producing an alternating voltage output. This principle
(or variations of it) is used in most brushless AC generators. These generators are common to many large
aircraft.
17.1.2 Rotating Armature Type
Rotating armature type AC generator is similar in construction to a DC generator in that the rotor rotates in
a fixed field with the emf picked off via slip rings. One voltage cycle is induced into the external circuit when
the armature windings move through 360° past one pair of poles. If there are two pairs of poles, then two
cycles of AC will be produced per revolution. The number of cycles of induced voltage per revolution of an
actual generator will correspond to the number of pairs of poles in the generator and is called the
frequency (f).
17.1.3 Rotating filed type
In a rotating field type generator, the DC field rotates and its’ field cuts the stationary output windings on
the stator. The output windings consist of a number of coils connected in series. If another set of singlephase windings at 90° to the first are added, then a two-phase output is produced (phases A and B) one
being 90° out-of-phase with the other.
The first AC generating systems on aircraft used rotating field AC generators in what was called a ‘frequency
wild’ system. The three-phase output was controlled and converted to DC and fed to the aircraft bus bar
(from which all DC services take their supplies). The generator output voltage was controlled to 200 V, but
the frequency varied with engine speed. Low engine RPM produced low frequency AC, and high engine
RPM produced a higher frequency. This frequency wild AC was fed to resistive loads only, such as heater
mats, where the variable frequency has no effect. Most AC generators are now driven at constant speed
irrespective of engine RPM.
The output of AC generators on most large aircraft today is three-phase 200/115 V 400 Hz (400 cycles). The
200 V or 115 V supply will depend on how the load is connected to the generator.
17.1.4 Connection of Phases
Each phase of a three-phase generator can be brought out to separate terminals and used to supply
separate loads independently, which will require six leads. This shows that one end of each of the three
windings is connected to one point and a cable is taken from that point to a busbar on the aircraft. This
configuration is called a 'star connection' and the point where they meet is called the star point, and the
cable taken from the star point is called the neutral.
The star connection shows that line current = the phase current.
The main advantage of the star connection is that with the neutral line we are able to provide two voltages,
200 V and 115 V. Most aircraft AC generators are connected in star.
Another form of connection of the three coils would be to connect them in Delta connection. In this case,
the three windings are connected in series to form a closed mesh, with the three output lines at the
junction points. The delta connection does not have a neutral and cannot provide two outputs and must be
connected to a balanced load, but does give a higher current output than a star connected system.
17.1.5 The Brushless Generator
In general, this generator unit consists of a permanent magnet generator, a rotating armature and rotating
field generators.
When the generator drive shaft (rotor) is turned (by the engine), the permanent magnet in the permanent
magnet generator end rotates and its field cuts the windings on the stator (3 stationary coils) and induces
an AC current into them. This is fed externally to the voltage regulator in the GCU to rectify it to a DC supply
for the stationary field winding in the generator. The GCU is the ‘brains’ of the system.
As the magnetic field of this winding is cut by the 3 rotating coils of the rotating assembly, a three-phase AC
output is generated. This AC is fed through the three-phase full wave rectifier bridge (also rotating) to
provide DC to the main generator field coil. This rotating field cuts the star connected stator windings to
produce a three-phase 200/115 V 400 Hz output to the aircraft system bus bars.
17.2 Three-phase supplies
The three-phase generator (star wound, which is most common) has three single-phase cables supplying 115 V
to each of three separate busbars. For services requiring a single-phase such as a lamp or a pitot head heater, a
single line is connected from one bus. Each bus will have its fair share of single-phase loads. The Transformer
Rectifier Unit (TRU) is connected to all three phases to produce 28 V DC - not because it needs the power, but
three-phase rectification produces a smoother DC output than single-phase rectification.
17.2.1 Power in a Three-phase system
18 AC Motors
18.1 Introduction
The main types of AC motors are:
 Induction (single-phase, two-phase and three-phase).
 Synchronous.
 Hysteresis.
 Shaded Pole.
18.2 Production of a Rotating Field from a Three-phase AC Supply
At any instant, the three magnetic fields will be 120° out-of-phase with each other and the resultant magnetic
field will be the vector sum of the three.
18.3 Induction Motors
18.3.1 The Three-phase Motor
Three-phase motor is the most common type of AC motor used on aircraft. The stator is responsible for the
production of a rotating magnetic field. The rotor consists of a series of copper or aluminium bars
connected at each end by a copper or brass ring. No insulation is required between the bars and the core on
which they are mounted because of the very low voltages generated into the rotor bars. Note that no
brushes or slip rings are involved and there are no external connections made to it. This type of rotor is
sometimes called a ‘squirrel cage’ rotor. The ratio of the slip speed to the rotating magnetic field speed is
known as slip and is normally given as a percentage. The starting torque of induction motors is low. On
start, the frequency is at its maximum in the rotor and the rotor has low resistance but high inductance.
This causes the rotor current to lag the induced emf by almost 90° so interaction between the rotor field
and the rotating field is poor. To improve the starting torque, it is necessary to bring rotor current and the
emf more into phase. This can be achieved by using aluminium bars on the rotor instead of copper bars.
18.3.2 Two-phase Type
In two-phase type motor, the windings are 90° displaced from one another. The rotor is of the normal
induction motor type. A rotating field can be produced if the supplies to the two phases are 90° out-ofphase with each other. The production of a two-phase rotating magnetic field is similar to the production of
a rotating field from a three-phase supply. The speed of the motor depends on the input frequency. These
motors are used extensively as servo-motors in instrument systems and other systems on aircraft.
18.3.3 The Split-phase Motor
To create a rotating field from a single-phase supply is not possible unless we modify the supply somehow.
If two windings are used and one produces a field out-of-phase from the other, then a rotating field can be
produced. To achieve this, we have to ‘split the phase’, i.e., split the single-phase supply into two currents
which are out-of-phase with each other.
Splitting can be achieved by placing a resistance in series with one winding, which would make it less
inductive than the other winding. It could also be achieved by placing more inductance in one winding than
the other to create an out-of-phase current. Usually a capacitor is placed across the coils. The rotor is of the
normal induction motor type. These motors are used extensively as AC actuators on aircraft.
18.4 The Synchronous Motor
The synchronous motor has the normal three-phase stator, but the rotor is basically an electromagnet with the
field windings being fed with DC via bushes and slip-rings. However the motor does have a problem in that it
will not start of its own accord (there is 100% slip on start). This is because the rotating field moves so quickly
that the rotor cannot ‘lock on’ to the field. With an input of 400 Hz from an aircraft system, it functions as a
constant speed machine and so was used to drive the earlier Flight Data Recorders (FDRs).
18.5 The Hysteresis Motor
This motor has two windings at 90° to each other and, has a ‘reference phase’ and a ‘control phase’ and is a
two-phase motor. The speed of the motor is dependent on the supply frequency. Reversal of rotation occurs by
changing the phase relationship of the control phase by 180°. These motors are used as servo motors and also
as motors in miniature rate gyros.
18.6 The Shaded Pole Motor
Each of the poles is split into two with one half fitted with a copper or aluminium ring (shading). The rotor is of
the normal induction motor design. They are used in some engine pressure indication instruments.