Download Circuit Components Lesson 4

Representation, Education, Infrastructure, Service
Radio Amateurs of Canada (RAC): Speaking on behalf of Canadian
Radio Amateurs, RAC provides liaison with government agencies and
carries the Amateur voice about regulatory and spectrum issues to the
discussion table with government and industry leaders, nationally and
internationally.
The Winnipeg Amateur Radio Club
(WARC): is your local RAC affiliated club.
From Bruxelles in the west to Falcon Lake in the east and Gimli in
the north to Morris in the south the Manitoba Repeater Society
(MRS) maintains a linked FM repeater system. By offering mutual
linking arrangements with the Brandon Amateur Radio Club (BARC),
and the Lake of the Woods Amateur Radio Society’s Pine Tree
system, coverage is extended to Brandon and to Dryden, Ontario.
Winnipeg Amateur Radio Emergency Service (WARES): to assist
the civil authorities with emergency communications in times of
disaster and when existing communications are inadequate; and to
train and educate licensed amateur radio operators in emergency
communications technique and organization.
1
Section 005 - Basic Electronics and Theory
*only 13 exam questions (roughly 130 questions in the exam bank)
1000 Question Exam Bank
Study Guide
Refer to the Section 5 (B-005) Questions in the Exam Bank (page 66
/112) and read the following Coax Publications Study Guide sections
• Chapter 2: Basic Electrical Theory
• Chapter 3: Ohm’s Law and Power
• Chapter 4: Inductors, Capacitors, Transformers
• Chapter (5.1-5.5): Waves, Period, Frequency (audio and radio),
Wavelength, and Harmonics
The study guide certainly has more information than is covered by the
exam questions.
RIC-7: Section B-005 = 13 Exam Questions
(One question on each of the following topics.)
•
•
•
•
•
•
•
•
•
•
•
•
•
B-005-001: Unit Conversions
B-005-002: Resistors, Conductors, Insulators, Resistance, Conductance
B-005-003: Electrical Power
B-005-004: Ohm’s Law
B-005-005: Resistors in Series and in Parallel
B-005-006: Power Dissipation using Resistors
http://shsballoonproject.
pbworks.com/w/page/70
B-005-007: Frequency and Wavelength
013917/SHARP%20Am
B-005-008: Decibels (dB), Power and RST reports
ateur%20Radio
B-005-009: Capacitors and Inductors
B-005-010: Reactance and Impedance
B-005-011: Transformers
B-005-012: Resonance and Tuned Circuits
B-005-013: Voltmeters, Ammeters, Multimeters
3
Common Radio Quantities and Their Symbols
Quantity
Quantity Symbol
electromotive force
E
volt
V
current
I
amp or ampere
A
resistance
R
ohm
W
power
P
watt
W
capacitance
C
farad
F
inductance
L
henry
H
impedance
Z
ohm
W
frequency
f
hertz
Hz
reactance
X
ohm
W
wavelength
l
wavelength
m
B-005-001
Unit
Base Unit Symbol
4
Metric Unit Conversions
1 Giga (G) = 1 billion = 1,000,000,000 = 109
1 Mega (M) = 1 million = 1,000,000 = 106
1 kilo (k) = 1 thousand = 1,000 = 103
1 centi (c) = 1 one-hundredth = 0.01 = 10-2
1 milli (m) = 1 one-thousandth = 0.001 = 10-3
1 micro (m) = 1 one-millionth = 0.000001 = 10-6
1 nano (n) = 1 one-billionth = 0.000000001 = 10-9
1 pico (p) = 1 one-trillionth = 0.000000000001 = 10-12
Unit Conversion Aide for Moving the Decimal
B-005-001
5
Metric Conversion Practice
14550 kHz = ________ MHz
155 mA = ________ A
2280 m = ________ km
0.004 V = ________ mV
45000 kW = ________ MW
5.50 pF = ________ nF
12,900 kHz = ________ GHz
147.390 MHz = ________ Hz
(Hz = hertz)
(A = amps)
(m = metres)
(V = volts)
( W = ohms)
(F = farads)
(CFRW)
(CKY-FM)
6
B-005-001
Atoms, Electrons & Current
A piece of copper wire contains enormous numbers of copper atoms.
Each atom contains many negatively charged electrons. Some of these
electrons will move along the wire when a voltage, say from a battery,
is placed across the ends of the wire. Electricity is an electron current
flowing in the wire.
-
+
An Atomic Model
B-005-002
A “conventional current, (I) is the
hypothetical flow of positive
charge from the positive terminal
of the battery to the negative
terminal; opposite in direction to
the electron current.
7
Conductor, Insulator, Voltage, Current &
Resistance
There are some materials that electricity flows through easily. These
materials are called conductors. Most conductors are metals.
Four good electrical conductors are copper, aluminum, gold and
silver.
Insulators are materials that do not let electricity flow through them.
Four good insulators are glass, air, plastic, and porcelain.
The outer jacket and dielectric in a
coaxial cable are insulators. Signal
travels along the centre conductor.
The braided shield is grounded.
Coax is a cylindrical capacitor used
for radio signal transmission.
B-005-002
8
Current, Voltage, Conductor, Insulator,
Resistance, Conductance and Current
The Water Analogy
Water flowing through a hose is a
good way to imagine electricity.
Water in a pipe is like electrons in
a wire (flowing electrons are called
current).
Pressure is the force pushing water
through a hose – voltage is the
force pushing electrons through a
wire.
Friction against the walls of the
hose slows the flow of water.
Resistance is an impediment that
slows the flow of electrons.
B-005-002
9
Ohm’s Law
(“The more the volts, the more the amps.”)
• E = electromotive force (a.k.a. voltage)
• I = current (the French term is intensity)
• R = resistance
• 𝑹=
𝑬
Resistance (R) is the ratio of
𝑰
voltage (E) applied to current (I) produced.
• Voltage: E = I x R (Volts)
𝐸
• Current: I = (Amps)
𝑅
𝐸
• Resistance: R =
(Ohms)
𝐼
B-005-004
10
Longer wires have greater resistance. Wider wires have less resistance.
Calculating Voltage and Current and
Resistance
Calculating Current (I)
There is a very easy way to determine how much current (I) will
flow through a circuit when the voltage (E) and resistance (R) is
known. This relationship is expressed in a simple equation (don't
let the word “equation” scare you... this is going to be easy as
"pie"...
Let's start with the "pie“ or actually E=IR.
This “pie” circle will help you calculate the answer to Ohm’s Law
problems. The three letters stand for...
E = electromotive force (a.k.a. voltage)
I = intensity (French term for current)
R = resistance
B-005-004
11
Electric Current Calculations
Lets say you have 200 volt source connected to a circuit with 100
ohms of resistance. How much current will flow?
Since our unknown value in this problem is the current, we put our
finger over the "I". What’s left is "E over R". This means you take
the voltage and divide it by the resistance. 200 V divided by 100 W.
The result is 2 amperes or a 2 A current.
E = voltage measured in volts (V)
R = resistance measured in ohms (W)
I = current measured in amps (A)
[Units such as these with capitalized symbols are named after
scientists. Alessandro Volta, Georg Ohm and André Ampère].
B-005-004
12
Calculating Voltage
What if you needed to find out the voltage in a circuit when we
know the current and resistance? Go back to the "pie" and cover up
the E. You're now left with I times R.
What voltage is needed across a 50 ohm circuit to make a 2 amp
current?
E = I R so E = 2A (50W) so E = 100 V
E = electric potential or voltage in volts (V)
I = electric current in amps (A)
R = electrical resistance in ohms (W)
B-005-004
13
Calculating Resistance
Finally, if you had a circuit with 9V and 300 mA (milliamps) and you
needed to find the resistance, you could cover up the R... the result is
E over I (voltage divided by current). R = E/I... R = 9V/0.3A. R = 30 W.
This circuit would have 30 ohms of resistance if it was hooked up to
90 volts and 3 amps flowed through the circuit. Note that you need
to be working in base units so the milliamps had to be converted to
amps first.
Ohm's Law
This relationship between voltage, current, and resistance is known as
Ohm's Law. This is in honour George Ohm who discovered this direct
relationship (his last name was Ohm). Note Ohm’s law is only valid for a
constant temperature. For most things, resistance tends to increase with
temperature increase. The relationship described in Ohm's Law is used
when working with almost any electronic circuit.
B-005-004
14
Ohm’s Law and A.C. Circuits
The familiar Ohm's Law pie or triangle used for DC circuits can only be
used with alternating current circuits or AC if the load is purely
resistive. Most AC circuits contain series or parallel combinations of
resistance, capacitance and inductance. This leads to the voltage and
current being out of phase and the load becomes complex. In purely
capacitive circuits the current waveform leads the voltage waveform,
whereas in inductive circuits the voltage will lead the current. Circuits
containing both inductors and capacitors, the voltage and current
waveform will not be in phase except at resonance. The general term
for AC resistance is impedance and given the symbol Z. The
impedance triangle is shown below.
More on A.C. later.
Generating A.C.
15
Resistance & Conductance
The resistance of a conductor is a measure of the difficulty to pass an
electric current. The inverse quantity is called conductance, the ease
with which an electric current passes. The unit of resistance is the ohm
1
(Ω), while electrical conductance is measured in reciprocal ohms (W) or
siemens (S).
All materials show some resistance, (except for superconductors, which
have zero resistance and infinite conductance). Copper and aluminum are
the most common conductors used in wiring.
The resistance (R) of a material is defined as the ratio of voltage across it
(V) to current through it (I), while the conductance (G) is the reciprocal so
𝑅=
𝑉
𝐼
and 𝐺 =
𝐼
𝑉
A resistance of 10 W is equal to a conductance of 1/10W or 0.1 S.
B-005-002
16
Electric Current ( I )
There are 2 types of current:
Direct Current (DC)
 Flows in only one direction. Electrons flow from negative toward
positive but conventional current (I) represented as positive to
negative pole of source.
Alternating Current (AC)
 Flows back and forth because the poles of the source as the
poles alternate between positive and negative.
B-005-002
17
Electric Energy & Power, Open & Short
Circuits
An Open Circuit
No current will leave the source or flow
anywhere because there is break in the circuit. A
good example is a light switch. When the switch
is off, the circuit is “open”. Closing the switch
turns the circuit and light on. Fuses and circuit
breakers are devices that will open the circuit if
too much current flows.
B-005-003
18
The Short Circuit
A short circuit can be caused by
incoming power wires coming in
contact with each other. Since a
circuit has resistance, and the power
wires that "short out" have very
little resistance, the current will
tend to flow through the path of
least resistance... the short.
Less resistance at the same amount of voltage will result in more
current to flow. Fuses and circuit breakers
near the source of electrical power can
prevent this. Broken insulation on a
wire can cause a hazardous short circuit.
B-005-003
19
Electrical Power
Circuits convert the energy of the flowing
electrons into more useful forms of
energy such as heat, light, radio waves or
motion. Power is the rate at which
electrical energy is converted.
When you switch on a light bulb, heat and light energy are released. This
is because of the resistance of the light bulb filament. The resistance of
the tungsten filament turns the electrical energy into heat and light.
Each light bulb has a certain power rating. This is how much energy the
bulb will use in a normal 110 volt house circuit. The most popular power
value for an incandescent light bulb is 60 watts. Power is measured in
watts. One watt represents 1 joule of energy converted per second. A 60
W bulb converts 60 J of electrical energy into heat and light energy each
second.
B-005-003
20
Electric Power Calculations
• Power is the rate at which energy is converted from one form into
another form e.g. from electrical energy into heat.
• The unit of power is the watt (W). One watt is equal to 1 joule of
energy converted per second.
• The power equation(s): 𝑃 = 𝐼𝐸, 𝑃 =
𝐼 2 𝑅, 𝑃
=
𝑉2
𝑅
B-005-003 A hydrometer measures the electrical energy converted by the home owner.
21
Electrical Power
Power calculations (continued)
 How much electrical power is dissipated as heat when a current
of 10 amps passes through a resistor if the voltage drop is 13.8
volts.
 P = I x E P = 10 A x 13.8 V = 138 W
B-005-006
 How much power is used by a 120 volt circuit when the current
is 2.5 amperes.
 P = I x E P = 2.5 A x 120 V = 300 watts
22
More Power Calculations (P = IE)
• You can determine the electrical power utilized by your
transceiver when you are transmitting by measuring the DC
voltage at the transceiver and multiplying by the current drawn
when you transmit.
• How many amps flow in a circuit when the applied voltage is
120 volts DC and the load is 1200 watts.
• I = P/E I = 1200/120 = 10 amperes
B-005-006
23
More Power Calculations
Power refers to the rate at which electrical energy is converted to heat or radio energy.
Power Formula P= I x E
Lets try some examples we are familiar with;
P = 60 watt light bulb
E = 120 volts
I = 0.5 amps
P = 100 watt light bulb
E = 120 volts
I = 0.83 amps
Electric Kettle consumes
P = 900 watts
E = 120 volts
I = 7.5 amps
Power: P = I x E (Watts)
Current: I = P / E (Amps)
Voltage: E = P/ I (Volts)
P = Power
E = Electromotive Force aka Volts
I = Current
Electric Toaster
P = 1200 watts
E =120 volts
I =10 amps
24
B-005-006
Series & Parallel Resistors
Resistors in Series
A series circuit is a circuit in which resistors are arranged in a chain,
so the current has only one path to take. The current is the same
through each resistor. The total resistance of the circuit is found by
simply adding up the resistance values of the individual resistors:
equivalent resistance of resistors in series : RS = R1 + R2 + R3 + ...
B-005-005
25
Resistors in Series
For Resistances in Series RS = R1 + R2 + R3 + ...
R1 = 100 W
R2 = 150 W
R3 = 370 W
RS = _________ ohms
A large resistor can dissipate heat energy faster
than a small one and has a larger power rating.
Resistors are often used to reduce potentially
damaging currents.
B-005-005
26
Resistors in Series
Add Resistances
A series circuit is shown in the diagram above. The current flows
through each resistor in turn. If the values of the three resistors are:
With a 10V battery connected, by E = I R, the total current in the
circuit is:
I = V / R = 10 / 20 = 0.5 A.
The current through each resistor would be 0.5 A.
B-005-005
27
Resistors in Series
Series Resistance Calculation
RS = R1 + R2 + R3 + ...
R1 = 100 W
R2 = 150 W
R3 = 370 W
RS = 620 W
(more than the most)
Compare the parallel circuit (left) and the series circuit.
B-005-005
28
Resistors in Parallel
Parallel Resistances (finding the reciprocal of the sum of the reciprocals)
A parallel circuit is a circuit in which the resistors are arranged with their
heads connected together, and their tails connected together. The current
in a parallel circuit breaks up, with some flowing along each parallel
branch and re-combining when the branches meet again. The voltage
across each resistor or parallel branch is the same.
The total resistance of a set of resistors in parallel is found by adding up
the reciprocals of the resistance values, and then taking the reciprocal of
the total.
equivalent resistance in parallel: 1/RP = 1/R1 + 1/R2 + 1 /R3 + ...
B-005-005
29
Calculating Parallel Resistance
Parallel Resistances
A parallel circuit is shown in the diagram above. The current supplied by the
battery splits up, and the amount going through each resistor depends on the
resistance. If the values of the three resistors are:
With a 10 V battery; by E = I R the total current in the circuit is: I = E/R = 10/2 =
5 A.
The individual currents can also be found using I = V / R. The voltage across
each resistor is 10 V, so:
I1 = 10 V /8 W = 1.25 A
I2 = 10 V/8 W = 1.25 A
I3=10 V/4 W = 2.5 A
Note that the currents add together to 5A, the total current.
30
B-005-005
More Resistors in Parallel
Parallel Resistors
1/RP = 1/R1 + 1/R2 + 1/R3 + ...
R1 = 300 W
R2 = 300 W
R3 = 300 W
RP = ______ ohms
B-005-005
31
Resistors in Parallel
For Parallel Resistances
1/RP = 1/R1 + 1/R2 + 1/R3 + ...
R1 = 300 W
R2 = 300 W
R3 = 300 W
1/300 + 1/300 + 1/300 =
3/300 so RP =
300/3 = 100 ohms
(less than the least)
The Circuit Diagram
B-005-005
32
Parallel Resistors
Short-cuts and Checks
If the resistors in parallel are identical, it’s easy to work out the equivalent
resistance. The equivalent resistance of N identical resistors is the
resistance of one resistor divided by N, the number of resistors. Two 40 W
resistors in parallel are equivalent to one 20 W resistor and five 50 W
resistors in parallel are equivalent to one 10 W resistor.
When calculating the equivalent resistance of a set of parallel resistors,
people often forget to flip the 1/R upside down e.g. writing the answer as
1/5 of an ohm instead of 5 ohms. Here's a check. If you have two or more
resistors in parallel, look for the one with the smallest resistance. The
equivalent resistance will always be less than the least resistance.
B-005-005
33
Series and Parallel Combined
Many circuits have a combination of series and parallel resistors. The total
resistance of a circuit like this is found by reducing the different series and
parallel combinations step-by step to end up with a single equivalent
resistance for the circuit. This allows the current to be determined easily.
The current flowing through each resistor can then be found by undoing
the reduction process.
Two (or more) resistors with their heads directly connected together and
their tails directly connected together are in parallel and they can be
reduced to one resistor using the equivalent resistance equation for
resistors in parallel.
Two resistors connected together so that the tail of one is connected
directly to the head of the next are in series and can be reduced to one
equivalent resistance.
Finally, remember that for resistors in series, the current is the same for
each resistor, and for resistors in parallel, the voltage is the same for
34
each one.
Frequency
AC, Radio Waves, Sound, Frequency & Frequency Units
The number of cycles per unit of time is called the frequency. For
convenience, frequency is most often measured in cycles per second
(cps) or the preferred hertz (Hz) (60 cps = 60 Hz), 1000 Hz is often
referred to as 1 kHz (kilohertz).
The range of human hearing in the young is approximately 20 Hz to 20
kHz—the higher number tends to decrease with age (11 kHz is my
threshold).
We call signals in the range of 20 Hz to 20,000 Hz audio frequencies
because the human ear can sense sounds in this range.
B-005-007
35
The Frequency – Wavelength Relationship
The distance a wave travels in one cycle is called wavelength ( l ).
“As frequency increases, wavelength decrease (previous diagram).”
B-005-007
Higher pitched sounds have shorter wavelengths. Higher frequency
radio waves have shorter wavelengths.
36
Frequency and Period
The time for one cycle or wavelength to pass a point in space is
called its period (T). Period is the reciprocal of frequency.
𝑓=
1
and
𝑇
𝑇=
1
.
𝑓
B-005-007-010 (from the exam question bank)
Current in an AC circuit goes through a complete cycle in 0.1
second. This means the AC has a frequency of:
A. 100 Hz
B. 1000 Hz
C. 10 Hz
D. 1 Hz
37
Names of Frequency Ranges & Types of
Waves
• Audible frequency range 20 – 20,000 Hz. (Voice
frequencies are sound waves in the range between 300
and 3000 Hz.)
• Electromagnetic waves that oscillate more than 20,000
times per second (20 kHz) as they travel through space
are generally referred to as radio waves.
sound waves are longitudinal pressure waves
B-005-007
radio waves are transverse electromagnetic waves
38
Relationship Between Frequency (f)
and Wavelength (l)
• Frequency describes number of times AC flows back and forth and
back (cycles) per second.
• Wavelength is distance a radio wave travels during one complete
cycle.
• As the frequency increases the wavelength decreases.
• The speed of the wave v or c is constant in a uniform medium.
• For EM waves; wavelength in metres equals 300 divided by
frequency in megahertz (MHz).
• A radio wave travels through space at c = 300,000,000 m/s (300
Mm/s).
𝑣 = 𝑓𝜆
B-005-007
39
Identification of Amateur Radio Bands
The property of a radio wave often used to identify the different
bands amateur radio operators use is the wavelength.
• The frequency range of the 2-metre band in Canada is 144
to 148 MHz.
• The frequency range of the 6-metre band in Canada is 50
to 54 MHz.
• The frequency range of the 70-centimetre band in Canada
is 420 to 450 MHz.
Note that the band wavelength is
approximate. E.g. 3Mm/s/2m = 1.5 MHz
B-005-005
Amateur radio band plans
40
Wave Harmonics
The lowest resonant frequency of a vibrating object is called its
fundamental frequency. Most vibrating objects have more than one
resonant frequency. Those used in musical instruments typically vibrate
at harmonics of the fundamental. A harmonic is an integer or whole
number multiple of the fundamental frequency. Harmonic frequencies
can be produced the electronic oscillator in a radio circuit converts
direct current (DC) from a power supply to an alternating current (AC)
signal.
The original wave is also called 1st harmonic, the following harmonics
are known as higher harmonics. For example, if the fundamental
frequency is 50 Hz, a common AC power supply frequency, the
frequencies of the first three higher harmonics are 100 Hz (2nd
harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any
addition of waves with these frequencies is periodic at 50 Hz.
41
Decibels (dB)
Decibels units are used to account
for the gains and losses of a signal
from a transmitter to a receiver
through some medium (e.g. air, coax
cable, fiber optics, etc.) The dB is a
logarithmic way of describing a
ratio.
In radio electronics, the decibel is
used to describe the ratio between
two measurements of electrical
power.
A 3 dB gain is a doubling of the
power. A 3 dB loss is ½ the power.
B-005-008
42
Decibels and Power / Intensity
The gains of amplifiers,
attenuation of signals, and
signal-to-noise ratios are often
expressed in decibels.
B-005-008
43
Decibels and Power Increases and Reductions
𝑃2
𝑑𝐵 = 10 𝑙𝑜𝑔 ( )
𝑃1
Remember These!
3 dB gain = 2x power
6 dB gain = 4x power
9 dB gain = 8x power
10 dB gain = 10x power
20 dB gain = 100x power
30 dB gain = 1000x power
44
B-005-008
https://www.youtube.com/watch?v=Dy7V517NfqQ
Decibels and Power Increases and Reductions
It is not necessary to do log calculations or bring a scientific calculator
to the exam (but feel free to bring a calculator if you wish).
3 Exam Bank Questions:
B-005-008-001 (B)
B-005-008-002 (D)
How can you decrease your
transmitter's power by 3 dB?
A two-times increase in power results in a
change of how many dB?
A. Divide the original power by 1.5
A. 1 dB higher
C. Divide the original power by 4
B. 3 dB higher
D. Divide the original power by 2
B. Divide the original power by 3
C. 6 dB higher
D. 12 dB higher
Remember:
2x power = 3 dB gain
4x = 6 dB gain
8x = 9 dB gain
10x = 10 dB, 100x = 20 dB, 1000x – 30 dB
(see S meter scale on next slide)
B-005-008-003 (A)
How can you increase your transmitter's
power by 6 dB?
A. Multiply the original power by 4
B. Multiply the original power by 3
C. Multiply the original power by 2
D. Multiply the original power by 1.5
45
Decibels (dB) and Power Changes
 A two-times increase in
power results in an increase
of 3 dB
Signal Strength or S Meter
 A decrease in a transmitter’s
power by one-half is a 3 dB
decrease (-3 dB).
 To increase your transmitter’s
power by 6 dB means the
power was increased by 4 (2
doublings)
 An 8 times power increase
results in +9 dB (3 doublings)
B-005-008
A radio receiver’s S meter is
shown above. The bottom units
are in dB indicating the power of
the radio signal being received 3
dB = 2x, 6 dB = 4x, 9 dB = 8x...
46
Signal Strength Reports
• A signal-strength report is “10dB over
S9”. If the transmitter power is
reduced from 1500 watts to 150 watts,
the report should now be S9 as 1/10
power = -10 dB.
• A signal-strength report is “20dB over
S9”. If the transmitter power is
reduced from 1500 watts to 150 watts
the report should now be S9 plus 10dB
“10 dB over S9”
S9 is considered very strong
signal (optimal)
• The power output from a transmitter increases from 1 watt to 2
watts. This represents an increase of 3 dB.
• The power output from a transmitter increases from 5 watts to
50 watts by a linear amplifier. The power gain would be 10 dB.
B-005-008
Actual exam bank questions - page 73.
47
Signal Strength
S stands for "Strength". When making signal strength reports,
strength is described on a scale of 1 to 9. Power levels beyond S9 at
the receiver are probably a waste. Reduce your transmitter’s power.
1. Faint signal, barely perceptible
2. Very weak
3. Weak
4. Fair
5. Fairly good
6. Good
7. Moderately strong
8. Strong
9. Very strong signals
48
Magnets
The Inductor
A Bar Magnet
The magnetic field (B)
runs from the North
Pole to the South Pole
(coils, solenoids and
toroids)
The magnetic field
is contained
within the
permeable core.
49
B-005-009
Electromagnetism
• Electric charges are surrounded by an electric field.
• A voltage across the ends of a wire produces an electric field in the
wire. The electric force field pushes the charges forward resulting in
an electric current.
• An electric current in a wire produces a magnetic field around the
wire that is perpendicular to the electric field and the current.
• An alternating current (AC) in a wire (antenna) produces an
oscillating electromagnetic wave that travels outward at the speed
of light (c = 300 000 000 m/s).
A Dipole Antenna Producing
Radiowaves
Stationary Electric Field (E)
B-005-008
Magnetic Field (B) Due to Moving
Electric Charges in a Wire
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Electromagnetic Induction
Electromagnetic induction is the production of an electromotive force
(EMF) or voltage (E) across a conductor exposed to changing magnetic
flux.
Above: Moving a conductor
perpendicular to the magnetic
field produces the greatest flux
change and greatest voltage.
No voltage is induced if the
wire moves parallel to the
field.
Above: Changing the magnetic flux through a loop or coil of wire
induces a voltage and produces an electric current (I).
Left: Changing flux in
an AC generator by coil
rotation. The AC motor
uses the reverse
process.
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Coils, Solenoids, Toroids or Inductors
There are two fundamental principles of electromagnetism:
1. Moving electrons create a magnetic field.
2. Moving or changing magnetic fields cause electrons to
move (in conductors).
An inductor is a coil of wire through which a current moves and
electrical energy is stored in the resulting magnetic field.
A voltage will be induced in
the coil by a constantly
changing magnetic flux
(Faraday’s Law of
Electromagnetic Induction). If
a battery replaces the meter,
current flows around the
inductor filling it with a
magnetic field.
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Inductor Performance With DC Currents
• When a DC current is applied to an inductor, the increasing
magnetic field opposes the current flow and the current
flow is at a minimum.
• Finally, the magnetic field is at its maximum and the current
flows to maintain the field.
• As soon as the current source is removed, the magnetic field
begins to collapse and creates a rush of current in the other
direction, sometimes at very high voltage.
• Otherwise, the inductor has no great resisting capability. It
can pass huge amounts of energy limited only by the supply
capability. An inductor in a DC system has to be used with
caution as it allows unrestricted flow of energy.
• You could say that inductors “like” DC.
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Inductor Performance With AC Currents
• When AC current is applied to an inductor, during the first half
of the cycle, the magnetic field builds as if it were a DC
current.
• During the next half of the cycle, the current is reversed and
the magnetic field first has to decrease and then reverse
polarity.
• These forces can work against each other resulting in a lower
current flow.
• You could say, inductors do not “like” AC, particularly high
frequency AC.
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Inductor Behavior
Consider the circuit shown. The coil of wire is an
inductor.
Without the inductor we would have a simple flashlight
circuit. If you close the switch, the bulb lights up. With
the inductor in the circuit, the behavior is completely
different.
The lightbulb is a resistor. The wire in the coil has much lower resistance than the
lightbulb, so what you would expect when you turn on the switch is for the bulb to glow
very dimly. Most of the current should follow the low-resistance path through the wire
loop avoiding the lightbulb. However, when you close the switch, the bulb burns
brightly and then gets dimmer. When you open the switch, the bulb burns very brightly
and then quickly goes out.
The reason for this is the inductor. When current starts flowing in the coil, a magnetic
field builds in the coil. While the field is building, the coil inhibits the flow of current
(resists change). This is called inductive reactance and is similar to resistance. Once the
field is established, current flows normally through the inductor. When the switch
opens, the magnetic field in the coil pushes current in the opposite direction until the
field collapses. This current keeps the bulb lit for a period of time even though the
switch is open. So, an inductor stores energy in its magnetic field, and an inductor
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resists a change in the current flowing through the bulb.
Inductors & Inductance
Inductance (L) refers to the capacity of a coil to develop a voltage in it
as the result of a changing magnetic flux. It is customary to use the
symbol L for inductance, in honour of the physicist Heinrich Lenz.
In the metric system, the unit
for inductance is the henry (H),
named in honor of Joseph
Henry.
The factors that determine the
inductance include the number
of loops of wire in the coil, the
diameter or area of the coil, the
length of the coil and the
permeability of the core
material.
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Inductance (L)
• The capacity or inductance (L) of an
inductor is determined by a few factors:
• NUMBER OF LOOPS, OR “TURNS”:
the more turns of wire on the coil,
the greater the inductance.
• COIL AREA: the greater the coil area,
the greater inductance.
• COIL LENGTH: the longer the length,
the less inductance.
• CORE MATERIAL: the magnetic
permeability of the core, the greater
the inductance.
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Inductors in Series and in Parallel
In Series: the combined inductance is
greater than the greatest.
In Parallel: the combined inductance is
less than the least.
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Capacitors
A capacitor is an electrical component used to store electrical energy
temporarily in an electric field. The forms of practical capacitors vary
widely, but all contain at least two electrical conductors (plates)
separated by a dielectric (i.e. an insulator that can store energy by
becoming polarized). The conductors are often thin metal films. The
nonconducting dielectric acts to increase the capacitor's charge
capacity or capacitance.
Materials commonly used as dielectrics
include ceramic, plastic and air.
Capacitors are widely used as parts of
electrical circuits.
Unlike a resistor, an ideal capacitor does
not dissipate energy. Instead, a capacitor
stores energy in the form of an
electrostatic field between its plates.
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The Capacitor
A device that stores energy in an
electric field.
•Two conductive plates separated
by a non conductive material.
•Electrons accumulate on one
plate forcing electrons away from
the other plate leaving a net
positive charge.
•Think of a capacitor as very
small, temporary storage battery.
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The Capacitor Physical Construction
Capacitors are rated by:
• Amount of charge they can
hold.
• Their voltage handling
capability.
• The insulating (dielectric)
material between plates.
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The Capacitor’s Ability to Hold a Charge
Ability of a capacitor to hold a
charge depends on:
• Conductive plate surface area.
• Space between plates.
• Material between plates.
Filling a Capacitor with Charge
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The Capacitor’s DC Behavior
• When connected to a DC source, the capacitor charges and holds
the charge as long as the DC voltage is applied.
• The capacitor essentially blocks DC current from passing through.
• You could say that capacitors do not “like” DC.
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The Capacitor’s AC Behavior
• When AC voltage is applied, during one half of the cycle the
capacitor accepts a charge in one direction.
• During the next half of the cycle, the capacitor is discharged then
recharged in the reverse direction.
• During the next half cycle the pattern reverses.
• It acts as if AC current passes through a capacitor.
• You might say, capacitors “like” AC, particularly high frequency AC.
Note that AC/DC behaviour
is opposite for inductors and
capacitors. Capactors
accept high frequency AC
while inductors do not.
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Capacitor Behavior
Consider the circuit shown here which includes a
parallel plate capacitor.
Without the capacitor branch; if you close the switch,
the bulb lights up. With the capacitor in the circuit, the
behavior is completely different.
You might be tempted to think that the capacitor represents a break in the circuit and
all the current passes through the bulb. However the capacitor charges quickly at first.
The plate connected to the negative battery terminal becomes negatively charged. The
other plate becomes positively charged. As the capacitor slowly nears its full charge, less
current can flow though that branch. More current flows through the bulb making it
brighter. So, when you close the switch, the bulb burns dimly but then gets brighter.
When you open the switch, the bulb burns very brightly and then quickly goes out as
the capacitor discharges.
When current first starts flowing in the “cap”, the capacitor builds up an electric field.
While the field is building, the capacitor increasingly inhibits the flow of current. Once
the capacitor is fully charged, no current can flow through it. When the switch opens,
the electric field in the capacitor keeps the current flowing until the field collapses. This
current keeps the bulb lit for a short period even though the switch is open. So, a
capacitor stores energy in its electric field.
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Capacitance (C)
A common form of capacitor is the parallel-plate capacitor, which
consists of two conductive plates insulated from each other, usually
sandwiching a dielectric material. The capacity or capacitance of a
capacitor, measured in Farads (F), depends on a few factors including
the area of plates, the permittivity of the dielectric material between
the plates (the dielectric constant) and the distance separating the
plates.
A 0.330 farad capacitor
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Capacitance Values
• The unit of capacitance is the farad (F).
• One farad is a huge amount of capacitance.
• Most electronic devices use capacitors that are a small
fraction of a farad.
• Common capacitance ranges are:
 micro (m) 10-6 F
 nano (n) 10-9 F
 pico, (p) 10-12 F
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Capacitors in Series & in Parallel
• In series, plates are far apart making capacitance less.
• In parallel, the surface area of the plates add up to be greater. This
makes the total capacitance higher.
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Capacitors in Series & in Parallel
• Two 10F capacitors in parallel = 20F
• Two 10F capacitors in series = 5F
10F + 10F = 20F
1/(1/10F + 1/10F) = 5F
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Capacitors or Series and Parallel
Capacitors
connected in
series (a) and
parallel (b).
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Electricity – The Water Analogy
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Inductive Reactance (XL)
Reactance (X) is the opposition of a circuit to a change in current due to
inductance (L) or capacitance (C). Just as resistance opposes the flow of
current through a resistor, inductive reactance opposes the flow of
current through an inductor.
The established magnetic field of an inductor resists the changing
voltage and current in AC circuits resulting in what is called inductive
reactance. The symbol for inductive reactance is XL. Reactance is
expressed in ohms, just like resistance.
Inductors drop voltage in proportion to the rate of change in the
current. The faster the change (higher frequency) the greater the
voltage drop and the greater the “resistance” or reactance. Therefore
reactance for an inductor is directly proportional to the frequency (f) of
the AC and the inductance of the coil (L).
𝑿𝑳 = 𝟐𝝅𝒇𝑳
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Ohm's Law for a resistor: E = IR, Ohms' Law for an inductor: EL = ILXL
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Inductive Reactance
Inductors do not behave the same as resistors. Whereas resistors
simply oppose the flow of electrons through them (by dropping a
voltage directly proportional to the current), inductors oppose
changes in current through them, by dropping a voltage directly
proportional to the rate of change of current. This induced voltage is
always of such a polarity as to try to maintain current at its present
value. That is, if current is increasing, the induced voltage will “push
against” the electron flow; if current is decreasing, the polarity will
reverse and “push with” the electron flow to oppose the decrease.
This results in a voltage that is 90° out of
phase with the current wave. For inductors
voltage leads the current by a quarter
cycle.
In a practical sense, the reactance of an
inductor dissipates a net energy of zero,
quite unlike the resistance of a resistor,
which dissipates energy in the form of heat.
Voltage leads current by 90o
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Capacitive Reactance (XC)
Reactance (X) is the opposition of a circuit to a change in current due
to inductance (L) or capacitance (C). Established electric fields and
magnetic fields resist the changing voltages and currents in AC
circuits. Reactance is measured in ohms (W).
Capacitive reactance (XC) is the opposition to the change in current
or voltage in a capacitor. Capacitive reactance is inversely
proportional to the signal frequency (f) and the capacitance, (C).
𝟏
𝑿𝑪 =
𝟐𝝅𝒇𝑪
Ohm's Law for a resistor: E = IR,
Ohms' Law for a capacitor: EC = ICXC
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Capacitive Reactance
As with the inductor, when a capacitor is connected to a circuit with an
alternating power supply, the voltage across the capacitor and the
current through the capacitor does not change simultaneously. The
potential difference across the capacitor is changing in response to the
alternating power supply. The rate at which charges accumulate/leave
the plates is greater when the potential difference is around 0 (this is
when the rate of change of potential difference is highest). We say that
the voltage lags current by a quarter-cycle (the maximum voltage
comes quarter-a-cycle after the current).
Unlike the resistance of a
resistor, which dissipates
energy in the form of
heat, the reactance of a
capacitor dissipates a net
energy of zero.
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Comparing the Effect of AC Frequency on
Inductors and Capacitors
“For an inductor, as frequency increases, reactance increases.”
𝑿𝑳 = 𝟐𝝅𝒇𝑳
Where:
XL = inductive reactance in ohms (W)
2p ≈ 6.28
F = frequency (Hz) L = inductance in henrys (H)
“For a capacitor, as frequency increases, reactance decreases.”
𝟏
𝑿𝑪 =
𝟐𝝅𝒇𝑪
Where:
XC = inductive reactance in ohms (W)
F = frequency in hertz (Hz)
2p ≈ 6.28
C = capacitance in farads (F)
For inductors, voltage leads the current by a quarter cycle.
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For capacitors, voltage lags the current by a quarter cycle.
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Impedance (Z)
Electrical impedance is the measure of the opposition that a circuit
presents to a current when a voltage is applied. Impedance extends
the concept of resistance to AC circuits as there are two additional
impeding mechanisms to be taken into account besides the normal
resistance of DC circuits: that is induction (L) and capacitance (C). The
symbol for impedance is Z and is given in ohms. Total circuit
impedance is the sum of resistance (R) and reactance (X).
Ohm’s Law for AC Circuits: EZ = IZ
In practical terms, impedance matching of components is important to
the radio operator. If for example 300 W transmission line is used to
connect a transmitter to a 50 W antenna, the impedance mismatch
causes the signal to be partially reflected instead of going out the
antenna. The reflected energy could seriously damage the transmitter.
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A Tuned or Resonant Circuit
An LC circuit, also called a resonant
circuit, tank circuit, or tuned circuit,
is an electric circuit consisting of an
inductor, represented by the letter L,
and a capacitor, represented by the
letter C. The circuit can act as an
electrical resonator, an electrical
analogue of a tuning fork, storing
energy oscillating at the circuit's
resonant frequency.
LC circuits are used either for generating signals at a particular
frequency, or picking out a signal at a particular frequency from a more
complex signal. They are key components in many electronic devices,
particularly radio equipment, used in circuits such as oscillators, filters,
tuners and frequency mixers.
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The Resonant Frequency of an LC Circuit
Resonance
An LC circuit, also called a resonant circuit, tuned circuit or tank circuit
is an electric circuit consisting of an inductor and a capacitor
connected together.
The LC circuit is resonant when the inductive reactance equals the
capacitive reactance:
XL = XC
2π𝑓𝐿 =
𝒇𝒓 =
1
2𝜋𝑓𝐶
𝟏
𝟐𝝅 𝑳𝑪
the electric pendulum
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Series and Parallel RLC Circuits
The RLC circuit forms a harmonic oscillator for current, and resonates
in a similar way as an LC circuit. Introducing the resistor increases the
decay of these oscillations, which is also known as damping. In circuit 1
below, the three components are all in series with the voltage source.
Circuit 2 is the parallel circuit.
• At resonance, the series circuit has low
impedance.
• At resonance, the parallel circuit has high
impedance.
Circuit 1: A Series RLC Circuit
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Circuit 2: A Parallel RLC Circuit
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Transformers
A transformer is an electrical device that transfers electrical energy
between two or more circuits by electromagnetic induction. AC
power is supplied to a primary coil. A secondary coil is magnetically
linked to the primary coil. The alternating magnetic field from the
primary coil induces an AC voltage in the secondary. The voltage and
current is thus “transformed”. If the secondary coil has more loops
than the primary, the voltage is stepped up or increased (and the
current is reduced). If the secondary coil has fewer loops than the
primary, the voltage is stepped down. In an efficient transformer the
output power from the secondary is nearly the same as the input
power on the primary (P1 = P2). The relationship for number of loops
N, voltages (V) and current (I) for a 100% efficient transformer is:
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Essential Workings of a Transformer
This diagram shows the basics of all transformers. A coil (the primary) is
connected to an AC voltage source - typically the mains for power
transformers. The flux induced into the core is coupled through to the
secondary, a voltage is induced into the winding, and a current is
produced through the load.
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Transformers
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Using Voltmeters
Potential difference (voltage) is measured with a voltmeter, the
voltmeter is connected to a circuit under test in parallel with the
circuit.
Voltmeter
Power
Supply
Transceiver
Potential difference refers to a
voltage difference
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Using Ammeters
The instrument to measure the flow of electric current is the ammeter.
An ammeter is connected to a circuit under test in series with the
circuit. The ammeter will act as a low value resistance.
Ammeter
Power
Supply
Transceiver
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Using Ohm Meters
The instrument to measure resistance is the ohmmeter. An ohm meter
is connected to a circuit under test in parallel with the circuit.
Ohmmeter
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Voltmeters, Ammeters and Multimeters
• Multimeters will measure voltage, current and resistance (and
possibly other things too).
• Be sure it is set properly to read what is being measured.
• If it is set to the ohms setting and voltage is measured the meter
could be damaged!
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