Section 005 - Basic Electronics and Theory (13 questions)

Canadian Amateur Radio Basic Qualification Study Guide

• Chapter 2: Basic Electrical Theory

• Chapter 3: Ohm’s Law and Power

• Chapter 4: Inductors, Capacitors, Transformers

1 Winnipeg Amateur

Radio Club

RIC-7: Section 5: 13 Exam Questions • 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

• B-005-007: Frequency and Wavelength

• B-005-008: Decibels (dB), Power and RST reports

• 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

2

http://shsballoonproject.

pbworks.com/w/page/70

013917/SHARP%20Am

ateur%20Radio

Common Radio Quantities and Their Symbols

Quantity Quantity Symbol Base Unit Base Unit 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

3 B-005-001

Metric Unit Conversions

4

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

14550. kHz = 14.5 MHz (Hz = hertz)

155 mA = ________ A (A = amps)

2280 m = ________ km (m = metres)

0.004 V = ________ mV (V = volts)

45000 kW = ________ MW ( W = ohms)

5.50 pF = ________ nF (F = farads)

1290 kHz = ________ MHz (CFRW)

102,300,000 Hz = ________ MHz (CKY-FM) 5

Metric Conversion Practice

B-005-001

The red arrow above tells us to move the decimal 3 places left to convert “kilo” to

“mega” as in the first example below. Memorize this conversions chart.

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 a current of flowing electrons in the wire.

6 B-005-002

The outer jacket and dielectric in a coaxial cable are insulators. Signal travels along the centre conductor. The braided shield is grounded.

Conductor, Insulator, Current, Voltage, Resistance

7

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.

B-005-002

Current, Voltage, Conductor, Insulator, Resistance, Conductance and Current

Water flowing through a hose is a

good way to imagine electricity. Water 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.

8 B-005-002

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

𝑰 Resistance (R) is the ratio of

voltage (E) applied to current (I) produced.

• Voltage: E = I x R (Volts)

• Current: I = E / R (Amps)

• Resistance: R = E / I (Ohms)

9 B-005-004 Longer wires have greater resistance. Wider wires have less.

Calculating Voltage and Current and Resistance

10

Calculating Current (I)

There is a very easy way to determine how much current will flow through a circuit when the voltage and resistance 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"... This circle will help you to know how to figure out 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

Electric Current Calculations

11

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. This is 200 V divided by 100 W. The result is 2 amperes or 2 amps (A).

E = voltage measured in volts (V) R = resistance measured in ohms (W) I = current measured in amps (A)

[Units that have capitalized symbols are named after scientists. Alessandro Volta, Georg Ohm and André Ampère]

B-005-004

Calculating Voltage

12

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 = in volts I = in amps R = in ohms

B-005-004

Calculating Resistance

13

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 of the man who discovered this direct relationship (his last name was Ohm). The relationship described in Ohm's Law is used when working with almost any electronic circuit.

B-005-004

Resistance & Conductance The electrical 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 electrical resistance is the ohm (Ω), while electrical conductance is measured in reciprocal ohms or siemens (S).

All materials show some resistance, (except for superconductors, which have a resistance of zero). Copper and aluminum are the most common conductors used in most wiring.

The resistance (R) of an object 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.

14 B-005-002

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.

15 B-005-002

16

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 break the circuit if too much current flows.

Electric Energy & Power, Open & Short Circuits

B-005-003

The Short Circuit

17

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

Electrical Power

18

Circuits convert the energy in flowing electrons into more useful forms of energy such as heat, light or motion. Power is the rate at which electrical energy is converted.

B-005-003

When you switch on a light bulb, light and heat energy are released. This is because of the current flowing through a resistor or 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 values for light bulbs 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.

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.

• 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 = 𝐼2𝑅, 𝑃 =𝑉2

𝑅

19 B-005-003

Electrical Power Power calculations (continued)

How much electrical power is dissipated as heat when a current of 10 amperes passes through a dummy load resistor if the voltage drop is 13.8 volts DC. (For testing purposes, a dummy load replaces the antenna. It simulates the electrical load of the antenna.)

P = I x E P = 10 A x 13.8 V = 138 W

How much power is being used in a circuit when the voltage is 120 volts DC and the current is 2.5 amperes.

P = I x E P = 2.5 A x 120 V = 300 watts

A dummy load with a PL259

connector (male UHF)

B-005-006 20

Power Calculations (P = IE )

• You can you determine power [consumed] 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

21 B-005-006

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

Electric Toaster P = 1200 watts E =120 volts I =10 amps

22

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

B-005-006

Series & Parallel Resistors

23

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

Resistors in Series

24

For Resistances in Series RS = R1 + R2 + R3 + ... R1 = 100 W

R2 = 150 W

R3 = 370 W

RS = _________ ohms

B-005-005

Resistors are often used to reduce potentially damaging currents.

Resistors in Series

25

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

Resistors in Series

26

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

Resistors in Parallel

27

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

Calculating Parallel Resistance

28

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.

B-005-005

Resistors in Parallel

29

Parallel Resistors 1/RP = 1/R1 + 1/R2 + 1/R3 + ... R1 = 300 W

R2 = 300 W R3 = 300 W

RP = ______ ohms

B-005-005

Resistors in Parallel

30

Parallel Resistance 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)

B-005-005

Parallel Resistors

31

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 smallest resistance.

B-005-005

Series and Parallel Combined

32

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 each one.

Frequency

33

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 interchangeable 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. It may be quite normal for a 60-year-old to hear a maximum of 14,000 Hz (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

The Frequency – Wavelength Relationship

The distance a wave travels in one cycle is called wavelength ( l ).

“As frequency increases, wavelength decrease (previous diagram).”

One Wavelength

time

V+

V-

0V

One Cycle

B-005-007 34

Higher pitched sounds have shorter wavelengths. Higher frequency

radio waves have shorter wavelengths.

Names of Frequency Ranges & Types of Waves

35

• 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 (hertz – Hz) as they travel through

space are generally referred to as radio waves.

B-005-007

sound waves are longitudinal waves

radio waves are transverse

Relationship Between Frequency (f) & Wavelength (l)

36

• 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 wavelength gets shorter as the frequency increases.

• Wavelength in metres equals 300 divided by frequency in megahertz (MHz).

• A radio wave travels through space at the speed of light. c = 300,000,000 m/s (300 Mm/s).

B-005-007

Identification of Amateur Radio Bands

37

The property of a radio wave often used to identify the

different bands amateur radio operators use is the physical

length of the radio wave.

• The frequency range of the 2-meter band in Canada is

144 to 148 MHz.

• The frequency range of the 6-meter band in Canada is

50 to 54 MHz.

• The frequency range of the 70-centimeter band in

Canada is 420 to 450 MHz.

B-005-005

Note that the band wavelength is approximate.

5.8 Decibels (dB)

38

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.

B-005-008

Decibels and Power / Intensity

39 B-005-008

Decibels and Power Increases and Reductions

40 B-005-008

9 dB gain = 8x power

10 dB gain = 10x power

20 dB gain = 100x power

3 dB gain = 2x power

6 dB gain = 4x power

Remember These!

Decibels (dB) and Power Changes

41

A two-times increase in

power results in an increase of 3 dB

A decrease in a transmitter’s power by one-half is a 3 dB decrease (-3 dB).

You can 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

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.

Signal Strength Reports

42

• 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 (1/10 power = -10 dB)

• If 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

• 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 form 5 watts to 50 watts by a linear amplifier. The power gain would be 10 dB.

B-005-008

43

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 is 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

Signal Strength

Magnets

44

A Bar Magnet

The magnetic field (B) runs from the North

Pole to the South Pole

An Inductor

The magnetic field is contained within the permeable core.

B-005-008

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).

45 B-005-008

Stationary Electric Field (E) Magnetic Field (B) Due to Moving

Electric Charges in a Wire

A Dipole Antenna Producing Radiowaves

Electromagnetic Induction Electromagnetic induction is the production of an electromotive force (EMF) or voltage (E) across a conductor exposed to changing magnetic flux.

46

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.

B-005-008

Coils, Solenoids 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).

B-005-008

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.

An inductor is a coil of wire through which a current moves and energy is stored in the resulting magnetic field.

47

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.

48

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, the coil wants to build up a magnetic field. While the field is building, the coil inhibits the flow of current (resists change). 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 resists a change in the current flowing through it.

Inductors & Inductance

49

Inductance (L) refers to the capacity of a coil 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.

B-005-009

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 cross-sectional area, the length of the coil and the permeability of the core material.

Inductance (L)

50 B-005-009

• 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.

Inductors in Series and in Parallel

51

In Series: the combined inductance is greater than the greatest.

In Parallel: the combined inductance is less than the least.

Capacitors

52

A capacitor is 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.

B-005-009

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.

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.

53

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.

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.

54 B-005-009

A 0.330 farad capacitor

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

55 B-005-009

Capacitors or Series and Parallel

56 B-005-009

Capacitors connected in series (a) and parallel (b).

57 B-005-009

Inductive Reactance (XL)

58 B-005-010

Inductive Reactance

59

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. 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.

Current lags voltage by 90o

B-005-010

Capacitive Reactance (XC)

60 B-005-010

Comparing the Effect of AC Frequency on Inductors and Capacitors

61 B-005-010

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).

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.

62 B-005-010

A Tuned or Resonant Circuit

63

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.

B-005-012

The Resonant Frequency of an RLC 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 circuit can act as an electrical resonator; an electrical analog of a tuning fork, 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 including radio equipment (oscillators, tuners, filters and frequency mixers.)

𝑓𝑟 =1

2𝜋 𝐿𝐶

64

Series and Parallel RLC Circuits In circuit 1 below, the three components are all in series with the voltage source. Circuit 2 is the parallel circuit.

Circuit 1: A Series RLC Circuit Circuit 2: A Parallel RLC Circuit

B-005-012

• At resonance, the series circuit has low impedance.

• At resonance, the parallel circuit has high impedance.

65

Transformers

66 B-005-011

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:

Essential Workings of a Transformer

67

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.

B-005-011

Transformers

68 B-005-011

Using Voltmeters

Potential difference (voltage) is measured with a voltmeter, the voltmeter is connected to a circuit under test in parallel with the circuit.

69

Power

Supply

Transceiver

Voltmeter

B-005-013

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.

70

Power

Supply

Transceiver

Ammeter

B-005-013

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.

71

Ohmmeter

B-005-013

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!

B-005-013 72