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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 50 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. 51 B-005-008 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. B-005-008 52 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. 53 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. 54 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 55 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. 56 B-005-009 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. 57 B-005-009 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. 58 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. B-005-009 59 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. 60 The Capacitor Physical Construction Capacitors are rated by: • Amount of charge they can hold. • Their voltage handling capability. • The insulating (dielectric) material between plates. 61 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 62 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. 63 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. 64 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. 65 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 B-005-009 66 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 B-005-009 67 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. 68 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 69 Capacitors or Series and Parallel Capacitors connected in series (a) and parallel (b). B-005-009 70 Electricity – The Water Analogy B-005-009 71 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 B-005-010 Ohm's Law for a resistor: E = IR, Ohms' Law for an inductor: EL = ILXL 72 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 B-005-010 73 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 B-005-010 74 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. 75 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. B-005-010 For capacitors, voltage lags the current by a quarter cycle. 76 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. B-005-010 77 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. B-005-012 78 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 79 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 B-005-012 Circuit 2: A Parallel RLC Circuit 80 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: B-005-011 81 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. B-005-011 82 Transformers B-005-011 83 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 B-005-013 84 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 B-005-013 85 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 B-005-013 86 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 87