1 chapter 4 “electrical principles ” bill ryan, kj6igx and glen rikerd, no6w discussion leader
TRANSCRIPT
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1
Chapter 4
“Electrical Principles” Bill Ryan, KJ6IGX and Glen
Rikerd, NO6W Discussion Leader
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Chapter 4
Radio Mathematics
2
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A General Principle
•Each question should be approximately as difficult as the other questions.
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General Principles
•Question statements that involve more difficult subjects generally can be expected to have easier answers.
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Look for Simplicity
•Calculations are set up to use simple numbers or combinations of values
•Estimate the answers
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Central Ideas
•Resonance•Triangles•Ratio•Handling Exponents
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Resonance
•Capacitive Reactance and Inductive Reactance cancel each other
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Triangles
•The test uses simple triangles that can be solved by sight
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Ratio
The ratio of a triangles sides often tells you how to find the answer
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Handling Exponents
• When multiplying, add the exponents
• When dividing, change the sign and then add the exponents
• For square roots, cut the exponent in half
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Question E5C11
• Impedance has a real part (resistance) and an imaginary part (reactance)
• The horizontal axis is the real part
• The vertical axis is the imaginary part
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Polar Coordinates
•Polar Coordinate System has same information as the rectangular axis
•Determined by a distance from a fixed point and an angle with a fixed direction
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Phase Angle
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Question E5B06: Time Constant
• Time it takes for a capacitor to charge or discharge by 63.2% is called the time constant
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Question E5B06: Time Constant
• Tau = Resistance x Capacitance
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Handling Exponents
•1 megohm x 1 microfarad =
•1 x 106 x 1 x 10-6 =
•106 + (-6) = 100 = 1 second
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E5B06: Time Constant Calculation
• Given 800 V DC charge decreases to 294 V DC. (Looks like – 63.2%)
• R x C = 1 megohm x 450 microfarads
• 1 x 106 x 450 x 10-6 = 450 seconds
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Phase
• Relationship of current and voltage is the phase of the two waves
• Phase means time
• The effect that occurs first leads the second, the trailing effect lags the first
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Voltage jumps from coil to coil
Since voltage does not travel along the whole wire, it moves faster than the current in an inductor
Voltage leads current in an inductor
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• Voltage must build up in a capacitor. This causes a delay. Current seems to go right through the capicator
Current leads voltage in a capacitor
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• When reactance is inductive, voltage leads current
• When reactance is capacitive, current leads voltage
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Question E5B10: Phase Relationship
What is the Relationship between current through and voltage across an inductor
• Voltage moves from loop to loop, current must move through the wire
• In this question, voltage leads current by 90 degrees
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Understanding Right Triangles:The central angle is the phase angle
• Two sides are equal: opposite angles = 45 degrees
• Opposite side longer than adjacent: central angle is more than 45 degrees
• Opposite side shorter: central angle is less than 45 degrees
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Equal sides of triangle, phase angle = 45
• When reactance and resistance are the same number of ohms, then the triangle has equal sides
• 100 ohms• 45• 100 ohms
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Reactance smaller, phase angle = <45
• When reactance is smaller than the resistance, the phase is less than 45
• 250 ohms• • < -45 100 ohms
• Net Capacitative Reactance is a negative phase angle
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Reactance larger than resistance
• When reactance is larger than the resistance, the phase is more than 45
• 100 ohms - > -45
• 250 ohms XC
• •
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Question E5B13
• Resistance = 1000 ohm• Reactance is inductive 250 ohms• Phase angle is less than 45 degrees
and voltage leads the current
• Inductive Reactance• 250 ohms• <45• Resistance 1000 ohms
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Question E5B07
Resistance = 1000 ohm• Reactance is capacitive 250 ohms• Phase angle is less than 45 degrees
and current leads the voltage 1000• <-45 250
• Capacitive reactance is always drawn downwards to show a negative angle
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Question E5B13 Complex Impedance
• Phase angle between voltage across and current through series RLC circuit
• XL =500 ohms, XC = 250 ohms R = 1000 ohms
• Net reactance: XL – XC = 250 ohms XL
• Phase angle is less than 45 degrees and voltage leads current
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Tank Circuits
• Parallel RLC circuits at resonance have a high impedance and appear as an open circuit.
• It also has a circulating current and builds a maximum voltage at resonance.
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3 4 5 Right Triangles
• Pythagorean Theorem for series RLC
• If shortest sides are 3 and 4 units long, then the longest side is 5 units
• Resistance = 400 ohms and • Reactance = 300 ohms
• Impedance = 500 ohms
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Pythagorean Triangles
• Any combination of 300 and 400 for the sides will produce an impedance of 500
• 500• 300•
• 400•
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30 60 90 Triangles
• When the phase angle is 30 degrees, the reactance is always half of the impedance
• 200 • 30 100• 186
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Equilateral Triangles
When the phase angle is 45 degrees, the impedance is 1.41 times either the reactance or resistance
141 100 45 100
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Question: E5D19 Power Factor
• Real Power = PF x Apparent Power
• Power Factor (PF) = 0.71
• Apparent Power = 500 watts
• Watts consumed = 0.71 x 500 watts = 355 watts
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Resonant Frequency
• Same for Series and Parallel Circuits•
Fr = 1
2 pi L x C
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Resonant Frequency Strategy
•Calculate L x C alone first•Take square root•Plug values into formula•Estimate the result
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Question E5A14 Resonant Freq
• L x C = • 40 microhenrys x 200 picofarads =
• 40 x 10-6 x 200 x 10-12 = 8,000 x 10-12
• Take square root of 8,000 x 10-18 =
• Square root of 80 x 10-16 = 9 x 10-8
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Plug in values and estimate for Fr
Fr = 1 = 10+8
6 x 9 x 10-8 50
Fr = .02 x 10+8 = 2 x 10+6 = 2 MHz estimate
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Answer to Question E5A14
•Estimate of Fr = 2 MHZ
•Actual value of Fr = 1.78 MHz
•Just estimate freely and pick the closest answer
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Q
• Q is a quality factor for a circuit for low resistive losses
• Q is the ratio of reactance to resistance
• Q = X • R
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Resonant Circuit Bandwidth
•Bandwidth is the freqency range within 3 dB below peak response
•Delta f = bandwidth = fr
• Q
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Question E5A13 Half Power BW
• Half Power BW of a parallel resonant circuit:
• Resonant Frequency = 14.25 MHz• Q = 187
• BW = 14.25 MHz = 15 MHz = 100 kHz• 187 150
• Actual answer: 76.2 kHz
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Encouraging Thoughts
• We want you to pass the Extra Exam
• Try to focus on simplifying methods
• True mastery of this material will take a long time
• Commit to taking the test at end of class despite whether feeling ready
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In Class Practice PRoblems
• Here is a list of possible in class seminar questions
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Chapter 4
E5C11 What do the two numbers represent that are used to define a point on a graph using rectangular coordinates?•The sine and cosine values•The tangent and cotangent values•The coordinate values along the horizontal and vertical axes•The magnitude and phase of the point
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Chapter 4
E5D05 What is a magnetic field?•The space between the plates of a charged capacitor, through which a magnetic force acts•The force that drives current through a resistor•The region surrounding a magnet through which a magnetic force acts•Electric current through the space around a permanent magnet 47
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Chapter 4
E5B05 (A) How long does it take for an initial charge of 20 V DC to decrease to 7.36 V DC in a 0.01-microfarad capacitor when a 2-megohm resistor is connected across it?•0.02 seconds•0.04 seconds•20 seconds•40 seconds 48
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Chapter 4
E5D13 (B) How many watts are consumed in a circuit having a power factor of 0.2 if the input is 100-V AC at 4 amperes?•2000 watts• 400 watts• 80 watts• 50 watts
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Chapter 4
E5C19 (B) Which point on Figure E5-2 best represents that impedance of a series circuit consisting of a 400 ohm resistor and a 38 picofarad capacitor at 14 MHz?•Point 6•Point 5•Point 4•Point 2 50
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Chapter 4
Figure E5-2 refers to question E5C19
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Chapter 4
• E5A12 What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 3.7 MHz and a Q of 118?
• 15.7 kHz• 31.4 kHz• 218.3 kHz• 436.6 kHz
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Next Class Session
• Study Chapter 5 “Components and Building Blocks”
• Study the Chapter 5 Question Pool questions found in the Blue Boxes
• Prepare your Chapter 5 Study Guide materials
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Chapter 4
E5C11 What do the two numbers represent that are used to define a point on a graph using rectangular coordinates?•The sine and cosine values•The tangent and cotangent values•The coordinate values along the horizontal and vertical axes•The magnitude and phase of the point
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Chapter 4
E5D05 What is a magnetic field?•The space between the plates of a charged capacitor, through which a magnetic force acts•The force that drives current through a resistor•The region surrounding a magnet through which a magnetic force acts•Electric current through the space around a permanent magnet
55
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Chapter 4
E5B05 (A) How long does it take for an initial charge of 20 V DC to decrease to 7.36 V DC in a 0.01-microfarad capacitor when a 2-megohm resistor is connected across it?•0.02 seconds•0.04 seconds•20 seconds•40 seconds 56
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Chapter 4
E5D13 (B) How many watts are consumed in a circuit having a power factor of 0.2 if the input is 100-V AC at 4 amperes?•2000 watts• 400 watts• 80 watts• 50 watts
57
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Chapter 4
E5C19 (B) Which point on Figure E5-2 best represents that impedance of a series circuit consisting of a 400 ohm resistor and a 38 picofarad capacitor at 14 MHz?•Point 6•Point 5•Point 4•Point 2 58
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Chapter 4
Figure E5-2 refers to question E5C19
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Chapter 4
• E5A12 (B) What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 3.7 MHz and a Q of 118?
• 15.7 kHz• 31.4 kHz• 218.3 kHz• 436.6 kHz
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Next Class Session
• Study Chapter 5 “Components and Building Blocks”
• Study the Chapter 5 Question Pool questions found in the Blue Boxes
• Prepare your Chapter 5 Study Guide materials
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