Amateur Extra License Class

Amateur Extra License Class Chapter 4 Electrical Principles

Chapter 4 Electrical Principles • Electric & Magnetic Fields • RC & RL Time Constants • Phase Angle • Radio Math • Complex Impedance • Plotting Impedance • Admittance • Real Power & Power Factor • Resonant Circuits • Q Factor • Magnetic Cores

Electric and Magnetic Fields • Field • Region of space where energy is stored and through which a force acts. • Energy stored in a field is called potential energy. • Fields are undetectable by any of the 5 human senses. • You can only observe the effects of a field. • Example: Gravity

Electric and Magnetic Fields Electric Field Magnetic Field Detected by effect on moving electrical charges (current). An electrical current has an associated magnetic field. Magnetic energy is stored by moving electrical charges to create an electrical current. A magnetostatic field is a magnetic field that does not change over time. Stationary permanent magnet Earth’s magnetic field • Detected by a voltage difference between 2 points. • Every electrical charge has an electric field. • Electrical energy is stored by moving electrical charges apart so that there is a voltage difference (or potential) between them. • Voltage potential = potential energy • An electrostatic field is an electric field that does not change over time.

Electric and Magnetic Fields Magnetic Field Direction: “Left-Hand Rule”

RC and RL Time Constants R-C Circuit R-L Circuit

RC and RL Time Constants

RC and RL Time Constants R-C circuit R-L Circuit In an R-C circuit, one time constant is defined as the length of time it takes the voltage across an uncharged capacitor to reach 63.2% of its final value. Time Constant, TC = R x C In an R-L circuit, one time constant is defined as the length of time it takes the current through an inductor to reach 63.2% of its final value. Time Constant, TC = R x L

RC and RL Time Constants Note: After a period of 5 time constants, the voltage or current can be assumed to have reached its final value. “Close enough for all practical purposes.”

E5D03 -- What device is used to store electrical energy in an electrostatic field? A battery A transformer A capacitor An inductor

E5D05 -- Which of the following creates a magnetic field? Potential differences between two points in space Electric current A charged capacitor A battery

E5D06 -- In what direction is the magnetic field oriented about a conductor in relation to the direction of electron flow? In the same direction as the current In a direction opposite to the current In all directions; omnidirectional In a direction determined by the left-hand rule

E5D07 -- What determines the strength of a magnetic field around a conductor? The resistance divided by the current The ratio of the current to the resistance The diameter of the conductor The amount of current

E5D08 -- What type of energy is stored in an electromagnetic or electrostatic field? Electromechanical energy Potential energy Thermodynamic energy Kinetic energy

E5B01 -- What is the term for the time required for the capacitor in an RC circuit to be charged to 63.2% of the applied voltage? An exponential rate of one One time constant One exponential period A time factor of one

E5B04 -- What is the time constant of a circuit having two 220-microfarad capacitors and two 1-megohm resistors, all in parallel? 55 seconds 110 seconds 440 seconds 220 seconds

E5B04 -- What is the time constant of a circuit having two 220-microfarad capacitors and two 1-megohm resistors, all in parallel? R1 = R2 = 1 x 106Ω C1 = C2 = 220 x 10-6 F

E5B05 -- 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

E5B05 -- 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? Percent of Discharge = 7.36 ÷ 20 = 0.368 = 36.8% Checking Table: 36.8% Discharge Occurs at One Time Constant Time Constant for RC Circuit = R x C = (2 x 106)(0.01 x 10-6) = 0.02 Seconds

Phase Angle • Difference in time between 2 signals at the same frequency. • Measured in degrees. θ= 45º

Phase Angle Leading signal is ahead of 2nd signal. Blue signal leads red signal. Lagging signal is behind 2nd signal. Blue signal lags red signal.

Phase Angle AC Voltage-Current Relationship in Capacitors Current leads the voltage by 90° Or Voltage lags the current by 90° AC Voltage-Current Relationshipin Inductors Current lags the voltage by 90° Or Voltage leads the current by 90° Blue = Voltage Red = Current

Phase Angle • Combining reactance with resistance. • In a resistor, the voltage and the current are always in phase. • In a circuit with both resistance and capacitance, the voltage will lag current by less than 90°. • In a circuit with both resistance and inductance, the voltage will lead current by less than 90°. • The size of the phase angle depends on the relative sizes of the resistance to the inductance or capacitance.

E5B09 -- What is the relationship between the current through a capacitor and the voltage across a capacitor? Voltage and current are in phase Voltage and current are 180 degrees out of phase Voltage leads current by 90 degrees Current leads voltage by 90 degrees

E5B10 -- What is the relationship between the current through an inductor and the voltage across an inductor? Voltage leads current by 90 degrees Current leads voltage by 90 degrees Voltage and current are 180 degrees out of phase Voltage and current are in phase

Radio Mathematics Basic Trigonometry • Sine sin(θ) = a/c or θ = ArcSin(a/c) • Cosine cos(θ) = b/c or θ = ArcCos(b/c) • Tangent tan(θ) = a/b or θ = ArcTan(a/b) c a θ b

Radio Mathematics • Coordinate Systems • Complex impedances can be plotted using a 2-dimensional coordinate system. • There are two primary types of coordinate systems used for plotting impedances. • Rectangular • Polar

Radio Mathematics Rectangular Coordinates • Also called Cartesian coordinates • A pair of numbers specifies a position on the graph: (x, y) • 1st number (x) specifies position along horizontal axis. • 2nd number (y) specifies position along vertical axis. Example A Example B

Radio Mathematics Polar Coordinates • A pair of numbers specifies a position on the graph: (r, θ) • (r) specifies distance from the origin. • (θ) specifies angle from horizontal axis. 90º 4/30º Vector: Line with BOTH length & direction. Represented by a single-headed arrow • Polar Coordinates used to specify a vector. • Length of vector is impedance. • Angle of vector is phase angle. • Angle always between +90⁰ and -90⁰. 0º 5/-45º -90º

Radio Mathematics ConvertingRectangular to Polar r = x2 +y2 θ = ArcTan (y/x) ConvertingPolar to Rectangular x = r * cos(θ) y = r * sin(θ) Working with Polar & Rectangular Coordinates 

Radio Mathematics Example Ain RectangularCoordinates Example Bin RectangularCoordinates Example Ain PolarCoordinates Example Bin PolarCoordinates 3.6 /33.7º 4.5 /-63.4º

Radio Mathematics • Complex Numbers • Also called “imaginary” numbers. • Represented by x + jy where j = • “x” is the “real” part. • “jy” is the “imaginary” part.

Radio Mathematics • Complex Numbers can be expressed in either rectangular or polar coordinates. • Adding/subtracting complex numbers more easily done using rectangular coordinates. (a + jb) + (c + jd) = (a+c) + j(b+d) (a + jb) - (c + jd) = (a-c) + j(b-d) • Multiplying/dividing complex numbers more easily done using polar coordinates. a/θ1 x b/θ2 = a x b /θ1 + θ2 a/θ1 / b/θ2 = a / b /θ1 - θ2

E5C11 -- What do the two numbers represent that are used to define a point on a graph using rectangular coordinates? The magnitude and phase of the point The sine and cosine values The coordinate values along the horizontal and vertical axes The tangent and cotangent values

Complex Impedance Capacitive Reactance Inductive Reactance • Reactance decreases with increasing frequency. • Capacitor looks like open circuit at 0 Hz (DC). • Capacitor looks like short circuit at very high frequencies. • Reactance increases with increasing frequency. • Inductor looks like short circuit at 0 Hz (DC). • Inductor looks like open circuit at very high frequencies.

Complex Impedance When resistance is combined with reactancethe result is called impedance, Z (Where X = XL – XC)

Plotting Impedance

Plotting Impedance Plot R=600 Ω and XL= j600 Ω |Z|= R2 + X2 θ = ArcTan(X/R) where: X = XL - XC X = XL - XC = 600-0 = 600 Ω |Z| =R2 + X2 = 6002 + 6002 = 360000 + 360000 = 720000 = 848.5Ω θ = ArcTan(X/R) = ArcTan(600/600) = ArcTan(1) = 45° Z = 848.5 Ω/45° R = 600Ω Z = 848.5Ω X = j600Ω Θ= 45º     

Plotting Impedance R = 600 Ω XC = -j600 Ω Z = 848.5 Ω/-45º Θ= -45º X = -j600Ω Z = 848.5Ω R = 600Ω

Plotting Impedance R = 600 Ω XL = j600 Ω XC = -j1200 Ω X = -j600 Ω Z = 848.5 Ω/-45º XL = j600Ω Θ= -45º XC = -j1200Ω Z = 848.5Ω X = -j600Ω R = 600Ω

E5C09 -- When using rectangular coordinates to graph the impedance of a circuit, what does the horizontal axis represent? Resistive component Reactive component The sum of the reactive and resistive components The difference between the resistive and reactive components

E5C10 -- When using rectangular coordinates to graph the impedance of a circuit, what does the vertical axis represent? Resistive component Reactive component The sum of the reactive and resistive components The difference between the resistive and reactive components

E5C12 -- If you plot the impedance of a circuit using the rectangular coordinate system and find the impedance point falls on the right side of the graph on the horizontal axis, what do you know about the circuit? It has to be a direct current circuit It contains resistance and capacitive reactance It contains resistance and inductive reactance It is equivalent to a pure resistance

E5C13 -- What coordinate system is often used to display the resistive, inductive, and/or capacitive reactance components of an impedance? Maidenhead grid Faraday grid Elliptical coordinates Rectangular coordinates

E5C14 -- What coordinate system is often used to display the phase angle of a circuit containing resistance, inductive and/or capacitive reactance? Maidenhead grid Faraday grid Elliptical coordinates Polar coordinates

Tips forCalculating Impedance • Impedances in series add together. • Inductive and capacitive reactance in series cancel. • Admittances in parallel add together.

Admittance Admittance , Y = 1/Z = G + j B Conductance, G = 1/R Susceptance, B = 1/X |Y| = G2 + B2 / Y = ArcTan(B/G) = ArcTan (-R/X)  Note: When taking the reciprocal of an angle, the sign changes from positive to negative or vice versa.

Admittance Unit of measurement for Y, G, & B are Siemens (S) Formerly “mho”. Example: An impedance of 141Ω @ /45° is equivalent to an admittance of 7.09 millisiemens @ /-45°

E5B07 -- What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms? 68.2 degrees with the voltage leading the current 14.0 degrees with the voltage leading the current 14.0 degrees with the voltage lagging the current 68.2 degrees with the voltage lagging the current Circuit is capacitive since capacitive reactance is larger than the inductive reactance. AC voltage-current relationship in capacitive circuits is voltage lagging current (negative phase angle), eliminating Choices A and B. Between choices C and D, Choice D has a phase angle greater than 45° indicating the Reactance is larger than the Resistance. Choice C has a phase angle less than 45° indicating a larger Resistance value than Reactance. In this problem, the Resistance is larger than the resultant reactance so the phase angle is expected to be less than 45°. Choice C is the correct answer.

E5B07 -- What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms? θ = ArcTan(X/R) where: X = XL - XC X = XL - XC = 250 - 500 = -250 Ω θ = ArcTan(X/R) = ArcTan(-250/1000) = ArcTan(-0.25) = -14.04° The phase angle is negative making this circuit capacitive. AC voltage-current relationship in capacitive circuits is voltage lagging current. Note that voltage is the reference point for phase angle polarity, so with a negative phase angle, voltage lags current.

Amateur Extra License Class