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electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA chapter 8 Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Sine waves The sinusoidal waveform (sine wave) is the fundamental alternating current (ac) and alternating voltage waveform. Electrical sine waves are named from the mathematical function with the same shape. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 A wave is a disturbance. Unlike water waves, electrical waves cannot be seen directly but they have similar characteristics. All periodic waves can be constructed from sine waves, which is why sine waves are fundamental. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Sine waves Sine waves are characterized by the amplitude and period. The amplitude is the maximum value of a voltage or current; the period is the time interval for one complete cycle. 20 V 15 V The amplitude (A) of this sine wave is 20 V The period is 50.0 s A 10 V 0V t (s) 25 0 37.5 50.0 -10 V -15 V -20 V Electronics Fundamentals 8th edition Floyd/Buchla T © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Sine waves The period of a sine wave can be measured between any two corresponding points on the waveform. TT T T A T T By contrast, the amplitude of a sine wave is only measured from the center to the maximum point. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Frequency Frequency ( f ) is the number of cycles that a sine wave completes in one second. Frequency is measured in hertz (Hz). If 3 cycles of a wave occur in one second, the frequency is 3.0 Hz 1.0 s Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Period and frequency The period and frequency are reciprocals of each other. 1 f T and T 1 f Thus, if you know one, you can easily find the other. (The 1/x key on your calculator is handy for converting between f and T.) If the period is 50 s, the frequency is 0.02 MHz = 20 kHz. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Sinusoidal voltage Generation of a sinesources wave Sinusoidal voltages are produced by ac generators and electronic oscillators. When a conductor rotates in a constant magnetic field, a sinusoidal wave is generated. C N D B S A B C D A Motion of conductor Conduc tor When theisconductor is moving parallel with When the loop moving perpendicular to the lines flux, no voltage is induced. lines of the flux, theofmaximum voltage is induced. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 AC generator (alternator) Generators convert rotational energy to electrical energy. A stationary field alternator with a rotating armature is shown. The armature has an induced voltage, which is connected through slip rings and brushes to a load. The armature loops are wound on a magnetic core (not shown for simplicity). Small alternators may use a permanent magnet as shown here; other use field coils to produce the magnetic flux. S N brushes arm ature slip rings Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 AC generator (alternator) By increasing the number of poles, the number of cycles per revolution is increased. A four-pole generator will produce two complete cycles in each revolution. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Readout Function generators Typical controls: Function selection Frequency Range Adjust Output level (amplitude) DC offset CMOS output Sine Electronics Fundamentals 8th edition Floyd/Buchla Square Outputs Duty cycle Triangle © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Sine wave voltage and current values There are several ways to specify the voltage of a sinusoidal voltage waveform. The amplitude of a sine wave is also called the peak value, abbreviated as VP for a voltage waveform. 20 V 15 V VP 10 V The peak voltage of this waveform is 20 V. 0V t (s) 0 25 37.5 50.0 -10 V -15 V -20 V Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Sine wave voltage and current values The voltage of a sine wave can also be specified as either the peak-to-peak or the rms value. The peak-topeak is twice the peak value. The rms value is 0.707 times the peak value. 20 V 15 V The peak-to-peak voltage is 40 V. The rms voltage is 14.1 V. 10 V Vrms 0V 0 VPP t (s) 25 37.5 50.0 -10 V -15 V -20 V Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Sine wave voltage and current values For some purposes, the average value (actually the halfwave average) is used to specify the voltage or current. By definition, the average value is as 0.637 times the peak value. 20 V 15 V The average value for the sinusoidal voltage is 12.7 V. 10 V Vavg 0V t (s) 0 25 37.5 50.0 -10 V -15 V -20 V Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Angular measurement Angular measurements can be made in degrees (o) or radians. The radian (rad) is the angle that is formed when the arc is equal to the radius of a circle. There are 360o or 2p radians in one complete revolution. R R 1.0 0.8 0.6 0.4 0.2 0 -0.2 -0.4 Electronics Fundamentals 8th edition Floyd/Buchla -0.6 0 p p 4 2 3p 4 p 5p 4 3p 2 © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Angular measurement There are 2p radians in one complete revolution and 360o in one revolution. To find the number of radians, given 2p rad the number of degrees: rad degrees 360 This can be simplified to: rad p rad 180 degrees To find the number of degrees, given the number of radians: 180 deg Electronics Fundamentals 8th edition Floyd/Buchla p rad rad © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Angular measurement How many radians are in 45o? rad p rad degrees 180 p rad = 45 0.785 rad 180 How many degrees are in 1.2 radians? 180 rad p rad 180 1.2 rad = 69 p rad deg Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Sine wave equation Instantaneous values of a wave are shown as v or i. The equation for the instantaneous voltage (v) of a sine wave is v V p sin where Vp = Peak voltage = Angle in rad or degrees If the peak voltage is 25 V, the instantaneous voltage at 50 degrees is 19.2 V Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Sine wave equation A plot of the example in the previous slide (peak at 25 V) is shown. The instantaneous voltage at 50o is 19.2 V as previously calculated. 90 Vp Vp = 25 V v = Vp sin = 19.2 V = 50 0 50 Vp Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Phasors The sine wave can be represented as the projection of a vector rotating at a constant rate. This rotating vector is called a phasor. Phasors are useful for showing the phase relationships in ac circuits. 90 180 Electronics Fundamentals 8th edition Floyd/Buchla 0 0 90 180 360 © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Phase shift The phase of a sine wave is an angular measurement that specifies the position of a sine wave relative to a reference. To show that a sine wave is shifted to the left or right of this reference, a term is added to the equation given previously. v VP sin f where f = Phase shift Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Example of a wave that lags the reference …and the equation Phase shift has a negative phase shift Referenc e 40 Peak voltage 30 v = 30 V sin ( - 45o) Voltage (V) 20 10 0 0 45 90 135 180 225 270 315 360 405 -20 -30 - 40 Notice that a lagging sine wave is below the axis at 0o Angle () Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Example of a wave that leads the reference Notice that a leading sine Referenc e wave is above the axis at 0o Phase shift 40 Peak voltage 30 Voltage (V) 20 v = 30 V sin ( + 45o) 10 -45 0 0 -10 -20 -30 -40 45 90 135 180 225 270 315 360 …and the equation has a positive phase shift Angle () Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Phase shift An important application of phase-shifted sine waves is in electrical power systems. Electrical utilities generate ac with three phases that are separated by 120° as illustrated. Normally, 3-phase power is delivered to the user with three hot lines plus neutral. The voltage of each phase, with respect to neutral is 120 V. 120o Electronics Fundamentals 8th edition Floyd/Buchla 120o 120o © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Power in resistive AC circuits The power relationships developed for dc circuits apply to ac circuits except you must use rms values in ac circuits when calculating power. The power formulas are: P Vrms I rms 2 Vrms P R 2 P I rms R Electronics Fundamentals 8th edition Floyd/Buchla For example, the dc and the ac sources produce the same power to the bulb: 120 Vdc 0V ac or dc source Bulb 170 Vp = 120 Vrms 0V © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Power in resistive AC circuits Assume a sine wave with a peak value of 40 V is applied to a 100 W resistive load. What power is dissipated? 40 30 Voltage (V) 20 10 0 -1 0 -2 0 -3 0 - 40 Vrms = 0.707 x Vp = 0.707 x 40 V = 28.3 V 2 Vrms 28.3 V 2 P 8W R 100 W Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Superimposed dc and ac voltages Frequently dc and ac voltages are together in a waveform. They can be added algebraically, to produce a composite waveform of an ac voltage “riding” on a dc level. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Alternators Alternators are ac generators. Utility companies use 3-phase alternators and deliver all three phases to industrial customers. A simplified 3-phase alternator is illustrated. Phase 1 Neutral N S Phase 2 Phase 3 Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Alternators In vehicles, alternators generate ac, which is converted to dc for operating electrical devices and charging the battery. A basic vehicle alternator is illustrated. AC is more efficient to produce and can be easily regulated, Housing hence it is generated and converted to Stator coils dc by diodes. The output is taken from the rotor through the slip rings. Rotor Diode plate Diodes Electronics Fundamentals 8th edition Floyd/Buchla Slip rings © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 AC Motors There are two major classifications of ac motors. These are the induction motor and the synchronous motor. Both types use a rotating field in the stator windings. Induction motors work because current is induced in the rotor by the changing current in the stator. This current creates a magnetic field that reacts with the moving field of the stator, which develops a torque and causes the rotor to turn. Synchronous motors have a magnet for the rotor. In small motors, this can be a permanent magnet, which keeps up with the rotating field of the stator. Large motors use an electromagnet in the rotor, with external dc supplied to generate the magnetic field. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Pulse definitions Ideal pulses Leading (rising) edge Leading (falling) edge Trailing (falling) edge Trailing (rising) edge Baseline Amplitude Amplitude Baseline Pulse width (a) Positive-going pulse Electronics Fundamentals 8th edition Floyd/Buchla Pulse width (b) Negative-going pulse © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Pulse definitions Non-ideal pulses A 0.9 A A 0.5 A 0.1A t tr (a) Rise and fall times t tW tf (b) Pulse width Notice that rise and fall times are measured between the 10% and 90% levels whereas pulse width is measured at the 50% level. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Triangular and sawtooth waves Triangular and sawtooth waveforms are formed by voltage or current ramps (linear increase/decrease) Triangular waveforms have positive-going and negativegoing ramps of equal duration. The sawtooth waveform consists of two ramps, one of much longer duration than the other. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Harmonics All repetitive non-sinusoidal waveforms are composed of a fundamental frequency (repetition rate of the waveform) and harmonic frequencies. Odd harmonics are frequencies that are odd multiples of the fundamental frequency. Even harmonics are frequencies that are even multiples of the fundamental frequency. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Harmonics A square wave is composed only of the fundamental frequency and odd harmonics (of the proper amplitude). Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Display section Vertical section Signal coupling Volts/Di v The oscilloscope is divided into From Analog Amp four main sections. vertic al only Oscilloscopes AC DC Ch 1 GND Signal coupling Volts/Di v AC DC Ch 1 GND AC Ch 2 Conversion/storage sec tion (Digital scopes only) Vertical section DC Trigger section DC GND Digital Display section To display sec tion only Amp GND position AC Ch 2 Vertical Conversion/storage position (Digital scopes only) Amp Vertical Amp Conversion/storage (Digital scopes only) External trigger coupling AC External trigger coupling DC External trigger AC DC Ch 1 Ext Line Intensity Digital only Trigger source Trigger source Analog only Horizontal From horizontal sec tion Conversion/storage (Digital scopes only) section Trigger Horizontal Control and proc ess and section level (Digital scopes only) Trigger section External trigger Intensity slope Trigger level and slope Ch 1 Ch 2 Ch 2 Control and process (Digital scopes only) Sec/Div Trigger Time base circuits Time base Sec /Div Ext Line Trigger circuits Horizontal position Horizontal position AC Power supply Electronics Fundamentals 8th edition Floyd/Buchla AC DC to all sec tions © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Vertical section Chapter 8 Signal coupling Volts/Di v AC DC Ch 1 AC Ch 2 DC GND Display section Amp GND Conversion/storage (Digital scopes only) Vertical position Amp Analog only Intensity Conversion/storage (Digital scopes only) Digital only Horizontal section Trigger section External trigger coupling External trigger Trigger source AC DC Ch 1 Ext Line Ch 2 Trigger level and slope Control and process (Digital scopes only) Sec /Div Trigger circuits Time base Horizontal position AC Power supply DC to all sec tions 8th ElectronicsFundamentals Fundamentals edition Electronics Floyd/Buchla Circuits, Devices and Applications - Floyd © 2010©Pearson Education, Upper Saddle Copyright 2007 Prentice-Hall River, NJ 07458. All Rights Reserved. Chapter 8 Oscilloscopes Display Vertical Horizontal Trigger VERT ICAL VERT ICAL HORIZONT AL HORIZONT AL TRIGGER TRIGGER CH HH CH11 CH CH22 BOT BOT SLOPE SLOPE ÐÐ POSIT ION POSIT ION POSIT ION POSIT ION VOLT S/DIV VOLT S/DIV VOLT S/DIV VOLT S/DIV ++ POSIT ION POSIT ION LEVEL LEVEL SEC/DIV SEC/DIV SOURCE SOURCE CH CH11 55VV 22mmVV COUPLING COUPLING AC-DC-GND AC-DC-GND 55VV 22mmVV COUPLING COUPLING AC-DC-GND AC-DC-GND 55ss 55ns ns CH CH22 EE XT XT LL INE INE TRIG TRIGCOUP COUP DC DC DISPLAY DISPLAY PPR OB R OBEECOMP COMP 55VV CH CH11 CH CH22 AC AC EXT EXTTRIG TRIG INT INTENSIT ENSITYY Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Selected Key Terms Sine wave A type of waveform that follows a cyclic sinusoidal pattern defined by the formula y = A sin . Alternating Current that reverses direction in response to a current change in source voltage polarity. Period (T) The time interval for one complete cycle of a periodic waveform. Frequency (f) A measure of the rate of change of a periodic function; the number of cycles completed in 1 s. Hertz The unit of frequency. One hertz equals one cycle per second. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Selected Key Terms Instantaneous The voltage or current value of a waveform at value a given instant in time. Peak value The voltage or current value of a waveform at its maximum positive or negative points. Peak-to-peak The voltage or current value of a waveform value measured from its minimum to its maximum points. rms value The value of a sinusoidal voltage that indicates its heating effect, also known as effective value. It is equal to 0.707 times the peak value. rms stands for root mean square. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Selected Key Terms Radian A unit of angular measurement. There are 2p radians in one complete 360o revolution. Phase The relative angular displacement of a time-varying waveform in terms of its occurrence with respect to a reference. Amplitude The maximum value of a voltage or current. Pulse A type of waveform that consists of two equal and opposite steps in voltage or current separated by a time interval. Harmonics The frequencies contained in a composite waveform, which are integer multiples of the pulse repetition frequency. Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 1. In North America, the frequency of ac utility voltage is 60 Hz. The period is a. 8.3 ms b. 16.7 ms c. 60 ms d. 60 s Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 2. The amplitude of a sine wave is measured a. at the maximum point b. between the minimum and maximum points c. at the midpoint d. anywhere on the wave Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 3. An example of an equation for a waveform that lags the reference is a. v = -40 V sin () b. v = 100 V sin ( + 35o) c. v = 5.0 V sin ( - 27o) d. v = 27 V Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 4. In the equation v = Vp sin , the letter v stands for the a. peak value b. average value c. rms value d. instantaneous value Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 5. The time base of an oscilloscope is determined by the setting of the a. vertical controls b. horizontal controls c. trigger controls d. none of the above Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 6. A sawtooth waveform has a. equal positive and negative going ramps b. two ramps - one much longer than the other c. two equal pulses d. two unequal pulses Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 7. The number of radians in 90o are a. p/2 b. p c. 2p/3 d. 2p Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 8. For the waveform shown, the same power would be delivered to a load with a dc voltage of a. 21.2 V 60 V 45 V b. 37.8 V 30 V c. 42.4 V 0V d. 60.0 V t (s) 0 25 37.5 50.0 -30 V -45 V -60 V Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 9. A square wave consists of a. the fundamental and odd harmonics b. the fundamental and even harmonics c. the fundamental and all harmonics d. only the fundamental Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz 10. A control on the oscilloscope that is used to set the desired number of cycles of a wave on the display is a. volts per division control b. time per division control c. trigger level control d. horizontal position control Electronics Fundamentals 8th edition Floyd/Buchla © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved. Chapter 8 Quiz Answers: Electronics Fundamentals 8th edition Floyd/Buchla 1. b 6. b 2. a 7. a 3. c 8. c 4. d 9. a 5. b 10. b © 2010 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved.