Presentation on theme: "1 of 77 Chapter 8 – AC Circuits electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA."— Presentation transcript:
1 of 77 Chapter 8 – AC Circuits electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA
AC Circuits 2 of 77 Alternating Voltage is a voltage that: 1.Continuously varies in magnitude 2.Periodically reverses in polarity
AC Circuits 3 of 77 Symbol for a sinusoidal voltage source.
AC Circuits 4 of 77 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 to alternating current. A wave is a disturbance.
AC Circuits 5 of 77 The sinusoidal waveform (sine wave) is the fundamental alternating current (ac) and alternating voltage waveform. Sine waves Electrical sine waves are named from the mathematical function with the same shape.
AC Circuits 6 of 77 Sinusoidal voltages are produced by ac generators and electronic oscillators. Sinusoidal voltage sources Generation of a sine wave A BC D When a conductor rotates in a constant magnetic field, a sinusoidal wave is generated. When the conductor is moving parallel with the lines of flux, no voltage is induced. When the loop is moving perpendicular to the lines of flux, the maximum voltage is induced.
AC Circuits 7 of 77 Sine waves are characterized by the amplitude and period. Sine waves The amplitude (A) of this sine wave is 20 V The period is 50.0 s A T 1.The amplitude is the maximum value of a voltage or current 2.The period is the time interval for one complete cycle.
AC Circuits 8 of 77 The period (T) of a sine wave can be measured between any two corresponding points on the waveform. Sine waves TTTT TT By contrast, the amplitude of a sine wave is only measured from the center to the maximum point. AA
AC Circuits 9 of 77
AC Circuits 10 of Hz 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 1.0 s
AC Circuits 11 of 77
AC Circuits 12 of 77 The period and frequency are reciprocals of each other. Period and frequency and If the period is 50 s, the frequency is 0.02 MHz = 20 kHz. (The 1/x key on your calculator is handy for converting between f and T.)
AC Circuits 13 of 77 Sine wave voltage and current values The peak voltage of this waveform is 20 V. VPVP vv Instantaneous value (v): Voltage or current at any point on the curve. Peak value (V P for voltage): The amplitude of a sine wave.
AC Circuits 14 of 77 The average value (actually the half-wave average) is used when comparing power supplies. Sine wave voltage and current values The average value for the sinusoidal voltage is 12.7 V. V avg
AC Circuits 15 of 77 Peak to peak value: Value from positive peak to negative peak. Equation = Sine wave voltage and current values RMS (root mean squared) value: Is the sinusoidal wave with the same heat value as a DC voltage source (known as the effective value)
AC Circuits 16 of 77 Sine wave voltage and current values The peak-to-peak voltage i s 40 V. The rms voltage is 14.1 V. V PP V rms V P = 20 volts This is magnitude V pp
AC Circuits 17 of 77 Degree: Angular measurement equal to 1/360 of the circumference of a circle. Radian (rad): Angle formed when the distance along the circumference of a circle equal the radius of the circle. PI ( ): The ratio of the circumference of a circle to its diameter. Has a constant value ≈ Angular Measurement
AC Circuits 18 of 77 Angular measurements can be made in degrees ( o ) or radians. There are 360 o or 2 radians in one complete revolution. Angular measurement
AC Circuits 19 of 77 Angular measurements
AC Circuits 20 of 77 There are 2 radians in one complete revolution and 360 o in one revolution. To find the number of radians, given the number of degrees: To find the number of degrees, given the number of radians: Angular measurement This can be simplified to:
AC Circuits 21 of 77 How many radians are in 45 o ? Angular measurement How many degrees are in 1.2 radians?
AC Circuits 22 of 77 Sine wave angles
AC Circuits 23 of 77 Phase of a Sine Wave Phase: Angular measurement that specifies the position on the sine wave relative to a reference point.
AC Circuits 24 of 77 Phase shift where = Phase shift Phase Shift of a sine wave is an angular measurement that specifies the position of a sine wave relative to a reference wave. Sine wave shifted right (lags) – Sine wave shifted left (leads) +
AC Circuits 25 of 77 Phase shifts Occurs when a sine wave is shifted right or left in relation to the base/reference sine wave.
AC Circuits 26 of 77 Phase shift – Lead/Lag Occurs when a sine wave is shifted right or left in relation to the base/reference sine wave. A - Leads B – Lags by 45 0 A - Lags B – Leads by 30 0
AC Circuits 27 of 77 Phase shift Notice that a lagging sine wave is below the axis at 0 o Example of a wave that lags the reference (not on guided notes) v = 30 V sin ( 45 o ) …and the equation has a negative phase shift
AC Circuits 28 of 77 Phase shift Notice that a leading sine wave is above the axis at 0 o Example of a wave that leads the reference (not on guided notes) v = 30 V sin ( + 45 o ) …and the equation has a positive phase shift
AC Circuits 29 of 77 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 o. PolyPhase power 120 o 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. 120 o 0o0o
AC Circuits 30 of 77 Instantaneous values of a wave are shown as v or i. The equation for the instantaneous voltage (v) of a sine wave is Sine wave equation If the peak voltage is 25 V, the instantaneous voltage at 50 degrees is where V p = theta = Peak voltage Angle in rad or degrees 19.2 V
AC Circuits 31 of 77 A certain sine wave has a positive-going zero crossing at 0° and an peak value of 40V. Calculate its instantaneous voltage for the degrees listed below for the sine wave below. Sine wave equation 45°, 125°, 180°, 220°,325° V p = theta = Peak voltage Angle in rad or degrees
AC Circuits 32 of 77 Sine wave equation A plot of the example in the previous slide (peak at 25 V). The instantaneous voltage at 50 o is 19.2 V as previously calculated. What is the voltage at 10 0 and 80 0 ? 4.34v 24.64v
AC Circuits 33 of 77 Phasor (aka Phase Vector): Representation of a sine wave whose amplitude (A) and angular frequency (ω - omega ) are a constant rate. Phasors
AC Circuits 34 of 77
AC Circuits 35 of 77 Power in resistive AC circuits A sinusoidal voltage produces a sinusoidal current
AC Circuits 36 of 77 Kirchhoff’s voltage law applies to AC circuits just like DC circuits Power in resistive AC circuits
AC Circuits 37 of 77 The power formulas are: Power in resistive AC circuits Power in AC circuits is calculated using RMS values for voltage and current. 0 V The dc and the ac sources produce the same power to the bulb: 120 V dc 170 V p = 120 V rms WHY?
AC Circuits 38 of 77 Assume a sine wave with a peak value of 40 V is applied to a 100 resistive load. What power is dissipated? Power in resistive AC circuits V rms = x V p = x 40 V = 28.3 V 8 W
AC Circuits 39 of 77 1.DC and AC voltages can be combined in a waveform. 2.Algebraically they produce a composite waveform of an AC voltage “riding” on a DC level. 3.If dc voltage > ac voltage, the sine wave never goes negative. Superimposed dc and ac voltages
AC Circuits 40 of 77 Superimposed dc and ac voltages
AC Circuits 41 of 77 Schematic for Superimposed DC and AC voltages
AC Circuits 42 of 77 Superimposed dc and ac voltages
AC Circuits 43 of 77 Superimposed dc and ac voltages V MAX = 22V V MIN = 2V V MAX = 16V V MIN = -4V
AC Circuits 44 of 77 Generators convert rotational energy to electrical energy. 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). AC generator (alternator) Small alternators may use a permanent magnet Others use field coils to produce the magnetic flux.
AC Circuits 45 of 77
AC Circuits 46 of 77 AC generator (alternator) Increasing the number of poles increases the number of cycles per revolution. A four-pole generator will produce two complete cycles in each revolution.
AC Circuits 47 of 77 Output Frequency of an AC Generator f – frequency (Hz) N – number of poles s - speed in RPM
AC Circuits 48 of 77 In vehicles, alternators generate ac, which is converted to dc for operating electrical devices and charging the battery. AC is more efficient to produce and can be easily regulated, hence it is generated and converted to DC by diodes. Alternators The output is taken from the rotor through the slip rings.
AC Circuits 49 of 77 There are two major classifications of ac motors. 1.Induction motor 2.Synchronous motor. 3.Both types use a rotating field in the stator windings. AC Motors 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.
AC Circuits 50 of 77 Rotating the stator produces a net magnetic field
AC Circuits 51 of 77 Rotating the stator produces a net magnetic field
AC Circuits 52 of 77 Induction vs. Stator Motors Squirrel Cage Rotor
AC Circuits 53 of 77 Induction vs. Stator Motors
AC Circuits 54 of 77 NONSINUSODIAL WAVE FORMS Pulse: Transition from one voltage/current level (baseline) to another level ( leading edge) and after an interval of time (t) transitioning back to the baseline (tailing edge) 1.Going positive – Rising edge 2.Going negative – Falling edge Rise Time (t r ) – Time required to go from 10% amplitude to 90% amplitude Fall time (t f )– Time to go from 90% amplitude to 10% amplitude Pulse width (t w ) - Interval of time from when t r is at 50% amplitude and t f is at 50% amplitude
AC Circuits 55 of 77 Pulse definitions Ideal pulses
AC Circuits 56 of 77 Pulse definitions Non-ideal pulses Notice that rise and fall times are measured between the 10% and 90% levels whereas pulse width is measured at the 50% level.
AC Circuits 57 of 77 Repetitive pulse waveforms Periodic waveforms repeat at fixed intervals. Pulse repetition frequency: Rate at which the pulses repeat. Duty Cycle – Ratio of pulse width (t w ) to the period (T) Percent Duty Cycle = V avg = baseline = (duty cycle)( amplitude)
AC Circuits 58 of 77 Nonsinusoidal Wave Forms Define terms on page 359 Rise time: Fall time: Pulse width:
AC Circuits 59 of 77 Voltage ramps Ramp – Linear increase or decrease in voltage or current. Slope =
AC Circuits 60 of 77 Triangular and Sawtooth waves Triangular and sawtooth waveforms are formed by voltage or current ramps (linear increase/decrease) Triangular waveforms have positive-going and negative-going ramps of equal duration (same slope either increasing or decreasing). The sawtooth waveform consists of two ramps, one of much longer duration than the other. (unequal slopes in either direction). T T T T
AC Circuits 61 of 77 Harmonics Repetitive non-sinusoidal waveforms are composed of: fundamental frequency (repetition rate of the waveform) & 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. Composite Waveform – Any deviation from a “normal” sine wave
AC Circuits 62 of 77 Harmonics A square wave is composed only of the fundamental frequency and odd harmonics (of the proper amplitude).
AC Circuits 63 of 77 Oscilloscope A device that traces the graph of a measured electrical signal on its screen.
AC Circuits 64 of 77 Oscilloscopes The oscilloscope is divided into four main sections.
AC Circuits 65 of 77 Video on Osciloscope on/yt/watch?v=8VEg6L2QG5ohttp://www.cleanvideosearch.com/media/acti on/yt/watch?v=8VEg6L2QG5o The name of video is: AC vs Dc explain how to use an oscilloscope
AC Circuits 66 of 77 Reading an Oscilloscope
AC Circuits 67 of 77 Calculate for each wave: Period, Peak, Peak to Peak, RMS T= 20 ms Vp = 1.5 v Vpp = 3.0 v RMS = 1.06 V 500 mv 0.5 ms 6 v 12 v15 µs 300 µs T= 3.0 ms Vp = 1250 mv Vpp = 2500 mv RMS = mV T= 6000 µs; 6 ms Vp = 20.4 v Vpp = 40.8 v RMS = 14.4 V T= 30 µs Vp = 24 v Vpp = 48 v RMS = V
AC Circuits 68 of 77 Sine wave Alternating current Period (T) Frequency (f) Hertz Current that reverses direction in response to a change in source voltage polarity. The time interval for one complete cycle of a periodic waveform. A type of waveform that follows a cyclic sinusoidal pattern defined by the formula y = A sin Selected Key Terms A measure of the rate of change of a periodic function; the number of cycles completed in 1 s. The unit of frequency. One hertz equals one cycle per second.
AC Circuits 69 of 77 Instantaneous value Peak value Peak-to-peak value rms value The voltage or current value of a waveform at its maximum positive or negative points. The voltage or current value of a waveform measured from its minimum to its maximum points. The voltage or current value of a waveform at a given instant in time. Selected Key Terms The value of a sinusoidal voltage that indicates its heating effect, also known as effective value. It is equal to times the peak value. rms stands for root mean square.
AC Circuits 70 of 77 Quiz 1. In North America, the frequency of ac utility voltage is 60 Hz. The period is a. 8.3 ms b ms c. 60 ms d. 60 s
AC Circuits 71 of 77 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
AC Circuits 72 of 77 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 ( + 35 o ) c. v = 5.0 V sin ( 27 o ) d. v = 27 V
AC Circuits 73 of In the equation v = V p sin , the letter v stands for the a. peak value b. average value c. rms value d. instantaneous value Quiz
AC Circuits 74 of 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 Quiz
AC Circuits 75 of 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 Quiz
AC Circuits 76 of The number of radians in 90 o are a. /2 b. c. 2 /3 d. 2 Quiz
AC Circuits 77 of For the waveform shown, the same power would be delivered to a load with a dc voltage of a V b V c V d V Quiz
AC Circuits 78 of 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 Quiz
AC Circuits 79 of 77 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
AC Circuits 80 of 77 Quiz Answers: 1. b 2. a 3. c 4. d 5. b 6. b 7. a 8. c 9. a 10. b