4A 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 to alternating current.
5Sine wavesThe 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.
6Generation of a sine wave Sinusoidal voltage sourcesSinusoidal voltages are produced by ac generators and electronic oscillators.When a conductor rotates in a constant magnetic field, a sinusoidal wave is generated.DBCAWhen the loop is moving perpendicular to the lines of flux, the maximum voltage is induced.When the conductor is moving parallel with the lines of flux, no voltage is induced.
7Sine waves Sine waves are characterized by the amplitude and period. The amplitude is the maximum value of a voltage or currentThe period is the time interval for one complete cycle.AThe amplitude (A) of this sine wave is20 VTThe period is50.0 ms
8Sine wavesThe period (T) of a sine wave can be measured between any two corresponding points on the waveform.TTTTATTABy contrast, the amplitude of a sine wave is only measured from the center to the maximum point.
12Period and frequencyThe period and frequency are reciprocals of each other.andIf the period is 50 ms, the frequency is0.02 MHz = 20 kHz.(The 1/x key on your calculator is handy for converting between f and T.)
13Sine wave voltage and current values Instantaneous value (v): Voltage or current at any point on the curve.Peak value (VP for voltage): The amplitude of a sine wave.VPvThe peak voltage of this waveform is20 V.v
14Sine wave voltage and current values The average value (actually the half-wave average) is used when comparing power supplies.The average value for the sinusoidal voltage isVavg12.7 V.
15Sine wave voltage and current values Peak to peak value: Value from positive peak to negative peak. Equation =RMS (root mean squared) value: Is the sinusoidal wave with the same heat value as a DC voltage source (known as the effective value)
16Sine wave voltage and current values VP = 20 voltsThe peak-to-peak voltage isVrms40 V.VPPThe rms voltage is14.1 V.This is magnitude Vpp
17Angular Measurement 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 ≈
18Angular measurementAngular measurements can be made in degrees (o) or radians.There are 360o or 2p radians in one complete revolution.
20Angular measurementThere are 2p radians in one complete revolution and 360o in one revolution. To find the number of radians, given the number of degrees:This can be simplified to:To find the number of degrees, given the number of radians:
21How many radians are in 45o? Angular measurementHow many radians are in 45o?How many degrees are in 1.2 radians?
23Phase of a Sine Wave Phase: Angular measurement that specifies the position on the sine wave relative to a reference point.
24Phase shiftPhase 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) +wheref =Phase shift
25Phase shiftsOccurs when a sine wave is shifted right or left in relation to the base/reference sine wave.
26Phase shift – Lead/LagOccurs when a sine wave is shifted right or left in relation to the base/reference sine wave.A - LeadsB – Lags by 450A - LagsB – Leads by 300
27Phase shiftExample of a wave that lags the reference (not on guided notes)…and the equation has a negative phase shiftv = 30 V sin (q - 45o)Notice that a lagging sine wave is below the axis at 0o
28Phase shiftExample of a wave that leads the reference (not on guided notes)Notice that a leading sine wave is above the axis at 0ov = 30 V sin (q + 45o)…and the equation has a positive phase shift
29PolyPhase powerAn important application of phase-shifted sine waves is in electrical power systems.Electrical utilities generate ac with three phases that are separated by 120o.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.120o120o120o0o
30Sine wave equation Instantaneous values of a wave are shown as v or i. The equation for the instantaneous voltage (v) of a sine wave iswhereVp =q (theta) =Peak voltageAngle in rad or degreesIf the peak voltage is 25 V, the instantaneous voltage at 50 degrees is19.2 V
31Sine wave equationA 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.Vp =q (theta) =Peak voltageAngle in rad or degrees45°, 125°, 180°, 220°,325°
32Sine wave equationA plot of the example in the previous slide (peak at 25 V).The instantaneous voltage at 50o is 19.2 V as previously calculated.4.34v24.64vWhat is the voltage at 100 and 800?
33Phasors Phasor (aka Phase Vector): Representation of a sine wave whose amplitude (A) and angular frequency (ω - omega) are a constant rate.
35Power in resistive AC circuits A sinusoidal voltage produces a sinusoidal current
36Kirchhoff’s voltage law applies to AC circuits just like DC circuits Power in resistive AC circuitsKirchhoff’s voltage law applies to AC circuits just like DC circuits
37Power in resistive AC circuits Power in AC circuits is calculated using RMS values for voltage and current.The power formulas are:The dc and the ac sources produce the same power to the bulb:120 Vdc0 V170 Vp= 120 Vrms0 VWHY?
38Power 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?Vrms = x Vp = x 40 V = V8 W
39Superimposed dc and ac voltages DC and AC voltages can be combined in a waveform.Algebraically they produce a composite waveform of an AC voltage “riding” on a DC level.If dc voltage > ac voltage, the sine wave never goes negative.
43Superimposed dc and ac voltages VMAX = 22VVMIN = 2VVMAX = 16VVMIN = -4V
44AC generator (alternator) 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).Small alternators may use a permanent magnetOthers use field coils to produce the magnetic flux.
46AC 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.
47Output Frequency of an AC Generator f – frequency (Hz)N – number of poless - speed in RPM1423
48AlternatorsIn 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.The output is taken from the rotor through the slip rings.
49AC Motors There are two major classifications of ac motors. Induction motorSynchronous 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.
50Rotating the stator produces a net magnetic field
51Rotating the stator produces a net magnetic field
54NONSINUSODIAL 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)Going positive – Rising edgeGoing negative – Falling edgeRise Time (tr) – Time required to go from 10% amplitude to 90% amplitudeFall time (tf)– Time to go from 90% amplitude to 10% amplitudePulse width (tw) - Interval of time from when tr is at 50% amplitude and tf is at 50% amplitude
56Pulse 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.
57Repetitive pulse waveforms Periodic waveforms repeat at fixed intervals.Pulse repetition frequency: Rate at which the pulses repeat.Duty Cycle – Ratio of pulse width (tw) to the period (T)Percent Duty Cycle =Vavg = baseline = (duty cycle)( amplitude)
58Nonsinusoidal Wave Forms Define terms on page 359Rise time:Fall time:Pulse width:
59Voltage rampsRamp – Linear increase or decrease in voltage or current.Slope =
60Triangular 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).TTThe sawtooth waveform consists of two ramps, one of much longer duration than the other. (unequal slopes in either direction).
61Harmonics 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
62HarmonicsA square wave is composed only of the fundamental frequency and odd harmonics (of the proper amplitude).
63OscilloscopeA device that traces the graph of a measured electrical signal on its screen.
64OscilloscopesThe oscilloscope is divided into four main sections.
65Video on OsciloscopeThe name of video is: AC vs Dc explain how to use an oscilloscope
68Selected Key Terms Sine wave Alternating currentPeriod (T)Frequency (f)HertzA type of waveform that follows a cyclic sinusoidal pattern defined by the formula y = A sin q.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 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.
69Selected Key Terms Instantaneous value Peak valuePeak-to-peak valuerms valueThe voltage or current value of a waveform at a given instant in time.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 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.
70Quiz1. In North America, the frequency of ac utility voltage is 60 Hz. The period isa. 8.3 msb msc. 60 msd. 60 s
71Quiz 2. The amplitude of a sine wave is measured a. at the maximum pointb. between the minimum and maximum pointsc. at the midpointd. anywhere on the wave
72Quiz3. An example of an equation for a waveform that lags the reference isa. v = -40 V sin (q)b. v = 100 V sin (q + 35o)c. v = 5.0 V sin (q - 27o)d. v = 27 V
73Quiz 4. In the equation v = Vp sin q , the letter v stands for the a. peak valueb. average valuec. rms valued. instantaneous value
74Quiz5. The time base of an oscilloscope is determined by the setting of thea. vertical controlsb. horizontal controlsc. trigger controlsd. none of the above
75Quiz 6. A sawtooth waveform has a. equal positive and negative going rampsb. two ramps - one much longer than the otherc. two equal pulsesd. two unequal pulses
76Quiz7. The number of radians in 90o area. p/2b. pc. 2p/3d. 2p
77Quiz8. For the waveform shown, the same power would be delivered to a load with a dc voltage ofa Vb Vc Vd V
78Quiz 9. A square wave consists of a. the fundamental and odd harmonics b. the fundamental and even harmonicsc. the fundamental and all harmonicsd. only the fundamental
79Quiz10. A control on the oscilloscope that is used to set the desired number of cycles of a wave on the display isa. volts per division controlb. time per division controlc. trigger level controld. horizontal position control