1 © Unitec New Zealand DE APTE 5601 I NTRODUCTION TO AC CIRCUIT THEORY

DC and AC DC stands for “Direct Current,” –voltage maintains constant polarity over time –current maintains constant direction over time. AC stands for “Alternating Current”: –voltage changes polarity over time –current changes direction over time 2 © Unitec New Zealand

Why AC? With AC, it is possible to build electric generators, motors and power distribution systems that are far more efficient than DC 3 © Unitec New Zealand War of Currents

AC is necessary because... AC generators and AC motors tend to be simpler than DC generators and DC motors. –This relative simplicity translates into greater reliability and lower cost of manufacture. The transformer's ability to step AC voltage up or down with ease gives AC an advantage unmatched by DC in the realm of power distribution. –When transmitting electrical power over long distances, it is far more efficient to do so with stepped-up voltages and stepped- down currents (smaller-diameter wire with less resistive power losses), then step the voltage back down and the current back up at the receiving end for consumer use. 4 © Unitec New Zealand

Main AC advantage: power distribution 5 © Unitec New Zealand

Can’t be done with DC Transformer technology has made long-range electric power distribution practical. Without the ability to efficiently step voltage up and down, it would be cost- prohibitive to construct power systems for anything but close-range (within a few miles at most) use. Transformers only work with AC, not DC. It works based on the phenomenon of mutual inductance, which relies on changing magnetic fields. Direct current (DC) can only produce steady magnetic fields, thus transformers simply will not work with direct current. 6 © Unitec New Zealand

Waveform of DC 7 © Unitec New Zealand

AC waveform: sine wave When graphed, the voltage produced by AC generator (alternator) takes on a distinct shape known as a sine wave: 8 © Unitec New Zealand One cycle of a wave is one complete evolution of its shape until the point that it is ready to repeat itself.

Sinewave Generation 9 © Unitec New Zealand

Sinewave Details 10 © Unitec New Zealand

Other waveforms 11 © Unitec New Zealand

Sinusoidal waveform Sinusoidal waveform is given by I = I o sin (ωt+ ϕ ) –Io is amplitude –ω is angular frequency in radian per second: ω = 2  / T –t is time and ϕ is the phase angle. The period T of a wave is the amount of time it takes to complete one cycle (unit is second s). 12 © Unitec New Zealand

Frequency Frequency is the number of complete cycles that a wave completes in a given amount of time. Standard unit for frequency is Hertz (abbreviated Hz). Frequency of 1 Hz represents the number of periods completed during one second of time. f = 1 / T  2  f 13 © Unitec New Zealand

Radians 14 © Unitec New Zealand

Conversions 15 © Unitec New Zealand

Some well known frequencies... In New Zealand, power system frequency is 50 Hz. This corresponds to the period T = 20ms. In US, power system frequency is 60 Hz. Audio frequencies: from 20 Hz to 20kHz A radio station broadcast at a frequency of 100 MHz. Microwave oven operates at 2.54 GHz k (kilo) = 1000 Hz; M (mega) = Hz; G(giga)= Hz. In music, frequency is the same as pitch, which is the essential property distinguishing one note from another 16 © Unitec New Zealand

AC generator in the laboratory In our lab, we will use an Audio Generator. This means that the frequency of an AC wave taken from the generator Output is within an audio range (frequencies we can hear). We can adjust both frequency (period) and magnitude of the wave 17 © Unitec New Zealand

Oscilloscope The main purpose of an oscilloscope is to give an accurate visual representation of electrical signals. 18 © Unitec New Zealand

Your instrument Every large instrument manufacturer has additional resources online: pdf files, videos, forums, FAQ –Get the model number of your instrument and find the manual online Tektronix: Agilent: 19 © Unitec New Zealand

Oscilloscope 20 © Unitec New Zealand

Measurement of AC amplitude With DC, where quantities of voltage and current are constant, we have little trouble expressing how much voltage or current we have in any part of a circuit. But how do you measure magnitude of something that is constantly changing? The amplitude of an AC waveform is its height as depicted on a graph over time. An amplitude measurement can take the form of peak, peak-to-peak, average, or RMS quantity. 21 © Unitec New Zealand

Peak amplitude Peak amplitude is the height of an AC waveform as measured from the zero mark to the highest positive or lowest negative point on a graph. Also known as the crest amplitude of a wave. 22 © Unitec New Zealand

Peak-to-peak amplitude Peak-to-peak amplitude is the total height of an AC waveform as measured from maximum positive to maximum negative peaks on a graph. Often abbreviated as “P-P”. 23 © Unitec New Zealand

Average value of all points ? 24 © Unitec New Zealand Average amplitude is the mathematical “mean” of all a waveform's points over the period of one cycle.

Average of absolute values Technically, the average amplitude of any waveform with equal-area portions above and below the “zero” line on a graph is zero. However, as a practical measure of amplitude, a waveform's average value is often calculated as the mathematical mean of all the points' absolute values (taking all the negative values and considering them as positive) –For a sine wave, the average value so calculated is approximately of its peak value. 25 © Unitec New Zealand

Ability to do useful work 26 © Unitec New Zealand

DC equivalent to AC assign a “DC equivalent” measurement to any AC voltage or current: – whatever magnitude of DC voltage or current would produce the same amount of heat energy dissipation through an equal resistance 27 © Unitec New Zealand An RMS voltage produces the same heating effect as a the same DC voltage

Root Mean Square For example, 10 volts AC RMS is the amount of voltage that would produce the same amount of heat dissipation across a resistor of given value as a 10 volt DC power supply. The qualifier “RMS” stands for Root Mean Square, and is a way of expressing an AC quantity of voltage or current in terms functionally equivalent to DC. –To calculate the Root Mean Square of a set of numbers, square all the numbers in the set and then find the arithmetic mean of the squares. Take the square root of the result. 28 © Unitec New Zealand

RMS for sine wave For a sine wave, the RMS value is approximately of its peak value 29 © Unitec New Zealand

RMS Peak Average Conversions 30 © Unitec New Zealand

Non Sinusoidal Average is Different 31 © Unitec New Zealand

RMS is most often stated When talking of AC, RMS values are so commonly used that, unless otherwise stated, you may assume that RMS values are intended*. For instance, normal domestic AC in New Zealand is 230 Volts AC with frequency 50 Hz. The RMS voltage is 230 volts, so: – the peak value V m = V.√2 = 325 volts. –So the active wire goes from +325 volts to -325 volts and back again 50 times per second. 32 © Unitec New Zealand

It depends on the use, though... For instance, when determining the proper size of wire to conduct electric power from a source to a load, RMS current measurement is the best to use, because the principal concern with current is overheating of the wire, which is a function of power dissipation caused by current through the resistance of the wire. However, when rating insulators for service in high- voltage AC applications, peak voltage measurements are the most appropriate, because the principal concern here is insulator “flashover” caused by brief spikes of voltage, irrespective of time. 33 © Unitec New Zealand

For other wave shapes.. Formulas for RMS and average value given above are for sine waves only. If you have other wave shapes, you cannot use these formulas! Find appropriate formula in literature or online OR calculate the value from definition 34 © Unitec New Zealand

Comparing two sine waveforms I = I o sin (ωt+ ϕ ) Looking at : –Amplitude –Frequency –Phase 35 © Unitec New Zealand

In Phase 36 © Unitec New Zealand

Pos Neg Phase 37 © Unitec New Zealand

Phase Difference 38 © Unitec New Zealand

Phase shift Phase shift occurs when two waveforms are “out of step” with each other. Calculations for AC circuit analysis must take into consideration both amplitude and phase shift of voltage and current waveforms to be completely accurate. This requires the use of complex numbers. 39 © Unitec New Zealand

Phase: always relative phase is always a relative measurement between two waveforms rather than an absolute property 40 © Unitec New Zealand

Revision Period Frequency For Sine wave: must know how to measure / read / calculate –Peak value –Peak-to-Peak value –Average value –RMS value Phase shift 41 © Unitec New Zealand