8. The AC Theory

Direct Current or D.C. as it is more commonly called, is a form of current or voltage that flows around an electrical circuit in one direction only, making it a "Uni-directional" supply. Generally, both DC currents and voltages are produced by power supplies, batteries, generators or solar cells, etc. A DC voltage and current has a fixed magnitude (amplitude) and a definite direction associated with it. For example, +12V represents 12 volts in the positive direction, or -5V represents 5 volts in the negative direction. We also know that DC power supplies do not change their value with regards to time; they are a constant value flowing in a continuous steady state direction. In other words, DC maintains its value for all times. A uni-directional or DC supply never becomes negative unless its connections are physically reversed. An example of a simple DC or direct current circuit is shown below.

a. DC Circuit and Waveform

An alternating function or AC Waveform on the other hand is defined as one that varies in both magnitude and direction in more or less an even manner with respect to time making it a "Bi-directional" waveform. An AC function can represent either a power source or a signal source with the shape of an AC waveform generally following that of a mathematical sinusoid as defined by

 The main characteristics of an AC Waveform are defined as:

• The Period, (T) is the length of time in seconds that the waveform takes to repeat itself from start to finish. This can also be called the Periodic Time of the waveform for sine waves, or the Pulse Width for square waves.
• The Frequency, (ƒ) is the number of times the waveform repeats itself within a one second time period. Frequency is the reciprocal of the time period, ( ƒ = 1/T ) with the unit of frequency being the Hertz, (Hz).
• The Amplitude (A) is the magnitude or intensity of the signal waveform measured in volts or amps.

Types of Periodic Waveform

The time taken for an AC Waveform to complete one full pattern from its positive half to its negative half and back to its zero baseline again is called a Cycle and one complete cycle contains both a positive half-cycle and a negative half-cycle. The time taken by the waveform to complete one full cycle is called the Periodic Time of the waveform, and is given the symbol T. The number of complete cycles that are produced within one second (cycles/second) is called the Frequency, symbol ƒ of the alternating waveform. Frequency is measured in Hertz, ( Hz ) named after the German physicist Heinrich Hertz.

Then we can see that a relationship exists between cycles (oscillations), periodic time and frequency (cycles per second), so if there are ƒ numbers of cycles in one second, each individual cycle must take 1/ƒ seconds to complete.

b. Relationship between Frequency and Periodic Time

Frequency is specified in units called Hertz and for the domestic mains supply this will be either 50Hz or 60Hz depending upon the country and is fixed by the speed of rotation of the generator. But one hertz is a very small unit so prefixes are used that denote the order of magnitude of the waveform at higher frequencies such as kHz, MHz and even GHz.

Prefix	Definition	Written as	Periodic Time
Kilo	Thousand	kHz	1mS
Mega	Million	MHz	1uS
Giga	Billion	GHz	1nS
Terra	Trillion	THz	1pS

c. The Average Value of an AC Waveform

The average or mean value of a continuous DC voltage will always be equal to its maximum peak value as a DC voltage is constant. This average value will only change if the duty cycle of the DC voltage changes. In a pure sine wave if the average value is calculated over the full cycle, the average value would be equal to zero as the positive and negative halves will cancel each other out. So the average or mean value of an AC waveform is calculated or measured over a half cycle only and this is shown below.

d. The RMS Value of an AC Waveform

For a pure sinusoidal waveform this effective or R.M.S.( Root Mean Squared) value will always be equal to 1/√2 x V_max which is equal to 0.707 x V_max and this relationship holds true for RMS values of current. The RMS value for a sinusoidal waveform is always greater than the average value except for a rectangular waveform.

One final comment about R.M.S. values. Most multimeters, either digital or analogue unless otherwise stated only measure the R.M.S. values of voltage and current and not the average. Therefore when using a multimeter on a direct current system the reading will be equal to I = V/R and for an alternating current system the reading will be equal to Irms = Vrms/R. Also, except for average power calculations, only use V_RMS to find I_RMS values, or peak voltage, Vp to find peak current, Ip values. Do not mix the two together average, R.M.S. or peak values as the results will be incorrect.

Next topic will be on Binary Numbers