Saturday, December 10, 2016
Introduction to Waveforms
Introduction to Waveforms
Typical Electrical Waveform
In Electronic Circuits we need to produce many different types, frequencies and shapes of Signal Waveforms such as Square Waves, Rectangular Waves, Triangular Waves, Sawtoothed Waveforms and a variety of pulses and spikes.
These types of signal waveform can then be used for either timing signals, clock signals or as trigger pulses. However, before we can begin to look at how the different types of waveforms are produced, we firstly need to understand the basic characteristics that make up Electrical Waveforms.
Technically speaking, Electrical Waveforms are basically visual representations of the variation of a voltage or current over time. In plain English this means that if we plotted these voltage or current variations on a piece of graph paper against a base (x-axis) of time, ( t ) the resulting plot or drawing would represent the shape of a Waveform as shown. There are many different types ofelectrical waveforms available but generally they can all be broken down into two distinctive groups.
- 1. Uni-directional Waveforms – these electrical waveforms are always positive or negative in nature flowing in one forward direction only as they do not cross the zero axis point. Common uni-directional waveforms include Square-wave timing signals, Clock pulses and Trigger pulses.
- 2. Bi-directional Waveforms – these electrical waveforms are also called alternating waveforms as they alternate from a positive direction to a negative direction constantly crossing the zero axis point. Bi-directional waveforms go through periodic changes in amplitude, with the most common by far being the Sine-wave.
Whether the waveform is uni-directional, bi-directional, periodic, non-periodic, symmetrical, non-symmetrical, simple or complex, all electrical waveforms include the following three common characteristics:
- 1). Period: – This is the length of time in seconds that the waveform takes to repeat itself from start to finish. This value can also be called the Periodic Time, ( T ) of the waveform for sine waves, or the Pulse Width for square waves.
- 2). Frequency: – This 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 standard unit of frequency being the Hertz, (Hz).
- 3). Amplitude: – This is the magnitude or intensity of the signal waveform measured in volts or amps.
Periodic Waveforms
Periodic waveforms are the most common of all the electrical waveforms as it includes Sine Waves. The AC (Alternating Current) mains waveform in your home is a sine wave and one which constantly alternates between a maximum value and a minimum value over time.
The amount of time it takes between each individual repetition or cycle of a sinusoidal waveform is known as its “periodic time” or simply the Period of the waveform. In other words, the time it takes for the waveform to repeat itself.
Then this period can vary with each waveform from fractions of a second to thousands of seconds as it depends upon the frequency of the waveform. For example, a sinusoidal waveform which takes one second to complete its cycle will have a periodic time of one second. Likewise a sine wave which takes five seconds to complete will have a periodic time of five seconds and so on.
So, if the length of time it takes for the waveform to complete one full pattern or cycle before it repeats itself is known as the “period of the wave” and is measured in seconds, we can then express the waveform as a period number per second denoted by the letter T as shown below.
A Sine Wave Waveform
Units of periodic time, ( T ) include: Seconds ( s ), milliseconds ( ms ) and microseconds ( ?s ).
For sine wave waveforms only, we can also express the periodic time of the waveform in either degrees or radians, as one full cycle is equal to 360o ( T = 360o ) or in Radians as 2pi, 2? ( T = 2? ), then we can say that 2? radians = 360o – ( Remember this! ).
We now know that the time it takes for electrical waveforms to repeat themselves is known as the periodic time or period which represents a fixed amount of time. If we take the reciprocal of the period, ( 1/T ) we end up with a value that denotes the number of times a period or cycle repeats itself in one second or cycles per second, and this is commonly known as Frequency with units ofHertz, (Hz). Then Hertz can also be defined as “cycles per second” (cps) and 1Hz is exactly equal to 1 cycle per second.
Both period and frequency are mathematical reciprocals of each other and as the periodic time of the waveform decreases, its frequency increases and vice versa with the relationship betweenPeriodic time and Frequency given as.
Relationship between Frequency and Periodic Time
Where: ƒ is in Hertz and T is in Seconds.
One Hertz is exactly equal to one cycle per second, but one hertz is a very small unit so prefixes are used that denote the order of magnitude of the waveform such as kHz, MHz and even GHz.
| Prefix | Definition | Written as | Time Period |
| Kilo | Thousand | kHz | 1ms |
| Mega | Million | MHz | 1us |
| Giga | Billion | GHz | 1ns |
| Tera | Trillion | THz | 1ps |
Square Wave Electrical Waveforms
Square-wave Waveforms are used extensively in electronic and micro electronic circuits for clock and timing control signals as they are symmetrical waveforms of equal and square duration representing each half of a cycle and nearly all digital logic circuits use square wave waveforms on their input and output gates.
Unlike sine waves which have a smooth rise and fall waveform with rounded corners at their positive and negative peaks, square waves on the other hand have very steep almost vertical up and down sides with a flat top and bottom producing a waveform which matches its description, – “Square” as shown below.
A Square Wave Waveform
We know that square shaped electrical waveforms are symmetrical in shape as each half of the cycle is identical, so the time that the pulse width is
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