Representation of Waveforms..?
Representation of Waveforms..?
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, ( Æ’ = 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 ( μs ).
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, 2Ï€ ( T = 2Ï€ ), then we can say that 2Ï€ 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: Æ’ 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 positive must be equal to the time that the pulse width is
negative or zero. When square wave waveforms are used as “clock” signals
in digital circuits the time of the positive pulse width is known as
the “Duty Cycle” of the period.
Then we can say that for a square wave waveform the positive or “ON”
time is equal to the negative or “OFF” time so the duty cycle must be
50%, (half of its period). As frequency is equal to the reciprocal of
the period, ( 1/T ) we can define the frequency of a square wave waveform as:
Electrical Waveforms Example No1
A Square Wave electrical waveform has a pulse width of 10ms, calculate its frequency, ( Æ’ ).
For a square wave shaped waveform, the duty cycle is given as 50%, therefore the period of the waveform must be equal to: 10ms + 10ms or 20ms
So to summarise a little about Square Waves. A Square Wave Waveform is
symmetrical in shape and has a positive pulse width equal to its
negative pulse width resulting in a 50% duty cycle. Square wave
waveforms are used in digital systems to represent a logic level “1”,
high amplitude and logic level “0”, low amplitude. If the duty cycle of
the waveform is any other value than 50%, (half-ON half-OFF) the
resulting waveform would then be called a Rectangular Waveform or if the “ON” time is really small a Pulse.
Rectangular Waveforms
Rectangular Waveforms are
similar to the square wave waveform above, the difference being that
the two pulse widths of the waveform are of an unequal time period.
Rectangular waveforms are therefore classed as “Non-symmetrical”
waveforms as shown below.
A Rectangular Waveform
The example above shows that the positive pulse width is shorter in time
than the negative pulse width. Equally, the negative pulse width could
be shorter than the positive pulse width, either way the resulting
waveform shape would still be that of a rectangular waveform.
These positive and negative pulse widths are sometimes called “Mark” and
“Space” respectively, with the ratio of the Mark time to the Space time
being known as the “Mark-to-Space” ratio of the period and for a Square
wave waveform this would be equal to one.
Electrical Waveforms Example No2
A Rectangular waveform has a positive pulse width (Mark time) of 10ms and a duty cycle of 25%, calculate its frequency.
The duty cycle is given as 25% or 1/4 and this is equal to the mark time
which is 10ms, then the period of the waveform must be equal to: 10ms (25%) + 30ms (75%) which equals 40ms (100%) in total.
Rectangular Waveforms can
be used to regulate the amount of power being applied to a load such as
a lamp or motor by varying the duty cycle of the waveform. The higher
the duty cycle, the greater the average amount of power being applied to
the load and the lower the duty cycle, the less the average amount of
power being applied to the load and an excellent example of this is in
the use of “Pulse Width Modulation” speed controllers.
Triangular Waveforms
Triangular Waveforms are
generally bi-directional non-sinusoidal waveforms that oscillate
between a positive and a negative peak value. Although called a
triangular waveform, the triangular wave is actually more of a
symmetrical linear ramp waveform because it is simply a slow rising and
falling voltage signal at a constant frequency or rate. The rate at
which the voltage changes between each ramp direction is equal during
both halves of the cycle as shown below.
A Triangular Waveform
Generally, for Triangular Waveforms the
positive-going ramp or slope (rise), is of the same time duration as
the negative-going ramp (decay) giving the triangular waveform a 50%
duty cycle. Then any given voltage amplitude, the frequency of the
waveform will determine the average voltage level of the wave.
So for a slow rise and slow delay time of the ramp will give a lower
average voltage level than a faster rise and decay time. However, we can
produce non-symmetrical triangular waveforms by varying either the
rising or decaying ramp values to give us another type of waveform known
commonly as a Sawtooth Waveform.
Sawtooth Waveforms
Sawtooth Waveforms are
another type of periodic waveform. As its name suggests, the shape of
the waveform resembles the teeth of a saw blade. Sawtoothed waveforms
can have a mirror image of themselves, by having either a slow-rising
but extremely steep decay, or an extremely steep almost vertical rise
and a slow-decay as shown below.
Sawtooth Waveforms
The positive ramp Sawtooth Waveform is
the more common of the two waveform types with the ramp portion of the
wave being almost perfectly linear. The Sawtooth waveform is commonly
available from most function generators and consists of a fundamental
frequency ( Æ’ ) and all its integer ratios of even harmonics only, 1/2, 1/4, 1/6 1/8 … 1/n etc. What this means in practical terms is that the Sawtoothed Waveform is
rich in harmonics and for music synthesizers and musicians gives the
quality of the sound or tonal colour to their music without any
distortion.
Triggers and Pulses
Although technically Triggers and Pulses are
two separate waveforms, we can combine them together here, as a
“Trigger” is basically just a very narrow “Pulse”. The difference being
is that a trigger can be either positive or negative in direction
whereas a pulse is only positive in direction.
A Pulse Waveform or
“Pulse-train” as they are more commonly called, is a type of
non-sinusoidal waveform that is similar to the Rectangular waveform we
looked at earlier. The difference being that the exact shape of the
pulse is determined by the “Mark-to-Space” ratio of the period and for a
pulse or trigger waveform the Mark portion of the wave is very short
with a rapid rise and decay shape as shown below.
A Pulse Waveform
A Pulse is
a waveform or signal in its own right. It has very different
Mark-to-Space ratio compared to a high frequency square wave clock
signal or even a rectangular waveform.
The purpose of a “Pulse” and that of a trigger is to produce a very
short signal to control the time at which something happens for example,
to start a Timer, Counter, Monostable or Flip-flop etc, or as a trigger
to switch “ON” Thyristors, Triacs and other power semiconductor devices.
Function Generator
A Function Generator or sometimes called a Waveform Generator is
a device or circuit that produces a variety of different waveforms at a
desired frequency. It can generate Sine waves, Square waves, Triangular
and Sawtooth waveforms as well as other types of output waveforms.
There are many “off-the-shelf” waveform generator IC’s available and all
can be incorporated into a circuit to produce the different periodic
waveforms required.
One such device is the 8038 a
precision waveform generator IC capable of producing sine, square and
triangular output waveforms, with a minimum number of external
components or adjustments. Its operating frequency range can be selected
over eight decades of frequency, from 0.001Hz to 300kHz, by the correct
choice of the external R-C components.
Waveform Generator IC
The frequency of oscillation is highly stable over a wide range of
temperature and supply voltage changes and frequencies as high as 1MHz
is possible. Each of the three basic waveform outputs, sinusoidal,
triangular and square are simultaneously available from independent
output terminals. The frequency range of the 8038 is voltage
controllable but not a linear function. The triangle symmetry and hence
the sine wave distortion are adjustable.
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