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4 : ignals


This Chapter uses voltage/time, V/t, graphs to describe the charactersitics of different types of signals. The Practical introduces the oscilloscope, a key instrument for measuring and displaying V/t graphs.

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Introducing signals Making waves
Sine waves Other signals
Listening to waves LINKS . . .

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Introducing signals

In electronic circuits things happen. Voltage/time, V/t, graphs provide a useful method of describing the changes which take place.

The diagram below shows the V/t graph which represents a DC signal:

V/t graph for a DC signal

This is a horizontal line a constant distance above the X-axis. In many circuits, fixed DC levels are maintained along power supply rails, or as reference levels with which other signals can be compared.

Compare this graph with the V/t graphs for several types of alternating, or AC, signals:

alternating signals

As you can see, the voltage levels change with time and alternate between positive values (above the X-axis) and negative values (below the X-axis). Signals with repeated shapes are called waveforms and include sine waves, square waves, triangular waves and sawtooth waves. A distinguishing feature of alternating waves is that equal areas are enclosed above and below the X-axis.

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Sine waves

A sine wave has the same shape as the graph of the sine function used in trigonometry. Sine waves are produced by rotating electrical machines such as dynamos and power station turbines and electrical energy is transmitted to the consumer in this form. In electronics, sine waves are among the most useful of all signals in testing circuits and analysing system performance.

Look at the sine wave in more detail:

sine wave

The terms defined below are needed to describe sine waves and other waveforms precisely:

1. Period: T : The period is the time taken for one complete cycle of a repeating waveform. The period is often thought of as the time interval between peaks, but can be measured between any two corresponding points in successive cycles.

2. Frequency: f : This is the number of cycles completed per second. The measurement unit for frequency is the hertz, Hz. 1 Hz = 1 cycle per second. If you know the period, the frequency of the signal can be calculated from:

Conversely, the period is given by:

Signals you are likely to use vary in frequeny from about 0.1 Hz, through values in kilohertz, kHz (thousands of cycles per second) to values in megahertz, MHz (millions of cycles per second).

3. Amplitude: In electronics, the amplitude, or height, of a sine wave is measured in three different ways. The peak amplitude, Vp , is measured from the X-axis, 0 V, to the top of a peak, or to the bottom of a trough. (In physics 'amplitude' usually refers to peak amplitude.) The peak-to-peak amplitude, Vpp , is measured between the maximum positive and negative values. In practical terms, this is often the easier measurement to make. Its value is exactly twice Vp .

Although peak and peak-to-peak values are easily determined, it is often more useful to know the root mean square, or rms amplitude of the wave, where:

or

and:

or

What is rms amplitude and why is it important?

KEY POINT: The rms amplitude is the DC voltage which will deliver the same average power as the AC signal.

To understand this, think about two lamps connected to alternative power supplies:

AC and DC compared

The brightness of the lamp illuminated from the AC supply looks constant but the current flowing in the lamp is changing all the time and alternates in direction, flowing first one way and then the other. There is no current flowing at the instant that the AC signal crosses the X-axis. What you see is the average brightness produced by the AC signal.

The second lamp is illuminated from a DC supply and its brightness really is constant because the current flowing is always the same. It is obviously possible to adjust the voltage of the DC supply until the two lamps are equally bright. When this happens, the DC supply is providing the same average power as the AC supply. At this point, the DC voltage is equal to the Vrms value for the AC signal.

A bit of mathematics is needed to explain why the equivalent DC value is called the root mean square value. If you want to know about this click here. What is important at this stage is to remember that the AC signal and its rms equivalent provide the same average power.

4. Phase: It is sometimes useful to divide a sine wave into degrees, ░ , as follows:

phase

Remember that sine waves are generated by rotating electrical machines. A complete 360░ turn of the voltage generator corresponds to one cycle of the sine wave. Therefore 180░ corresponds to a half turn, 90░ to a quarter turn and so on. Using this method, any point on the sine wave graph can be identified by a particular number of degrees through the cycle.

If two sine waves have the same frequency and occur at the same time, they are said to be in phase:

in phase and out of phase

On the other hand, if the two waves occur at different times, they are said to be out of phase. When this happens, the difference in phase can be measured in degrees, and is called the phase angle, . As you can see, the two waves in part B are a quarter cycle out of phase, so the phase angle = 90░.

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Listening to waves

It can be helpful in understanding what is meant by 'frequency' and 'amplitude' to compare the sounds produced when different waves are played through a loudspeaker.

Not all frequencies are audible. The hi-fi range is defined as from 20 Hz to 20 kHz, approximately the same as the range of frequencies which can normally be detected. As you get older, you will find it more and more difficult to hear higher frequencies. Experience suggests that, by the time you are able to afford a decent hi-fi system, you will probably be unable to fully appreciate its performance.

ALTERNATIVE
     NAMES
The pitch of a musical note is the same as its frequency
The intensity or loudness of a musical note is the same as its amplitude

Your ears are particularly sensitive to sounds in the middle range, from about 500 Hz to 2 kHz, corresponding with the range of frequencies found in human speech. Telephone systems have a poor high frequency performance but do work effectively in this middle range.

When you design an alarm system with an audible output, it is important to keep the frequency of the alarm sounds within this middle range.

The graphs below show waveforms of different frequency and amplitude. Click on the button below each graph to listen to the corresponding sounds:

   Play sound    Play sound
   Play sound    Play sound
   Play sound    Play sound

These sine wave signals produce a 'pure' sounding tone. If the amplitude is increased, the sound is louder. If the frequency is increased, the pitch of the sound is higher.

Other shapes of signal generate sounds with the same fundamental pitch, but can sound different. Compare the sine wave sounds with square signals at 500 Hz and 1 kHz:

   Play sound    Play sound

The square wave sound is harsher because the signal contains additional frequencies which are multiples of the fundamental frequency. These additional frequencies are called harmonics. Sounds from different musical instruments are distinguished by their harmonic content.

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Making waves

Sine waves can be mixed with DC signals, or with other sine waves to produce new waveforms. Here is one example of a complex waveform:

complex waveform

'Complex' doesn't mean difficult to understand. A waveform like this can be thought of as consisting of a DC component with a superimosed AC component. It is quite easy to separate these two components using a capacitor, as will be explained in Chapter 5.

More dramatic results are obtained by mixing a sine wave of a particular frequency with exact multiples of the same frequency, in other words, by adding harmonics to the fundamental frequency. The V/t graphs below show what happens when a sine wave is mixed with its 3rd harmonic (3 times the fundamental frequency) at reduced amplitude, and subsequently with its 5th, 7th and 9th harmonics:

constructing a square wave

As you can see, as more odd harmonics are added, the waveform begins to look more and more like a square wave.

This surprising result illustrates a general principle first formulated by the French mathematician Joseph Fourier, namely that any complex waveform can be built up from a pure sine waves plus particular harmonics of the fundamental frequency. Square waves, triangular waves and sawtooth waves can all be produced in this way.

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Other signals

This part of the Chapter outlines the other types of signal you are going to meet. Circuits which generate these signals are versatile building blocks and many practical examples are given later in Design Electronics.

1. Square waves: Like sine waves, square waves are described in terms of period, frequency and amplitude:

square waves and rise time

Peak amplitude, Vp , and peak-to-peak amplitude, Vpp , are measured as you might expect. However, the rms amplitude, Vrms , is greater than that of a sine wave. Remember that the rms amplitude is the DC voltage which will deliver the same power as the signal. If a square wave supply is connected across a lamp, the current flows first one way and then the other. The current switches direction but its magnitude remains the same. In other words, the square wave delivers its maximum power throughout the cycle so that Vrms is equal to Vp . (If this is confusing, don't worry, the rms amplitude of a square wave is not something you need to think about very often.)

Although a square wave may change very rapidly from its minimum to maximum voltage, this change cannot be instaneous. The rise time of the signal is defined as the time taken for the voltage to change from 10% to 90% of its maximum value. Rise times are usually very short, with durations measured in nanoseconds (1 ns = 10-9 s), or microseconds (1 Ás = 10-6 s), as indicated in the graph.

2. Pulse waveforms: Pulse waveforms look similar to square waves, excpet that all the action takes place above the X-axis. At the beginning of a pulse, the voltage changes suddenly from a LOW level, close to the X-axis, to a HIGH level, usually close to the power supply voltage:

pulse waveform

Sometimes, the 'frequency' of a pulse waveform is referred to as its repetition rate. As you would expect, this means the number of cycles per second, measured in hertz, Hz.

The HIGH time of the pulse waveform is called the mark, while the LOW time is called the space. The mark and space do not need to be of equal duration. The mark space ratio is given by:

A mark space ratio = 1.0 means that the HIGH and LOW times are equal, while a mark space ratio = 0.5 indicates that the HIGH time is half as long as the LOW time:

mark space ratio

A mark space ratio of 3.0 corresponds to a longer HIGH time, in this case, three times as long as the space.

Another way of describing the same types of waveform uses the duty cycle, where:

When the duty cycle is less than 50%, the HIGH time is shorter than the LOW time, and so on.

A subsystem which produces a continuous series of pulses is called an astable. Chapter ? describes pulse waveforms in more detail and explains how to build a variety of astable circuits. As you will discover, it is useful to be able to change the duration of the pulse to suit particular applications. Other pulse-producing subsystems include monostables, Chapter ?, and bistables, Chapter ?.

3. Ramps: A voltage ramp is a steadily increasing or decreasing voltage, as shown below:

positive and negative ramps

The ramp rate is measured in units of volts per second, V/s. Such changes cannot continue indefinitely, but stop when the voltage reaches a saturation level, usually close to the power supply voltage. Ramp generator circuits are described in Chapter ?.

4. Triangular and sawtooth waves: These waveforms consist of alternate positive-going and negative-going ramps. In a triangular wave, the rate of voltage change is equal during the two parts of each cycle, while in a sawtooth wave, the rates of change are unequal (see graph at the beginning of the Chapter). Sawtooth generator circuits are an essential building block in oscilloscope and television systems.

5. Audio signals: As already mentioned, sound frequencies which can be detected by the human ear vary from a lower limit of around 20 Hz to an upper limit of about 20 kHz. A sound wave amplified and played through a loudspeaker gives a pure audio tone. Audio signals like speech or music consist of many different frequencies. Sometimes it is possible to see a dominant frequency in the V/t graph of a musical signal, but it is clear that other frequencies are present.

audio signal

6. Noise: A noise signal consists of a mixture of frequencies with random amplitudes:

noise

Noise can originate in various ways. For example, heat energy increase the random motion of electrons and results in the generation of thermal noise in all components, although some components are 'noisier' than others. Additional sources of noise include radio signals, which are detected and amplified by many circuits, not just by radio receivers. Interference is caused by the switching of mains appliances, and 'spikes' and 'glitches' are caused by rapid changes in current and voltage elesewhere in an electronic system.

Designers try to eliminate or reduce noise in most circuits, but special noise generators are used in electronic music synthesisers and for other musical effects.

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Links

Click on the icon to transfer to the WWW pages:



Heinrich Hertz: brief biography



Joseph Fourier: biography



Demonstrations in auditory perception from McGill University:



Fascinating information on the perception of speech:


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