Introduction


This unit uses voltage–time graphs to describe the characteristics of different types of signal. The supporting practical, Using an Oscilloscope, introduces the oscilloscope, a key instrument for measuring and displaying voltage–time graphs.

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

Fig.2 shows the voltage–time graph that represents a direct

current

Current I is a flow of charged particles, usually electrons.

current (

d.c.

In a d.c., or direct current, circuit, current always flows in the same direction.

d.c.) signal.



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

Compare Fig.2 with Fig.3, which shows the voltage–time graphs for several types of alternating current (

a.c.

In an a.c., or alternating current, circuit, current flows first in one direction, then in the other.

a.c.) signals.



As you can see, the

voltage

Potential difference, or voltage V is a measure of the difference in energy between two points in a circuit. Charges gain energy in the battery and lose energy as they flow round the rest of the circuit.

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, triangle waves, and sawtooth waves. A distinguishing feature of alternating waves is that equal areas are enclosed above and below the x-axis.

You can investigate some of these waveforms in the simulation of Fig.4.


Click on the figure below to interact with the model.




Move the probe to a new location to see each waveform.

In electronics, sine waves are among the most useful of all signals in testing circuits and analysing system performance.

Fig.5 shows a sine wave in more detail.





You can find out more about each these by working through the rest of this section.


Period and frequency

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

The frequency f 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 waveform can be calculated from:



Conversely, the period is given by:



In rearrangeable format:



Signals you are likely to use vary in frequency 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.


Amplitude

In electronics, the amplitude, or height, of a sine wave is measured in three different ways:

The peak amplitude V_p 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 V_pp 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 V_p.

Although peak and peak-to-peak values are easily determined, it is sometimes more useful to know the root mean square (r.m.s.) amplitude V_rms of the wave, where:



and



In rearrangeable format:



Just why the r.m.s. amplitude is useful will be explained shortly.



Move the probe in Fig.6 to see the V–t graph of each signal.


Click on the figure below to interact with the model.





Phase

It is sometimes useful to divide a sine wave into degrees, °, as follows:



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 half a 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:



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, θ. As you can see, the two waves in the second part of the diagram are a quarter cycle out of phase, so the phase angle θ = 90°.

Fig.9 shows another example of sine waves that are out of phase.

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



The brightness of the lamp connected to the a.c. 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 at the instant the a.c. signal crosses the x-axis. What you see is the average brightness produced by the a.c. signal.

The second lamp is powered by a d.c. 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 d.c. supply until the two lamps appear equally bright.

When this happens, the d.c. supply is providing the same average power as the a.c. supply. At this point, the d.c. voltage is equal to the V_rms value for the a.c. signal.


Nevertheless, the average power in the two circuits is the same.

A bit of mathematics is needed to explain why the equivalent d.c. voltage is called 'root mean square'. You don't need to know anything about this.

To help you with waveform calculations, you might like to use the Absorb Electronics calculators shown below:



Use the calculator to answer the following questions:


To convert from peak amplitude to r.m.s. amplitude, or from r.m.s. to peak, use this calculator:

You can understand what is meant by 'frequency' and 'amplitude' by comparing the sounds produced when different waves are played through a loudspeaker.




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

The animation below can show waveforms of different frequencies and amplitudes. Click on the buttons next to the graph to listen to the corresponding sounds:



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. Comparing one note with another that is double the frequency, you should notice that they sound similar – the sounds are an octave apart.

Other shapes of signal generate sounds with the same fundamental frequency, but which can sound different. Switch to square wave signals in Fig.14. 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 (or overtones). Sounds from different musical instruments are distinguished by their harmonic content:



The distinctive sound of the bagpipes depends on the fundamental frequency of the note played and the harmonics produced. Additional pipes, called drones, generate sounds so that the overall effect is rich and complex. Some people like it.

You may be interested to know that an electronic device for checking the pitch of the drones is available.

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



'Complex' doesn't mean difficult to understand. A waveform like this can be thought of as consisting of a d.c. component with a superimposed a.c. component. It is quite easy to separate these two components using a capacitor, as is explained in the unit on Capacitors.

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. Click the button at lower left in the V–t graph below to find out what happens when a sine wave is mixed with its 3rd harmonic (3 times the fundamental frequency) at reduced amplitude:



Keep clicking the button to see the effect of adding the 5th, 7th, and 9th harmonics. The waveform begins to look more and more like a square wave as more odd number harmonics are added in.

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

This part of the unit 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 elsewhere in Absorb Electronics.


Square waves

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



Peak amplitude V_p and peak-to-peak amplitude V_pp are measured as you might expect. However, the r.m.s. amplitude V_rms of a square wave is bigger than that of a sine wave.




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



Pulse waveforms

Pulse waveforms look similar to square waves except 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:



The low voltage level is often called logic 0, or just 0, while the high voltage is called logic 1, or just 1. Pulses are fundamental in

digital

In a digital circuit, information is represented by discrete voltage levels. A high voltage is called logic 1, or 1, while a low voltage is called logic 0, or 0.

digital systems.

Sometimes the 'frequency' of a pulse waveform is called its repetition rate. This means the number of pulses per second, measured in hertz, Hz.

The length of time for which the pulse voltage is high is called the mark, while the length of time for which it is low is called the space. The mark and space do not need to be equal. The mark-space ratio is given by:



A mark-space ratio = 1.0 means that the high and low times are equal. A mark‑space ratio = 0.5 indicates that the high time is half as long as the low time.



A mark-space ratio of 3.0 indicates that the mark period is three times as long as the space period. In general, a mark-space ratio greater than 1 indicates that the high time is longer.


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