ELEC3242 Communications Engineering Laboratory 1 ---- Amplitude Modulation (AM) 1. Objectives 1.1 Through this the laboratory experiment, you will investigate demodulation of an amplitude modulated (AM) signal using an envelope detector and subsequent filtering; investigate demodulation of an AM signal using a product detector and subsequent filtering; and investigate the spectrum of an AM signal. 1.2 On completion of this laboratory experiment, you will be able to: understand the concept of multiplying two sinusoidal waveforms; recognize that the result of such a multiplication is amplitude modulation; and determine the modulation index of an AM signal. 2. Theory 2.1 Concepts of Modulation A carrier is simply a single frequency of constant amplitude, phase and frequency. More properly, this is called an un-modulated or plain carrier. In itself, it does not carry any information. However, when referred to as an un-modulated carrier, the implication is that some information will be carried on it at some time. The carrier transports the information to be carried, hence the name. As it is an oscillation, it is sometimes also referred to as a wave. How is information to be carried? This information can be of many forms and can, by the time it reaches the carrier, be either analogue or digital in form. Even if the information is digital the process of transmission is analogue, because the real world is analogue. So, in general, there is no difference between the processes involved in carrying analogue or digital information. Information to be carried is often referred to as baseband. The reason for this name will become clearer later on. In order to be decoded at the receiving end of a communications channel, some characteristics of the carrier has to be varied to represent differences in the baseband signal. There are only three carrier characteristics that can be varied: its amplitude, its frequency and its phase. Some schemes vary more than one of these characteristics and also, as you will see, in some cases varying one will inadvertently vary the others. So it is important not to think of each in isolation. The term modulation arises from the implication that some part of the carrier characteristic is changing. When carrying information, the carrier is said to be modulated, and the sub system responsible for doing this is called a modulator. Page 1
The opposite process to modulation is demodulation, in which the baseband signal is recovered. The trick is to try and recover the baseband signal so that it is as near as possible to the original signal, even when it has been severely weakened and distorted during transmission. Another consideration is to use as little transmission bandwidth as possible, so that as many signals as possible can be sent down a cable or via a radio link. Transmission power is also important. Usually the minimum power that can be used to achieve a usable output is desirable. The concept of signal-to-noise ratio will also be introduced and how it is a measure of the quality of both the modulated and baseband signals. The assignments will introduce the modulation and demodulation concepts vital to an understanding of information transmission. 2.1 Equations of Amplitude Modulation The equation of a sinusoidal voltage waveform is given by : v = V maxsin(ωt + ) (1) where: v is the instantaneous voltage, Vmax is the maximum voltage amplitude, ω is the angular frequency in rad/s is the phase A steady voltage corresponding to the above equation conveys little information. To convey information the waveform must be made to vary so that the variations represent the information. This process is called modulation. From the above equation, the basic parameters of such a waveform are: its amplitude, Vmax its frequency, ω in rad/s (or f in Hz ) its phase, Any of these may be varied to convey information 2.1.1 Amplitude Modulation (AM) Amplitude modulation uses variations in amplitude (Vmax) to convey information. The wave whose amplitude is being varied is called the carrier wave. The signal doing the variation is called the modulating signal. For simplicity, suppose both carrier wave and modulating signal are sinusoidal, i.e.: Page 2
vc = Vc sin ωc t (c denotes the carrier) and (2) vm = Vm sin ωmt (m denotes modulation) (3) We want the modulating signal to vary the carrier amplitude, Vc, so that: vc = (Vc + Vm sin ωmt). sinωc t (4) where (Vc + Vm sin ωmt) is the new and varying carrier amplitude. Expanding (4) gives: vc = Vc sin ωc t + Vm sin ωc t. sin ωmt (5) which may be rewritten as vc = Vc [sin ωc t + m sin ωc t. sin ωmt] (6) where m = Vm/ Vc and is called the Modulation Index. Now sin ωc t. sin ωmt = ½ [cos(ωc ωm) t cos(ωc + ωm) t] (7) so, we can express (6) as: vc = Vc sin ωc t + ½ (m Vc )[cos(ωc - ωm) t] ½(m Vc)[cos(ωc + ωm) t] (8) This expression for vc has three terms:- 1) The 1 st term is the original carrier waveform at frequency ωc, which contains no variations and thus carries no information. 2) The 2 nd term is a component at frequency (ωc ωm), whose amplitude is proportional to the modulation index. This is called the lower-side frequency. 3) The 3 rd term is a component at frequency (ωc + ωm), whose amplitude is proportional to the modulation index. This is called the upper-side fre4quency. It is the upper and lower side frequencies that carry the information. This is shown by the fact that only these 2 terms include the modulation index m. Because of this, the amplitudes of the side frequencies vary in proportion to that of the modulating signal; the amplitude of the carrier does not. 2.1.2 Sidebands If the modulating signal is a more complex waveform, for instance an audio voltage from a speech amplifier, there will be many side frequencies present in the total waveform. This gives Page 3
rise to components 2 and 3 in the last equation being bands of frequencies, known as sidebands. Hence we have the upper sideband and the lower sideband, together with the carrier. 3. Theory on Frequency Translation 3.1 Translating from zero frequency Baseband signal can be thought of a signal having 0 Hz (i.e. dc) as the carrier frequency and the baseband signal is the upper sideband. However, through Fourier Transform and in the frequency domain, the signal will have positive and negative frequency sidebands, each having a half of the total power. The modulation process can be thought of as that of frequency translation. Through modulation, the upper and lower sidebands of the baseband signal are moved up in positive and negative frequency by an amount equal to the carrier frequency. 4. Theory on the Experimental Determination of the Modulation Index This is most easily done by measuring the maximum and minimum values which the instantaneous amplitude of the carrier reaches. Let us call these x and y. Taking (6) for a sinusoidal carrier modulated by a sinusoidal waveform (see the Modulation Maths Concept): vc = Vc [sin ωc t + m sin ωc t. sin ωmt] and re-arranging it, vc can be expressed as vc = Vc sin ωc t [1+ m sin ωmt] (9) so that the instantaneous amplitude of the carrier is Vc [1+ m sin ωmt] Since sin ωmt can only vary between +1 and 1, x = Vc (1+ mvc ) and y = (1 mvc ). (10) To obtain the value of modulation index m from x and y, Vc can be eliminated between these equations by division, i.e., y/x = (1 m)/(1 + m). (11) Solving for m gives: m = (x y)/ (x + y) (12) Page 4
5. Practical 1: Double-Sideband Amplitude Modulation with Full Carrier 5.1 Background In this practical work, you will investigate how two sinusoidal signals are multiplied together to produce a modulated signal. The two signals are generated on the workboard. The signal that is to be modulated onto the carrier is usually refer to as the baseband signal, as it often has frequencies close to dc and sometimes a dc component. In the simplest amplitude modulator, the carrier is multiplied by only positive magnitudes of baseband signal. The baseband signal is usually bipolar so, when a true, four-quadrant multiplier is used as a modulator, an offset has to be added to change the baseband signal to unipolar, so that the carrier is only multiplied by positive values. The result of this is usually referred to as amplitude modulation with full carrier, as the amplitude of the carrier signal is controlled, or modulated, by the baseband. The frequency of the carrier is determined by the transmission method. For example, it might be a particular radio frequency. The modulating signal may take many forms: a complex digital signal or simply audio speech for example. As you can see the modulating signal is being carried by the carrier. In the practical work, you will be using simple sine waves so that the principles are easier to understand. In this simplest form of amplitude modulation, the instantaneous amplitude of the modulated waveform is proportional to the instantaneous amplitude of the modulating signal. The diagram shows such a signal in the time domain. Figure 1 AM Modulated signal Notice that when the modulating signal is at its maximum amplitude, the modulated waveform amplitude is at maximum, and that when the modulation is minimum, the modulated waveform amplitude is zero. Because most modulating signals have no dc component, the carrier is at half the modulated waveform s peak amplitude when the modulating signal is zero. Mathematically, amplitude modulation is the result of multiplying the two signals together. However such a process would not produce exactly the signal seen above. Imagine two sine waves with peak amplitudes of 1, i.e. their instantaneous values vary between +1 and 1. Page 5
If they were multiplied together, the output would also vary between +1 and 1. However, during the time that the modulation was -1, the output would not be 0 but would be the carrier multiplied by 1; i.e. its phase would be reversed. Hence the need for a modulating signal that varies between 0 and +1. This would be produced by adding a constant of value +1 to the modulating signal in the mathematics. This is equivalent to adding a dc offset voltage to the modulating signal. The example shows the maximum amount of modulation that can be applied to the carrier. The amplitude of the modulated waveform varies from zero to twice its mean value. The amount of modulation is referred to as modulation index and it is expressed as a parameter between 0 to 1. It is sometimes expressed as a percentage. 5.2 Sidebands If the modulation process were simply an addition of the two signals, the output would consist only of the two frequency components put in. However, as the process is that of multiplication, the output consists of some new frequency components: the carrier frequency plus the modulating frequency and the carrier frequency minus the modulating frequency. These are called sidebands. Their existences can easily be proved mathematically by multiplying two sine wave equations together (see the Modulation Maths Concept). In the case of having a dc offset, the output will contain a component at the carrier frequency. The diagram shows such a signal in the frequency domain. Figure 2 Carrier and two sidebands In a real system, the modulating signal would comprise a band of frequencies rather than simply one frequency. The diagram below shows how the spectrum would look. Figure 3 Spectrum display of carrier and two sidebands This type of transmission is called amplitude modulation with full carrier. The reason for this is obvious, in that the carrier is transmitted as well as the two sidebands. Historically, it has been used extensively, as the equipment needed to produce it and to receive it is very simple. Page 6
In the practical work, you will use a balanced modulator to generate the modulated signal and use a dc offset on the baseband signal. Note that there is a low pass filter at the output of the modulator, before it reaches the instrumentation. This is so you can see more clearly the modulated signal on the spectrum analyser without having to be concerned about the second harmonic of the carrier frequency that is caused by small, but inevitable, distortion in the modulator. 5.3 Block Diagram Figure 4 Block diagram of practical 1 5.4 Make Connections Diagram Figure 5 Connections made on the workboard for practical 1 5.5 Perform Practical Use the Make Connections diagram to make the required connections on the hardware. 1. Open the voltmeter and use it to set the dc Source voltage to give a Carrier offset of approximately +0.25 volts. 2. Set the modulating signal amplitude (I Mod) by adjusting the Signal Level Control to half scale. Page 7
3. In the IQ Modulator block, set all of the controls to half scale. 4. Open the oscilloscope and note the waveform on the upper trace (the modulated waveform). Compare it to that on the lower trace (the modulating waveform). 5. Connect the voltmeter probe (green) to the modulating signal (monitor point 3) and set the voltmeter functions to ac p-p. Use the Signal Level Control to set the amplitude of the modulating signal to 0.25 volts peak to peak. 6. Use the oscilloscope cursors to measure the values A1 and A2 shown below. 7. Use the formula to calculate modulation index m. Figure 6 Computing modulation index 8. Try other values of modulation signal amplitude and measure A1 and A2 and thus calculate m. Compare the values with the ratios of the modulation signal peak value to the dc offset. Launch an Excel spreadsheet to tabulate your results. Note that the voltmeter reads peak to peak values. 9. Open the spectrum analyser and observe the spectrum of the modulated signal (monitor point 4). Adjust the modulation amplitude using the Signal Level Control and observe the spectrum. Use the cursors to measure the relative levels of the two sidebands to the carrier at m=1, 0.5 and 0. 10. Move the spectrum analyser probe (orange) to the modulation source (monitor point 3). Measure modulating frequency using the cursor. 11. Return to the modulated output (monitor point 4) and measure the frequencies of the two sidebands. Calculate the frequency difference between the carrier and the upper sideband, and the carrier and the lower sideband. 12. Now measure the modulating frequency on the second channel. Compare the values. 13. Set the modulation index to 1 using the oscilloscope display. 14. Open the phasescope. Move the reference probe (yellow) to the carrier source (monitor point 1) and the input probe (blue) to the modulated signal (monitor point 4). Note that the display shows a signal with constant phase changing in amplitude between a radial point to zero. 15. Change the modulation amplitude and note that the phase does not change but the variation in amplitude does. What happens when the amplitude is zero? 16. Change the modulation source from the 62.5 khz Locked Sine Source to the Function Page 8
Generator. Set the Function Generator to Fast and the output to a sine wave. Adjust the Frequency control and observe the spacing of the sidebands from the carrier on the spectrum analyzer. 5.6 Questions for practical 1: (a) Use your own words and the figures shown in practical 1 to describe the AM process. (b) From the spectrum analyzer, you can see that there are two sidebands in the signal spectrum. Use equations to explain how the carrier frequency relates to the uppersideband frequency and the lower-sideband frequency. (c) Use screenshot or photograph to record the spectra and waveforms of the modulated signal with m=1, 0.5 and 0. (d) Compute m for maximum percentage of power in the sidebands. (e) Compute the percentage of power used to send the carrier signal in a DSB AM with full carrier signal using equation and the spectrum. Comment on the difference. (f) Is DSB AM with full carrier a power efficient modulation scheme? Suggest ways to improve the efficiency. (g) With your suggestions, how much power you can save in transmission? 6. Practical 2: Demodulation with an Envelope Detector 6.1 Background Demodulation Demodulation is the reverse process to modulation. It takes the carrier and two sidebands of the modulated signal and extracts the modulating signal from it. In this instance, this can be done very simply. If the modulated signal is passed through either a full or half wave rectifier, followed by a filter that passes only the modulation, then the output follows the amplitude of the carrier. The resulting signal is the modulating plus the dc offset, which can be removed. This type of demodulator is called an envelope detector. Figure 9 shows the output of the rectifier for an AM signal. Page 9
Figure 7 Output from a rectifier Note that the filter is usually simply a resistor-capacitor network and the time constant of the filter is important, as it determines the magnitude of the residual carrier, or twice-carrier frequency components. Mathematically, this demodulator can also be thought of as a multiplier that takes the signal and multiplies it by its own carrier (this is because the carrier is switching the diodes in the rectifier). The result of multiplying the two sidebands is the demodulated signal and multiplying the carrier produces the dc offset in the output. In other words, the envelope detector uses the carrier component to demodulate the signal. In this Practical Work, you will use the same set-up as in Practical 1 to generate an AM double sideband (DSB) signal and use an envelope detector to demodulate it. The envelope detector uses a full wave rectifier, so that both positive and negative peaks of the modulated signal contribute. You will also see how the addition of a filter removes much of the twice carrier component. 6.2 Block Diagram Figure 8 Block diagram of practical 2 6.3 Make Connections Diagram Figure 9 Connections made on the workboard for practical 2 6.4 Perform Practical Page 10
Use the Make Connections diagram to make the connections on the hardware that are required. This practical work uses the same AM generator circuit as Practical 1. 1. Use the voltmeter to set the dc carrier offset to 0.25 volts. 2. Use the oscilloscope and the Signal Level Control to set the modulation index to approximately 0.5. 3. In the IQ Modulator block, set all of the controls to half scale. 4. Observe the output of the Envelope Detector (monitor point 5). Note that it reproduces the modulating signal. 6.5 Questions (a) Use screenshots or photographs to record the demodulated waveforms from the Envelope Detector for m=0, 0.5 and 1. (b) Use screenshots or photographs to record the spectra from the Envelope Detector for m=0, 0.5 and 1. (c) Compare the spectra of the demodulated signals with the modulating signals and comment. 7. Practical 3: Demodulation with a Product Detector 7.1 Background An alternative type of demodulator is called a product detector. Here the demodulating process requires the modulated signal to be multiplied with a reference signal having the frequency and phase equal to those of the carrier. In the envelope detector, the modulated signal is simply multiplied by itself to achieve this. In the product detector, the source of the reference signal is obtained from an external oscillator. This results in better demodulation because the multiplying signal is not varying in amplitude and does not contain so much noise. The action of such a demodulator is achieved by using a balanced modulator fed from an oscillator. This oscillator is often referred to as a local oscillator as in a link it is, as viewed from the receiver point of view, local as opposed to remote at the transmitting end. The process of having a reference signal at the receiver at the same frequency and phase as the original carrier is used in many demodulator processes. 7.2 Synchronising Although it has been stated that the local oscillator needs to be on frequency and in phase, so far it has not been explained how this is achieved. It is, in fact not easy. Other assignments show how this can be achieved for other types of demodulators, but in this assignment, for simplicity, a sample of the original carrier is used to synchronise the local oscillator. In practice, AM double sideband with full carrier is usually demodulated with derivatives of the envelope detector. Page 11
As you will see later, the product detector is used for suppressed carrier single sideband transmission. However, it is important that you understand that a product detector can be used to detect full carrier AM. Figure 10 Output from the multiplier You will also see how the addition of a filter can remove much of the twice carrier component. A filter in this position is often referred to as a post detection filter. 7.3 Block Diagram 7.4 Make Connections Diagram Figure 13 Block diagram of practical 3 Page 12
Figure 11 Connections made on the workboard for practical 3 7.5 Perform Practical 3 Use the Make Connections diagram to make the connections on the hardware that are required. Again, you use the same generator configuration to generate the AM waveform. 1. Use the voltmeter to make sure that the dc carrier offset is set to 0.25 volts. 2. Use the Signal Level Control to set the modulation index to approximately 0.5. 3. In the IQ Modulator block, set all of the controls to half scale. 4. Use the oscilloscope to observe the output of the product detector (monitor point 5) and the spectrum analyser to note the twice carrier frequency component. Observe the output after the post detection filter (monitor point 6). 7.6 Questions for practical 3: (a) Describe the operations of an envelope detector and a product detector. (b) Use screenshot or photograph to record the waveform and spectrum at the input of the lowpass filter. (c) Use screenshot or photograph to record the waveform and spectrum at the output of the lowpass filter. (d) What is the function of filter in demodulation? (e) What is the advantage of product detector compared to envelop detector? Page 13