Pulse amplitude modulation experiment

Introduction

The majority of Telecommunication systems are concerned with the transfer of the information signal between points which are impossible or impractical to connect by cables. Even when cable is used, there may be many different information signals to send along that route. Hence the various transmission media may be required to pass several information channels simultaneously. It is necessary, therefore, for each particular information channel to be amended (or modulated) in a known way, so that the reception point can resolve the required information channel without interference from other channels.

A major constraint on the transmission of information through one widely used medium – free space – is that speech will not propagate easily, without frequency translation. Indeed, the lowest practical broadcast transmission is at about 200kHz. Therefore the information signal needs to be translated to at least this higher frequency. Indeed, if each information channel is translated to a different higher frequency, then the channels can be resolved after passing through the common medium.

This chapter deals with the most common type of translation (modulation) method used both in commercial broadcasting and in transmission by cable – that of Amplitude Modulation. A high frequency sinusoid (the carrier) has an amplitude which is defined by the information signal waveform. The outline shape of the high frequency signal is called the envelope. A major distinction between types of amplitude modulation hinges around whether the carrier signal remains when the information signal is reduced to zero.

The pulse amplitude modulation experiment studies the properties of amplitude modulated carrier, and demonstrates the different forms of demodulation required to detect both the ‘with carrier’ and the ‘suppressed carrier’ form of modulation.

The Apparatus

It comprises an amplitude modulator with an internally generated carrier, a tuned circuits spectrum analyzer, and two forms of amplitude demodulator. One of these demodulators uses an envelope detector while the other utilizes a synchronous oscillator. The following additional equipment is required :

1. Audio Signal Generator.
2. Audio amplifier and speaker.
3. An oscilloscope.

The Amplitude Modulator

A carrier wave Vc cos(ωc t) when amplitude modulated by a sinusoidal signal Vm cos(ωc t) is described by the general expression :

v= Vc (1+m cos ωm t) cos ωc t …………. (1)

In the experiment to obtain the waveform of equation (1), a constant level Vdc is added to the modulating signal to give (Vdc + cos m t), and this multiplied by (Vc cos c t), in the modulator, giving a resultant.

v = Vc (Vdc + Vm cos ωm t) cos ωc t ……………. (2)

Vc and ωc are fixed by the apparatus, but Vdc can be varied (DC level) and Vm and ωm are controlled by the external oscillator.

We will now examine theoretically how variation of these controls affects the output from the transmitter.

Double Sideband Suppressed Carrier

If the dc level is zero, then Vdc=0 in equation (2). In this case.

v = Vc Vm cos(ωm t) cos(ωc t) ……. (3)

v = Vc Vm ½ [cos(ωc + ωm) t + cos(ωc - ωm) t] …….. (4)

thus the envelope of the carrier varies like a rectified sinusoid of frequency ωm, see figure 2.2, while the composite waveform comprises only two frequencies, at (ωc + ωm) and (ωc - ωm) radians/sec. This is known as Double Sideband - Suppressed Carrier (DSB-SC) modulation.

To observe the modulation waveform, attach the external oscillator (2Vp-p, 250Hz for example) between the AF input terminals. With the oscilloscope set to 0.5 V/cm amplitude and 1ms/cm time base, the input signal can be observed at the AF input terminals. The periodicity and amplitude should be noted. The carrier wave can be observed at the terminal ‘RF input fc’, with the time base set to 1 μs/cm and the amplitude at 1 V/cm. Again note the periodicity.

With the dc level control fully anticlockwise to zero, use the oscilloscope to examine the modulator output waveform (red transmitter terminal) . With the time base at 1ms/cm measure the periodicity of the envelope of the amplitude modulated waveform. The level and frequency of external oscillator (modulating signal ) can be varied to show that the amplitude of the modulator output signal is proportional to that of the modulating signal, and the period of its envelope is half that of the modulating signal. This completes the examination of equation 3.

To determine the frequency components of the modulator output signal connect the modulator output loosely to the tuned circuit input (black terminal).

Double Sideband Modulation

If the modulator output signal is again examined, with the dc level increased from zero, it can be seen that the envelope of the signal has a constant voltage added to it. As the dc level is increased, so a point is reached where Vdc = Vm , and the envelope looks approximately like that shown in figure 2.3. At this point the modulation index,(m) in equation (1), is unity – compare equations 1 and 2 with Vdc = Vm. This is often referred to as 100 per cent modulation.

A.M. Synchronous Detection

Synchronous detection is needed when DSB.SC modulation is used. The advantage of DSB.SC is transmitted power is saved by not transmitting the carrier. The disadvantage is that the receiver has to multiply the incoming signal by a replica of the original carrier and this carrier has to be inserted correctly in frequency and phase. The receiver therefore has a local oscillator frequency is correct, i.e. fc, then the output of the multiplier is :

v = (V1 cos (ωc t)) (Vc Vm cos (ωm t) cos (ωc t)) ……

= V1 Vc Vm cos(ωm t) (1 + cos (2ωc t)) / 2 … (5)

let us now assume that the local oscillator is free – running with a frequency error ωe. Derive a calculation similar to 5 for this case. Switch to ‘Free’, and listen to and observe the difference.

A.M. Envelope Detection

In the DSB experiment it was noticed that with sufficient D.C. the envelope of the r.f. waveform looked like the modulating sine waveform. This property of DSB with carrier allows a very simple detector to be devised. This is the envelope detector, and simply consists of a diode and smoothing circuit. Thus the advantage of DSB with carrier is that the detection circuit is very simple. Commercial broadcast transmitters use this type of modulation (even though it requires higher transmitter power) because commercial radio receivers can then be made cheaply.

Return to the 100 per cent modulation point and reduce the audio signal level. Why does the speaker output alter in magnitude only, and not in frequency ? Remove the oscilloscope. Increase the audio level slowly. Can you hear when 100 per cent modulation is reached ? Check by using the oscilloscope.

Suggestion for Further Experiments

Connect a microphone across the modulator input. Listen to the effects of overmodulation on speech using each of the demodulators by varying the DC level while speaking into the microphone. Listen to the effect on speech of allowing the local in the modulator signal ?

Place the DC level at its maximum with a 5V peak modulating signal at about 5kHz. Loosely couple to the tuned circuit. How many component frequencies can you detect in the modulated signal ?

Insert a square wave modulating signal and repeat the above exercise to determine the number of side – frequencies and their relative amplitudes .

Results and Conclusion

When the Frequency is constant:

When the Amplitude is constant:

Using the DC switch:

• Amplitude modulation with suppressed carrier provide us with convenient means to observe the complete frequency spectrum of a given signal.
• Single-sideband modulation is efficient because it requires no more bandwidth than that of the original signal and only half that of the corresponding DSB signal.