# Delta modulation lab experiment

### Introduction

The two forms of modulating (A.M. & FM) are closely related in that each impresses the modulating signal on a carrier waveform by means of varying one parameter of that waveform. In each case the waveform is sinusoid. As with the sinusoid, the modulating signal can be impressed upon any parameter of the pulse train such as freq., duration or amplitude.This delta modulation lab experiment deals with a form of pulse freq. modulation called delta modulation. The first step in the process is a form of pulse amplitude modulation. In pulse code modulation the pulse amplitude is then encoded into train of equi-amplitude pulses, which improve the transmission quality of the signal. It can, therefore, be seen that the two classes of sinusoidal of pulse modulation represented in this series differ more widely than two classes of sinusoidal modulation.

A part from being merely a representative of all the possible members of the pulse parameter modulation class, delta modulation has some very attractive attributes. These hinge around the simplicity and cheapness of the delta demodulator. The disadvantages are the relatively wide bandwidth required for given quality of modulating signal reproduction.

Costly modulating and demodulating equipment is normally only attractive when it forms a relatively small part of the total system cost, which is usually when the information content transmission distance product is high. In the telephone network this product is low when interconnecting telephone subscribes or groups of subscribes with exchanges, and this is one area of application where some telecommunications administrations, including the U.K., the U.S.A. and the USSR, are conducting extensive studies to determine the role of delta modulation in their network of future.

### The apparatus

It is comprises the two basic forms of delta modulator together with their corresponding demodulators, provision is made for a local D.C. supply to be applied to the signal input, together with an externally provided signal. To allow evaluation of the distortion inherent in the delta modulation process under a wide variety of conditions the difference amplifier is included in the equipment so that the demodulator output may be compared directly with, and subtracted from the modulator input. The conditions that can be varied widely are the clock freq., the gain of the output amplifier and the D.C. level, which varies from corresponding to above positive clipping to one corresponding to below negative clipping. The two forms of modulator provided are the delta modulator and sigma delta modulators.#### The following additional equipment is required:

- Audio signal generator.
- Oscilloscope.

### The Modulation Process

In delta modulation, the existence or non-existence of individual pulses conveys information. The width and amplitude of each pulse is constant. The modulator output is a three level signal as it contains positive and negative going pulses as well as a zero level. The sum of the modulator output pulses at any instant is compared with the level of the analog signal to be modulated and if this sum is less than the analog signal level a positive pulse is sent so that the sum increases towards the analog level, while in the case of a negative difference going pulse is sent to decrease the sum total.To illustrate this concept suppose that as the modulator is switched on, a sinusoidal signal of zero level at the time of switch on is applied to the modulator input. As there has been no modulator output prior to switch on the sum is zero. Assuming that the sinusoid is positive going at this instant, the difference between the sinusoid and the modulator output after one pulse duration is positive and therefore a positive going delta pulse is transmitted by the modulator.

1. After another pulse period the sinusoid has risen further and this level has the average pulse height subtracted from it. Let us suppose that this difference is positive that the applied sinusoid amplitude is very large compared to the amplitude of a delta pulse. The modulator will therefore transmit another positive pulse, and indeed, may continue to transmit positive pulses for some time while the sinusoid amplitude rises steeply.

2. There are as many negative delta of pulses as positive delta pulses if the mean level of the input signal is 0, and that in the example shown the first negative pulse will occur when the sum of all the previous positive pulses first exceeds the amplitude of the input signal.

3. It is quite possible that the rate of increase of the input signal amplitude outstrips that of the sum of the delta pulses, and this gives rise to one form of distortion. It is clear that under all conditions of input signal waveform a basic form of distortion exits because the shape of the waveform of the sum of the delta pulses cannot be an exact replica of the modulating signal due to the basic shape. It is intuitively clear from this discussion that if the demodulator includes a low pass filter as well as the integrator the level of quantization noise can be significantly reduced.

4. Because the maximum slope of a sine wave is proportional to amplitude and freq. this type of pre-emphasis is conveniently achieved by passing the input through an ideal integrator before modulation and omitting the integrator in the demodulator.

This power is the average of the amplitude squared over the duration of the triangle. This integration results in a total quantization noise of

These results can be extended to the sigma delta modulator by considering it as a delta modulator with the signal integrated before the input.

The sigma delta modulator limits the amplitude and acts as a limiter of maximum amplitude Vc. if fm is the maximum modulating freq. the noise due to clipping should decrease as the ration fc/fm becomes larger. In general with this apparatus the ratio used will be much higher than two so that the noise level will in general be less than that calculated.

When an error occurs and a pulse is changed from + to – the mean square wave error noise added will be

(b) In each case with the modulator output applied to an oscilloscope, the way in which the ratio of the number of positive to the number of positive to the number of negative pulses varies as a function of applied voltage should be observed. Plot the ratio as a function of applied voltage over the range –5V to 5V. note that in one case this is not smooth curve but consists of a series steps. Using a description in the section on the modulation process, explain the variation in step size. The difference between the observations in the two cases should be clearly described and the reason for these differences thoroughly explained.

(c) The procedure is to apply a constant amplitude signal to the demodulator input with the integrator short-circuited. With the amplifier gain at maximum the signal should be varied in freq. from 0 to 10kHz and the output amplitude plotted against input frequency.

(d) Apply 1kHz signal of less than 3 volt peak to peak amplitude to the input of the modulator when I a delta configuration. The clock freq. should be at 100kHz. The modulator and demodulator should be connected and the integrator included in the circuit.

(e) The demodulator output and the signal input should be connected to the A and B inputs to the difference amplifier, the output of which should be applied to an oscilloscope. The demodulator output should also connected to the oscilloscope.

(f) The signal amplitude should be varied slightly and the demodulator output signal observed to check that clipping is not occurring. Decrease the clock freq. while observing the quntisation noise level and using the relevant equation given previously explain the results obtained.

(g) Increase the signal freq. and taking into account the low pass filter characteristic and the effective reduction of clock freq. check that the conclusions are unaffected by slope limiting.

(h) With the equipment set to the sigma delta modulator position and the integrator short circuited the above procedure should be repeated, a part from the final pre emphasis characteristic experiment, with peak limiting replacing slope limiting.

1. After another pulse period the sinusoid has risen further and this level has the average pulse height subtracted from it. Let us suppose that this difference is positive that the applied sinusoid amplitude is very large compared to the amplitude of a delta pulse. The modulator will therefore transmit another positive pulse, and indeed, may continue to transmit positive pulses for some time while the sinusoid amplitude rises steeply.

2. There are as many negative delta of pulses as positive delta pulses if the mean level of the input signal is 0, and that in the example shown the first negative pulse will occur when the sum of all the previous positive pulses first exceeds the amplitude of the input signal.

3. It is quite possible that the rate of increase of the input signal amplitude outstrips that of the sum of the delta pulses, and this gives rise to one form of distortion. It is clear that under all conditions of input signal waveform a basic form of distortion exits because the shape of the waveform of the sum of the delta pulses cannot be an exact replica of the modulating signal due to the basic shape. It is intuitively clear from this discussion that if the demodulator includes a low pass filter as well as the integrator the level of quantization noise can be significantly reduced.

4. Because the maximum slope of a sine wave is proportional to amplitude and freq. this type of pre-emphasis is conveniently achieved by passing the input through an ideal integrator before modulation and omitting the integrator in the demodulator.

### Quantizing and clipping noise

In order to establish the noise from the quantization effect in a delta modulator it must be assumed that the slope of the input signal doesn’t exceed the max. permitted slope. Effectively a delta modulator re-establishes an output level one-quantization increment, s. from its exiting level at each sampling instant. If the clock freq. is fc then this interval between sampling instants is**. without getting involved in complicated mathematics it is intuitively clear that although the base of each quantization noise triangle. The mean quantization noise power is the mean power of a triangle of quantization noise.***1/fc*This power is the average of the amplitude squared over the duration of the triangle. This integration results in a total quantization noise of

**. If it can be assumed that the noise has a flat freq. spectrum then the spectral density of the noise is given by:***s²/3**N∆q = s²/3fc*These results can be extended to the sigma delta modulator by considering it as a delta modulator with the signal integrated before the input.

*N∑∆q = s²(2Ï€f)²/3fc*

The sigma delta modulator limits the amplitude and acts as a limiter of maximum amplitude Vc. if fm is the maximum modulating freq. the noise due to clipping should decrease as the ration fc/fm becomes larger. In general with this apparatus the ratio used will be much higher than two so that the noise level will in general be less than that calculated.

### Noise due to errors

In practice the modulator and demodulator are normally separated by a transmission medium which introduced impairments into the signal. At the receiver these impairments occasionally result in the detector making an error in its decision about the existence of a pulse. Although errors should not occur in transmission across this apparatus, for completeness it is worth commenting upon this noise source. If the probability of error is pc then the spectral density of noise due to errors becomes:*Nc = 4PcVc²/fc*

When an error occurs and a pulse is changed from + to – the mean square wave error noise added will be

**.***(2Vc)²*### Observation of waveforms

(a) the locally generated D.C. supply should be connected to the signal input and the modulator switch placed firstly in the delta position, and then in the sigma-delta modulator position.(b) In each case with the modulator output applied to an oscilloscope, the way in which the ratio of the number of positive to the number of positive to the number of negative pulses varies as a function of applied voltage should be observed. Plot the ratio as a function of applied voltage over the range –5V to 5V. note that in one case this is not smooth curve but consists of a series steps. Using a description in the section on the modulation process, explain the variation in step size. The difference between the observations in the two cases should be clearly described and the reason for these differences thoroughly explained.

(c) The procedure is to apply a constant amplitude signal to the demodulator input with the integrator short-circuited. With the amplifier gain at maximum the signal should be varied in freq. from 0 to 10kHz and the output amplitude plotted against input frequency.

(d) Apply 1kHz signal of less than 3 volt peak to peak amplitude to the input of the modulator when I a delta configuration. The clock freq. should be at 100kHz. The modulator and demodulator should be connected and the integrator included in the circuit.

(e) The demodulator output and the signal input should be connected to the A and B inputs to the difference amplifier, the output of which should be applied to an oscilloscope. The demodulator output should also connected to the oscilloscope.

(f) The signal amplitude should be varied slightly and the demodulator output signal observed to check that clipping is not occurring. Decrease the clock freq. while observing the quntisation noise level and using the relevant equation given previously explain the results obtained.

(g) Increase the signal freq. and taking into account the low pass filter characteristic and the effective reduction of clock freq. check that the conclusions are unaffected by slope limiting.

(h) With the equipment set to the sigma delta modulator position and the integrator short circuited the above procedure should be repeated, a part from the final pre emphasis characteristic experiment, with peak limiting replacing slope limiting.

### Results and Conclusions

- In the telephone network the product is low interconnecting telephone subscribers or groups of subscribers with exchanges, and this is one area of application where some telecommunication administrations are conducting extensive studies to determine the role of delta modulation in their network of the future.
- There are two forms of modulating additional to delta modulation, these forms are closely in that each impresses the modulating signal on a carrier waveform by means of varying one parameter of that waveform.
- In this experiment, the two forms of modulator provided are the delta modulator and sigma delta modulator which are comprised in the apparatus.
- The maximum slope of a sine wave is proportional to amplitude and frequency.

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