PULSE MODULATION
Table of Contents
INTRODUCTION..
PULSE MODULATION..
ANALOGUE-OVER-ANALOGUE METHODS:
ANALOG-OVER-DIGITAL METHODS:
REVIEW OF LITERATURE.
ANALOGUE-OVER-ANALOGUE METHODS:
1. PULSE AMPLITUDE MODULATION:
2. PULSE WIDTH MODULATION..
3. PULSE POSITION MODULATION..
ANALOG-OVER-DIGITAL METHODS:
1. PULSE CODE MODULATION..
2. DELTA MODULATION..
3. PULSE DENSITY MODULATION..
WORKING..
APPLICATIONS.
BIBLIOGRAPHY.
INTRODUCTION
PULSE MODULATION
Pulse modulation schemes aim at transferring a narrowband analog signal over an analog lowpass channel as a two-level quantized signal, by modulating a pulse train. Some pulse modulation schemes also allow the narrowband analog signal to be transferred as a digit signal(i.e. as a quantized discrete-time signal) with a fixed bit-rate, which can be transferred over an underlying digital transmission system, for example some line code. They are not modulation schemes in the conventional sense since they are not channel coding schemes, but should be considered as source coding schemes, and in some cases analog-to-digital conversion techniques.
ANALOGUE-OVER-ANALOGUE METHODS:
- 1. PULE AMPLITUDE MODULATION
- 2. PULSE WIDTH MODULATION
- 3. PULSE POSITION MODULATION
- 1. PULSE CODE MODULATION
- 2. DELTA MODULATION
- 3. PULSE DENSITY MODULATION
ANALOG-OVER-DIGITAL METHODS:
REVIEW OF LITERATURE
ANALOGUE-OVER-ANALOGUE METHODS:
1. PULSE AMPLITUDE MODULATION:
Pulse-amplitude modulation, acronym PAM, is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses.
Demodulation is performed by detecting the amplitude level of the carrier at every symbol period.
Pulse-amplitude modulation is widely used in baseband transmission of digital data, with non-baseband applications having been largely Principle of PAM; (1) original Signal, superseded by pulse-position modulation. (2) PAM-Signal, (a) Amplitude of Signal,
(b) Time
In particular, all telephone modems faster than 300 bit/s use quadrature amplitude modulation (QAM). (QAM uses a two-dimensional constellation).
2. PULSE WIDTH MODULATION
Pulse width-modulation (PWM) of a signal or power source involves the modulation of its duty cycle, to either convey information over a communications channel or control the amount of power sent to a load.
In pulse width modulation(PWM), the width of each pulse is made directly proportional to the amplitude of the information signal.
The resulting signal, PWM, has an average voltage proportional to the time difference between the PPM pulses and the references clock pulses.
Time-averaging (integration) of the output produces the analog variations.
A PWM waveform consists of a sequence of pulses, each of which have a width that is proportional to the values of a message signal at the sampling instants.
Since the width of a pulse cannot be negative, a dc bias is added to the message signal prior to modulation.
Procedure for generating the PWM signal:
- A PAM waveform is generated from x(t)+K.
- A sequence of synchronized triangular pulses is then added to the PAM signal xPAM(t). This yield a signal xPAM(t)+TR(t).
- The resulting signal is the PWM waveform.
- A PWM waveform can be demodulated by low-pass filtering.
3. PULSE POSITION MODULATION
Pulse-position modulation is a form of signal modulation in which M message bits are encoded by transmitting a single pulse in one of 2M possible time-shifts. This is repeated every T seconds, such that the transmitted bit rate is M/T bits per second. It is primarily useful for optical communications systems, where there tends to be little or no multipath interference.
One of the key difficulties of implementing this technique is that the receiver must be properly synchronized to align the local clock with the beginning of each symbol. Therefore, it is often implemented differentially as Differential Pulse-Position modulation, where by each pulse position is encoded relative to the previous pulse, such that the receiver must only measure the difference in the arrival time of successive pulses. It is possible to limit the propagation of errors to adjacent symbols, so that an error in measuring the differential delay of one pulse will affect only two symbols, instead of effecting all successive measurements.
ANALOG-OVER-DIGITAL METHODS:
1. PULSE CODE MODULATION
Pulse code modulation was developed in 1937 at the Paris Laboratories of AT & T. Alex H. Reeves was the inventor.
Reeves conducted several successful transmission experiments across the English Channel using various modulation techniques, including pulse-width modulation (PWM), pulse-amplitude modulation (PAM) and pulse modulation (PPM).
Circuitry was quite complex and expensive in the early stages of development. In the 1960s, the evolution of the semiconductor industry permitted low cost circuits to be fabricated. PCM became the preferred method of transmitting over the PSTN.
PCM is a method of serially transmitting an approximate representation of an analogue signal.
The PCM is itself a succession of discrete numerically encoded binary values derived from digitizing the analogue signal. The maximum expected amplitude of the magnitude of the analogue signal is quantized. That is, divided into discrete numerical levels. The number of discrete levels depends on the resolution (number of bits) of the analogue-to-digital(A/D) converted used to digitize the signal.
The essential operations in the transmitter of a PCM system are sampling, quantizing, and encoding.
The quantizing and encoding operations are usually performed in the same circuit, which is called an analogue-to-digital converter.
The essential operations in the receiver are regeneration of impaired signals, decoding and demodulation of the train of quantized samples.
2. DELTA MODULATION
Delta-Modulation is an analog to digital and digital to analog signal conversion technique used for transmission of voice information where quality is not of primary importance. DM is the simplest form of the pulse-code modulation where the difference between successive samples is encoded into n-bit data streams. In delta modulation, the transmitted data is reduced to a 1-bit data stream.
Its main feature are:
- The analog signal is approximated with a series of segments.
- Each segment of the approximated signal is compared to the original analog wave to determine the increase or decrease in relative amplitude.
- The decision process for establishing the state of successive bits is determined by this comparison.
- Only the change of information is sent, that is, only an increase or decrease of the signal amplitude from the previous sample is sent whereas a no-change condition causes the modulated signal to remain at the same 0 or 1 state of the previous sample.
To achieve high signal-to-noise ratio, delta modulation must use oversampling techniques, that is, the analog signal is sampled at a rate several times higher than the Nyquist rate.
3. PULSE DENSITY MODULATION
Pulse-density modulation, or PDM, is a form of modulation used to represent an analog signal in the digital domain. In a PDM signal, specific amplitude values are not encoded into pulses as they would be in PCM. Instead it is the relative density of the pulses that corresponds to the analog signal’s amplitude. Pulse-width modulation (PWM) is the special case of PDM where all the pulses corresponding to one sample are contiguous in the digital signal.
In an pulse-density modulation bitstream a 1 corresponds to a pulse of positive polarity (+A) and a 0 corresponds to a pulse of negative polarity (-A).
WORKING
In digital modulation, an analog carrier signal is modulated by a digital bit stream. Digital modulation methods can be considered as digital-to-analog conversion, and the corresponding demodulation or detection as analog-to-digital conversion. The changes in the carrier signal are chosen from a finite number of M alternative symbols.
Fundamental digital modulation methods
These are the most fundamental digital modulation techniques:
- In the case of PSK, a finite number of phases are used.
- In the case of FSK, a finite number of frequencies are used.
- In the case of ASK, a finite number of amplitudes are used.
- In the case of QAM, a finite number of at least two phases, and at least two amplitudes are used.
In QAM, an in-phase signal (the I signal, for example a cosine waveform) and a quadrature phase signal (the Q signal, for example a sine wave) are amplitude modulated with a finite number of amplitudes, and summed. It can be seen as a two-channel system, each channel using ASK. The resulting signal is equivalent to a combination of PSK and ASK.
In all of the above methods, each of these phases, frequencies or amplitudes are assigned a unique pattern of binary bits. Usually, each phase, frequency or amplitude encodes an equal number of bits. This number of bits comprises the symbol that is represented by the particular phase.
For example, with an alphabet consisting of 16 alternative symbols, each symbol represents 4 bits. Thus, the data rate is four times the baud rate.
In the case of PSK, ASK or QAM, where the carrier frequency of the modulated signal is constant, the modulation alphabet is often conveniently represented on a constellation diagram, showing the amplitude of the I signal at the x-axis, and the amplitude of the Q signal at the y-axis, for each symbol.
Modulator and detector principles of operation
PSK and ASK, and sometimes also FSK, are often generated and detected using the principle of QAM. The resulting so called equivalent lowpass signal or equivalent baseband signal is a representation of the real-valued modulated physical signal.
These are the general steps used by the modulator to transmit data:
- Group the incoming data bits into codewords, one for each symbol that will be transmitted.
- Map the codewords to attributes, for example amplitudes of the I and Q signals (the equivalent low pass signal), or frequency or phase values.
- Adapt pulse shaping or some other filtering to limit the bandwidth and form the spectrum of the equivalent low pass signal, typically using digital signal processing.
- Perform digital-to-analog conversion (DAC) of the I and Q signals (since today all of the above is normally achieved using digital signal processing, DSP).
- Generate a high-frequency sine wave carrier waveform, and perhaps also a cosine quadrature component. Carry out the modulation, for example by multiplying the sine and cosine wave form with the I and Q signals, resulting in that the equivalent low pass signal is frequency shifted into a modulated passband signal or RF signal. Sometimes this is achieved using DSP technology, for example direct digital synthesis using a waveform table, instead of analog signal processing. In that case the above DAC step should be done after this step.
- Amplification and analog bandpass filtering to avoid harmonic distortion and periodic spectrum
At the receiver side, the demodulator typically performs:
- Bandpass filtering.
- Automatic gain control, AGC (to compensate for attenuation, for example fading).
- Frequency shifting of the RF signal to the equivalent baseband I and Q signals, or to an intermediate frequency (IF) signal, by multiplying the RF signal with a local oscillator sinewave and cosine wave frequency (see the superheterodyne receiver principle).
- Sampling and analog-to-digital conversion (ADC) (Sometimes before or instead of the above point, for example by means of undersampling).
- Equalization filtering, for example a matched filter, compensation for multipath propagation, time spreading, phase distortion and frequency selective fading, to avoid intersymbol interference and symbol distortion.
- Detection of the amplitudes of the I and Q signals, or the frequency or phase of the IF signal.
- Quantization of the amplitudes, frequencies or phases to the nearest allowed symbol values.
- Mapping of the quantized amplitudes, frequencies or phases to codewords (bit groups).
- Parallel-to-serial conversion of the codewords into a bit stream.
- Pass the resultant bit stream on for further processing such as removal of any error-correcting codes.
As is common to all digital communication systems, the design of both the modulator and demodulator must be done simultaneously. Digital modulation schemes are possible because the transmitter-receiver pair have prior knowledge of how data is encoded and represented in the communications system. In all digital communication systems, both the modulator at the transmitter and the demodulator at the receiver are structured so that they perform inverse operations.
Non coherent modulation methods do not require a receiver reference clock signal that is phase synchronized with the sender carrier wave. In this case, modulation symbols (rather than bits, characters, or data packets) are asynchronously transferred. The opposite is coherent modulation.
Pulse-width modulation uses a square wave whose pulse width is modulated resulting in the variation of the average value of the waveform.
A simple method to generate the PWM pulse train corresponding to a given signal is the intersective PWM: the signal (here the green sinewave) is compared with a sawtooth waveform (blue). When the latter is less than the former, the PWM signal (magenta) is in high state (1). Otherwise it is in the low state (0).
The simplest way to generate a PWM signal is the intersective method, which requires only a sawtooth or a triangle waveform (easily generated using a simple oscillator) and a comparator. When the value of the reference signal is more than the modulation waveform (blue), the PWM signal (magenta) is in the high state, otherwise it is in the low state.
Delta
The output signal is compared with limits, which correspond to a reference signal offset by a constant. Every time the output signal reaches one of the limits, the PWM signal changes state.
Principle of the delta PWM. The output signal (blue) is compared with the limits (green). These limits correspond to the reference signal (red), offset by a given value. Every time the output signal reaches one of the limits, the PWM signal changes state.
Sigma-Delta
The output signal is subtracted from a reference signal to form an error signal. This error is integrated, and when the integral of the error exceeds the limits, the output changes state.
Principle of the sigma-delta PWM. The top green waveform is the reference signal, on which the output signal (PWM, in the middle plot) is subtracted to form the error signal (blue, in top plot). This error is integrated (bottom plot), and when the integral of the error exceeds the limits (red lines), the output changes state.
Digital
Many digital circuits can generate PWM signals (e.g. many microcontrollers have PWM outputs). They normally use a counter that increments periodically (it is connected directly or indirectly to the clock of the circuit) and is reset at the end of every period of the PWM. When the counter value is more than the reference value, the PWM output changes state from high to low (or low to high).
The incremented and periodically reset counter is the discrete version of the intersecting method’s sawtooth. The analog comparator of the intersecting method becomes a simple integer comparison between the current counter value and the digital (possibly digitized) reference value. The duty cycle can only be varied in discrete steps, as a function of the counter resolution.
Types
Three types of PWM signals (blue): leading edge modulation (top), trailing edge modulation (middle) and centered pulses (both edges are modulated, bottom). The green lines are the sawtooth signals used to generate the PWM waveforms using the intersective method.
Three types of pulse-width modulation (PWM) are possible:
- The pulse center may be fixed in the center of the time window and both edges of the pulse moved to compress or expand the width.
- The lead edge can be held at the lead edge of the window and the tail edge modulated.
- The tail edge can be fixed and the lead edge modulated.
Spectrum
The resulting spectra (of the three cases) are similar, and each contains a dc component, a base sideband containing the modulating signal and phase modulated carriers at each harmonic of the frequency of the pulse. The amplitudes of the harmonic groups are restricted by a sinx / x envelope (sin function) and extend to infinity
Analog-to-digital conversion
A PDM bitstream is encoded from an analog signal through the process of delta-sigma modulation. This process uses a one bit quantizer that produces either a 1 or 0 depending on the amplitude of the analog signal. A 1 or 0 corresponds to a signal that is all the way up or all the way down, respectively. Because in the real world analog signals are rarely all the way in one direction there is a quantization error, the difference between the 1 or 0 and the actual amplitude it represents. This error is fed back negatively in the ΔΣ process loop. In this way every error successively influences every other quantization measurement and its error. This has the effect of averaging out the quantization error.
Digital-to-analog conversion
The process of decoding a PDM signal into an analog one is amazingly simple. One only has to pass that signal through an analog low-pass filter. This works because the function of a low-pass filter is essentially to average the signal. The density of pulses is measured by the average amplitude of those pulses over time, thus a low pass filter is the only step required in the decoding process.
Examples
A single period of the trigonometric sine function, sampled 100 times and represented as a PDM bitstream, is:
0101011011110111111111111111111111011111101101101010100100100000010000000000000000000001000010010101
An example of PDM of 100 samples of one period a sine wave. 1s represented by blue, 0s represented by white, overlaid with the sine wave.
Two periods of a higher frequency sine wave would appear as: 0101101111111111111101101010010000000000000100010011011101111111111111011010100100000000000000100101 or
In pulse-density modulation, a high density of 1s occurs at the peaks of the sine wave, while a low density of 1s occurs at the troughs of the sine wave.
Algorithm
Pulse-density modulation of a sine wave using this algorithm.
A digital model of pulse-density modulation can be obtained from a digital model of the delta-sigma modulator.
Using the inverse Z-transform, we may convert this into a difference equation relating the input of the delta-sigma modulator to its output in the discrete time domain,
y[n] = x[n] + e[n] − e[n − 1]
There are two additional constraints to consider: first, at each step the output sample y[n] is chosen so as to minimize the “running” quantization error e[n]. Second, y[n] is represented as a single bit, meaning it can take on only two values. We choose for convenience, allowing us to write
e[n] = y[n] − x[n] + e[n − 1]
This, finally, gives a formula for the output sample y[n] in terms of the input sample x[n]. The quantization error of each sample is fed back into the input for the following sample.
APPLICATIONS
PDM is the encoding used in Sony’s Super Audio CD (SACD) format, under the name Direct Stream Digital.
In telecommunications, the widths of the pulses correspond to specific data values encoded at one end and decoded at the other.
Pulses of various lengths (the information itself) will be sent at regular intervals (the carrier frequency of the modulation).
PWM can be used to reduce the total amount of power delivered to a load without losses normally incurred when a power source is limited by resistive means.
PWM is also used in efficient voltage regulators. By switching voltage to the load with the appropriate duty cycle, the output will approximate a voltage at the desired level. The switching noise is usually filtered with an inductor and a capacitor.
PWM is sometimes used in sound synthesis, in particular subtractive synthesis, as it gives a sound effect similar to chorus or slightly detuned oscillators played together.
BIBLIOGRAPHY
www.wikipedia.org
www.johnwileyproject.org
www.masseyuniversity.edu
www.queenslanduniversity.edu
www.uow.edu.au
www.web.uct.ac.za/depts/commnetwork/achan.html
www.chengkunguniversity.edu
www.google.com
