Digital to Analog Conversion Techniques

The continued use of digital electronics calls for the use of Digital-to-Analog converters. To send digital data over analog media, data should be transformed into an analog signal.

Digital-to-analog conversion happens when digital data is transformed into a bandpass analog signal while analog-to-analog conversion happens when the low-pass analog signal is changed into a bandpass analog signal. There are two cases of data formatting, Band-pass and Low-pass.

Band-pass signal

A band-pass is a filter utilized in filtering and passing frequencies under consideration.  The distinguishing characteristic of bandpass signal is that its one-sided energy spectrum does not extend in frequency to zero and is centered at a non-zero frequency. The signal also has Hermitian Symmetry

Low-pass

Low-pass passes low-frequency signals and has its spectrum located around the zero frequency. Signal processing occurs at the baseband rather than the passband. The representation of low pass signal is complex

The formula   depicts the relationship between a digital signal and its analog equivalent in the case of a 3-bit DAC.

Where:

  • VDAC is the analog voltage
  • K1 is the scale factor
  • bn is the nth converter bit and,
  • VREF is the reference voltage

An analog carrier is used in the conversion of data from one computer to another. The process involves modifying analog signals to digital data. The characteristics of analog data include phase, frequency, and amplitude. Three major types of digital-to-analog conversions exist; Amplitude Shift Keying, Frequency Shift, and Phase Shift Keying.

Amplitude Shift Keying

Amplitude Shift Keying is a form of Amplitude Modulation where binary data is represented in the form of variations in the breadth of a signal. The conversion technique involves modifying the amplitude of an analog carrier signal to reflect binary data.

The amplitude is held when binary data represents digit 1, else it is set to 0. Phase and frequency remain the same similar to the ones reflected in the original carrier wave. The technique is one of the simplest and earliest digital modulations. ON-OFF keying is one of the forms of Amplitude Shift Keying. M‐ary Amplitude Shift Keying (MASK) has to be used to improve bandwidth efficiency. It is possible to coherently or non-coherently modulate MASK.

In this technique, only the amplitude of the carrier signal is modified during modulation. During an Amplitude Shift Keying Modulation, an uninterrupted high-frequency carrier is sent by the carrier generator.

The modulated carrier takes one or two different forms. One state represents a 0 while the other represents a 1.  The carrier states, 0 and 1 are also referred to as symbols.  In some situations, there may be two possible symbols or carrier states.  Therefore, it is possible each state or symbol to represent a number of bits.

The unipolar input experienced is either high or low depending on the binary sequence from the message signal. The switch closes due to the high signal, consequently allowing a carrier wave.

The resulting output is the carrier signal at high input. In the case of low input, the switch opens and allows no voltage to pass. The outcome is the form of a low output. Depending on the phase and amplitude traits of the pulse-shaping filter or band-limiting filter, the band-limiting filter shapes the pulse.

The alternate process is known as demodulation. Amplitude Shift Keying demodulation techniques come into two forms; Asynchronous and Synchronous. In the Synchronous method, the clock frequency at the receiver matches with the clock frequency at the transmitter.

Without matching, it is referred to as Asynchronous. The Synchronous Amplitude Shift Keying detector is made up of a voltage limiter, a low pass filter, a comparator, and Square law detector. The Asynchronous Amplitude Shift Keying detector consists of a comparator, a low pass filter, and a half-wave rectifier.

The modulated ASK signal is passed to the half-wave rectifier, which carries a positive half output. Higher frequencies are suppressed by the low pass filter and produce an envelope detected output from which the digital output is delivered.

Frequency Shift Keying (FSK)

The conversion technique involves modifying the frequency of the analog carrier to reflect binary data. The frequency of a sine wave carrier is moved above or below to represent a specific bit pattern or a single binary value.

Two frequencies, f1 and f2, are used. One frequency is set to represent binary digit 1 while the other is set to represent binary digit 0. The phase and amplitude of the carrier signal remain intact.

The technique came into being in 1900 for use in the mechanical teleprinters. The standard speed of mechanical teleprinters was 45 baud. With the advent of personal computers, the signaling speed became slow and tedious compared to the networks that characterized the introduction of personal computers.

As a result, the transmission of programs, images, and large texts would take long. In response, Engineers in the 1970s began to develop modems to improve the speed. Since then, the search for ever-greater bandwidth has been constant.

Currently, the standard modem functions at thousands of bits per a second. However, the foundation principle of Frequency Shift Keying modulation has not changed in more than half a century.

The binary frequency shift keying is the simplest form of frequency shift keying. In this form, the binary logic values of 1 and 0 are symbolized by the carrier frequency being shifted up or down the center frequency.

In a standard binary frequency shift keying system, the higher frequency embodies 1 and is called the mark frequency while the lower frequency represents 0 and is known as the space frequency. The distance of the two frequencies from the center frequency is equal.

Where there is a discontinuity in phase during the shifting of the frequency between space and mark values, the frequency shifting used is regarded as non-coherent. Else it is seen to be coherent. Additional frequencies are utilized in complex schemes, for representation of several bits through each frequency utilized.

The aim is to provide a higher data rate with more bandwidth. Additionally, it increases the likelihood of transmission errors arising and heightens the complexity of the demodulator or modulator and circuitry.

A common application of the Frequency Shift Keying is found in the transmission on analog telephone lines through the process of Audio frequency-shift keying. In this process, changes in the frequency of an audio tone characterize the modulation technique in which binary data is denoted.

The representation of space and mark values is done through two tones. Conventional analog modems employed Audio frequency-shift keying to convey data at rates of up to roughly 300 bits per second. In addition, a modified form of Audio frequency-shift keying was used by some early microcomputers to store data on audio cassettes.

Today, Frequency Shift Keying technique is used in the in communication systems such as urgent situation broadcasts, caller ID, and amateur radio, where a pair of discrete frequencies is used to transmit binary information.

Frequency Shift Keying Modulation involves two oscillators with the input binary sequence and a clock. The oscillators produce a higher and lower frequency signals, are linked to a switch together with the clock. A clock is used for both oscillators to prevent the unexpected discontinuation of the phase during message transmission. Selecting the frequencies in line with the binary output requires application of the binary input sequence.

On the other hand, demodulation of Frequency Shift Keying takes two forms. The main forms of detection are; a synchronous detector and asynchronous detector. The asynchronous detector is a non-coherent one while the synchronous detector is a coherent one.

Synchronous Frequency Shift Keying Detector comprises of a decision circuit, two bandpass filters and, two mixers with local oscillator circuits. A signal input is passed to the two mixers, connected to two bandpass filters, with local oscillator circuits.

The most likely output is then selected from one of the detectors by the decision circuit. The bandwidth of each demodulator is dependent on the bit rate. The asynchronous demodulator is less complex compared to the synchronous demodulator.

For the asynchronous Frequency Shift Keying Detector, the block diagram comprises of a decision circuit, two envelope detectors, and two bandpass filters. Two Band Pass Filters are tuned to Space and Mark frequencies to allow the signal to pass.

The output from the two Band Pass Filters symbolizes Aptitude Shift Keying signal, which is passed to the envelope detector where signals are modulated asynchronously.

The role of the decision circuit is to re-shape the waveform to a rectangular one and select which output has the most prospective from either of the envelope detectors. It also re-shapes the waveform to a rectangular one.

Phase Shift Keying

This conversion technique involves the alteration of the original carrier to reflect the binary data. The phase of the signal changes when a new binary symbol is stumbled upon. Frequency and amplitude of the original carrier wave remain the same.

The baseband signal controls the phase shift of the signal in a Phase Shift Keying system. The amplitude a(t) = a and carrier frequency f(t) = f are constant, while phase functions carry a finite period of time. Two types of Phase Shift Keying are Binary Phase-Shift Keying (BPSK) and Quadrature Phase-Shift Keying (QPSK).

Binary Phase-Shift Keying (BPSK)

The type of Phase Shift Keying uses two separate phases. The technique is characterized by a sine wave carrier with two-phase reversals. The reversal may be 0° and 180°.

A set of basic functions is selected for a specific modulation scheme. As a rule, the functions are orthogonal to each other and are often derived using the Gram Schmidt orthogonalization process.

Upon selection of the functions, vectors in the signal space are denoted as linear combinations of the functions. A single sinusoid is used as the basis function. Changing the phases of the sinusoid causes modulation. Four phases may be used for data transmission in more complex Phase-Shift Keying schemes. The maximum that can be used is eight.

Quadrature Phase-Shift Keying (QPSK)

Quadrature Phase Shift Keying is a variation of Binary Phase-Shift Keying that also uses a Double Side Band Suppressed Carrier modulation scheme to pass two bits of information at a particular time.

Digital streams are converted into bit pairs rather than a sequence of the digital stream. The process helps in decreasing the bit rate by a half, allowing space for other users. This process occurs in two separate phases. In the first phase, the binary data is separated into two equal sub-streams.

In the second phase, each stream is transformed into a digital signal after the conversion of serial data in both sub-streams. The digital signals are then merged together following the completion of the second phase.

In this technique, four quadrants or spaces called constellations are used. The tendency of the technique to use individual points or quadrants improves the performance and quantity even despite possible signal intrusion from status, lighting systems, electrical noise, and other sources.

The application of Constellations is extensive in modem technology due to its abilities to improve speed while reducing errors. Evidently, Quadrature Phase Shift Keying is better bandwidth efficiency when compared to modulation schemes that pass one bit per symbol.

Binary Phase-Shift Keying can transmit a single bit per symbol given that it uses two possible phase shifts as compared to four as used in Quadrature Phase Shift Keying. In the Quadrature Phase Shift Keying, two bits are transmitted during each symbol period even with a baseband signal of the same frequency. Therefore, the technique’s bandwidth efficiency is relatively two times higher.

Analog signals demonstrate incessant variations in the area of wired electronics. On the other hand, digital signal schemes have a single or two discrete states.  The distinction is extended to analog to digital conversion systems to allow the transmission of data through electromagnetic radiation in the place of electric current through wires.

When utilized in the passage of analog signals, amplitude modulation and frequency modulation result in continuous variations in the amplitude or frequency of a carrier wave. The modulation technique can also be employed in digital communication to allow for the variations of the carrier in accordance with the discrete information being conveyed.