Mixed Signal Electronics

3.3 Mixed Signal Electronics

This section introduces the concept “digital”, and presents Mixed Signal Electronics as the specialty of electronics found on the border between the analog and the digital worlds. Consequently, mixed signal electronics also cover the procedures for converting analog signals into digital and vice versa.

3.3.1 Towards the Digital World

In contrast to the analog world, a digital signal is discretized, that is, it is discontinuous. The representation of information, regardless of its origin or purpose, is reduced to a stream of binary data called “bits”. In other words, the world is reduced to ones and zeros, ‘1’s and’ 0’s from now on. The procedure to carry out this simplification of reality will be revealed as the text progresses.

Comparisson between ideal and impaired digital transmission
Figure 5: Transmission of digital signal: ideal (a) and with defects (b)

The basics of digitizing information are explained with an example. Figure 5(a) shows an ideal analog signal s(t) that transmits a stream of bits, specifically 10110010. Figure 5(b) shows the same analog signal, after having been affected by the impediments associated with a transmission channel, in in this case noise and frequency distortion. In both cases, using the red line as a threshold, the bit string can also be retrieved without errors, 10110010. This example allows us to conclude that the digital implementation has the following properties:

  • Analog: A digital signal is always analog in its most fundamental state. In the same way that analog electronics abstracts from low-level electrons to work with voltages and currents, some specialties of digital electronic engineering allow us to abstract from voltages and currents to work only with bits.
  • Robust: Despite the impediments and noise suffered by the signal, the bit stream can be perfectly recovered. This cannot be achieved in a purely analog transmission of information, since the added defects in the transmission will irreparably affect the quality of the information received. In other words, digital signals are more robust against transmission channel impediments.
  • Ideal for storage: the example has focused on the transmission of a signal but is equally valid for the storage of information. Any storage method can be subject to some kind of corruption. If the stored signal is analog, this corruption results in loss of quality. However, if the information is digital, it is potentially recoverable if the corruption does not exceed a certain threshold.

3.3.2 Signal Integrity

Signal integrity is the specialty of mixed electronics in charge of guaranteeing the correct transmission of bits between components or integrated circuits within electronic equipment. As the generation and quality of digitally stored information increases, and to minimize the number of lines between components, it is necessary to squeeze the maximum number of bits per second (bit/s) that can be transmitted on a transmission line between components. These links work at very high frequencies, so it is necessary to apply microwave theory.

An electronic engineer specialized in signal integrity must guarantee that all the bits that are transmitted in a link of the equipment using a voltage v(t), are read correctly by the element or destination circuit. During transmission, v(t) can suffer a high number of impairments such as thermal noise, noise from adjacent channels, or rebounds associated with high transmission speed, among others. The quality of the link can be visualized with a tool known as “Eye Diagram”, where the voltages associated with all the bits received at the destination are superimposed on each other, showing something similar to an eye. If the defects accumulated by the signal are under control, the eye will remain open, guaranteeing that in the center, the ideal sampling moment, the receiver can read the bits correctly. As an example, Figure 6 shows the eye diagram associated with Figure 5(b). In this case the eye is completely open since it is a simple example. This eye diagram would be any engineer’s dream for a high speed link. In practice, digital transmissions usually work in the limit to maximize the speed of the link without generating bit errors in the receiver.

Eye diagram example
Figure 6: Eye diagram example

3.3.3 Analog-to-Digital and Digital-to-Analog Conversion

Until now, the digital signal has been presented in its simplest variant, as a simple stream of bits. In this way, a digital signal (‘1’s and‘ 0’s) became analog by alternating an output between two values or voltages. And an analog signal (originally square and two-level) was converted to digital (‘1’s and’ 0’s) with a simple threshold comparator. But how is the continuous and variable information from a source digitized, for example the audio from a microphone? On the other hand, can a multilevel digital signal, for example the digitized audio from the previous microphone after being transmitted on a channel, be transformed into the original analog signal to be emitted by a speaker at the destination?

The issues raised in the previous paragraph are resolved by continuing with the example of the microphone and the speaker. Figure 7 shows the analog signal generated by the microphone on the left. This signal is digitized with an analog to digital converter (ADC). The ADC in the figure has 3 bits that allow to represent 8 levels of the original signal. The generated bit-stream (set of samples of 3 bits each) is transmitted through one channel. Here we abstract from the analog voltages and currents associated with said transmission because the defects introduced by our channel are under control, so that we send and receive exactly the same bits without errors. At the receiver, a digital-to-analog converter (DAC), also working with 3-bit per sample, recovers the original analog signal that feeds the loudspeaker so that the audio can be heard at the destination. Obviously, to ensure everything works in this example, it is necessary that both the sample rate of the signals and the number of conversion bits of the ADC and DAC meet a series of mathematical criteria. But those details are beyond the scope of this text.

 Practical example of ADC and DAC in a transmission scheme.
Figure 7: Practical example of ADC and DAC in a transmission scheme.

In communications, for example a computer sending digital data at high speed to another computer, it is common to find schemes where the location of ADC and DAC is the opposite. In effect, the bits that the computer wants to send can be “modulated” with complex mathematical operations that give rise to apparently analog continuous signals, which are generated with a DAC. Said signals are transmitted, received at destination and digitized with an ADC to be finally “demodulated” with digitally implemented mathematical operations, so that the original bits are extracted [1]. It is precisely in communications applications where ADCs and DACs are required to work at higher sample rates with higher number of bits of resolution.

The design and manufacturing of latest generation ADCs and DACs is very complex [2]. Simplifying to the maximum, it can be said that these converters are integrated circuits that include active and passive elements for the bidirectional transformation between analog and digital voltages/currents.

Bibliography
[1]: Sklar, Bernard, Digital Communications: Fundamentals and Applications:, 2020.
[2]: Carbone, Paolo, Design, Modeling and Testing of Data Converters, 2013.


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