# 12.1: Introduction to Analog to Digital to Analog Conversion

Up to now, all of the circuits you have studied in this book were analog circuits. That is, the input waveforms were time-continuous and had infinite resolution along the time and amplitude axes. That is, you could discern increasingly smaller and finer changes as you examined a particular section. No matter whether the circuit was a simple amplifier, function synthesizer, integrator, filter, or what have you, the analog nature of the signal was always true. Fundamentally, the universe is analog in nature (at least as far as we can tell - until someone discovers a quantum time particle). Our only real deviation from the pure analog system was the use of the comparator. Although the input to the comparator was analog, the output was decidedly digital; its output was either a logic high $$(+V_{sat})$$ or a logic low $$(−V_{sat})$$. You can think of the comparator's output as having very low resolution, as only two states are possible. The comparator's output is still time-continuous in that a logic transition can occur at any time. This is in contrast to a pure digital system where transitions are time-discrete. This means that logic levels can only change at specific times, usually controlled by some form of master clock. A purely digital system then, is the antithesis of a pure analog system. An analog system is time-continuous and has infinite amplitude resolution. A digital system is time-discrete and has finite amplitude resolution (two states in our example).

As you have no doubt noticed in your parallel work, digital systems have certain advantages and benefits relative to analog systems. These advantages include noise immunity, storage capability, and available numeric processing power. It makes sense, then, that a combination of analog and digital systems could offer the best of both worlds. This chapter examines the processes of converting analog signals into a digital format and turning digital words into an analog signal. A few representative examples of processing the signal in the digital domain are presented as well. Some examples with which you might already be familiar include the stereo compact disk (CD) and the digital storage oscilloscope. We will break down this topic into two broad sections: analog-to-digital conversion (AD) and digital-to-analog conversion (DA). Since many AD systems require digital-to-analog converters, we will examine DA systems first.

## 12.1.1: The Advantages and Disadvantages of Working in the Digital Domain

Given enough time, an analog circuit may be designed and manufactured for virtually any application. Why, then, would anyone desire to work in the digital domain? Perhaps the major reason for working in the digital domain is the flexibility it offers. Once signals are represented in a digital form, they may be manipulated by various means, including software programs. You have probably discovered that replicating a computer program is far easier than replicating an analog circuit. What's more, a program is much easier to update and customize than a hardware circuit. Because of this, it is possible to manipulate a signal in many different ways with the same digital/computer hardware; all that needs to be altered is the manipulation instructions (i.e., the program). The analog circuit, in contrast, needs to be re-wired, and extra components need to be added or old portions removed. This can be far more costly and time-intensive than just updating software. By working in the digital domain, processing circuits do not exist per se; rather, a generic IC such as a CPU is used to create a “virtual circuit”. With a certain amount of intelligence in the system design, the virtual circuit may be able to alter its own performance in order to precisely adapt to various signals. This all boils down to the fact that a digital scheme may offer much greater flexibility for involved tasks and allows a streamlined, generic hardware solution for complex applications. Because of this attribute, the digital solution may wind up being significantly less expensive than its analog counterpart.

When an analog signal is transferred to the digital domain, it is represented as a series of numbers (usually, high/low binary logic levels). One nice property of this representation is that it is exactly repeatable. In other words, an infinite number of copies of the data may be generated, and no distortions or deviations from the original will appear. The last copy will be identical to the first. Compare this to a simple analog copy. For example, if you were to record a song with a cassette recorder and then make a copy of the tape, the second-generation copy would suffer from increased noise and distortion. A copy of the second copy would produce even worse results. Every time the signal is copied, some corruption occurs. It is for this reason that early long distance telephone calls were of such low quality. Modern communications systems employ digital techniques that allow much higher quality, even if one person is in New York and the other is in Australia, halfway around the planet.

Besides being a desirable mathematical attribute, repeatability also lends itself to the problem of long term storage. A storage medium for a binary signal only needs to resolve two levels, whereas the analog medium needs to resolve very fine changes in signal strength. As you might guess, deterioration of the analog medium is a serious problem and results in information loss. The digital medium can theoretically survive a much higher level of deterioration without information loss. In a computerized system, data may be stored in a variety of formats including RAM (Random Access Memory) and magnetic tape or disk. For playback only (i.e., read only), data may be stored in ROM (Read Only Memory) or laser disk formats (such as DVD or audio CD).

As always, the benefits of the digital scheme arrive with specific disadvantages. First, for simpler applications, the cost of the digital approach is very high and cannot be justified. Second, the process of converting a signal between the analog and digital domains is an inexact one. Some information about the signal will be lost during the conversion. This is because the digital representation has finite resolution. This means that only signal changes larger than a certain minimum size (the resolution step size) are discernable, and therefore, some form of round-off error is inevitable. This characteristic helps determine the range of allowable signals, from the smallest detectable signal to the maximum signal before overload occurs. Third, analog systems are inherently faster than digital systems. Analog solutions can process input signals at much higher frequencies than digital schemes. Also, analog systems work in real-time, whereas digital systems might not. Digital systems can only perform in real-time if the input signal is not a very high frequency, if the processing task is not overly complex, or if specialized processing circuits are added. Not all applications require real-time performance, so this limitation is not always a problem. Also, because we can expect computing power to get less and less expensive in the coming years, cost-effective digital processing will undoubtedly expand into new areas.