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Digital-to-Analog Fundamentals
February 1967 Radio-Electronics

February 1967 Radio-Electronics

February 1967 Radio-Electronics Cover - RF Cafe[Table of Contents]

Wax nostalgic about and learn from the history of early electronics. See articles from Radio-Electronics, published 1930-1988. All copyrights hereby acknowledged.

Irwin Math - what a great last name. My preferred last name list also includes Piper, Cessna, Rockett, Wright, Goddard, Einstein, Marconi, Hertz, Coulomb, Ampere, Edison, de Forest. That is not to disparage other worthy names like Bell, Moore, and Franklin, it's just that the latter are common enough that they would not likely illicit an association with an accomplished scientist. If I can't have fame in common with a great person, at least the name would be somewhat of a consolation. ...but I digress. This "Digital-to-Analog Fundamentals" article authored by Mr. Math appeared in a 1967 issue of Radio-Electronics magazine. With the advent of transistors and a growing selection of integrated circuits, digital signaling and processing was getting a lot of attention. Univac-size vacuum tube computers were being compacted into a small fraction of the volume, consuming a small fraction of the power, and requiring a small fraction of the maintenance. History shows that rapid progress ensued in both digital circuitry and the application thereof.

Digital-to-Analog Fundamentals

Output from the counting system - RF Cafe

Fig. 2a - Simple digital counting system.

Fig. 2b - The output from the counting system.

By Irwin Math

In today's sophisticated world of electronic computers, automatic control systems and complex communication networks, many physical and electrical quantities must be measured and processed with electronics. At present, there are two ways for handling such information - the analog and the digital methods.

When the value of quantities such as temperature, fluid flow and illumination level change, they do so gradually and continuously. To measure such analog quantities, certain sensing devices - thermocouples, flow meters, and photocells, for instance - are used. The output of a thermocouple is a continuously varying voltage; there are no jumps or breaks between one point and the next. For example, Fig. 1 is a graph of the temperature variations during a normal summer day, as measured by a thermocouple calibrated in degrees F. Notice that the curve is smooth - all temperatures from the high of the day to the low have been recorded.

Other values - such as the number of boxes on an assembly line or the number of automobiles passing a toll booth - are called digital quantities. They are composed of distinct, separate units, never varying continuously but always in discrete steps. The output of digital sensing devices such as electronic counters, proximity detectors or photoelectric relays are usually pulses or steps in voltage. Fig. 2-a shows a high-speed production line with a photoelectric counter, while Fig. 2-b illustrates the output of the photoelectric cell. Every time an object interrupts the light beam, a pulse is produced and the counter is triggered. This output, unlike the analog output, is abrupt. An increase in the number of items passing the photocell increases only pulse rate. Amplitude remains the same.

Digital-pulse information, unlike continuously varying analog data, is more easily processed in electronic devices. Flip-flops can quickly count pulses, digital computers can readily add, subtract, multiply and divide them; and punch cards and magnetic tapes can store them. It is therefore often desirable to convert analog information to digital signals. Many devices have been developed to accomplish this, and if you understand how analog-to-digital converters work, you'll know more about today's industrial measuring and control systems.

Temperature on a summer day - RF Cafe

Fig. 1 - Temperature on a summer day.

Simple digital-to-analog converter; temperature controls heating or cooling - RF Cafe

Fig. 3 - Simple digital-to-analog converter; temperature controls heating or cooling.

Basic form of an electronic analog-digital conversion system - RF Cafe

Fig. 4 - This is the basic form of an electronic analog-digital conversion system.

Automobile tachometer uses one kind of digital-to-analog conversion - RF Cafe

Fig. 5 - An automobile tachometer uses one kind of digital-to-analog conversion.

Rocket-borne telemetry transmitter uses analog-to-digital conversion - RF Cafe

Fig. 6 - This rocket-borne telemetry transmitter uses analog-to-digital conversion.

As an example, suppose it's desired to keep the temperature of a room at 75°F. Since temperature is an analog quantity, what's needed is a device to sense 75°F, to turn on a heater if the temperature falls or a cooling device if it rises. Fig. 3 shows the system. A bimetallic strip is used as the analog-digital converter. When the temperature is below 75°F, the strip bends up (the analog input) and the heater is connected in the circuit (the digital output). As the temperature rises, the strip slowly bends down until, at exactly 75°F, the contact is broken and the heater turns off. If the temperature should rise above 75°F, the bimetallic strip bends further down and turns on the air conditioner. Now the cycle reverses, the contact being broken when 75°F is reached. By varying the settings of either contact point, various temperatures can be sensed and controlled.

Most analog-to-digital converters are more complex than the previous example. Consider Fig. 4. In this circuit an analog input of 0-10 volts changes the bias on Q1 (an npn transistor), thereby varying emitter-to-collector resistance r2. This change in resistance varies the total resistance (R1 + r2) in the Q2 emitter circuit, altering the number of pulses per second produced by pulse generator Q2. As a result, each analog change produces a definite change in the number of pulses. Since fractions of a pulse cannot be produced, the output is a true digital signal.

Using this system, analog temperature information can be read out on a numbered display device. A thermocouple's output can be fed to the converter and the resultant pulses used to trigger illuminated numerals.

When an analog quantity has been put in digital form for processing and storing, it's often desirable to recover the information by using a digital-to-analog converter. The automobile tachometer is an example. Engine revolutions - analog data - are translated into digital form by the breaker points, which produce pulses used to fire the sparkplugs. A DC meter is used to indicate engine rpm, but the meter can't respond to pulses. It needs a DC voltage, furnished by the circuit of Fig. 5.

An input pulse causes C1 to charge through D1 with indicated polarity. While this happens, D2 is reverse-biased and therefore nonconducting. After the pulse has passed, the voltage on C1 reverse-biases D1 and discharges through D2 (which is now forward-biased). C2 charges until the voltages across both capacitors are equal. The next input pulse causes exactly the same sequence of events, adding more voltage to C2. But meter resistance RM is in parallel with, and constantly discharging, C2. As a result, the meter indicates the average voltage across C2. The faster the engine turns, the more pulses per second are fed to the circuit, the more quickly C2 is charged, and the higher the meter reads. Thus meter indication is proportional to engine speed.

The preceding examples are employed in certain simple devices but have limited application in industry and communications. More complex systems, combining several functions. are used extensively for special applications.

Figs. 6 and 7 are simplified diagrams of a telemetry system used to obtain fuel-tank information from a rocket in flight. All values to be measured are analog, so the sensing devices produce continuously varying output voltages, each proportional to the parameter being measured. One important item is the rate of fuel flow. To sample the flow, a paddle wheel in the fuel line drives the armature of a DC generator (Fig. 6). Hence, the DC voltage is proportional to the rate of fuel flow.

It's also desirable to know how much fuel remains in the tank at any time. The task is accomplished with an unusual capacitor. Again referring to Fig. 6, a rod is suspended in the middle of the tank, forming one plate of the capacitor. The walls of the tank form the other plate. The value of this capacitor is determined by the dielectric constant of the liquid (which is known for each fuel type) and by the amount of liquid in the tank.

Since the capacitance is very small, special techniques must be used to measure any change. The tank capacitor is placed in series with an external fixed-value capacitor, forming a voltage divider. An AC generator places a voltage across this divider so that any change in the value of the tank capacitor changes the AC voltage amplitude. This AC output is rectified to produce a DC voltage for further processing.

Resistive voltage dividers fed by DC sources are used to measure fuel temperature and pressure. One divider contains a thermistor in the tank, monitoring the temperature and varying DC output voltage proportionately. Fuel pressure is measured by a carbon block between two metal plates in another voltage divider. Any increase in tank pressure compresses the carbon material, altering the output voltage.

The output from each sensing device is tapped down to a convenient range for conversion to digital form. It would be desirable to monitor all parameters continuously, but only a single transmitting channel is available: consequently, time multiplexing must be used. Switch S1 connects each sensor output to the converter for a short period, then moves on to the next one.

The analog-to-digital converter operates just like the one shown in Fig. 4. Its pulse output - which is proportional to the quantity being measured - is fed to a pulse modulator. This stage modulates the transmitter of the rocket, which sends the telemetry information to the receiving station. Note the sync inserter - this device adds a sync signal to furnish a reference point for locating the position of switch S1. Thus at the receiver it's possible to determine which quantity is being measured at any time.

Fig. 7 shows how the telemetered information is processed by the receiver. RF is processed by a conventional methods, and a pulse detector recovers the original pulses. These pulses go through the digital-to-analog converter, and the continuously varying DC output is fed to sampler S2, identical to and synchronized with S1 in the rocket. S2 feed analog data to the various indicating meters, which are calibrated in gallons per second, pounds per square inch, etc.

For permanent reference, a tape recorder stores the pulse information. At any later time, the tape may be played back and used to drive the converter, S2 and the readout meters.

For greater resolution, sometimes the pulses are fed directly to electronic counters with numerical display readouts. At other times the analog outputs of S2 are fed to oscilloscopes or ink-chart recorders.

The system described in Figs. 6 and 7 is necessarily simplified; most systems are more complicated and sophisticated. However, the same basic principles are employed in both.

There are many other types of converters and sensors - time encoders, shaft-angle decoders and weighted decoders. All accomplish similar tasks. A continuously varying quantity is monitored by a sensor, the information changed to pulses, and these pulses used to control some portion of a production process. For human monitoring of the quantity, the pulses are converted back into continuously varying voltages, where they drive meters.

Digital and analog systems are like two languages. The converters are really translators. They're useful because two different systems can then exchange information. It's a lot like two persons from different countries talking to each other through an interpreter. Without him, there'd be no communication.



Posted April 11, 2023

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Kirt Blattenberger,


RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while tying up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived...

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