CSE, Software Development: Signal Paths from Analog to Digital (DACs)

The concept of a programmable system-on-chip (SoC) started in 1972 with the advent of the unassuming 4-bit TMS1000 microcomputer —the perfect fit for applications such as calculators and microwave ovens that required a device with everything needed to embed "electronic intelligence".

Microcomputers changed the way engineers approached equipment design;

for the first time they could reuse proven electronics hardware, needing only to create software specific to the application.
The result of microcomputer-based designs has been a reduction in both system cost and time-to-market.

In 2005 many things have changed, but many things remain the same. The term microcomputer has been replaced with microcontroller unit (MCU) —a name more descriptive of a typical application.
Today’s MCU, just like yesterday’s microcomputer, remains the heart and soul of many systems.

But over time the MCU has placed more emphasis on providing a higher level of integration and control processing and less on sheer computing power.
The race for embedded computing power has been won by the dedicated digital signal processor (DSP), a widely used invention of the ‘80s that now dominates high-volume, computing-intensive embedded applications such as the cellular telephone. But the design engineer’s most used tool, when it comes to implementing cost effective system integration, remains the MCU. The MCU allows just the right amount of intelligent control for a wide variety of applications.
Today there are hundreds of MCUs readily available, from low-end 4-bit devices like those found in a simple wristwatch, to high-end 64-bit devices. But the workhorses of the industry are still the versatile 8/16-bit architectures. Choices are available with 8 to 100+ pins and program memory ranging from 1 kb to 64 KB.
The MCU’s adoption of mixed-signal peripherals is an area that has greatly expanded, recently enabling many new SoC solutions. It is common today to find MCUs with 12-bit analog-to-digital and digital-to-analog converters combined with amplifiers and power management, all on the same chip in the same device. This class of device offers a complete signal-chain on a chip for applications ranging from energy meters to personal medical devices.
Modern MCUs combine mixed-signal integration with instantly programmable Flash memory and embedded emulation.
In the hands of a savvy engineer, a unique MCU solution can be developed in just days or weeks compared to what used to take months or years.
You can find MCUs everywhere you look from the watch on your wrist to the cooking appliances in your home to the car you drive. An estimated 20 million MCUs ship every day(2005), with growth forecast for at least a decade to come. The march of increasing silicon integration will continue offering an even greater variety of available solutions—but it is the engineer’s creativity that will continue to set apart particular system solutions.

Analog system designers many times in the past avoided the use of electronics for their system functions because electronic circuits could not provide the dynamic range of the signal

without severe nonlinearity, or
because the circuits drifted or became unstable with temperature, or
because the computations using analog signals were quite inaccurate.

As a result, the design shifted to other disciplines, for example, mechanical.

Today, young engineers requested by their superiors to design an analog control system, have an entirely new technique available to them to help them design the system and overcome the “old” problems.
The design technique is this:

sense the analog signals and convert them to electrical signals;
condition the signals so they are in a range of inputs to assure accurate processing;
convert the analog signals to digital; make the necessary computations using the very high-speed IC digital processors available with their high accuracy;
convert the digital signals back to analog signals; and
output the analog signals to perform the task at hand.

Here we try to explain the functions that are in the signal chain, and explain how to design electronic circuits to perform the functions. What we have to know are:

different types of sensors and their outputs.
different techniques of conditioning the sensor signals, especially amplifiers and op amps.
techniques and circuits for analog-to-digital and digital-to-analog conversions, and what a digital processor is and how it works.
data transmissions and power control
assembly-language programming, and also
hands on experience on building a working project.
ability on choosing a digital processor. We choose to use TI MSP430 microcontroller because of its design, and because it is readily available, it is well supported with design and applications documentation, and it has relatively inexpensive evaluation tools.

The goal here is to provide understanding and learning of the new design technique available to analog system designers and the tools available to provide system solutions.

Intro

Designers of analog electronic control systems have continually faced the following obstacles in arriving at a satisfactory design:

Instability and drift due to temperature variations.
Dynamic range of signals and non-linearity when pressing the limits of the range.
Inaccuracies of computation when using analog quantities.
Adequate signal frequency range.

Today’s designers, however, have a significant alternative offered to them by the advances in integrated circuit technology, especially low-power analog and digital circuits.
The alternative new design technique for analog systems is to

sense the analog signal,
convert it to digital signals,
use the speed and accuracy of digital circuits to do the computations, and
convert the resultant digital output back to analog signals.

The new design technique requires that the electronic system designer interface between two distinct design worlds.

First, between analog and digital systems, and
second, between the external human world and the internal electronics world.

Various functions are required to make the interface.

First, from the human world to the electronics world and back again and,
in a similar fashion, from the analog systems to digital systems and back again.

Here we identify:

the electronic functions needed, and
describe how electronic circuits are designed and applied to implement the functions,and
give examples of the use of the functions in systems.

A Refresher

Since we deal with the electronic functions and circuits that interface or couple analog-to-digital circuits and systems, or vice versa, a short review is provided so it is clearly understood what analog means and what digital means.

Analog

Analog quantities vary continuously, and
analog systems represent the analog information using electrical signals that vary smoothly and continuously over a range.

A good example of an analog system is the recording thermometer shown in Figure 1-1. The actual equipment is shown in Figure 1-1a.

An ink pen records the temperature in degrees Fahrenheit and plots it continuously against time on a special graph paper attached to a drum as the drum rotates.
The record of the temperature changes is shown in Figure 1-1b.

Note that the temperature changes smoothly and continuously. There are no abrupt steps or breaks in the data.

Another example is the automobile fuel gauge system shown in Figure 1-2.

The electrical circuit consists of a potentiometer, basically a resistor connected across a car battery from the positive terminal to the negative terminal, which is grounded. The resistor has a variable tap that is rotated by a float riding on the surface of the liquid inside the gas tank.
A voltmeter reads the voltage from the variable tap to the negative side of the battery (ground) abbreviated as GND (black), 0V, usually connected to the vehicle's metal chassis and body.
The voltmeter indicates the information about the amount of fuel in the gas tank.

It represents the fuel level in the tank.The greater the fuel level in the tank the greater the voltage reading on the voltmeter.

The voltage is said to be an analog of the fuel level.

An analog of the fuel level is said to be a copy of the fuel level in another form—it is analogous to the original fuel level.

The voltage (fuel level) changes smoothly and continuously so the system is an analog system, but is also an analog system because the system output voltage is a copy of the actual output parameter (fuel level) in another form.

Digital

Digital quantities vary in discrete levels.

In most cases, the discrete levels are just two values—ON and OFF.

Digital systems carry information using combinations of ON-OFF electrical signals that are usually in the form of codes that represent the information.

The telegraph system is an example of a digital system.
The system shown in Figure 1-3 is a simplified version of the original telegraph system, but it will demonstrate the principle and help to define a digital system.

The electrical circuit (Figure 1-3a) is a battery with a switch in the line at one end and a light bulb at the other.

The person at the switch position is remotely located from the person at the light bulb.
The information is transmitted from the person at the switch position to the person at the light bulb by coding the information to be sent using the International Morse telegraph code.
Morse code uses short pulses (dots) and long pulses (dashes) of current to form the code for letters or numbers as shown in Figure 1-3b. As shown in Figure 1-3c, combining the codes of dots and dashes for the letters and numbers into words sends the information.
The sender keeps the same shorter time interval between letters but a longer time interval between words. This allows the receiver to identify that the code sent is a character in a word or the end of a word itself. The T is one dash (one long current pulse). The H is four short dots (four short current pulses). The R is a dot-dash-dot. And the two Es are a dot each.
The two states are ON and OFF—current or no current. The person at the light bulb position identifies the code by watching the glow of the light bulb. In the original telegraph, this person listened to a buzzer or “sounder”to identify the code.
Coded patterns of changes from one state to another as time passes carry the information.
At any instant of time the signal is either one of two levels. The variations in the signal are always between set discrete levels, but, in addition, a very important component of digital systems is the timing of signals. In many cases, digital signals, either at discrete levels, or changing between discrete levels, must occur precisely at the proper time or the digital system will not work.
Timing is maintained in digital systems by circuits called system clocks.

This is what identifies a digital signal and the information being processed in a digital system.

Binary

The two levels—ON and OFF—are most commonly identified as 1(one) and zero (0) in modern binary digital systems, and the 1 and 0 are called binary digits or bits for short.

Since the system is binary (two levels), the maximum code combinations 2^n depends on the number of bits, n, used to represent the information.

For example, if numbers were the only quantities represented, then the codes would look like Figure 1-4, when using a 4-bit code to represent 16 quantities.

To represent larger quantities more bits are added.
For example, a 16-bit code can represent 2^16=65,536 quantities.

The first bit at the right edge of the code is called the least significant bit (LSB). The left-most bit is called the most significant bit (MSB).

Binary Numerical Quantities

Our normal numbering system is a decimal system. Figure 1-5 is a summary showing the characteristics of a decimal and a binary numbering system.

Note that each system in Figure 1-5 has specific digit positions with specific assigned values to each position. Only eight digits are shown for each system in Figure 1-5.

Note that in each system, the LSB is either 100 in the decimal system or 20 in the binary system.
Each of these has a value of one since any number to the zero power is equal to one.

The following examples will help to solidify the characteristics of the two systems and the conversion between them.

Example 1. Identifying the Weighted Digit Positions of a Decimal Number
Separate out the weighted digit positions of 6524.

Solution:
6524 = 6 × 10^3 + 5 × 10^2 + 2 × 10^1 + 4 × 10^0
6524 = 6 × 1000 + 5 × 100 + 2 X 10 + 4 × 1
6524 = 6000 + 500 + 20 + 4

Can be identified as 6524₁₀ since decimal is a
base 10 system. Normally 10 is omitted since
it is understood.

Example 2. Converting a Decimal Number to a Binary Number
Convert 103 to a binary number.

Solution:
103₁₀/ 2 = 51 with a remainder of 1
51/2 = 25 with a remainder of 1
25/2 = 12 with a remainder of 1
12/2 = 6 with a remainder of 0
6/2 = 3 with a remainder of 0
3/2 = 1 with a remainder of 1
1/2 = 0 with a remainder of 1 (MSB)
103₁₀ = 1100111

Example 3. Determining the Decimal Value of a Binary Number
What decimal value is the binary number 1010111?

Solution:
Solve this the same as Example 1, but use the binary digit weighted position values.
Since this is a 7-bit number:
And since the MSB is a 1, then MSB = 1 × 2^6 = 64
and (next digit)                                     0 × 2^5 = 0
and (next digit)                                     1 × 2^4 = 16
and (next digit)                                     0 × 2^3 =   0
and (next digit)                                     1 × 2^2 =   4
and (next digit)                                     1 × 2^1 =   2
and (next digit, LSB)                            1 × 2^0 =    1
                                                                               ----------
                                                                             87

                              Binary Alphanumeric Quantities

If alphanumeric characters are to be represented, then Figure 1-6, the ASCII table defines the codes that are used.
For example, it is a 7-bit code, and capital M is represented by 1001101. Bit #1 is the LSB and bit #7 is the MSB.

As shown, upper and lower case alphabet, numbers, symbols, and communication codes are represented.

Accuracy vs. Speed — Analog and Digital

Quantities in nature and in the human world are typically analog. The temperature, pressure, humidity and wind velocity in our environment all change smoothly and continuously, and in many cases, slowly.

Instruments that measure analog quantities usually have slow response and less than high accuracy.

To maintain an accuracy of 0.1% or 1 part in 1000 is difficult with an analog instrument.

Digital quantities, on the other hand, can be maintained at very high accuracy and measured and manipulated at very high speed.

The accuracy of the digital signal is in direct relationship to the number of bits used to represent the digital quantity.

For example, using 10 bits, an accuracy of 1 part in 1024 (2^10=1204) is assured.
Using 12 bits gives four times the accuracy (1 part in 4096, 2^12=4096), and
using 16 bits gives an accuracy of 0.0015%(2^16=65536), or
1 part in 65,536.

And this accuracy can be maintained as digital quantities are manipulated and processed very rapidly, millions of times faster than analog signals.

The advent of the integrated circuit has propelled the use of digital systems and digital processing.

The small space required to handle a large number of bits at high speed and high accuracy, at a reasonable price, promotes their use for high-speed calculations.

As a result, if analog quantities are required to be processed and manipulated, the new design technique is to

first convert the analog quantities to digital quantities,
process them in digital form,
reconvert the result to analog signals and
output them to their destination to accomplish a required task.

The complete procedure is indicated in Figure 1-7, and the need for analog circuits, digital circuits and the conversion circuits between them is immediately apparent.

Interface Electronics

The system shown in Figure 1-7 shows the major functions needed to couple analog signals to digital systems that

perform calculations,
manipulate, and
process the digital signals and
then return the signals to analog form.

In that article we deal with the analog-to-digital portion of Figure 1-7, and in a later article we'll deal with the digital-to-analog portion.

The Basic Functions for Analog-to-Digital Conversion

Sensing the Input Signal

Figure 1-8 separates out the analog-to-digital portion of the Figure 1-7 chain to expand the basic functions in the chain.

Most of nature’s inputs such as temperature, pressure, humidity, wind velocity, speed, flow rate, linear motion or position are not in a form to input them directly to electronic systems.

They must be changed to an electrical quantity—a voltage or a current—in order to interface to electronic circuits.

The basic function of the first block is called sensing. The components that sense physical quantities and output electrical signals are called sensors.

The sensor illustrated in Figure 1-8 measures pressure. The output is in millivolts and is an analog of the pressure sensed. An example output plotted against time is shown.

Conditioning the Signal

Conditioning the signal means that some characteristic of the signal is being changed. In Figure 1-8, the block is an amplifier that increases the amplitude of the signal by 1,000 times so that the output signal is now in volts rather than millivolts.

The amplification is linear and the output is an exact reproduction of the input, just changed in amplitude.

Other signal conditioning circuits may

reduce the signal level, or
do a frequency selection (filtering), or
perform an impedance conversion.

Amplification is a very common signal conditioning function. Some electronic circuits handle only small-signal signals, while others are classified as power amplifiers to supply the energy for outputs that require lots of joules (watts are joules/second).

Analog-to-Digital Conversion

In the basic analog-to-digital conversion function, as shown in Figure 1-7, the analog signal must be changed to a digital code so it can be recognized by a digital system that processes the information.

Since the analog signal is changing continuously, a basic subfunction is required. It is called a sample-and-hold function.

Timing circuits (clocks) set the sample interval and the function takes a sample of the input signal and holds on to it.
The sample-and-hold value is fed to the analog-to-digital converter that generates a digital code whose value is equivalent to the sample-and-hold value. This is illustrated in Figure 1-8 as the conditioned output signal is sampled at intervals 0, 1, 2, 3, and 4 and converted to the 4-bit codes shown.
Because the analog signal changes continually, there maybe an error between the true input voltage and the voltage recorded at the next sample.

Example 4. A to D Conversion
For the analog signal shown in the plot of voltage against time and the 4-bit codes given for the indicated analog voltages, identify the analog voltage values at the sample points and the resultant digital
codes and fill in the following table.

Obviously, one would like to increase the sampling rate to reduce this error.
However, depending on the code conversion time, if the sample rate gets to large, there is not enough time for the conversion to be completed and the conversion function fails.

Thus, there is a compromise in the analog-to-digital converter between the speed of the conversion process and the sampling rate.

Output signal accuracy also plays a part. If the output requires more bits to be able to represent the magnitude and the accuracy required, then higher-speed conversion circuits and more of them are going to be required.

Thus, design time, cost, and all the design guidelines enter in.

As shown in Figure 1-8, the bits of the digital code are presented all at the same time (in parallel) at each sample point.
Other converters may present the codes in a serial string. It depends on the conversion design and the application.

Summary

So far we reviewed

analog and digital signals and systems,
digital codes,
the decimal and binary number systems, and
the basic functions required to convert analog signals to digital signals.

In a next article we'll complete the look at the basic functions required to convert digital signals to analog signals. It will be
important to have these basic functions in mind as the electronic circuits that perform these functions are the "core business" of our work.__

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Wednesday, January 2, 2019

Signal Paths from Analog to Digital (DACs)

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