1) Digital-to-Analog Conversion (D/A conversion)

2) Analog-to-Digital Conversion (A/D conversion)

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Analog Signals vs. Digital Signals

• Despite what you hear in the media, we don’t live in a digital world!
• Electricity by its nature is analog!
• Analog electrical signals have a continuous voltage and current range.
• When analog signals are restricted to one of a series of discrete voltages, we can map each of these voltage levels to one of n numbers. When we do this, we call it digital.
• Numbers are made up of digits—hence why it is called digital.
• Today, almost all digital systems operate on two discrete voltage levels. This maps nicely into a binary domain. Because of this, people will use the terms binary and digital interchangeably although they don’t technically have to mean the same thing.

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Analog Signals vs. Digital Signals

• Different logic families (TTL, CMOS, ECL, et cetera) map different voltages to logic 0 and logic 1:
• TTL: 0V = logic 0, +?V = logic 1
• CMOS: 0V = logic 0, +?V = logic 1
• ECL: -?V = logic 0, 0V = logic 1

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• When negative logic is employed, the voltages that normally correspond to logic 0 and logic 1 are reversed!
• On our breadboard in the lab, we treat +3.3V as a logic 1 and 0V as a logic 0.
• Acronyms:

TTL = Transistor-to-Transistor Logic

CMOS = Complementary Metal Oxide Semiconductor Logic

ECL = Emitter-Coupled Logic

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Digital-to-Analog Conversion (D/A)

• Digital-to-analog conversion is the process of mapping a number to an analog voltage.
• A single binary digit (bit) maps to one of two discrete voltages.
• A series of binary digits (bits) maps to series of discrete voltages (resolution/precision):
• An n-bit binary number can map to 2ⁿ voltage levels.
• An 8-bit binary number can map to 256 voltage levels.
• A device that takes a series of bits and outputs a voltage is called a digital-to-analog converter, D/A converter, or DAC.
• These binary digits can be fed to the D/A converter as a serial bit stream or as a set of parallel inputs.
• There are many ways to design D/A converters. The design of the D/A converter determines what range of analog voltages you will get for a set of digital inputs…

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Digital-to-Analog Conversion (D/A)

• Assume an 8-bit D/A converter is designed to output an analog voltage between 0 and +5V:

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0 = 00000000 -> 0V

63 = 00111111 -> +1.25V

127 = 01111111 -> +2.5V

255 = 11111111 -> +5V

• Basic equation: V_out = D_in/(2ⁿ - 1) * V_max
• The output of a D/A converter can be shifted or amplified using additional analog circuitry.

Lecture #18

ECE 3430 – Intro to Microcomputer Systems

Fall 2014

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Voltage is proportional

to number magnitude.

�Dividing number by two

will divide the output voltage

in half.

Digital-to-Analog Conversion (D/A)

• Simple example of a serial, pulse-width modulated (PWM) D/A converter:

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• This D/A converter is simply a low-pass filter with rolloff frequency defined as follows:

f_rolloff = 1/(2*π*R*C)

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where: R = resistor value (Ohms)

C = capacitor value (Farads)

Lecture #18

ECE 3430 – Intro to Microcomputer Systems

Fall 2014

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Digital-to-Analog Conversion (D/A)

• The low-pass (RC) filter will be driven with a serial stream of bits (voltage fluctuations between 0V and Vcc/Vdd).
• A low-pass filter will pass frequencies below the rolloff frequency and attenuate frequencies above the rolloff frequency.
• Rolloff frequency is also sometimes called cutoff or turnover frequency.
• To use this kind of serial D/A converter, we must use digital electronics to convert a binary number into a periodic square wave.
• If we drive the bits at the filter at a rate much lower than the rolloff frequency, we would expect to see a square wave at the output of the D/A converter (clearly not what we want).
• If we drive the bits at the filter at a rate much higher than the rolloff frequency, we would expect to see no oscillation on the output (high frequency is being filtered—what we want).

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Digital-to-Analog Conversion (D/A)

• However, the RC filter has a DC offset (due to charge accumulated on the capacitor). When a non-zero voltage is applied to the top terminal of the capacitor, it slowly starts charging to match that voltage.
• When a zero voltage is applied to the top terminal of the capacitor, the capacitor starts discharging.
• The voltage at the output of the D/A converter is simply the average voltage presented at V_in.
• The average voltage of a square wave is proportional to the duty cycle.

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So, does the frequency matter at all?

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Digital-to-Analog Conversion (D/A)

• The frequency must simply stay much greater that the rolloff frequency. We just vary the duty cycle of the input waveform to control the analog output:

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0% duty cycle -> 0V

25% duty cycle -> +1.25V

50% duty cycle -> +2.5V

100% duty cycle -> +5V

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How would you recommend we generate a waveform with fixed

frequency and variable duty cycle in the MSP430?

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Digital-to-Analog Conversion (D/A)

• We could use output compare to generate a square wave with a programmable duty cycle and fixed frequency.

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A parallel D/A converter:

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• Each combination of bits yields a discrete voltage output…
• Examples: R-2R Ladder DAC
• Vref defines the maximum analog output (mapping to all 1’s).

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Parallel Digital Input

(n-bit input)

Analog Output

D/A

Vref

Digital-to-Analog Conversion (D/A)

R-2R ladder:

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• Works well if all resistors (values of R) are “exactly the same”.
• Each input is GND or Vcc/Vdd.
• Current division (KCL) principles at play here.
• Vout is proportional to the binary number provided on a(0)-a(n-1).
• “Instantaneous” conversion time.

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Digital-to-Analog Conversion (D/A)

• 00000000 -> 0V

00000001 -> ~0.02V

00000010 -> ~0.04V

11111111 -> +5V

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Granularity in the output voltages. What if we needed 0.03V?

• Use smaller voltage reference (assign smaller voltage to

11111111).

• Use more bits.
• With this kind of parallel D/A converter, we don’t need to create a

periodic waveform.

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For the serial, PWM D/A, why not use a large capacitor to establish a low

rolloff frequency so we don’t have to generate such a high-

frequency square wave?

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Analog-to-Digital Conversion (A/D)

• Analog-to-digital conversion is the process of mapping an arbitrary voltage to one of n discrete numbers.
• As with D/A converters, A/D converters are designed to work with a specific number of bits (resolution/precision).
• An n-bit A/D converter will map a voltage to one of 2ⁿ numbers.
• A device that accepts an analog voltage and produces a corresponding number to represent that voltage is called an analog-to-digital converter, A/D converter, or ADC.
• The binary output of an A/D converter can be handed to another device in parallel or as a serial bit stream.
• As with D/A converters, there are many ways to design A/D converters.
• A/D converters use a reference voltage to define what voltage will yield the maximum binary output…

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Analog-to-Digital Conversion (A/D)

• An 8-bit A/D converter with +5V tolerant inputs and a voltage reference set to +5V will produce output as follows:

0V -> 0 = 00000000

+1.25V -> 63 = 00111111

+2.5V -> 127 = 01111111

+5V -> 255 = 11111111

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• If the reference voltage were changed to +2.5V, then the digital output for +2.5V would be 11111111.
• Some A/D converters have differential inputs (the input voltage is the difference between two input pins).
• Some A/D converters have differential voltage references (to establish both a high and low voltage reference).

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Number magnitude is

proportional to input voltage.

�Dividing voltage in half will

yield a binary output half as big.

Analog-to-Digital Conversion (A/D)

• Basic equation (for single input, single voltage reference):

D_out = V_in/V_ref * (2ⁿ - 1)

• Basic equation (for differential input, single voltage reference):

D_out = (V_+in - V_-in)/V_ref * (2ⁿ - 1)

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• Applied voltages to an A/D converter can be scaled and shifted using additional analog circuitry to meet the requirements of the A/D converter.
• A/D converters suffer from a phenomenon known as quantization error. A specific voltage will be “rounded” to the nearest whole number. This means that the digital output is not entirely accurate for all voltage inputs.

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What can be done to reduce quantization error?

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Analog-to-Digital Conversion (A/D)

So how does an analog-to-digital converter work?

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• One very common technique for doing analog-to-digital conversion is called the successive approximation method.
• This method involves the use of an analog comparator, a D/A converter, control logic, and storage for a digital approximation (SAR):

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Analog-to-Digital Conversion (A/D)

• The successive approximation method executes sequentially (it takes a clock cycle for each bit in the final result). An 8-bit A/D would take 8 cycles to calculate the 8-bit result.

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• The approximation register is first cleared, then the most-significant bit is calculated first…then the others:
• Guess bit to be 1.
• Provide current value in approximation register to D/A converter.
• Analog comparator compares D/A output with externally provided analog input.
• Control logic clears the bit that it set if D/A output is larger than externally provided input (the initial guess was wrong).

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• Repeat above steps for all the other bits.

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Lecture #18

ECE 3430 – Intro to Microcomputer Systems

Fall 2014

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Analog-to-Digital Conversion (A/D)

• MSP430 ADC10 and ADC12 module use successive approximation.
• More specifically, the MSP430 ADC10/12 modules use a

switched-capacitor DAC scheme instead of an older R-2R DAC

approach.

• The MSP430 also has an A/D module based on a Sigma-Delta

(sometimes called Delta-Sigma) A/D converter scheme.

• Called the SD16_A module.
• This A/D scheme is very complicated (w/r/t SAR) and beyond the scope of this course.
• This type of converter gives you more precision—but slower to stabilize.
• On the MSP430, this module is about 100 times slower than the ADC10/12.
• The only A/D converter we have on the G2553 part is the ADC10.

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Analog-to-Digital Conversion (A/D)

Another alternative…

Flash ADC:

• Produces digital result “in a flash”!
• Instantaneous output change.
• Lots of circuitry required however.
• Required in multimedia applications

or any time rapid conversions are

required.

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A/D and D/A General Issues

A/D and D/A General Issues:

• Accuracy
• How consistent are repeated conversions with a constant analog or digital input?

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• Resolution/Precision
• If the analog or digital input changes very slightly, will the digital or analog output reflect the change?

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A/D and D/A Uses

• We live in an analog world, so input from many different sensors are analog in their nature.
• Many forms of stimulus that a microcontroller needs to monitor are not electrical in nature:
• Temperature
• Pressure
• Light
• Weight
• Airflow
• Humidity
• Et cetera
• Transducers are used to transform the non-electrical quantities mentioned above into analog voltages (and vice-versa).
• Now if a microcontroller is expected to understand this analog information (i.e. detect the temperature, pressure, amount of light, et cetera) it needs an A/D converter to convert this quantity to a number.

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A/D and D/A Uses

• Transducers are devices that convert one form of energy to another form of energy. For our purposes we are typically interested in converting non-electrical energy into electrical energy and vice-versa.
• Examples of transducers:
• Piezoelectric materials
• Microphone/speakers
• Photoelectric cells/light bulbs/LEDs
• Electrical generators/electrical motors
• …and the list goes on forever…
• If a microcontroller expects to make sound, move an object with a motor, generate light, and so on, the digital information it contains must be translated. First a D/A converter converts digital information into a pure form of electricity (analog voltage). Then a transducer can change electrical energy into some other form of energy.

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A/D and D/A Uses

• The analog input to an A/D or the analog output of a D/A may

not meet the electrical requirements for the transducer.

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• Signal conditioning (amplification and shifting) can be applied

to these analog signals.

• Operational amplifier circuits are often used for this.
• The A/D or D/A voltage references may need to change for different applications.

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• Noise can be an issue.
• Digital clock lines contain very high frequency components and can “rattle”

nearby analog voltages.

• AC sources are a common source of 50 or 60 Hz noise.
• Noise can be dampened with capacitors and mitigated by decoupling analog and digital voltage rails.

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The MSP430 (D/A and A/D)

• Some varieties of the MSP430 have a built-in A/D converter.
• May have ADC10, ADC12, or SD16_A module.
• Can reconfigure port pins to become analog inputs.
• Our MSP430 (G2553) has only one ADC10 module.
• Some MSP430s (not ours) have a 12-bit D/A converter (DAC12).
• If an A/D converter or D/A converter is not built into your microcontroller, then you have to interface one externally (but this generally isn’t a big deal).
• There are many standalone A/D and D/A converters on the market to choose from.

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