Analog to Digital (and back again)
Interfacing a microprocessor-based system to the real
world.
• Analog and digital signals
• The bridge: Sampling Theorem
• Conversion concepts
• Conversion circuitry
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Analog to Digital - Microcontroller Systems - Lecture Slides, Slides of Microcontrollers
In the class of computer sciences, we have a special class for the Microcontroller Systems. The main points in these slides are:Analog to Digital, Microprocessor-Based System, Sampling Theorem, Analog and Digital Signals, Conversion Concepts, Conversion Circuitry, Data Transmission, Interface Microprocessors, Digital Conversion
Typology: Slides
2012/2013
1 / 17
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Analog to Digital (and back again)
Interfacing a microprocessor-based system to the real
world.
• Analog and digital signals
• The bridge: Sampling Theorem
• Conversion concepts
• Conversion circuitry
Analog Signals
- The real world is analog.
- Signals vary continuously with time.
- Analog signals take arbitrarily many values.
- Examples:
- audio signal from microphone or cassette player
- video signal from VCR or video camera
- x/y voltage outputs from joystick
time
x(t) continuous range
Analog vs. Digital
To compute on a Microprocessor, we need a digital value.
And by “compute”, we mean:
- making decisions based on signals
- combining multiple signals together
- analyze the signal for a data transmission
- generate a modification of the signal
Signal Conversion
- To interface microprocessors to real-world (analog) systems, we need converters.
- Digital to Analog Converters (DAC): Convert a digital input (e.g. binary word) to analog output (e.g. current or voltage).
- Analog to Digital Converters (ADC): Convert an analog input to digital output.
analog digital
ADC
DAC
mP
mic
speaker
mechanical
mechanical
electrical
electrical electrical
electrical
Conversion of Signals over Time
- Must hold input signal while converting.
- “Sample and hold” circuit takes in (samples) analog value and holds it still while A to D conversion is taking place.
- What is the minimum rate S at which the analog input should be sampled?
- Minimum sampling rate S determines the minimum acceptable speed of A to D conversion.
Sample and hold
n-bit ADC
n analog analog (^) digital
Sampling
- Sampling rate must be high enough so that “no information is lost”.
- What is the information of a signal?
Basic Converter Characteristics
Resolution : Fraction of analog range as defined by the number of bits on the digital side of the converter.
- An n-bit ADC divides analog voltage range [0 , Vmax] into _____ sections and its resolution is _____ of Vmax.
Error : Difference between analog value you believe a digital value represents and what that analog value actually is.
- Even ideal converters introduce some error.
Quantization Error
0
Vmax
¾ Vmax
½ Vmax
¼ Vmax
00 01 10 11
analog input
quantization error
- Inherent in converting continuous values to a finite number of discrete values.
- Every voltage in the range [1/2 Vmax , ¾ Vmax) is mapped to “10”.
- To minimize worst-case error, we assume that “10” means _____ Vmax.
- Worst-case error is __________.
- For normalization, quantization error is expressed in terms of the ideal analog difference represented by a unit change in the digital value, referred to as LSB.
- Quantization error is always equal to +/- ½ LSB.
ADC #2: Single-Slope Integration
+_
Vin
n-bit counter CLK
EN*
Vcc
done
- Start: Reset counter, discharge C.
- Charge C at fixed current I until Vc > Vin. How should C, I, n, and CLK be related?
- Final counter value is Dout.
- Conversion may take several milliseconds.
I C
ADC #3: Successive Approximation (1/2)
+_ Vin
DAC
Vref
n
CLK^ control
successive approximation register
Dout
- Binary search to match input voltage.
- Conversion time > n times DAC settling time.
- Input should stay stable throughout conversion.
DAC #1: Voltage Divider
2-to-4 decoder
2
Din
Vout
Vref
R
R
R
R
DAC #2: R/2R Ladder
D3 (MSB) D2 D1 D0 (LSB)
2R 2R 2R 2R
R R R 2R
Iout
Vref