ECE 3450 M. A. Jupina, VU, 2014 Analog-to-Digital and Digital-to-Analog Conversion Introduction...
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Transcript of ECE 3450 M. A. Jupina, VU, 2014 Analog-to-Digital and Digital-to-Analog Conversion Introduction...
ECE 3450 M. A. Jupina, VU, 2014
Analog-to-Digital and
Digital-to-Analog Conversion
Introduction (Applications and S/H Circuit)
DAC ADC
ECE 3450 M. A. Jupina, VU, 2014
Computerized Motor Control Through the Use of a DAC
ECE 3450 M. A. Jupina, VU, 2014
Example: Function Generator Using a ROM and a DAC
TCLK
TSIGNAL
2 1
2
2 1
PP
N
OUT REFN
N
V V
V
Low PassFilter
N=8 and 5
5256
B is a value between
0 and 255 stored in a ROM register
REF
A
For V V
BV t V
where
ECE 3450 M. A. Jupina, VU, 2014
What clock frequency will result in a 100 Hz sine wave at the output?
What method could be used to vary the peak-to-peak amplitude of the sine wave?
100 256 25.6KHz
Adjust the reference voltage of the DAC.
ECE 3450 M. A. Jupina, VU, 2014
Programmable Gain Amplifier with a DACAC Input Signal
AC Output Signal
Digital Inputs
IO
IO
14
O O
O DC AC
SREFO
S
R I
R I I t
V tVR A A
R R
DC Input Signal
DC Blocking Capacitor
SO O
S
V tV R A
R
ECE 3450 M. A. Jupina, VU, 2014
DVM Using an ADC
ECE 3450 M. A. Jupina, VU, 2014
Real World Applications
Analog-to-digital converters (ADC) and digital-to-analog converters (DAC) are used to interface a computer to the analog world so that the computer can monitor and control a physical variable.
ECE 3450 M. A. Jupina, VU, 2014
Data Sampling System Block Diagram
ECE 3450 M. A. Jupina, VU, 2014
Simplified Diagram of a Sample-and-Hold Circuit
ECE 3450 M. A. Jupina, VU, 2014
LF398 Sample-and-Hold (S/H) Circuit
F
ECE 3450 M. A. Jupina, VU, 2014
Block Diagram of a Digital Storage Oscilloscope
ECE 3450 M. A. Jupina, VU, 2014
Digital Signal Processor (DSP) Architecture
ECE 3450 M. A. Jupina, VU, 2014
Ideal FIR LP Filter
Digital Filter (FIR Low Pass) Implementation on UP1 Board
ECE 3450 M. A. Jupina, VU, 2014
Example Filter Measurements on a Scope
ALL Pass Filter (Sampling Effects) ALL Pass Filter (Alias Signal)
FIR Low Pass Filter (Gain and Phase Measurements)
Vinpp
Voutpp
0360 S
pp
pp
VoutGain
Vin
Phase hift tT
ECE 3450 M. A. Jupina, VU, 2014
Digital-to-AnalogConversion
Definitions Example Problems Various DAC Circuitries DAC0808
ECE 3450 M. A. Jupina, VU, 2014
Four-Bit DAC with Voltage Output
VREF = 16 V
2 1 2FS REF
STEP N N
V VV
ECE 3450 M. A. Jupina, VU, 2014
Output Waveform of a 4-Bit DAC with a Binary Counter Supplying the Input
ECE 3450 M. A. Jupina, VU, 2014
DAC Transfer Function
ECE 3450 M. A. Jupina, VU, 2014
Definitions• Full Scale Output – the maximum value that the D/A converter can produce.• Resolution or Step Size – the smallest change that can occur in the analog
output as a result of a change in the digital input.
where N is number of bits
• Analog Output = K • decimal value of the digital input• Percentage Resolution
• Accuracy Full Scale Error – maximum deviation of the DAC’s output from its ideal value. Linearity Error – maximum deviation in step size from the ideal step size. Offset Error – the small output voltage that exists when all inputs are “0”
• Settling Time – the time required for the DAC output to go from zero to full scale as the binary input goes from all 0’s to all 1’s.
100%
resolution
full scale
2 1FS
N
AK
ECE 3450 M. A. Jupina, VU, 2014
Example Problems1) An eight-bit DAC produces an output voltage of 2.0 V for an input
code of 01100100. What will the value of VOUT be for an input code of 10110011?
011001002 = 10010
101100112 = 17910
(179/100) = (X/2V)X = 3.58V
2) What is the resolution of the DAC in the previous? Express it in volts and as a percentage. Determine the weight of each input bit.
Resolution = 2V/100 = 20mV Full Scale Voltage = 20mV (28 -1) = 5.1V% Resolution = [20mV / {20mV (28 -1) }] x 100% 0.4%LSB = 2V/100 = 20mVOther bits: 40mV, 80mV, 160mV, 320mV, 640mV, 1280mV, and 2560mV.
ECE 3450 M. A. Jupina, VU, 2014
Example Problems3) What is the resolution in volts of a 10-bit DAC whose Full-Scale
output is 5 V?
10 bits---> 210 -1 = 1023 steps
Resolution = 5V/1023 = 4.89 mV 5mV
4) How many bits are required for a DAC so that its Full-Scale output is 10 mA and its resolution is less than 40 A?
The maximum resolution is 40µA. The number of steps required to produce 10mA full scale will be at least 10mA/40µA = 250.
Therefore, it requires at least 8 bits.
ECE 3450 M. A. Jupina, VU, 2014
Example Problems5) Assuming a 12-bit DAC with perfect accuracy, how close to 250 rpm can the motor speed be adjusted for the motorized system below?
12-bit DAC gives us 212 -1 steps = 4095. Step-Size = 2mA/4095 = 488.4nA
To have exactly 250 RPM the output of the DAC must be(250 RPM x 2mA) / 1000 RPM = 500µA.
In order to have 500µA at the output of the DAC, the computer must increment the input of the DAC to the count of 500µA/488.4nA = 1023.75.
Thus, the motor will rotate at (1024/4095) x 1000 RPM = 250.061 RPM when the computer's output has incremented 1024 steps.
ECE 3450 M. A. Jupina, VU, 2014
Example Problems6) An eight-bit DAC has a full-scale error of 0.2% F.S. If the DAC has a full-
scale output of 10 mA, what is the most that it can be in error for any digital input? If the DAC output reads 50 A for a digital input of 00000001, is this within the specified range of accuracy? (Assume no offset error.)
Full Scale error = 0.2% x 10mA = 20µA
Step-Size = 10mA/255 = 39.2µA. Ideal output for 000000012 is 39.2µA.
The possible range is 39.2µA ± 20µA = 19.2µA to 59.2µA.
Thus, 50µA is within this range.
ECE 3450 M. A. Jupina, VU, 2014
Example Problems7) A particular 6-bit DAC has a full-scale output rated at 1.260 V. Its accuracy is
specified as ± 0.1% F.S., and it has an offset error of ±1 mV. Assume that the offset error has not been zeroed out. Consider the measurements made on this DAC in the table below, and determine which of them are not within the device’s specifications.
Step-Size = 1.26V/63 = 20mV
±0.1% F.S. = ±1.26mV
Thus, maximum error will be ±1.26mV ±1mV = ±2.26 mV.
0000102 --> 2 x 20mV = 40mV [41.5mV is within specs.] .0001112 --> 7 x 20mV = 140mV [140.2mV is within specs.] .0011002 --> 12 x 20mV = 240mV [242.5mV isn't within specs.] .1111112 --> 63 x 20mV = 1.260V [1.258 V is within specs.] .
Input Code Output
000010 41.5 mV
000111 140.2 mV
001100 242.5 mV
111111 1.258 V
ECE 3450 M. A. Jupina, VU, 2014
Simple DAC Using an Op-Amp Summing Amplifier with Binary-Weighted Resistors
1 1 12 4 8
F F F FOUT D C B A
D C B A
D C B A
R R R RV V V V V
R R R R
V V V V
1 K
2 K
1 K
4 K
8 K
ECE 3450 M. A. Jupina, VU, 2014
Improved DAC using Summing Amplifier with Precision Voltage Source
1 K2 K
1 K
4 K
8 K
ECE 3450 M. A. Jupina, VU, 2014
Basic R/2R Ladder DAC
ECE 3450 M. A. Jupina, VU, 2014
DAC0808 R/2R Ladder DAC with Current Output
ECE 3450 M. A. Jupina, VU, 2014
DAC0808 Block Diagram
ECE 3450 M. A. Jupina, VU, 2014
DAC0808 Specifications
• The DAC0808 is an 8-bit monolithic DAC• Full Scale Error: ±0.19% • Offset current levels less than 4 A for • Maximum output current: 2 mA.• Fast settling time: 150 ns typical• Power supply voltage range: ±4.5V to ±18V• Low power consumption: 33 mW @ ±5V
REFI 2 mA
ECE 3450 M. A. Jupina, VU, 2014
DAC Circuit
MSB
LSB
F ref
O ref
Assuming matched resistors (R = R ),
A1 A2 A3 A4 A5 A6 A7 A8thus E = V
2 4 8 16 32 64 128 256
ECE 3450 M. A. Jupina, VU, 2014
Analog-to-DigitalConversion
Definitions Effects of Sampling Various ADC Circuitries Example Problems ADC0804
ECE 3450 M. A. Jupina, VU, 2014
General Diagram of One Class of ADCs
ECE 3450 M. A. Jupina, VU, 2014
Typical Computer Data Acquisition System
Waveforms showing how the computer initiates each new conversion cycle andthen loads the digital data into memoryat end of conversion (EOC).
ECE 3450 M. A. Jupina, VU, 2014
ADC Ideal Linear Transfer Function
ECE 3450 M. A. Jupina, VU, 2014
Definitions• Full Scale Input – the maximum value that the A/D converter can accept.
• Resolution or Step Size – the smallest change that can occur in the analog input to produce a change in the digital output.
where N is number of bits
• Accuracy Quantization Error – the maximum difference between the actual analog input
voltage and the digital output value representing it. This is equal to the resolution. Full Scale Error – maximum deviation in the ADC’s comparator reference voltage
or the internal DAC’s output voltage from the ideal value.
• Conversion Time – the time required for the ADC to convert an analog input voltage into a digital output.
2 1FS
N
AK
ECE 3450 M. A. Jupina, VU, 2014
Digitizing an Analog Signal
fed through a DAC
ADC
DAC
LPF
ECE 3450 M. A. Jupina, VU, 2014
Nyquist Criterion
In order to avoid loss of information, the incoming signal must be sampled at a rate greater than two times the highest frequency component in the incoming signal.
Example: CD Audio, FSAMPLING = 44 KHz since FMAX = 22 KHz
A signal alias is produced by sampling the signal at a rate less than the minimum rate (twice the highest frequency).
SAMPLING MAXF 2 F
ECE 3450 M. A. Jupina, VU, 2014
An Alias Signal Due to Under-Sampling
Sine wave frequency is 1.9 KHz. This signal is sampled every 500 s (FSAMPLING = 2 KHz). Data samples are indicated by square dots. These square dots form a sinusoidal waveform with a period of 10 ms or a frequency of 100 Hz.. The alias frequency is the difference between the sampling frequency and the frequency of the incoming signal.
ECE 3450 M. A. Jupina, VU, 2014
Digital-Ramp ADC
ECE 3450 M. A. Jupina, VU, 2014
Three-Bit Flash ADC3 K
1 K
1 K
1 K
1 K
1 K
1 K
1 K
ECE 3450 M. A. Jupina, VU, 2014
Four-Bit Successive-Approximation ADC
ECE 3450 M. A. Jupina, VU, 2014
Example Problems1) An eight-bit digital ramp ADC with a 40 mV resolution uses a clock
frequency of 2.5 MHz. Determine the following values:a) the digital output for an analog voltage of 6.005 Vb) the digital output for an analog voltage of 6.035 Vc) the maximum and average conversion times
a) 6.005 V / 40 mV = 150.125 = 15110 = 100101112.
b) Using same method as in (a) the digital value is again 100101112.
c) Maximum conversion time = (max. # of steps) x (TCLOCK) tmax_conv = (28-1) x (0.4µs) = 102µs. Average conversion time = 102µs/2 = 51µs
ECE 3450 M. A. Jupina, VU, 2014
Example Problems
2) Why were the digital outputs the same for parts a) and b) of question 1?
Because the difference in the two values of VA was smaller than the resolution of the converter.
ECE 3450 M. A. Jupina, VU, 2014
Example Problems3) An ADC has the following characteristics: resolution of 12
bits, full scale error of 0.03%, and full scale input of 5 V. What is the quantization error in volts? What is the total possible error in volts?
With 12 bits, percentage resolution is (1/(212-1)) x 100% = 0.024%.
Thus, quantization error = 0.024% x 5V = 1.2mV.
Error due to 0.03% inaccuracy is0.03% x 5V = 1.5mV.
Total Error = 1.2mV + 1.5mV = 2.7mV.
ECE 3450 M. A. Jupina, VU, 2014
Example Problems
4) A data acquisition system is being used to digitize an audio signal. The sampling frequency is 20 KHz. Determine the output frequency that will be heard for each of the following input frequencies?
a) 5 KHz < FMAX, 5 KHzb) 10.1 KHz > FMAX, 9.9 KHzc) 10.2 KHz > FMAX, 9.8 KHzd) 15 KHz > FMAX, 5 KHze) 19.1 KHz > FMAX, 900 Hzf) 19.2 KHz > FMAX, 800 Hz
ECE 3450 M. A. Jupina, VU, 2014
Example Problems5) The figure below shows the waveform at VAX for a 6-bit successive
approximation ADC with a step size of 40 mV during a complete conversion cycle. Examine this waveform and describe what is occurring at times t0 to t5. Then determine the resultant digital output.
ECE 3450 M. A. Jupina, VU, 2014
Example Problems5)
Full scale input = (26-1) 40mV = 2.52V
t0: Set MSB (bit 5); t1: Set bit 4; clear bit 4; t2: Set bit 3; clear bit 3;
t3: Set bit 2; t4: Set bit 1; clear bit 1; t5: Set LSB;
Digital result = 1001012 = 3710 Thus 1.48 V < VA < 1.52 V
ECE 3450 M. A. Jupina, VU, 2014
ADC0804 Eight-Bit Successive-Approximation ADC with Tri-State Outputs
ECE 3450 M. A. Jupina, VU, 2014
ADC0804 Block Diagram
ECE 3450 M. A. Jupina, VU, 2014
ADC0804 Specifications• It has two analog inputs, VIN(+) and VIN(-), to allow
differential inputs.
• Eight bit resolution at the output. The digital outputs are tri-state buffered for bus interfacing.
• VREF/2 pin is for a precision voltage source.
• Separate ground connections for digital and analog voltages (for noise considerations).
• It has an internal Schmitt Trigger oscillator that can be configured with an external R and C for self-clocking or an external clock can be used. Typical clock frequency is 640 KHz. Higher frequencies possible but error increases.
• Typical conversion time is 100 s or 0.1 ms.
ECE 3450 M. A. Jupina, VU, 2014
ADC0804 Control PinsINPUTS
• Chip Select, , must be LOW for and inputs to have any
effect. With HIGH, the digital outputs are in the Hi-Z state and
no conversions can take place.
• READ, , must be LOW to enable the digital output buffers.
• WRITE, , when a LOW pulse is received at this input, a new
conversion starts.
OUTPUT
• INTERRUPT, , will go HIGH at the start of a conversion and
will return LOW to signal the end of a conversion.
CS RD
CS
WR
RD
WR
INTR
ECE 3450 M. A. Jupina, VU, 2014
Self-Clocking the ADC0804
sampling rate = conversion rate = fCLK/64.
ECE 3450 M. A. Jupina, VU, 2014
An Application of an ADC0804
ECE 3450 M. A. Jupina, VU, 2014
MSB
LSB
8 Clocks
ADC Circuit in Free Running Mode
sampling rate = conversion rate = fCLK/72
ECE 3450 M. A. Jupina, VU, 2014
Appendix: Schmitt-Trigger Inverter
(a) If input transition times are too long, a standard logic device-output might oscillate or change erratically; (b) a logic device with a Schmitt-trigger type of input will produce clean, fast output transitions.
ECE 3450 M. A. Jupina, VU, 2014
Schmitt-Trigger Inverter Operation
• As VIN increases, VOUT = VOH until VIN > VTH then VOUT = VOL
• When VIN begins to decrease, VOUT = VOL until VIN < VTL then VOUT = VOH
VOH
VOL
VTL VTH
VOUT
VIN
ECE 3450 M. A. Jupina, VU, 2014
Schmitt-Trigger Oscillator
IIN
ECE 3450 M. A. Jupina, VU, 2014
Analysis of a Schmitt-Trigger Oscillator
Capacitor Discharging Capacitor Charging
VC(t) VTH
VTL
VOH
VOUT(t) VOL
t
t
TL TH
Assume Iin = 0, thus IR(t) = IC(t)
t = 0 t = 0'
VOL
VC(t)VOH
VC(t)
ECE 3450 M. A. Jupina, VU, 2014
Analysis of a Schmitt-Trigger OscillatorContinued
Capacitor Discharging Capacitor Charging
I.C. (0)
( )
( ) ( )
( ) ( )
( )
ln( )
tRC
TLRC
TH OL
TL OL
C TH
C L TL
OL C C
C OL OL TH
TL OL OL TH
V VL V V
V V
V T V
V V t dV tC
R dt
V t V V V e
V V V V e
T RC
I.C. (0 )
( )
( ) ( )
( ) ( )
( )
ln( )
tRC
THRC
OH TL
OH TH
C TL
C H TH
OH C C
C OH OH TL
TH OH OH TL
V VH V V
V V
V T V
V V t dV tC
R dt
V t V V V e
V V V V e
T RC
1 1 , H
L H
TOSC T T T Tf Duty Cycle
ECE 3450 M. A. Jupina, VU, 2014
Example: Show how to use a 74LS14 Schmitt-trigger inverter to produce an approximate square wave with a frequency of 10 KHz.
Solution:
ECE 3450 M. A. Jupina, VU, 2014
PSPICE Simulation of a Schmitt-Trigger Oscillator (7414)