Analog to Digital Converters (ADCs) Digital to Analog Converters (DACs)
111
Digital Output Dout
110 VFSR
101
100 ΔV, VLSB
011
010
001
000
Vref 4 7
Vref Vref
8 8 8
Analog Input Vin
Any analog quantity can be represented by a binary number. Longer binary
numbers provide higher resolution, which gives a more accurate representation
of the analog quantity.
1
Analog to Digital Converters
Objective: Representing an analog varying physical quantity by a
sequence of discrete numerical values.
01 07 10 15 09 03 00 05
Analog Digital
Sample
& Hold
Quantization
fsample
2
Digitization Process
3
Sample-and-Hold
A number of problems exist with the previous sample and
hold circuit
Load placed on the input of the circuit by charging the
capacitor during the sample phase.
Current flowing from the capacitor used in the conversion
will reduce the voltage stored on the capacitor
-
-
+
+
C
sample/hold
control line
Sample and Hold Circuits
• Sample and hold circuits hold signal constant for conversion
• A sample and a hold device (mostly switch and capacitor)
Demands:
– Small RC-settling-time (voltage over hold capacitor has to
be fast stable at < 1 LSB)
– Exact switching point
– Stable voltage over hold capacitor
– No charge injection by the switch.
If you can exactly
reconstruct the
signal from the
samples, then you
have done a proper
sampling and
captured the key
signal information
6
Accuracy
xq(t)
t
Ts
Higher Sampling Rate Higher Resolution
xq(t) xq(t)
t t
Ts
Resolution
Suppose a binary number with N bits is to represent an analog
value ranging from 0 to A; There are 2N possible numbers.
Resolution = A / 2N
Example 1: Temperature range of 0 K to 300 K to be linearly
converted to a voltage signal of 0 to 2.5 V, then digitized with an
8-bit A/D converter.
2.5 / 28 = 0.0098 V, or about 10 mV per step
300 K / 28 = 1.2 K per step
Example 2: Temperature range of 0 K to 300 K to be linearly
converted to a voltage signal of 0 to 2.5 V, then digitized with a
10-bit A/D converter
2.5 / 210 = 0.00244V, or about 2.4 mV per step
300 K / 210 = 0.29 K per step
Is the noise present in the system well below 2.4 mV ?
Successive Approximation ADC
• Generate internal analog signal VD/A
• Compare VD/A with input signal Vin
• Modify VD/A by D0D1D2…DN-1 until closest possible value to Vin
is reached
Vin S&H
Logic
D0 D1 DN-1
VD/A
DAC
Vref
9
Ladder Comparison
The counter, through a digital-to-analog converter, produces a stair-step of increasing
voltage. At each step the input signal is compared to the current step level. If the input is
higher, then continue to step, if the input is equal or lesser, then stop and read the
counter. The count value is read as numeric value of the input.
Calculate the maximum conversion time of a 8-bit staircase ramp ADC.
The maximum number of count is nc = 28 = 256. The maximum conversion time is:
nc 256
Tc 128 10 6
s 128s
f 2 10 6
10
Flash ADC
Vref • Vin connected with 2N
Vin
R/2 comparators in parallel
Over range
• Comparators connected to
R
resistor string
R
R D0
N D1
If Output
R (2 -1) to N
encoder
R
VIN > VREF High
DN-1
R VIN < VREF Low
R
R/2
Binary Encoder
Electronics 7 12
Priority Encoder
13
An ADC is usually in form of an integrated circuit (IC). ADC0808
and ADC0809 are two typical examples of 8-bit ADC with 8-
channel multiplexer using successive approximation method for its
conversion.
ADC0809
National
Semiconductor
14
Selection of ADC
The parameters used in selecting an ADC are very similar to those
considered for a DAC selection:
• Error/Accuracy: Quantizing error represents the difference
between an actual analog value and its digital representation.
Ideally, the quantizing error should not be greater than ± ½
LSB.
• Resolution: DV to cause 1 bit change in output
• Output Voltage Range Input Voltage Range
• Output Settling Time Conversion Time
• Output Coding (usually binary)
The Nyquist Rate: A signal must be sampled at a rate at least twice
that of the highest frequency component that must be reproduced.
Example: Hi-Fi sound (20-20,000 Hz) is generally sampled at about
44 kHz.
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Digital to Analog Converters (DACs)
Binary Weighted Resistor
Voltages V1 through Vn are Vref
either Vref if corresponding V1 R
bit is high or ground if Rf
V2 2R I
corresponding bit is low
V3 4R
V1 is most significant bit - Vout
n-1
+
Vn 2 R
Vn is least significant bit
MSB
V1 V2 V3 Vn LSB
Vout IRf Rf n -1
R 2R 4R 2 R
Binary-Weighted Digital-to-Analog Converters
Sum of the currents from the input resistors; Consider binary weighting factor.
Advantages: Simple Construction/Analysis; Fast Conversion
Disadvantages: Requires large range of resistors (2000:1 for 12-bit DAC)
with necessary high precision for low resistors; Requires low switch
resistances in transistors
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Binary Weighted Resistor
B3 B2 B1 B0
I VREF R 2R 4R 8R
B2 B1 B0
VOUT I R f VREF B3
2 4 8 Rf = R
Bi
VOUT VREF
2 n i 1 I i
VREF Digital Value Resolution
R 2R 4R 8R Vo
MSB
LSB
-VREF
R-2R Ladder
• The less significant the bit, the more resistors the signal muss
pass through before reaching the op-amp
• The current is divided by a factor of 2 at each node
LSB MSB
R-2R Ladder
The current is divided by a factor of 2 at each node; Analysis for
current from (001)2 shown below
I0 I0 I0
2 4 8
R R R 2R
R 2R 2R 2R
I0
Op-Amp input
VREF B1 B2 “Ground”
VREF VREF
B0 I0
2 R 2 R 2 R 3R 20
R-2R Ladder: An Example
Find the output voltage of the Op-Amp for the following DAC
• Given Values VREF VREF
– Input = (101)2 I0 1.67 mA
– VREF = 10 V
2 R 2 R 2 R 3R
I0 I0
– R=2Ω I opamp 1.04 mA
– Rf = 2R 8 2
VOUT I opamp R f 4.17 V
R R R 2R
R 2R 2R 2R
I0 I0
Op-Amp input
VREF VREF
“Ground”
B0 B2
21
Resolution
V Ref
Resolution V LSB N
2
Poor Resolution(1 bit) Better Resolution(3 bit)
Vout Vout
Desired Analog Desired Analog signal
signal
111
110 110
8 Volt. Levels
2 Volt. Levels
1
101 101
100 100
011 011
010 010
001 001
0 0 000
000
Digital Input Approximate Digital Input
Approximate
22 output
output
Digital to Analog Converters
Selection Criteria of DAC
Resolution
The number of bits making up the input data word that will ultimately determine
the output step voltage as a percentage of full-scale output voltage.
Example: Calculate the resolution of an 8-bit DAC.
Resolution = 8 bits
1 1
Percentage resolution = 8
100% 100% 0.391%
2 256
Output Voltage Range
This is the difference between the maximum and minimum output voltages
expressed in volts.
Example: Calculate the output voltage range of a 4-bit DAC if the output
voltage is +4.5V for an input of 0000 and +7.5V for an input of 1111.
Output voltage range = 7.5 – 4.5 = 3.0V
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Summary
• Operational amplifiers are important building blocks in analog-to-digital
(A/D) and digital-to-analog (D/A) converters. They provide a means for
summing currents at the input and converting a current to a voltage at the
output of converter circuits.
• The methods of A/D conversion used are many! In the successive method,
bits are tested to see if they contribute an equivalent analog value that is
greater than the analog input to be converted. If they do, they are returned
to zero. After all bits are tested, the ones that are left ON are used as the
final digital equivalent to the analog input.
• The R/2R ladder D/A converter uses only two different resistor values, no
matter how many binary input bits are included. This allows for very high
resolution and ease of fabrication in integrated-circuit form.
• The DAC0808 (or MC1408) IC is an 8-bit D/A converter that uses the
R/2R ladder method of conversion. It accepts 8 binary input bits and
outputs an equivalent analog current. Having 8 input bits means that it can
resolve up to 256 unique binary values into equivalent analog values.
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