Module 6

ADCandDAC
 Data conversion Systems
• Both data about the physical world and control
signals sent to interact with the physical world are
typically "analog" or continuously varying quantities.

• In order to use the power of digital electronics, one

must convert from analog to digital form on the
experimental measurement end and convert from
digital to analog form on the control or output end of
a laboratory system.
Data Collection and Control
 What is a DAC?
• A digital to analog converter (DAC) converts adigital
signal to an analog voltage or currentoutput.

100101…
DAC
3 bit DACoutput waveform
 Digital-to-Analog Conversion

• Data in clean binary digital form can be

converted to an analog form by using a
summing amplifier.
• For example, a simple 4-bit D/A converter can
be made with a four-input summingamplifier.
Summing Amplifier
Inverting summer circuit is an
operational amplifier using
negative feedback for controlled
gain, with several voltage inputs
and one voltage output.
The output voltage is the inverted
(opposite polarity) sum of all input
voltages:
Applying kcl at the junction
V 1 V 2 V 3  Vout
  
R R R R
Vout  (V 1  V 2  V 3)
 Digital-to-Analog Conversion

• 2 BasicApproaches

– Weighted SummingAmplifier
– R-2R Network Approach
 Weighted Resistor DAC
• For a simple inverting summer circuit, all resistors mustbe
of equal value.
• If any of the input resistors were different, the input
voltages would have different degrees of effect on the
output, and the output voltage would not be a true sum.
• Suppose, input resistor values at multiple powers oftwo:
R, 2R, and 4R, instead of all the same value R:
 Binary Weighted Resistor DAC
Voltages V1 through Vn are
Vref
Vref if corresponding bit ishigh V1
or R
ground if corresponding bit islow V2 2R I Rf
V3 4R
V1 is most significant bit
- Vout
Vn is least significantbit +
Vn 2n-1R

MSB
Vout   IR f LSB
V1 V 2 V 3 Vn
Vout   R f (         n1 )
1 2 4 2
3 bit binary-weighted DAC
 Binary Weighted Resistor
R
IfR f 
2
Vout   IR f
V1 V 2 V 3 Vn
Vout  (    n )
2 4 8 2

For example, a 3-Bit converter

Vout = - Vref (b3/2+ b2/4+ b1/8)

No B3 B2 B1 Analog Output

0 0 0 0 0

1 0 0 1 -V/8

2 0 1 0 -V/4 or -2V/8

3 0 1 1 -3V/8

4 1 0 0 -V/2 or -4V/8

5 1 0 1 -5V/8

6 1 1 0 -3V/4 or -6V/8

7 1 1 1 -7V/8
 3 bit DACoutputwaveform
With Vref negative (-10V) and Rf=R/2
Input Discrete
States output
Voltage (V)
000 0.0
001 1.25
010 2.50
011 3.75
100 5.00
101 6.25
110 7.50
Vout = - Vref (b3/2+ b2/4+ b1/8) 111 8.75
 Weighted Resistor D/A Converter
• Uses a parallel network of binary-weighted
resistors to feed the op-amp.
• Seldom used since a wide range of resistor
values is required for a large number of bits.
• Difficult to achieve accuracy for a highnumber
of bits.
 Weighted Resistor D/A Converter
• Advantages
– Simple Construction/Analysis
– Fast Conversion
– Cost is low
• Disadvantages
– Requires large range of resistors (2000:1 for 12-bitDAC)
with necessary high precision for lowresistors
– Expensive. Therefore, usually limited to 8-bitresolution.
– Supply voltage has to be constant
 R-2R Ladder DAC
• Produces an analog current that is the sumof
binary-weighted currents.
• Uses only two values of resistors.
• Easily modified to add additional bits – each
new bit requires 2 resistors, values Rand2R.
 R-2R Ladder
• Advantages
– Only two resistor values (R and 2R)
– Does not require high precision resistors
– Accuracy better than weighted resistor
• Disadvantage
– Lower conversion speed than binary weighted
DAC
– More number of resistors to be used compared
to weighted resistor
R-2R Ladder DAC
R-2R Ladder DAC
 R-2R Ladder DAC

 The summing amplifier with the R-2R ladder of

resistances shown produces the output where the
D's take the value 0 or 1.
 The digital inputs could be TTLvoltages which close
the switches on a logical 1 and leave it grounded
for a logical 0.
 This is illustrated for 4 bits, but can be extended to
any number with just the resistance values Rand
2R.
 R-2RLadder
For 0001 only D0=Vref, all other inputs are at 0V and canbe
treated as ground.
So finally Vref/16 volt is appearing as the input toop amp.
This value gets multiplied by the gain of op amp circuit – (Rf/Ri).
If we proceed in this manner (Thevenin equivalent reduction),
we will get

For a 4-Bit R-2RLadder

 1 1 1 1
Vout  Vref b3  b2  b1  b0 
 2 4 8 16 
For general n-Bit R-2R Ladder or Binary Weighted Resister DAC

n 1
Vout  Vref  b n  i
2i
i1
 Important Specifications of DACs
• Resolution
• Speed
• Linearity
 Resolution
• Smallest analog increment corresponding to 1
LSBchange
• An N-bit resolution can resolve 2N distinct
analog levels
• Common DAChas a 8-16 bit resolution

Vref
Resolution  V LSB  N
2
where N  number of bits
 Speed
• Rate of conversion of a single digital input to
its analog equivalent
• Conversion rate depends on
– clock speed of input signal
– settling time of converter
• When the input changes rapidly, the DAC
conversion speed must be high.