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N: Number of Bits in Digital Code

This document discusses digital to analog converters (DACs). It describes key DAC characteristics like offset, span or range, step size, and how analog value relates to digital number. It then explains the two main types of DAC circuits: binary weighted and R-2R ladder. Diagrams of 8-bit examples of each type are shown and their output voltage equations are given. The document also includes a short example problem calculating quantization values for an analog-to-digital converter.

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Shimaa Barakat
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105 views4 pages

N: Number of Bits in Digital Code

This document discusses digital to analog converters (DACs). It describes key DAC characteristics like offset, span or range, step size, and how analog value relates to digital number. It then explains the two main types of DAC circuits: binary weighted and R-2R ladder. Diagrams of 8-bit examples of each type are shown and their output voltage equations are given. The document also includes a short example problem calculating quantization values for an analog-to-digital converter.

Uploaded by

Shimaa Barakat
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Digital to Analog (DAC) Converters

DAC Characteristic:
Offset: minimum analog value. (= Vmin)
Span (or Range): V max −V min
n: number of bits in digital code.
V max −V min
Step Size (or Resolution):Q=
2n
Let AV be Analog Value; DN be Digital Number:
AV = DN * Step Size + Offset = (DN / 2n )* Span + Offset
DN = (AV - Offset) / Step Size = (AV - Offset) * 2n / Span
Digital to Analog Converter (DAC) types:
There are two methods of constructing a DAC; Binary Weighted type, and R-2R Ladder
type. Figure 1 displays an 8-bit binary weighted type DAC circuit. The output voltage for
a binary weighted DAC is found using the following equation.

1
Figure 2 displays an 8-bit R-2R Ladder type DAC circuit. In order to analyze the circuit,
assume that all bits except one are connected to the ground. Then, equivalent
resistance is calculated by realizing that two 2R resistors are in parallel, which will
generate an equivalent value of R. Next, this equivalent resistor is in series with
another R to produce an equivalent resistance of 2R. This process continues until the
number of resistors in the circuit are reduced to a couple of 2R resistors.

Figure 3 displays the equivalent circuit when D7 is connected to +5V. Now we can find
the Thevenin Equivalent Circuit of the section to the left of the Operational Amplifier
(Op-Amp), and proceed to calculate the output voltage generated by the associated bit.
The following equation represents the DAC output voltage for the R-2R Ladder type
circuit.

2
Sheet 2
1. An analog-to-digital converter (ADC) converts voltages in the range of ± 24 volts
(nominal input range) to 16-bit positive integer codes.
a) Calculate the quantization interval of the ADC.
b) Determine the maximum quantization error.
solution:
V max −V min 24−(−24) 48
a) Q= n
= 16
= =732.4 μV
2 2 65536
b) Maximum quantization error = Q/2 = 366.2 μV

2. A 4 bit digital to analog converter is shown. R = 100K ohm, V ref = 12v.


a. What is the quantization voltage?
b. What is the value of the
feedback resistor for a full
scale output voltage of -
1.0v; Rf=??

solution:
V max −V min 12
a. Q= n
=0.75 V
=
2 24
V × Rf D 3 D 2 D 1 D 0
b . V out = ref
2R (+ + +
20 21 22 23 )
2 R × V out 2× 100× 1
Rf= =
D D D D 1 1 1 1
(
V ref 03 + 12 + 21 + 30
2 2 2 2 ) (
12× 0 + 1 + 2 + 3
2 2 2 2 )
200
¿ =8.89 Ω
12×1.875

3
3.

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