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Final Lect 7 Dac

The document discusses Digital to Analog Conversion in Digital Signal Processing, focusing on two types of Digital to Analog Converters: Binary Weighted DAC and R-2R Ladder DAC. It explains the workings of a 4-bit Binary Weighted DAC, including current calculations for each input and the challenges of constructing it, while highlighting the advantages of the R-2R Ladder DAC. Additionally, it provides a formula for calculating the resolution of n-bit DACs and examples for 8-bit and 12-bit converters.

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12 views13 pages

Final Lect 7 Dac

The document discusses Digital to Analog Conversion in Digital Signal Processing, focusing on two types of Digital to Analog Converters: Binary Weighted DAC and R-2R Ladder DAC. It explains the workings of a 4-bit Binary Weighted DAC, including current calculations for each input and the challenges of constructing it, while highlighting the advantages of the R-2R Ladder DAC. Additionally, it provides a formula for calculating the resolution of n-bit DACs and examples for 8-bit and 12-bit converters.

Uploaded by

magentamadlen
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Lecture -8

Introduction to Digital Signal


Processing: 2
Prepared By: Asif Mahfuz
Introduction
• Digital to analog conversion is an important part of digital signal processing.
• Once the digital signal has been processed, it is further needed to be converted back to
the analog form.
• A Digital to Analog Converter (DAC) is an electronic device, often an integrated circuit,
which converts a digital signal to its corresponding analog signal.
• Two types of DAC will be studied:
• Binary Weighted DAC
• R-2R Ladder DAC
Binary Weighted DAC
• The figure shows a 4-bit DAC.
• The resistors have a specific
value depending on the binary
weights.
• The resistor corresponding to
MSB have the lowest value
• The resistor corresponding to
LSB have the highest value.
• The output depends on the
presence or absence of current
in the branches.
𝐈𝐟 = 𝐈𝟎 + 𝐈 𝟏 + 𝐈𝟐 + 𝐈𝟑
𝐕𝐎 𝐕 𝐕 𝐕 𝐕
= + + +
𝐑 𝐟 𝟖𝐑 𝟒𝐑 𝟐𝐑 𝐑
Now if 𝐑 𝐟 = 𝐑
𝐕 𝐕 𝐕 𝐕
𝐕𝐎 = + + +
𝟖 𝟒 𝟐 𝟏
Binary Weighted DAC
Determine the output of the DAC if the waveform representing a sequence of 4-bit numbers are applied to the
inputs. Input DO is the least significant bit(LSB)
Binary Weighted DAC
• First we need to determine the current for each of the weighted inputs.
5V
I0 = = 0.0025mA
200k
5V
I1 = = 0.05mA
100k
5V
I2 = = 0.1mA
50K
5V
I3 = = 0.2mA
25K
• Now we will calculate the output contribution for each of the weighted inputs. Since no
current goes through the inverting input, the current only flows through the feedback
path.
VO D0 = 10k −0.025mA = −.25V
VO D1 = 10k −0.05mA = −0.5V
VO D2 = 10k −0.1mA = −1V
VO D3 = 10k −0.2mA = −2V
Binary Weighted DAC
R-2R Ladder DAC
• Though binary-weighted DAC is simple to understand, construction of it is hectic.
• For binary-weighted DAC we need exact multiples of the resistors (R, 2R, 4R, 8R, 16R).
• For DAC of higher bits, the construction becomes practically infeasible.
• However, R-2R DAC solves this problem.
• The construction only require resistors of value R and 2R
R-2R Ladder DAC

Contribution of D3.
R-2R Ladder DAC

Contribution of D2.
R-2R Ladder DAC

Contribution of D1.
R-2R Ladder DAC

Contribution of D0.
DAC
Resolution of a n-bit DAC:
1
2𝑛 − 1
Determine the resolution expressed as a percentage of the following:
a) An 8-bit DAC
b) A 12-bit DAC
Solution:
a) Resolution for 8-bit converter,
1 1
8
× 100 = × 100 = 0.392%
2 −1 255
b) Resolution for 12-bit converter,
1 1
12
× 100 = × 100 = 0.0244%
2 −1 4095
References
1. Thomas L. Floyd, “Digital Fundamentals” 11th edition, Prentice Hall – Pearson Education.

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