DE UNIT-4

R-2R Ladder DAC

A R-2R ladder digital-to-analog converter (DAC) is a popular type of DAC used to convert digital
signals into analog voltages. It operates on the principle of binary-weighted resistor networks and is
relatively straightforward to understand. Here's how a R-2R ladder DAC works:

Components of a R-2R Ladder DAC:

1. Resistors: The key components in a R-2R ladder DAC are two types of resistors, R ohms and
2R ohms. The R resistors have a resistance of R ohms, and the 2R resistors have a resistance
of 2R ohms.

2. Binary Input: The digital input is applied to the DAC in binary form, with each bit of the
digital signal controlling whether a particular resistor is part of the circuit or not. A '1' bit
connects the corresponding resistor, and a '0' bit disconnects it.

3. Summing Amplifier (Op-Amp): The output of the resistor ladder network is connected to a
summing amplifier or operational amplifier (op-amp). The op-amp sums the voltages at the
nodes of the resistor ladder and produces the analog output voltage.

Working of the R-2R Ladder DAC:

1. Digital Input: The digital input is applied to the DAC. Each bit of the input corresponds to a
specific resistor in the ladder network. The most significant bit (MSB) is connected to a 2R
resistor, and the least significant bit (LSB) is connected to an R resistor.

2. Node Voltages: As the digital input is applied, the voltage at each node between the
resistors is determined by the binary weighting of the bits. If a bit is '1', it contributes to the
voltage at the corresponding node.

3. Voltage Summation: The voltages at the intermediate nodes are summed by the op-amp.
The op-amp amplifies and combines these voltages to produce the analog output voltage at
its output.

4. Output Voltage: The analog output voltage is a weighted sum of the voltages at the
intermediate nodes, where the weighting factor is determined by the binary values of the
input bits. The output voltage corresponds to the weighted sum of the input bits, with the
MSB having the most significant influence on the output voltage.

Advantages and Disadvantages:

 Advantages:

 Simplicity in design and operation.

 High-speed operation, suitable for applications that require rapid analog output
updates.

 Good linearity can be achieved when properly designed and calibrated.

 Relatively low power consumption when not all bits are toggling frequently.

 Disadvantages:
  Achieving high resolution with R-2R ladder DACs can be challenging due to the need
for precise resistor values and complex ladder structures for many bits.

 Specific resistor values (R and 2R) are required, which may not be readily available,
necessitating custom or trimmed resistor networks.

 R-2R ladder DACs are most suitable for applications that don't require extremely
high resolutions or low total harmonic distortion (THD).

 Non-negligible non-linearity may be present due to component tolerances and

resistor matching issues.

R-2R ladder DACs are commonly used in various applications, especially when moderate resolution
and speed are sufficient. However, for applications demanding higher resolution and precision,
alternative DAC architectures may be more appropriate.

BINARY WEIGHTED DAC

A binary weighted digital-to-analog converter (DAC) is a type of DAC that operates based on binary-
weighted current sources to produce an analog output voltage. It's a relatively simple and common
architecture for converting digital data into analog voltages. Here's how a binary weighted DAC
works:

Components of a Binary Weighted DAC:

1. Binary Input: The digital input to the DAC is represented as a binary number, with each bit
(from the most significant bit, MSB, to the least significant bit, LSB) controlling a different
current source. Each bit is associated with a weight that is a power of 2 (e.g., 2^0, 2^1, 2^2,
etc.).

2. Current Sources: The DAC includes a set of current sources, with each source providing a
specific current level. The currents from these sources are binary-weighted, meaning that
each current source corresponds to a specific bit and has a current value equal to 2^n times
a reference current (where 'n' is the position of the bit, starting from 0 for the LSB).

3. Summing Node: The currents from the individual current sources are combined at a
summing node. This node serves as the input to an operational amplifier (op-amp).

4. Operational Amplifier (Op-Amp): The summing node's output is connected to the inverting
input of an op-amp. The op-amp amplifies the current sum and converts it into an analog
voltage at the output.

Working of the Binary Weighted DAC:

1. Digital Input: The binary input code is applied to the DAC. Each bit of the digital input
corresponds to a specific current source, and the weight of the bit determines the current
level generated by that source.

2. Current Summation: The current sources corresponding to '1' bits in the binary input code
contribute their current values to the summing node. The sum of these currents at the
summing node represents the binary-weighted sum of the input code.
 3. Op-Amp Amplification: The op-amp amplifies the current sum. The voltage at the op-amp's
output is directly proportional to the sum of the weighted currents. The op-amp output
voltage becomes the analog representation of the digital input.

4. Output Voltage: The analog output voltage is the amplified representation of the digital
input. The voltage at the output is a binary-weighted combination of the reference current
sources.

Advantages and Disadvantages:

 Advantages:

 High linearity and accuracy when precision current sources are used.

 Simple and straightforward architecture.

 Fast response and good settling time.

 Disadvantages:

 The architecture becomes impractical for high-resolution DACs due to the need for a
large number of current sources with binary weighting.

 Non-linearities may occur if the current sources are not precisely matched.

 The precision of the current sources and resistors is crucial for achieving high
accuracy.

Binary weighted DACs are suitable for applications that require good accuracy, speed, and moderate
resolution. However, as the resolution requirements increase, other DAC architectures, such as R-2R
ladder DACs or sigma-delta DACs, become more practical choices.

COMAPRITIVE STUDY OF BOTH

A comparative study of binary weighted DACs and R-2R ladder DACs can help you understand their
differences and choose the appropriate one for your specific application. Here's a comparison
between the two:

1. Resolution:

 Binary Weighted DAC: Well-suited for moderate resolutions, but becomes impractical for
high resolutions due to the need for a large number of current sources.

 R-2R Ladder DAC: Can achieve higher resolutions without an excessive increase in
complexity, making it suitable for a wider range of applications.

2. Linearity:

 Binary Weighted DAC: Offers excellent linearity when precision current sources are used.

 R-2R Ladder DAC: Can achieve good linearity but may require calibration to correct for
component tolerances.

3. Speed:
  Binary Weighted DAC: Typically has a fast response and settling time.

 R-2R Ladder DAC: Also capable of high-speed operation, making it suitable for applications
requiring rapid analog output updates.

4. Complexity:

 Binary Weighted DAC: Simple in terms of concept and fewer components, but can become
complex when implementing a large number of current sources.

 R-2R Ladder DAC: Simpler in terms of component count for a given resolution, but may
become more complex for high resolutions due to resistor matching.

5. Component Tolerance Sensitivity:

 Binary Weighted DAC: Sensitive to variations in current source values, requiring precise
matching for high accuracy.

 R-2R Ladder DAC: Sensitive to resistor tolerances and requires well-matched resistors for
optimal performance.

6. Availability of Component Values:

 Binary Weighted DAC: Requires precise current source values, which may not be readily
available off-the-shelf.

 R-2R Ladder DAC: Requires specific resistor values (R and 2R), which may also require
custom or trimmed resistor networks.

7. Area and Power Consumption:

 Binary Weighted DAC: Requires a larger area and may consume more power when
implementing a large number of current sources.

 R-2R Ladder DAC: May be more area-efficient and power-efficient for high resolutions.

8. Application Suitability:

 Binary Weighted DAC: Suitable for applications that demand high accuracy, moderate
resolution, and speed. It is commonly used in high-speed data converters.

 R-2R Ladder DAC: Suitable for a wider range of applications, including those that require
high resolutions and relatively good linearity without excessive complexity.

In summary, both binary weighted DACs and R-2R ladder DACs have their strengths and weaknesses.
The choice between them depends on the specific requirements of your application, including the
desired resolution, linearity, speed, and available component values. Binary weighted DACs are a
good choice for moderate-resolution, high-precision applications with well-matched current sources,
while R-2R ladder DACs are more versatile and can handle a broader range of resolutions and
applications.

Circuitry:

1. Binary Weighted DAC:

 In a binary weighted DAC, the individual bits of the digital input control separate
current sources.
  The most significant bit (MSB) controls the largest current source, while the least
significant bit (LSB) controls the smallest current source.

 The outputs of these current sources are summed, and the summing node is
connected to an operational amplifier to produce the analog output voltage.

2. R-2R Ladder DAC:

 In an R-2R ladder DAC, a ladder-like network of resistors is used.

 Two types of resistors are used: R ohms and 2R ohms, forming a ladder with a
reference voltage (Vref) applied at the top.

 The digital input bits are connected to the ladder, and the voltages at the
intermediate nodes are generated based on the binary weighting of the bits.

 These voltages are summed up by an operational amplifier (op-amp) to produce the

analog output voltage.

Key Formulas:

1. Binary Weighted DAC:

 The output voltage (Vout) can be calculated as follows: Vout = (Iref / 2^N) * [bN *
2^N + b(N-1) * 2^(N-1) + ... + b1 * 2^1 + b0 * 2^0] Where:

 Iref is the reference current.

 N is the number of bits.

 bN, b(N-1), ..., b1, b0 are the binary values of the digital input bits.

 The resolution (N) represents the number of bits in the digital input, which directly
determines the number of discrete output voltage levels and can be calculated as
2^N.

 Differential Non-Linearity (DNL) and Integral Non-Linearity (INL) are measures of the
DAC's linearity and can be calculated by comparing the actual output values to their
expected values.

2. R-2R Ladder DAC:

 The output voltage (Vout) is given by the formula: Vout = Vref * (D0/2^1 + D1/2^2 +
D2/2^3 + ... + Dn/2^(n+1)) Where:

 Vref is the reference voltage.

 D0, D1, D2, ..., Dn are the digital input bits (0 or 1).

 The resolution (N) is the number of bits in the digital input, which is directly related
to the number of available discrete output voltage levels and can be calculated as
2^N.

 Differential Non-Linearity (DNL) and Integral Non-Linearity (INL) are measures of the
DAC's linearity and can be calculated by comparing the actual output values to their
expected values.
Comparative Analysis:

 Binary Weighted DACs are characterized by varying current sources, while R-2R ladder DACs
use a resistor ladder structure.

 The formulas for both types of DACs relate the digital input to the analog output, with
different parameters, such as reference current (Iref) for binary weighted DACs and
reference voltage (Vref) for R-2R ladder DACs.

 Both DAC types can achieve high linearity and good resolution, but the choice depends on
the specific application and requirements.

 Binary weighted DACs are typically more suitable for applications that demand high
precision, while R-2R ladder DACs are versatile and can handle a broader range of
resolutions and applications.

Sure, here’s an in-depth comparison of RTL, DTL, TTL, IIL, and ECL logic families based on their
characteristics and working:

1. Resistor Transistor Logic (RTL):

 Components Used: Resistor and transistor1.

 Fan Out: Low1.

 Propagation Delay: 12 ns1.

 Noise Margin: Poor1.

 Power Dissipation: 30 mW1.

 Speed Power product: 144 pJ1.

 Circuit complexity: Not Complex1.

 Basic gate: NOR Gate1.

 Application: Not Used1.

2. Diode Transistor Logic (DTL):

 Components Used: Diodes and transistors1.

 Fan Out: Moderate1.

 Propagation Delay: 10 ns1.

 Noise Margin: Moderate1.

 Power Dissipation: 10 mW1.

  Speed Power product: 100 pJ1.

 Circuit complexity: Complex1.

 Basic gate: NAND Gate1.

 Application: Lab and demonstration equipment1.

3. Transistor Transistor Logic (TTL):

 Components Used: Transistor, diodes, and resistor1.

 Fan Out: Moderate1.

 Propagation Delay: 10ns1.

 Noise Margin: Moderate1.

 Power Dissipation: 10 mW1.

 Speed Power product: 100 pJ1.

 Circuit complexity: Complex1.

 Basic gate: NAND Gate1.

 Application: Lab and demonstration equipment1.

4. Integrated Injection Logic (IIL):

 Components Used: Transistor1.

 Fan Out: Low1.

 Propagation Delay: 25-100 ns1.

 Noise Margin: High1.

 Power Dissipation: 5-20 mW1.

 Speed Power product: 4 pJ1.

 Circuit complexity: Not Complex1.

 Basic gate: NAND Gate1.

 Application: LSI and VLSI applications due to high packaging density1.

5. Emitter Coupled Logic (ECL):

 Components Used: Resistor and transistor1.

 Fan Out: High1.

 Propagation Delay: 2 ns1.

 Noise Margin: Low1.

 Power Dissipation: 40-50 mW1.

 Speed Power product: 40-100 pJ1.

  Circuit complexity: Complex1.

 Basic gate: OR Gate / NOR Gate1.

 Application: High-speed switching applications due to high speed1.

Each of these logic families has its own advantages and disadvantages, and they are used in different
applications based on their characteristics.