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A 6-bit ladder D/A converter has a maximum output of 10 V. The output for input 101001 is approximately
- a)4.2
- b)6.5
- c)5.5
- d)9.2
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A 6-bit ladder D/A converter has a maximum output of 10 V. The output ...
Concept:
For a ladder-type D/A Converter:
Output Voltage (V0) = Resolution × Decimal Equivalent of binary input.
Where Resolution is given by:
Where, Vfs = Full scale voltage or maximum voltage
Application:
Given n = 6 and the Digital input = 101001
∵ The Resolution will be:
Since the decimal Equivalent of 101001 = 41
So, V0 = 41 × 0.1587
V0 = 6.5067 V
V0 ≈ 6.5 V
Note: If the reference voltage is given, then:
For a ladder-type D/A Converter:
Output Voltage (V0) = Resolution × Decimal Equivalent of binary input.
Where Resolution is given by:
Where, Vfs = Full scale voltage or maximum voltage
Application:
Given n = 6 and the Digital input = 101001
∵ The Resolution will be:
Since the decimal Equivalent of 101001 = 41
So, V0 = 41 × 0.1587
V0 = 6.5067 V
V0 ≈ 6.5 V
Note: If the reference voltage is given, then:
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A 6-bit ladder D/A converter has a maximum output of 10 V. The output ...
To find the output voltage for the given input in a 6-bit ladder D/A converter, we need to understand how the converter works and how the binary input is converted to an analog output.
1. Understanding the 6-bit ladder D/A converter:
- A 6-bit ladder D/A converter consists of a ladder network of resistors and switches that convert a binary input to an analog output voltage.
- The ladder network consists of 2^6 = 64 equal-value resistors, each connected to a switch that can be either in an ON (connected to ground) or OFF (disconnected) state.
2. Conversion process:
- The binary input, 101001, represents the decimal number 41.
- The ladder network is designed such that each ON switch corresponds to a binary 1 and each OFF switch corresponds to a binary 0.
- The ladder network sums the currents flowing through the ON switches, which in turn determines the output voltage.
3. Calculation of output voltage:
- The ladder network has 64 resistors, and each resistor value is determined based on the maximum output voltage of 10 V.
- To calculate the output voltage, we need to determine the current flowing through the ON switches corresponding to the binary input 101001.
- For the given input, the switches corresponding to the bits 1, 3, 4, and 6 are ON, while the switches corresponding to bits 2 and 5 are OFF.
- The current flowing through the ON switches is given by the formula I = V/R, where V is the voltage across the resistors and R is the resistance value.
- Since all resistors are equal, the current flowing through each ON switch is the same, and we can calculate the total current flowing through the ON switches.
4. Calculation of total current:
- In the given input 101001, there are 4 ON switches and 2 OFF switches.
- The total current flowing through the ON switches can be calculated as (4/6) * I_max, where I_max is the maximum current that flows when all switches are ON.
- Since the output voltage is directly proportional to the total current, we can calculate the output voltage as (4/6) * V_max, where V_max is the maximum output voltage of 10 V.
5. Calculation of output voltage:
- Substituting the values, the output voltage for the given input is (4/6) * 10 V = 6.67 V.
- Rounding off to the nearest decimal, the approximate output voltage is 6.7 V.
Therefore, the correct answer is option 'B', 6.5 V.
1. Understanding the 6-bit ladder D/A converter:
- A 6-bit ladder D/A converter consists of a ladder network of resistors and switches that convert a binary input to an analog output voltage.
- The ladder network consists of 2^6 = 64 equal-value resistors, each connected to a switch that can be either in an ON (connected to ground) or OFF (disconnected) state.
2. Conversion process:
- The binary input, 101001, represents the decimal number 41.
- The ladder network is designed such that each ON switch corresponds to a binary 1 and each OFF switch corresponds to a binary 0.
- The ladder network sums the currents flowing through the ON switches, which in turn determines the output voltage.
3. Calculation of output voltage:
- The ladder network has 64 resistors, and each resistor value is determined based on the maximum output voltage of 10 V.
- To calculate the output voltage, we need to determine the current flowing through the ON switches corresponding to the binary input 101001.
- For the given input, the switches corresponding to the bits 1, 3, 4, and 6 are ON, while the switches corresponding to bits 2 and 5 are OFF.
- The current flowing through the ON switches is given by the formula I = V/R, where V is the voltage across the resistors and R is the resistance value.
- Since all resistors are equal, the current flowing through each ON switch is the same, and we can calculate the total current flowing through the ON switches.
4. Calculation of total current:
- In the given input 101001, there are 4 ON switches and 2 OFF switches.
- The total current flowing through the ON switches can be calculated as (4/6) * I_max, where I_max is the maximum current that flows when all switches are ON.
- Since the output voltage is directly proportional to the total current, we can calculate the output voltage as (4/6) * V_max, where V_max is the maximum output voltage of 10 V.
5. Calculation of output voltage:
- Substituting the values, the output voltage for the given input is (4/6) * 10 V = 6.67 V.
- Rounding off to the nearest decimal, the approximate output voltage is 6.7 V.
Therefore, the correct answer is option 'B', 6.5 V.
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A 6-bit ladder D/A converter has a maximum output of 10 V. The output for input 101001 is approximatelya)4.2b)6.5c)5.5d)9.2Correct answer is option 'B'. Can you explain this answer?
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