An analog voltage in the range 0 to 5V is divided into 10 equal interv...
Concept:
Maximum Quantization error =
Step size= (Vmax - Vmin)
Calculation:
Given
Analog voltage ranging from 0 V (Vmin) to 5 V (Vmax)
No. of interval or number of steps = 10
Step size = (5 - 0) = 5 V
Maximum quantization error = 1/2 × (5/10) = 0.25 V
An analog voltage in the range 0 to 5V is divided into 10 equal interv...
Given:
- Analog voltage range: 0 to 5V
- Divided into 10 equal intervals
- Conversion into 4-bit digital output
To find:
- Maximum quantization error
Solution:
To understand the solution, we need to first understand the concept of quantization and quantization error.
Quantization:
Quantization is the process of converting a continuous range of values into a discrete set of levels. In this case, the analog voltage range of 0 to 5V is divided into 10 equal intervals, resulting in 11 possible discrete levels.
Quantization Error:
Quantization error is the difference between the original continuous value and the quantized value. It occurs because the quantized value can only represent one of the discrete levels and not the exact continuous value.
Calculation:
In this case, we have a 4-bit digital output, which means we can represent a maximum of 2^4 = 16 levels. However, we are dividing the analog voltage range into only 10 levels.
To calculate the maximum quantization error, we need to consider the worst-case scenario. In this case, the worst-case scenario would be when the actual analog voltage is at the boundary of two adjacent levels.
The size of each interval can be calculated as follows:
Interval size = (Maximum voltage - Minimum voltage) / Number of intervals
= (5V - 0V) / 10
= 0.5V
The maximum quantization error would occur when the actual analog voltage is at the boundary of two adjacent levels. So the maximum quantization error can be calculated as half of the interval size.
Maximum quantization error = Interval size / 2
= 0.5V / 2
= 0.25V
Therefore, the maximum quantization error is 0.25V, which corresponds to option 'c'.