Solved step by step with explanation- Controller Circuit Design: Summary

Question

Solved step by step with explanation- Controller Circuit Design: Summary

The formula to calculate the smallest measurable voltage change (also known as the least significant bit or LSB) can be calculated using the following equation:

\[ \text{LSB} = \frac{\text{Full Scale Range}}{2^\text{Resolution}} \]

a. To calculate the input voltage applied to the set point, we can use the given transfer function:

\[ \text{TF} = \frac{5 \, \text{V}}{3 \, \text{V}} = \frac{\text{Input Voltage}}{\text{Set Point Voltage}} \]

In this case, we want the output voltage to be \(3 \, \text{V}\) (as per the transfer function). The input voltage (\(V_{\text{in}}\)) is \(5 \, \text{V}\), and we'll let \(R1\) and \(R2\) be the two resistors in the voltage divider.

Substitute the values into the voltage divider equation:

\[ 5R2 = 3R1 + 3R2 \]

\[ 2R2 = 3R1 \]

- \(R1 = 2.2 \, \text{k}\Omega\)

- \(R2 = 3.3 \, \text{k}\Omega\)