Question

A dual-slope ADC has a fixed integration time of 100 ms. The reference voltage of the ADC is \(-5 \, {V}\). The time taken by the ADC to measure an input voltage of \(1.25 \, {V}\) is ________ ms (rounded off to the nearest integer).

Hint:

In a dual-slope ADC, the measurement time is proportional to the ratio of the input voltage to the reference voltage, multiplied by the fixed integration time.

Answer 1

Step 1: Formula for the dual-slope ADC. For a dual-slope ADC, the time taken to measure the input voltage is given by: \[ t_{{meas}} = t_{{int}} \times \frac{|V_{{in}}|}{|V_{{ref}}|} \] where:
\( t_{{meas}} \) is the measurement time,
\( t_{{int}} \) is the fixed integration time,
\( V_{{in}} \) is the input voltage,
\( V_{{ref}} \) is the reference voltage.
Step 2: Substitute the given values.
From the question, we know:
\( t_{{int}} = 100 \, {ms} \),
\( V_{{in}} = 1.25 \, {V} \),
\( V_{{ref}} = -5 \, {V} \) (take the absolute value of \( V_{{ref}} \)).
Substitute these values into the formula: \[ t_{{meas}} = 100 \times \frac{1.25}{5} \] Step 3: Calculate the measurement time.
Simplifying:
\[ t_{{meas}} = 100 \times 0.25 = 125 \, {ms} \] Thus, the time taken by the ADC to measure the input voltage of 1.25 V is \( \boxed{125} \, {ms} \).