Question

An engineer is measuring an unsteady voltage with a DAQ. The signal of interest is typically below 100 Hz, so they sample at 250 Hz to avoid aliasing. They want to construct a passive first-order lowpass filter with a cutoff frequency of 100 Hz to get rid of high frequency electronic noise in the system. They have a 0.20μF capacitor and a decade resistance box available for this filter.

a) Sketch the circuit diagram for the first-order filter. What resistance should be dialed into the decade resistance box?

Answer 1

The engineer should dial in a resistance of approximately 7.96 kΩ into the decade resistance box to construct the lowpass filter using the 0.20µF capacitor, aiming for a cutoff frequency of 100 Hz.

Step-by-step explanation:

To construct a first-order lowpass filter with a cutoff frequency of 100 Hz using a 0.20µF capacitor, we'll base our calculations on the standard formula for the cutoff frequency (fc) of a first-order RC lowpass filter, which is fc = 1 / (2πRC). We need to solve for R when fc = 100 Hz and C = 0.20µF.

R = 1 / (2πfcC) = 1 / (2π×100 Hz×0.20µF) = 1 / (2π×100×0.20×10-6) ≈ 7.96 kΩ

The engineer should dial approximately 7.96 kΩ into the decade resistance box to achieve the desired cutoff frequency. The circuit diagram for the lowpass filter would show the resistor and capacitor in series, with the input voltage across the series combination and the output taken across the capacitor.