3. High-Pass Filters (20 points) An engineer is measuring an unsteady voltage with low- frequency interference at 10 Hz, and high-frequency vibrations at 1000 Hz. They want to construct a passive

first-order high-pass filter with a cutoff frequency of 300 Hz to attenuate the low-frequency interference. They have a 1.00 uF 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? b) Sketch the Bode magnitude plot for the fist-order filter, with gain |G(jw)| with a log scale on the vertical axis and frequency in Hz with a log scale on the horizontal axis. c) Calculate the gain of the filter for both the 10 Hz interference and the 1000 Hz vibrations. d) Suppose the unfiltered signal has a DC offset of approximately 4.50 V, about which it oscillates with a maximum amplitude of approximately 3.00 V. The filtered signal is to be measured with a DAQ that can be configured with a voltage range of ether 0 to 10 V or -5 to 5 V. Which configuration should the engineer choose? Hint: Recall the effect of high-pass filters on DC signals.