Question

A common use of capacitors as a reactive component is in a low-pass or high-pass filter, both of which contain a resistor and a capacitor. A low-pass filter is one that passes through signals with frequencies lower than a particular cutoff frequency and causes attenuation in signals of higher frequency. A high-pass filter is one that passes through signals with frequencies higher than a certain cutoff and causes lower frequencies to attenuate, giving the two configurations their names. The cutoff frequency for both circuits is given by ω_c = (RC)^-1

In the interference lab later this quarter, a photometer will be used to convert light

intensity measurements to voltages in order to digitize a double slit interference pattern.

This device takes incoming photons, and converts them into a voltage proportional to

the number of photons (which can be thought of as intensity). When using this device,

the double slit pattern will be scanned very slowly, so that the voltage signal coming

from the photometer changes slowly. Unfortunately, the photometer output has a lot

of residual noise coming from the outlet it is plugged into (120 VAC, 60 Hz AC with

noise superimposed at much higher frequencies of order kHz or MHz). Given this,

which type of filter should be used to filter the photometer output before allowing the

myDAQ to measure the signal? With R = 1kΩ, suggest a capacitance C assuming

that the signal we care about has a frequency of about 3 Hz.

Additionally, suppose we have a noisy signal (superposition of many frequencies), but

we are only concerned with a particular part of the signal within the noise at a frequency

of the signal in the context of this problem. Assuming the noise is far from the desired

signal in frequency (≥ ±200 MHz from f_desired), suggest component values that should

achieve this effect.

Answer 1

Since the signal we care about is about 3Hz and the noise is of order KHz or MHz, we need to attenuate the signals with higher frequencies.

Therefore we need to use a low pass filter.

Cutoff Frequency F_c = 1 / (2πRC)

Therefore 3 = 1 / 2*3.14*1000*C

C = 53uF

In the next part, the signal is again around 3Hz, noise is ≥ ± 200MHz. Here again we need a low pass filter to filter the noise at higher frequency. Assuming R = 1KΩ and C = 53uF we can set up a low pass filter to obtain the desired results.