Filters and Attenuators Questions and Answers

Answer: A

The cut off frequency of a first order RC low pass filter is the frequency at which the output has fallen to \(1/\sqrt{2}\) of its low frequency value, \(f_c = \dfrac{1}{2\pi R C}\).

\[ \begin{aligned} f_c \\ &= \frac{1}{2\pi \times 1200 \times 0.02 \times 10^{-6}} \\ &= \frac{1}{1.508 \times 10^{-4}} \\ &= 6631\ \text{Hz} \approx 6.63\ \text{kHz} \end{aligned} \]

The other values are 10, 10 and 100 times off, which would come from a slip of a power of ten in the capacitance (0.02 microfarad is \(2 \times 10^{-8}\) F). The answer is 6.63 kHz, option A.

Answer: A

An ideal filter has zero attenuation in the pass band.

An ideal filter passes every frequency in its pass band without any loss and completely blocks every frequency in its stop (reject) band, with an abrupt transition between them. Zero attenuation in the pass band is therefore one defining property; the other is infinite attenuation in the reject band.

Zero attenuation in the reject band would let unwanted frequencies through, infinite attenuation in the pass band would block the wanted ones, and finite attenuation in the reject band is what practical, not ideal, filters show.

Answer: C

The circuit is a band pass filter.

This is the Wien network: a series R-C arm feeding a parallel R-C arm, with the output across the parallel arm.

At low frequencies the series capacitor has a very high reactance and blocks the signal, so the output falls towards zero. At high frequencies the parallel capacitor has a very low reactance and shorts the output, so it again falls towards zero. In between, at \(f_{0} = 1/(2\pi RC)\), the output is greatest (one third of the input, with zero phase shift).

A response that is small at both ends and peaks in the middle is a band pass response. A low pass or high pass filter would pass one end of the spectrum, and a band reject filter would dip, not peak, in the middle.