(Solved): Problem 1: Given this filter, a. Sketch its transfer function (response). b. Calculate its break fr ...

Expert Answer

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B)Cutoff frequency (fC) calculation: The cutoff frequency of a simple RC low-pass filter can be calculated using the following formula: fC = 1 / (2?RC) where R is the resistance in ohms and C is the capacitance in farads. Using the given component values, we have: R = 2.2k? + 2.2k? = 4.4k? C = 33nF = 33 x 10^-9 F Substituting these values into the formula, we get: fC = 1 / (2? x 4.4k? x 33 x 10^-9 F) ? 113 kHz Therefore, the cutoff frequency of the filter is approximately 113 kHz. C)Passband gain calculation: The passband gain of the filter is the ratio of the output voltage to the input voltage, expressed in linear units (not in decibels). In a simple RC low-pass filter, the passband gain is given by: Gain = Vout / Vin = 1 / ?(1 + (f/fC)^2) where f is the frequency of the input signal. At low frequencies (i.e., f << fC), the denominator of the above equation approaches 1, so the passband gain is approximately 1 (i.e., the output voltage is approximately equal to the input voltage). At high frequencies (i.e., f >> fC), the denominator approaches (f/fC)^2, so the passband gain approaches 0 (i.e., the output voltage is much smaller than the input voltage). At the cutoff frequency (i.e., f = fC), the passband gain is approximately 0.707, which is equivalent to a power gain of approximately 0.5 (i.e., the output power is half of the input power). Therefore, the passband gain of the filter is approximately 1 at low frequencies, and decreases gradually as the frequency approaches the cutoff frequency. At the cutoff frequency, the gain is approximately 0.707.