Final answer:
To design the requested high-pass filter, calculate the resistor value using the capacitor provided and the cutoff frequency formula. With a 75 nF capacitor, the resistor needed is approximately 212 Ohms. Set the feedback resistor to about 636 Ohms for a gain of 4.
Step-by-step explanation:
To design an op amp-based high-pass filter with a cutoff frequency of 10 kHz and a passband gain of 4 using a 75 nF capacitor, you can use a non-inverting high-pass filter configuration. The cutoff frequency (φc) is determined by the formula φc = 1/(2πRC). Given the value of the capacitor (C = 75 nF), you can solve for R to find the resistance needed to achieve the desired cutoff frequency.
Using the cutoff frequency formula and rearranging for R gives us R = 1/(2πφcC) = 1/(2π × 10^4 Hz × 75 × 10^-9 F) ≈ 212 Ohms. To achieve a passband gain of 4, the ratio of the feedback resistor (Rf) to the series resistor (R1) should be 3, because the gain in a non-inverting amplifier is 1 + (Rf/R1).
If we choose R1 = 212 Ohms, then Rf = 3 × R1 = 3 × 212 Ohms ≈ 636 Ohms. The output voltage (Vout) can be taken from the output of the op amp.
Component values are as follows: C = 75 nF, R1 = 212 Ohms, and Rf = 636 Ohms.