Question

Design a high pass filter.

Use a series RC circuit with R=100 ohms.
Measure the voltage across the resistor to find the output signal. You want to ensure that frequencies below a certain value (in this case, 2000 Hz is a common frequency for a treble speaker) are attenuated by at least 30% (i.e. they are 70% of the input voltage), which is a common threshold that sound engineers use when designing filters.
Use the 2000 Hz frequency for design, but also test the output voltage at a very low frequency (25 Hz) and a high frequency (10000 Hz).

Answer 1

To design an RC high pass filter with a cutoff at 2000 Hz and R=100 ohms, capacitance C is calculated using the formula for the cutoff frequency, resulting in attenuation of frequencies below the threshold while allowing higher frequencies to pass with minimal attenuation.

Step-by-step explanation:

To design a high pass filter using a series RC circuit with R=100 ohms, we first need to find the required capacitance. The filter should attenuate frequencies below 2000 Hz by at least 30%, which translates to allowing 70% of the input voltage through. To calculate the desired capacitance (C), we use the formula for the cutoff frequency (fc) of an RC high pass filter, which is fc = 1/(2πRC). Substituting fc with 2000 Hz and R with 100 ohms, we can solve for C.

The capacitance C required is therefore C = 1/(2π*2000*100) farads. At 25 Hz, which is well below the cutoff frequency, the output voltage across the resistor would be significantly attenuated. Conversely, at 10,000 Hz, which is well above the cutoff frequency, the filter would allow the voltage across the resistor to be closer to the input voltage.