What is the roll-off rate of the filter described with R = 2.2k and C = 0.0015 picofarad?
To find the roll-off rate of a filter, we need to determine its cutoff frequency first. The cutoff frequency, denoted as ƒc, is defined as the frequency at which the filter attenuates the input signal by 3 dB (half-power point).
The cutoff frequency can be calculated using the formula:
ƒc = 1 / (2πRC)
Given the values, R = 2.2k (kilohms) and C = 0.0015 picofarad, we need to convert them to standard units before substituting them into the formula.
1 kilohm = 1000 ohms
1 picofarad = 0.000000000001 farads
So, R = 2.2k ohms = 2200 ohms
And C = 0.0015 picofarad = 0.0000000000015 farads
Now we can compute the cutoff frequency:
ƒc = 1 / (2π * 2200 * 0.0000000000015) = 1 / (2π * 3.3 * 10^(-9))
By evaluating this expression, we can find the cutoff frequency.