Hihave been trying to follow this example in the book (page 411, figure 11-28) on calculating cutoff frequency for an low pass active filter (using the formula on page 412, figure 11-4). I have tried by calculating 1000pF * 470pF to get 4.7*10 -19 and multiplying by 33k ohms * 3.14 *2 = 9.74028 ^-14 (9.74028 * 10^-14) and I hit the 1/X key and still get the wrong answer.. any ideas on how to enter these numbers to get it correct?

I know 33k ohms is 33,000 ohms and pico (pF) is *10^-12

 

Sorry, what’s wrong? Are my eyes tired or do I see the same number on the calculator as in the book? 7,000?

 

You forgot to take the square root.
Remember to track your units. pF x pF gives pF squared.
Hence you need to take the square root to get back to pF.

Here is another tip.
The square root of pico x pico must be pico.
Hence, just compute the square root of 1000 x 470, which is the square root of 47, which is close to 7, then multiply with 100 and then append pF to the result.

So mentally, it is 700 pF.

Also, with mental math, 33 x 3 = 99
Hence, 33 x 3.14 x 2 is about 200.

So now, in the denominator, we have:

k x 200 x 700 x pico =
k x 14 x 10000 x pico =
14 x 10^(-5)

take the reciprocal and get
1/14 x 10^5

14 x 7 = 98
1/14 is close to 0.07
The approximate answer is 7000 Hz or 7 kHz.
All done without having to touch a calculator.