Problem 59-1    Source:   Adapted from Problem 20 - page 731 - BOYLESTAD, Robert L. - Book: Introdução à Análise de Circuitos - Ed. Prentice Hall - 10ª edição - 2008.

For the circuit shown in the Figure 59-1.1:

a) Determine V_o to a frequency one octave above the cutoff frequency.

b) Determine V_o to a frequency a decade below the cutoff frequency.

Solution of the Problem 59-1   

Item a   

This setting is that of a low-pass circuit. Knowing that one frequency is one octave higher than another, means that it is twice as large. Therefore, we have to by the statement f = 2 f_c. Using the eq. 59-06 which relates the output voltage of a low pass circuit to the frequencies, we get:

Performing the calculation, we find:

Item b   

If f is a decade below the cutoff frequency, it means f = f _c / 10 . Therefore, using eq. 59-06 and making the calculation, we find: