Problem 58-7    Source:   Example 17.8 - page 376 - HUGGES, A. E. - Book: Electrical and Eletronic Technology - 10ª ed. - Editora Pearson - 2008.

For the series RLC circuit shown in Figure 58-07.1 calculate:

a) the resonant frequency and bandwidth of the circuit;

b) the output voltage, V_o, at resonance and side frequencies;

c) the value of the side or half power frequencies.

Solution of the Problem 58-7   

Item a   

We can calculate the resonant frequency of a series RLC circuit through the equation reproduced below.

Substituting the variables for their respective numerical values, we have:

Carrying out the calculation, we find:

Bandwidth can be calculated using the equation reproduced below.

Making the substitution of the variables for their respective numerical values ​​and, remembering that R = R₁ + R₂ = 20  Ω, we have:

Item b   

As studied in the theoretical part, we know that when an RLC circuit is in resonance, the impedance of the inductor is exactly the same as the impedance of the capacitor. This causes these impedances to cancel each other out and can be replaced by a short circuit. Then, applying a voltage divider, we get:

Carrying out the calculation, we find:

The voltage value for the side frequencies is equal to 70.7% of the V_o value. Therefore:

Item c   

So, knowing the bandwidth and resonance frequency: