# Just one little question on the frequency band of the series RLC filter

1. May 7, 2006

### Lisa...

Hey! I really need to find out how the width of the frequency band rejected depends on the resistance R of the following circuit:

http://img418.imageshack.us/img418/8168/rlc2wf.gif [Broken]

I've done the following:
$$Q= \frac{\omega_0}{\Delta \omega}$$

so

$$\Delta \omega = \frac{\omega_0}{Q}$$

with

$$Q= \frac{\omega_0 L}{R}$$

Substitution gives:

$$\Delta \omega = \frac{\omega_0}{\frac{\omega_0 L}{R}}$$

$$=\frac{R}{L}$$

$$\Delta f= \frac{\Delta \omega}{2 \pi}$$

$$= \frac{\frac{R}{L}}{2 \pi}$$

$$= \frac{R}{2 \pi L}$$

Though my textbook says that

$$\Delta \omega = \frac{R}{2L}$$

... and it defines the delta omega as the frequency difference between the two points on the average power vs generator frequency curve where the power is half its maximum value...

So am I wrong or is the textbook's answer just confusing?

Last edited by a moderator: May 2, 2017
2. May 7, 2006

### Lisa...

Anybody?! Please... it's due to tomorrow!