Question

The cross-over frequency $f_c$ is

• A. $\frac{1}{2\pi \sqrt{LC}}$
• B. $\frac{1}{2\pi RC}$
• C. $\frac{R}{2\pi L}$
• D. $none$

Answer 1

The correct option is A $\frac{1}{2\pi \sqrt{LC}}$

Since R and C are in series the effective resistance of tweeter branch would be $R-\frac{j}{\omega C}$.

Effective resistance in woofer arm is $R+j\omega L$.

Since both of these are in parallel the net effective resistance is given by: $\frac{r^2\omega C+Rj{\omega }^{2}LC-jR+\omega L}{R\omega C+j({\omega }^{2}LC-1)}$

Cross-over frequency is the frequency when imaginary part of effective resistance becomes 0 or the when reactance becomes zero.

Therefore, ${\omega }^{2}LC-1$ = 0 which gives is $\omega$ = $\sqrt{\frac{1}{LC}}$.

Therefore, cross-over frequency, $f=\frac{1}{2\pi }$$\sqrt{\frac{1}{LC}}$.