Cascading low pass op amps, derive expression for f3db

[donpacino]

Homework Statement

consider the cascading of two non identical amplifiers stages, each having a low-pass STC frequency response. STage 1 has a low freqency gain of A_LF1 and a 3 dB frequency of f₁. Stage 2 has a low frequency gain of A_LF2 and a 3 dB frequency of f₂. Derive a polynomial expression for f_3dB, the 3 dB frequency of the cascaded amplifier, in terms of f1 and f2. Express f_3dB in the following form.

a₀ +a₁f_3dB+a₂f²_3dB+...=0

find a₀,a₁,a₂...etc

Homework Equations

Av=gain
f=frequency
Av=A_LF1/(sqrt(1+(f/f1)))

The Attempt at a Solution

i truly don't know where to start. if anyone knows how to start the problem or has any tips to point me in the right direction it would be greatly appreciated.

 

[NascentOxygen]

It's a while since I've looked at this stuff, so check this over carefully. But -3db point is defined as the frequency where the gain has fallen to $\tfrac{1}{\sqrt{2}}$ of its low-frequency gain. So you need to involve a fraction that looks like this:

$$3dB\;\; point\;\; \overset{ \mathrm{ \triangle} } {=}\; \frac{1} {\left |(1+j\frac{{\omega}} {\omega _1})\cdot (1+j\frac{{\omega}}{\omega_2})\right |}\;=\;\frac{1}{\sqrt{2}}$$

One equation, only one unknown, solve for w.