# Cascading low pass op amps, derive expression for f3db

1. Sep 11, 2011

### donpacino

1. The problem statement, all variables and given/known data
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 ALF1 and a 3 dB frequency of f1. Stage 2 has a low frequency gain of ALF2 and a 3 dB frequency of f2. Derive a polynomial expression for f3dB, the 3 dB frequency of the cascaded amplifier, in terms of f1 and f2. Express f3dB in the following form.

a0 +a1f3dB+a2f23dB+...=0

find a0,a1,a2...etc

2. Relevant equations
Av=gain
f=frequency
Av=ALF1/(sqrt(1+(f/f1)))

3. The attempt at a solution
i truly dont 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.

Last edited: Sep 11, 2011
2. Sep 12, 2011

### Staff: Mentor

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.

Last edited: Sep 12, 2011