bandwidth of amplifiers in cascade

[abishek]

bandwidth of am

if there are n stages of amplification each with bandwidth = b what is the effective b.w of all n amplifiers in cascade?........

i found it as b.(2^1/n -1 )^.5......how?

 

[neils_arm_strong]

Re: bandwidth of am

For amplifiers the gain and bandwidth product remains constant.As the gain increases (due to number of stages) the bandwidth decreases.
suppose there are n identical amplifier stages connected in cascade each with gain A.And also let us take for simplicity the upper cut-off frequency be fh anf lower cut-off fl be≈0.then bandwidth b≈fh.
The frequency dependence of amplifier gain is given by

A(f)=A/√(1+(f/fh)²)-----------(1)
Gain of the multi stage amplifier will be then
A(total)=A×A×A................(n times)
A(total)=A^n---------------------(2)
let upper cutoff of this multi stage amplifier be F.Then
A(total)/√(1+(f/F)²)=(A/√(1+(f/fh)²))^n
simplifying this equation

F=fh×(2^1/n-1)^0.5 where fh is the bandwidth of single stage amplifier

I think this might be of help to you.
Regards.