Open Loop vs Closed Loop Inverting Op Amp Bandwidth

[BitShard]

Hi all,

This is (part of) a question for an Electronics Fundamentals class for uni. I've had a crack at it, but am not quite sure if I'm doing this right, if you guys could help point me in the right direction, it would be enormously helpful.

The question asks us to compare the bandwidth of an inverting Op Amp between open loop and closed loop configurations, there are no set values, but arather the question is looking for a generalised answer. (So the equation simply has to imply that the closed loop bandwidth is always going to be bigger than the open loop bandwidth).

I achieved this for a non inverting amplifier using the following equation:

??₀ = ?₀(1+A₀(R₁/(R₁+R₂)))

Where:
??₀ is the closed loop bandwidth
?₀ is the open loop bandwidth
A₀ is the open loop gain

Since (1+A₀(R₁/(R₁+R₂))) is always greater than 0, I could infer that ??₀ will always be larger than ?₀ since it's being multiplied by some greater than 1 number.

What I can't seem to derive is the corresponding equation for the inverting configuration of the Op Amp, would anyone be able to point me in the right direction?

Thanks!

[owiecc]

This picture you can find anywhere on google:



To understand it, it comes down to control theory. The equation to convert an open loop tf to closed loop tf is:



G is your open loop tf. For now assume H is 1. Now think about two cases:

1. G >> 1
2. G << 1

How will your closed loop transfer function look for these two cases? Where, on the frequency spectrum are these two cases located?