Bandwidth and GBW relations

[ahmed_hussein5]

Greetings,

I've heard that there is some relation between open loop GBW and Closed loop BW, what is it exactly, and if possible I want a proof on it.

thanks.

 

[KlausST]

Hi,

GBW = Gain Band Width. (usually open loop)

BW = Band Width (without gain)

Example:
if an OPAMP has an open loop GBW = 1MHz and you use it with Gain = 20 then the output bandwidth can be estimated by BW = GBW/Gain = 1MHz / 20 = 50 kHz

Klaus

 

[LvW]

Greetings,
I've heard that there is some relation between open loop GBW and Closed loop BW, what is it exactly, and if possible I want a proof on it.
thanks.

If you know the meaning of GBW (Gain-Bandwidth-Product) it should be clear that the closed-loop BW can be calculated using the relation
Bandwidth=GBW/Acl with Acl being the closed-loop gain.
Comment: This applies only as long as the opamp gain has a single pole response (slope -20dB/dec)

 

[crutschow]

As LvW noted, the GBW relation only applies to standard op amps with a single-pole roll-off of the open-loop response. Other types, such as current-feedback op amps, do not exhibit this variation in bandwidth with close-loop gain.

If you look at the open-loop response of such a single-pole op amp you will see a constant rolloff of gain versus frequency. The closed-loop frequency response is simply the intersection of a horizontal straight line from the closed-loop gain with the open-loop response. This can be calculated as GBW / Av where Av is the closed loop gain.