Re: Op amp newbie

In article <1120051752.650007.244640@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Yvan <kayoux@xxxxxxxxxxx> wrote:
>Hi,
>
>I have a very simple question to ask. Say my required Gain-bandwidth
>product is 1kHz * 1 = 1k, what is the minimum gain-bandwidth product of
>the op amp in order to assume an infinite gain?

The actual gain of the circuit is:

G / (1 + GH)

Where:
G is the gain of the op-amp
H is the gain of the feedback section

If G is very large, the one in the denom doesn't matter much and can be
ignored. If yoy do a little math, you will see that the overal gain ends
up as 1/H in that case.

If G is not very large, we can work out what the G has to be to get the
accuaracy we need. For most op-amp, you assume that the G has a phase
shift of 90 degrees.


Take the case of the non-inverting unity gain amplifier working at 1kHz.
In this case, the H is simply 1. Lets assume that we want the overal gain
to be at least 0.99 for a 1% error.

Remember that the phase angle of result is not know until we calculate it.
We use | X | to say ignoring the phase.

0.99 = | G/(1+GH) | = | G/(1+G) |

0.99|(1+G)| = |G|

Remember that we said "assume G is at 90 degrees"

0.99 * sqrt(1^2 + G^2) = | G |

Square both sides:

0.99^2 * (1 + G^2) = G^2

0.99^2 + 0.99^2 * G^ = G^2

0.99^2 = G^2 - 0.99^2 * G^2

0.99^2 = G^ * (1 - 0.99^2)

0.99^2 / (1 - 0.99^2) = G^2

sqrt(0.99^2 / (1 - 0.99^2)) = G

G = 7.018

Given this we check the data sheets to see that the op-amp we have
selected has a gain of at least 7 at 1kHz.

>In the book "sensors and signal conditioning", they gave an example of
>an application that had a GBW of 30 Khz. It mentioned that a opamp GBW
>of 5 Mhz was large enough to assume infinite gain. 5 Mhz/30khz=167
>times. Is there a rule of thumb would help in figuring if a given
>opamp is suitable for my application in terms of GBW?


A good rule of thumb is that an op-amp for a filter must have a GBP
greater than:

GWP > 10 * Q^2 * Fc

The G/(1 +GH) still works here but for a filter, the H is complex value
instead of siply being one.

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