Hey guys, I am trying to study my notes for Opamp circuits and am a bit confused, especially with instability. My lecturer explained that when "a 40db rolloff" occurs, like that with cascaded inverting opamp circuits, this leads to instability. Could someone please explain to me how this occurrs. From what i understand, due to the internal compensating capacitor in the opamp, the maximum phase shift of an inveting amplifier is 270 degrees. So if this output gets fed into the 2nd opamp, the phase shift out of the 2nd opamp could be around 360 degrees. But i dont understand how this is a problem leading to instability as the output of this opamp is not being fed back to the 1st one?

 

Here is a link to a brief article that discusses opamp stability.

A fairly intuitive graphical method is to use the "rate-of-closure" to detemine whether the amplifier is conditionally or unconditionally stable.

hgmjr

 

Ok i have made an effort trying to read the contents of that pdf link but its quite heavy going. I am now even more confused that i was before.

By definition, the
3dB bandwidth limit occurs where ACL drops from its DC
value to 0.707 times that value. Analysis shows that this
condition results at the intersection of the A and 1/b curves.
These curves are actually magnitude responses and, at their
intersection, their magnitudes are the same or |A| = |1/b|.
Rearranging this result shows that the intercept occurs where
the loop gain is |Ab| = 1 at the frequency fi. A phase shift of
–90° accompanies this unity gain magnitude because of the
single-pole roll off of gain A. Then, Ab = –j1, at the
intercept, and the denominator of the ACL equation becomes
1 + 1/Ab = 1 + j1.

Ok the quote above says that at the 3dB gain occurs at the intersection of Acl and A (closed loop gain and open loop gain), is this always the case? no matter what the closed loop gain is?

 

Ok the quote above says that at the 3dB gain occurs at the intersection of Acl and A (closed loop gain and open loop gain), is this always the case? no matter what the closed loop gain is?

The answer is a qualified yes. If a significant amount of capacitance is introduced into the opamp's negative feedback path, it is possible to roll off the closed loop gain earlier than it would roll off under the influence of the opamp's inherent open loop gain.

hgmjr

 

Ok fair enough thanks for that. Do you think you could give me a hint about this 40db rate of closure thing? Its driving me nuts!

I just cant see how instability can arise because the opamps are not feeding back to the same opamp... the feedback paths are independent!

As mentioned, the
intercept corresponds to a loop gain magnitude of |Ab| = 1. If
the loop phase shift reaches 180°, the loop gain at the intercept
becomes Ab = –1. Then, the denominator of ACL equation
reduces to 1 + 1/Ab = 0 making ACL infinite. With infinite gain,
a circuit supports an output signal in the absence of an input
signal. In other words, the circuit oscillates and it does so at the
intercept frequency fi.

I have no idea what this means??

 

Figure 6 illustrates the concept by showing the opamp's open loop gain overlayed with the opamp's closed loop response.

You can see from the graph that as the example opamp's closed loop gain is increased the resulting bandwidth decreases and as the opamp's closed loop gain decreases the resulting bandwith increases. This behaviour is often discussed in the context of the constant gain-bandwith product.

hgmjr

 

You can find additional information here.

http://www.en-genius.net/site/zones/acquisitionZONE/technical_notes/acqt_092407

 

That link looks very accessable to a student like me without much knowledge of opamps. i shall read it as soon as i get a chance thank you!