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Y

Yvan

Jan 1, 1970
0
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?

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?

Thank you,

Yvan
 
K

Ken Smith

Jan 1, 1970
0
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.
 
P

Pooh Bear

Jan 1, 1970
0
Yvan said:
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?

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?

The voltage gain of *all* op-amps rolls off rapidly from bizarrely large
numbers at DC / LF towards one @ the gain-bandwidth product frequency.

No op-amp has *infinite* gain but it makes the basic sums easier to
understand if you pretent they do. ;-)

Another poster appears to have given you the full and correct equations for
calculating closed-loop gain.

As you'll see, the simplistic 'theoretical' gain such as the classis - Rf /
Rin for a simple inverting stage is subject to a term that takes account of
the open-loop gain of the op-amp ( or indeed any other amplifer section )
being finite.

In practice I would advise that the gain of the op-amp should be
significantly greater than the closed-loop gain at any frequency that you
desire some accuracy at.

For example. Many popular bi-fet op-amps used in audio have a GBW product
of 4MHz.

The highest frequency normally considered relevant for audio is 20kHz. At
this frequency such an op-amp has an open-loop gain of 200 or 46dB.

It would be inadvisable to expect to use such an op-amp for closed-loop
gains greater than say 30dB in audio use. In practice I'd be likely not use
it for > 20dB. Clearly the closed-loop gain also can't exceed the open-loop
gain !


Graham
 
M

Mac

Jan 1, 1970
0
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?

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?

Thank you,

Yvan

It depends somewhat on what you are doing.

10 or even less might be good in some cases. I imagine that 1000 would be
good enough all the time.

The problem is that as you get closer and closer to the limit, then there
will be less and less feedback available to linearize the circuit at
higher frequencies and you will have more and more distortion. If the
op-amp is followed by an aggressive low-pass filter, the distortion might
be tolerable, since the filter will knock it down quite a bit.

--Mac
 
P

Pooh Bear

Jan 1, 1970
0
Mac said:
It depends somewhat on what you are doing.

10 or even less might be good in some cases. I imagine that 1000 would be
good enough all the time.

The problem is that as you get closer and closer to the limit, then there
will be less and less feedback available to linearize the circuit at
higher frequencies and you will have more and more distortion. If the
op-amp is followed by an aggressive low-pass filter, the distortion might
be tolerable, since the filter will knock it down quite a bit.

Filter ?

What filter ?

Graham
 
M

Mac

Jan 1, 1970
0
Filter ?

What filter ?

Graham

Graham, I said "if the op-amp is followed by an aggressive low-pass
filter, the distortion might be tolerable since the filter will knock it
down quite a bit."

I don't know why I'm quoting it; it is still visible above. ;-)

But anyway, does it make sense now? If not, I really don't know what to
say!

--Mac
 
P

Pooh Bear

Jan 1, 1970
0
Mac said:
Graham, I said "if the op-amp is followed by an aggressive low-pass
filter, the distortion might be tolerable since the filter will knock it
down quite a bit."

I don't know why I'm quoting it; it is still visible above. ;-)

But anyway, does it make sense now? If not, I really don't know what to
say!

It sounded like an odd thing to do. Can't say I've ever seen such an
arrangement. Have you ? The cost of a passive LP filter would be such that it
would simply make sense to use a better op-amp I would have thought.

Graham
 
M

Mac

Jan 1, 1970
0
It sounded like an odd thing to do. Can't say I've ever seen such an
arrangement. Have you ?

Yes. In a sampled IF system. IF bandwidth is 50 MHz.
The cost of a passive LP filter would be such that it
would simply make sense to use a better op-amp I would have thought.

Well, since it is a sampled IF system, a brickwall anti-aliasing filter
is mandatory anyway. And finding op-amps which can drive 50 Ohms at 50
MHz with low distortion is not necessarily trivial.

--Mac
 
Pooh said:
it for > 20dB. Clearly the closed-loop gain also can't exceed the open-loop
gain !

It may surprise you to hear that it can. Use of positive feedback makes
that happen. And yes, there are real world practical circuits that use
it.

NT
 
K

Ken Smith

Jan 1, 1970
0
It may surprise you to hear that it can. Use of positive feedback makes
that happen. And yes, there are real world practical circuits that use
it.

In practically all unity gain buffers it happens at the gain cross over
frequency so it isn't even rare.
 
P

Pooh Bear

Jan 1, 1970
0
It may surprise you to hear that it can.

Maybe the OP should have said NFB. I rather think that's what he meant.
Use of positive feedback makes
that happen. And yes, there are real world practical circuits that use
it.

I don't think that's what the OP had in mind though. Can you give an example of
one btw ?

Graham
 
Maybe the OP should have said NFB. I rather think that's what he meant.

indeed, but even with nfb it can happen, as Ken explained.

I don't think that's what the OP had in mind though. Can you give an example of
one btw ?

reactions receivers are back in fashion, aka regenerative receivers.

pfb is also used when starting sine oscillators, with feedback dropping
to 1 only once oscillation has built up. A whole lotta goods use
oscillators.


NT
 
P

Pooh Bear

Jan 1, 1970
0
indeed, but even with nfb it can happen, as Ken explained.



reactions receivers are back in fashion, aka regenerative receivers.

Using op-amps ?

pfb is also used when starting sine oscillators, with feedback dropping
to 1 only once oscillation has built up. A whole lotta goods use
oscillators.

Indeed, I've used that myself. Gain > 3 for the Wein Bridge arrangement to ensure
start-up. I don't see how a discussion of this is relevant to the OP's interest in
GBW product vs practical gains though.

Graham
 
K

Ken Smith

Jan 1, 1970
0
Use of positive feedback makes
that happen. And yes, there are real world practical circuits that use
it.

I don't think that's what the OP had in mind though. Can you give an example of
one btw ?[/QUOTE]
---------------------------
! !
--- !
--- !
! !\ !
----/\/\/----+---/\/\/----+-----! >------+------
! !/
--- AV=1
 
Ken said:
---------------------------
! !
--- !
--- !
! !\ !
----/\/\/----+---/\/\/----+-----! >------+------
! !/
--- AV=1

Indeed. Now also consider an nfb'ed opamp with a tight phase margin. At
hf, closed loop gain can exceed 1 without instability, since there is
phase shift along with that >1 gain. >1 gain only causes oscillation
when your phase shift is zero: the further from zero that shift goes,
the more gain can be tolerated before oscillation occurs.

Think about it: how much gain could be tolerated when phase shift is 90
deg? Would a closed loop gain of 1.1 be stable?


NT
 
K

Ken Smith

Jan 1, 1970
0
Indeed. Now also consider an nfb'ed opamp with a tight phase margin. At

Yes, as I pointed out elesewhere, almost all unity gain buffers peak at
the gain cross over point for this reason.
 
R

Rich Grise

Jan 1, 1970
0
Using op-amps ?


Indeed, I've used that myself. Gain > 3 for the Wein Bridge arrangement to ensure
start-up. I don't see how a discussion of this is relevant to the OP's interest in
GBW product vs practical gains though.

It isn't, but bigcat said that closed-loop gain can exceed the open-loop
gain. I think the oscillator example is irrelevant to that, and I'm a
little shaky on regenerative (q-multiplier) circuits - in a setting like
that, don't the definitions of "open-loop gain" and "closed-loop gain"
get a little foggy?

Thanks,
Rich
 
Rich said:
It isn't, but bigcat said that closed-loop gain can exceed the open-loop
gain. I think the oscillator example is irrelevant to that, and I'm a
little shaky on regenerative (q-multiplier) circuits - in a setting like
that, don't the definitions of "open-loop gain" and "closed-loop gain"
get a little foggy?

Thanks,
Rich

Why would they get foggy? More complex I guess, as there are 3 gain
figures not 2. With regen a single valve stage can give you gains of
1000, which demonstrates that closed loop can by far exceed open loop.

With opamps it gets more complex, but closed can still exceed open
IIUC.


NT
 
P

Pooh Bear

Jan 1, 1970
0
Rich said:
It isn't, but bigcat said that closed-loop gain can exceed the open-loop
gain. I think the oscillator example is irrelevant to that, and I'm a
little shaky on regenerative (q-multiplier) circuits - in a setting like
that, don't the definitions of "open-loop gain" and "closed-loop gain"
get a little foggy?

Not to me but maybe I'm being very literal in my interpetation of their meaning ?

Graham
 
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