Summing Amplifier with non-ideal op-amp

[Dave]

If an OP-77 connected as simple inverting summing op-amp stage has N
inputs, how could you estimate the practical limit for N ? I think if
all but one input is grounded you have the worst case, but where would
you go from there?

Thanks,
Dave

 

[Jim Thompson]

If an OP-77 connected as simple inverting summing op-amp stage has N
inputs, how could you estimate the practical limit for N ? I think if
all but one input is grounded you have the worst case, but where would
you go from there?

Thanks,
Dave

Just sum up the offset voltage contributions.

...Jim Thompson

 

[Tim Shoppa]

If an OP-77 connected as simple inverting summing

op-amp stage has N inputs,
how could you estimate the practical limit for N ?

What's your worry? Offset voltage? Noise? Either way source
impedance is a vital factor.

Depends largely on the source impedances driving the summing resistors
and the resistor scale used.

For typical input voltages say -10 to +10V, the output of a
hypothetical preceding op-amp can probably source several mA to 10mA.
So you're looking at summing resistors in the 1K range at the low end.
The OP-77 has an offset current in the nA range and offset voltage in
the uV range, so few-K resistors for summing is pretty good.

If the summing inputs have radical ratios (one is weighted 1000 times
another) then this will become the limiting factor.

Tim.

 

[Larry Brasfield]

If an OP-77 connected as simple inverting summing op-amp stage has N
inputs, how could you estimate the practical limit for N ? I think if
all but one input is grounded you have the worst case, but where would
you go from there?

In addition to the issues mentioned by Mr. Grise and Mr. Shoppa,
as N approaches the open loop gain of the op-amp divided by
the hoped-for realized gain from each input, the loop gain will
approach something near 1, leading to limited accuracy of the
actual closed loop gain and increased distortion.

 

[Dave]

I think if all but one input is grounded you have
the worst case

What's your worry? Offset voltage? Noise? Either way
source impedance is a vital factor. [...]

As my initial concern what happens in my suggested test case when the
parallel equivalent resistance to ground gets small?

 

[Terry Given]

If an OP-77 connected as simple inverting summing op-amp stage has N
inputs, how could you estimate the practical limit for N ? I think if
all but one input is grounded you have the worst case, but where would
you go from there?

Thanks,
Dave

It also depends on the required response - as the summing-point is *not*
0V, each input resistor affects the transfer function. conventional
analysis ignores this, but if you calculate alpha and beta (a-la Dostal
or Graeme) it shows up quite clearly. I recently completed a design that
was a summing BPF, having 15 inputs, each fed from 100k. The feedback
network was a bridged-T, and the difference between 1 and 15 inputs
shifted the centre frequency by about 3%. I can show you how if you want
- its not very hard, and implicitly deals with much of the non-ideal
behaviour of the opamp.

Another design I did a few years back had 144 inputs (100k each)
measuring a whole bunch of LED Vf's. The practical limit was actually 3
Vfs at once, given the gain for one Vf and the power supply limits (any
more than 3 and the amp clipped at the +ve rail). In this app it was OK
- uP controlled LEDs so only did one at a time. Of course > 3 faulty LED
drivers would make it saturate regardless of what the uP did, but it was
a faulty LED detector, so that was acceptable.

So there's a couple more things, in addition to offset voltage & noise.

Cheers
Terry

 

[John Larkin]

It also depends on the required response - as the summing-point is *not*
0V, each input resistor affects the transfer function. conventional
analysis ignores this, but if you calculate alpha and beta (a-la Dostal
or Graeme) it shows up quite clearly. I recently completed a design that
was a summing BPF, having 15 inputs, each fed from 100k. The feedback
network was a bridged-T, and the difference between 1 and 15 inputs
shifted the centre frequency by about 3%. I can show you how if you want
- its not very hard, and implicitly deals with much of the non-ideal
behaviour of the opamp.

Another design I did a few years back had 144 inputs (100k each)
measuring a whole bunch of LED Vf's. The practical limit was actually 3
Vfs at once, given the gain for one Vf and the power supply limits (any
more than 3 and the amp clipped at the +ve rail). In this app it was OK
- uP controlled LEDs so only did one at a time. Of course > 3 faulty LED
drivers would make it saturate regardless of what the uP did, but it was
a faulty LED detector, so that was acceptable.

So there's a couple more things, in addition to offset voltage & noise.

Cheers
Terry

We've got a box where we need to precisely sum ten 50-ohm signals with
a bandwidth of almost-DC to 1.5 GHz. All sorts of interesting things
happen: noise, reflections, crosstalk, oscillation, nonlinearity,
heat. Our third iteration looks pretty good, but the inputs do reflect
a bit. #4 should do it.

John

 

[Terry Given]

We've got a box where we need to precisely sum ten 50-ohm signals with
a bandwidth of almost-DC to 1.5 GHz. All sorts of interesting things
happen: noise, reflections, crosstalk, oscillation, nonlinearity,
heat. Our third iteration looks pretty good, but the inputs do reflect
a bit. #4 should do it.

John

Hi John,

that sounds like a pretty neat trick. Can you actually do it with a
single summing amp? sounds like you would need to terminate then buffer
each line, to prevent the summing-point impedance from screwing up your
termination. And that would be the least of the problems....

Cheers
Terry

 

[John Larkin]

Hi John,

that sounds like a pretty neat trick. Can you actually do it with a
single summing amp? sounds like you would need to terminate then buffer
each line, to prevent the summing-point impedance from screwing up your
termination. And that would be the least of the problems....

The current incarnation is a single common-source PHEMT, with a 45-ohm
resistor from each signal (10 MCX connectors in a circle) dumping into
the source node, and the summed output from the drain. This is fair,
and gain is good, but the fet source impedance is about 10 ohms
(1/Gm), so it's not a perfect summing point, so there's a bit of
crosstalk. Signal comes in on one line, wiggles the PHEMT source a
bit, so some goes out the other nine. They get back to the signal
generators on the other end of the cables, bounce a little, and
return. It's less than ideal.

If this has more reflection than the customer can tolerate, I guess
we'll have to redesign the summer/amp board (again!) and go to 10
mmics, one to receive each signal. Each of them will probably need an
input attenuator pad, since it's hard to get a mmic to be a true 50
ohm load (you're lucky to hit 40 on most of them.) So now we're
throwing away gain, begging for noise, and we still have to sum the
ten mmic outputs. Crowd ten of these in a circle, converging on a
summing node in the center, and this starts looking like a microwave
ring oscillator.

Oh, MCXs are great coax connectors. Small, easy to mate, cheap, and
you can get tons of test cables for the lab on ebay.

John

 

[Fred Bloggs]

If an OP-77 connected as simple inverting summing op-amp stage has N
inputs, how could you estimate the practical limit for N ? I think if
all but one input is grounded you have the worst case, but where would
you go from there?

There is absolutely no limitation whatsoever if you scale the input
summing resistors appropriately. For example, an inverting opamp with a
a single 1K ohm input resistor is no different than a inverting summing
amplifier with one thousand inputs using 1M ohm input resistors and all
inputs driven by the single source. There will be no measurement you can
make that will be able to distinguish the two if you "black box" the
input circuits driving the OA inverting input.

 

[Fred Bloggs]

In addition to the issues mentioned by Mr. Grise and Mr. Shoppa,
as N approaches the open loop gain of the op-amp divided by
the hoped-for realized gain from each input, the loop gain will
approach something near 1, leading to limited accuracy of the
actual closed loop gain and increased distortion.

Oh yeah- people are running that check all the time in their
calculations. Why don't you review OpAmps 101 before you post your
irrelevant pedantic drivel........

 

[Larry Brasfield]

Larry Brasfield wrote:

(Responding to the question: "If an OP-77 connected as simple
inverting summing op-amp stage has N inputs, how could you
estimate the practical limit for N ?")

Oh yeah- people are running that check all the time in their calculations. Why don't you review OpAmps 101 before you post your
irrelevant pedantic drivel........

You amaze me, Fred. You show signs of some
intelligence but seem to have never applied it to
understanding your own limitations.

Do you deny that loop gain imposes a practical
limit on how many inputs a summing op-amp
circuit can have? If so, you are the one that
needs remedial training in op-amp theory.

If you are merely suggesting that the limit I have
stated is never applicable, why have you not
given some hint as to what the real limit on N is?
My bet is that you cannot.

 

[John Woodgate]

I read in sci.electronics.design that Larry Brasfield <donotspam_larry_b

Do you deny that loop gain imposes a practical limit on how many inputs
a summing op-amp circuit can have?

I must say that I don't understand your *explanation* of this limit. If
I have an op-amp with a feedback resistor of value R and N inputs also
fed through resistors of value R, I don't see any deleterious loop gain
effect that depends on N. In audio, the usual limitation of this type of
circuit is noise.

 

[Larry Brasfield]

I read in sci.electronics.design that Larry Brasfield <donotspam_larry_b


I must say that I don't understand your *explanation* of this limit. If
I have an op-amp with a feedback resistor of value R and N inputs also
fed through resistors of value R, I don't see any deleterious loop gain
effect that depends on N. In audio, the usual limitation of this type of
circuit is noise.

For that topology, the feedback gain is:
(1/N) / (1 + 1/N) == 1 / (N + 1)
Clearly, as N approaches the open loop
gain of the op-amp, the loop gain will be
approaching 1. This means that the gain
accuracy will be reduced relative to the
usual case where loop gains exceed one
by quite a bit. Consider the formula for
closed-loop gain:
Avcl = G / (1 + GH) == 1 / (1/G + H)
Usually, we neglect the 1/G term because
it is small relative to H. But as N becomes
comparable to the open-loop gain (G), that
simplifying assumption becomes invalid.

 

[John Woodgate]

I read in sci.electronics.design that Larry Brasfield <donotspam_larry_b

For that topology, the feedback gain is:
(1/N) / (1 + 1/N) == 1 / (N + 1)

What do you mean by 'feedback gain'? The closed-loop gain is 1 for each
input. If any number up to N-1 inputs are grounded, they make no
difference to the gain from the active input(s) but can do nasty things
to the noise.

 

[Fred Bartoli]

For that topology, the feedback gain is:
(1/N) / (1 + 1/N) == 1 / (N + 1)
Clearly, as N approaches the open loop
gain of the op-amp, the loop gain will be
approaching 1. This means that the gain
accuracy will be reduced relative to the
usual case where loop gains exceed one
by quite a bit. Consider the formula for
closed-loop gain:
Avcl = G / (1 + GH) == 1 / (1/G + H)
Usually, we neglect the 1/G term because
it is small relative to H. But as N becomes
comparable to the open-loop gain (G), that
simplifying assumption becomes invalid.

There's a very simple and neat workaround for this: another opamp and 3
resistors.

Works also for the simple high gain inverter.

Now you'll have to guess how to connect them

 

[Fred Bartoli]

I read in sci.electronics.design that Larry Brasfield <donotspam_larry_b


What do you mean by 'feedback gain'? The closed-loop gain is 1 for each
input. If any number up to N-1 inputs are grounded, they make no
difference to the gain from the active input(s) but can do nasty things
to the noise.

.... and also to loop gain, which is I guess what he's reffering to.

 

[Spehro Pefhany]

I read in sci.electronics.design that Larry Brasfield <donotspam_larry_b


What do you mean by 'feedback gain'? The closed-loop gain is 1 for each
input. If any number up to N-1 inputs are grounded, they make no
difference to the gain from the active input(s) but can do nasty things
to the noise.

The open-loop signal at the input is reduced by a factor of 1/(N+1),
so not only is the noise increased by a factor of N+1, but also the DC
offset voltage (by the same factor). And the closed-loop DC gain
accuracy will be affected-- eg. if (1/(accuracy)) * N starts to
approach the open-loop gain of the chosen op-amp. Also the -3dB
frequency etc.

The OP77 is a fairly good op-amp- it has a Vos of 0.1mV max, and an
open loop gain of 1e6 min, and a GBW of 700kHz (typical), so even if
those numbers were effectively knocked down by an order of magnitude
by N~=10, it would still be pretty good in most applications.


Best regards,
Spehro Pefhany

 

[John Woodgate]

I read in sci.electronics.design that Fred Bartoli <fred._canxxxel_this_
bartoli@RemoveThatAlso_free.fr_AndThisToo> wrote (in <422f0555$0$30556$6
[email protected]>) about 'Summing Amplifier with non-ideal op-amp',

... and also to loop gain, which is I guess what he's reffering to.

But that's the point; HOW is loop gain affected? Is this due to the op-
map not being 'perfect' or what? If the summing junction really is a
virtual ground, then there is no voltage across any of the N-1
resistors.

 

[John Woodgate]

I read in sci.electronics.design that Spehro Pefhany <speffSNIP@interlog

The open-loop signal at the input is reduced by a factor of 1/(N+1)

Sorry, where does 1/(N+1) come from? This 'open loop signal' is due to
the op-amp open loop gain not being infinite?