Transimpedance Amplifier & OpAmp's Slew-Rate: how to do the math?

[Bigman]

Hi!

in my simulation a current ramps-up from 0 Amps to 3.3uA within 20uS.
Since I have a feedback-resistor of 1MegOhm, this results into a voltage of 3.3V (which equals within those 20uS an increase-rate of 0.165V/us).
When I am using the LMV793 OpAmp (Slew-Rate approx. 24V/us) everything is fine.

But when I change to the slower OpAmp OPA347 (Slew-Rate 0.17V/us), the OpAmp is struggling to provide the output-voltage fast enough, which results in a very high voltage at the OpAmp-Input.
However, even with it's 0.17V/us as a Slew-Rate the OPA347 should still be  fast enough to catch up with the input ... but it isn't ... what am I missing here?
I am certain it has something to do with the gain-conditions stated in the datasheet:
LMV793 24V/us @ Av=+10
OPA 0.17V/us @ Gain +1

Thanks in advance for all you tipps and hints!

[TimFox]

Since the slew-rate-limited output could not keep up initially, the input voltage at the inverting input went very negative (as you noted).  Assuming the op amp did not draw current under this condition, the current flows into the feedback network, but the "left" side of the network is not at virtual ground, rather at a substantial negative voltage (since the output is wimpy, the input current flowing into the feedback network with the "right" side near zero forces the input voltage negative.

[Bigman]

Since the slew-rate-limited output could not keep up initially, the input voltage at the inverting input went very negative (as you noted).  Assuming the op amp did not draw current under this condition, the current flows into the feedback network, but the "left" side of the network is not at virtual ground, rather at a substantial negative voltage (since the output is wimpy, the input current flowing into the feedback network with the "right" side near zero forces the input voltage negative.

yes, this describes why we see the negative swing of Usj ... but why is the LMV793 capable to avoid this negative swing and the OPA347 not. I assume the OPA347 is just too slow ... but why? It's Slew-Rate should be still high enough to keep the voltage at the left-network-side in check.
(or to ask the way around: how can I calcluate the min. needed Slew-rate of an OpAmp, which would be able to handle my situation?)

[TimFox]

What is the open-loop frequency response (usually specified by the unity-gain frequency) of the slower device?  Ignoring slew rate, that would limit the closed-loop response.

[Bigman]

What is the open-loop frequency response (usually specified by the unity-gain frequency) of the slower device?  Ignoring slew rate, that would limit the closed-loop response.

Slower device: Open-Loop voltage gain Aol = 115dB
Fast device: 98dB

to be honest: now I am a bit like a duck in a thunderstorm.
Pls. allow me to ask if the following thinking is correct (it's my first time, thinking through this):

---- start of crazy thinking -----------------------
Aol=115dB means
115dB = 20*lg(Vout/Vin) <-> Vin=1.75*Vout

Above I assumed, my voltage at the left-side of the network would rise to 3.3V within 20uS.
But indeed it's not 3.3V it's 1.75*3.3V=5.78V ... which equals 0.29V/us which would be too fast for that slow OpAmp.
... but this thinking must be wrong: a simulation where  I ramped up the current within 50uS (equals 0.12V/us) still shows the negative swing.

---- end of crazy thinking --------------------------

It's obvious, I am thinking in the wrong direction, and somehow my brain is blocked. Sorry, but I still would need a further push to bring me into the right direction

[mikerj]

What is the open-loop frequency response (usually specified by the unity-gain frequency) of the slower device?  Ignoring slew rate, that would limit the closed-loop response.

  Slew rate is not the limiting factor here, once the output of the OPA347 gets moving it's slewing at the appropriate rate.  This is what happens when compared an 88MHz op-amp to a 350kHz device.

[MatthewEveritt]

Aol=115dB means
115dB = 20*lg(Vout/Vin) <-> Vin=1.75*Vout

You took the log when you should have exponentiated, the ratio is about 10^5

[Marco]

It's funny that it's slewing at almost exactly 0.017 V/us, even if it was slewing at 0.17 you'd still have to add input capacitance so you didn't drive the input into input protection before it reacts (which is a function of bandwidth rather than slew rate). What happens with enough input capacitance so you don't ram it outside of it's specifications?

[Bigman]

Aol=115dB means
115dB = 20*lg(Vout/Vin) <-> Vin=1.75*Vout

You took the log when you should have exponentiated, the ratio is about 10^5

I have to excuse, this was a stupid miscalculation. To make it right: 115dB = 20*log(Vout/Vin) <-> Vout/Vin = 5*10^5
(anyhow, I still have to work out, why this Open-Loop-Gain has to be considered here ... I still have some questions, which I will ask below).

[Bigman]

What is the open-loop frequency response (usually specified by the unity-gain frequency) of the slower device?  Ignoring slew rate, that would limit the closed-loop response.

  Slew rate is not the limiting factor here, once the output of the OPA347 gets moving it's slewing at the appropriate rate.  This is what happens when compared an 88MHz op-amp to a 350kHz device.

It's funny that it's slewing at almost exactly 0.017 V/us, even if it was slewing at 0.17 you'd still have to add input capacitance so you didn't drive the input into input protection before it reacts (which is a function of bandwidth rather than slew rate). What happens with enough input capacitance so you don't ram it outside of it's specifications?

First: thanks for all your replies and patience. To sum up your replies about what I missed: open-loop frequence response, unity-gain-frequency, bandwith. I think all this is more or less the same and I could re-phrase my question like this: how do I calculated the needed unity-gain-frequency?

Now, my starting point is:
unity-gain-frequency x gain = cutoff frequency

• The unity-gain-frequency, I get from the OpAmp's specification, which is for the OPA347 350kHz;
  
• About the gain I am uncertain. Well, in this circuit both VOLTAGES at the inverting-input and at the OpAmp's output should be the same at the end, hence: gain=1

So, I have: 350kHz x 1 = 350kHz as my cutoff frequency

... But what is the frequency generated by my electrical current ramp? When I hear "frequency" I have a full sinus-wave in mind. Okay, I will tread this as a triangle-wave, whose first quarter-wave is done within 20uS (since my ramp finishes within 20uS). So, a theoretical full-wave would take 4 times as long = 80uS = 12.5kHz ... which is significantly lower than the allowed 350kHz. So the 350kHz of the slower device should be still sufficient.

[Marco]

You're right, either the model is wrong or my interpretation of the function of the opamp is naive.

My best guess, both are true to an extent ... even if you take it away from the rails a bit (slew rate specs are only valid with common mode halfway between the rails) it just doesn't get nearly the slewrate it should. The model for a MCP6231 with similar specs gives a response like you would expect purely from slewrate if you give it a bit of negative supply.

I'd say build it on a breadboard and see (you probably will have to move the common mode voltage away from the rails a bit).

[Bigman]

You're right, either the model is wrong or my interpretation of the function of the opamp is naive.

My best guess, both are true to an extent ... even if you take it away from the rails a bit (slew rate specs are only valid with common mode halfway between the rails) it just doesn't get nearly the slewrate it should. The model for a MCP6231 with similar specs gives a response like you would expect purely from slewrate if you give it a bit of negative supply.

I'd say build it on a breadboard and see (you probably will have to move the common mode voltage away from the rails a bit).

Marco, thanks for your reply. I really appreciate it!
I also tried now further OpAmp-models with almost similar unity-gain-bandwidth and slew-rate. And those others behaved as expected. However, this was a very good lesson also about OpAmp's theory (e.g. your statement "slew rate specs are only valid with common mode halfway ..." is a kind of knowledge I need to aquire to avoid future potential problems.)

Attached a simulation with the TLV2761:
TLV2761's slew rate = 0,2V/us.
My voltage at the inverting input should increase with a speed of 0.165V/us (same simulation condition as above), so the TLV2761 should be fast enough ... and indeed it is: the Output-Voltage curve slews with 0.165122V/us.
Regarding the voltage at the inverting-input (Usj), we see only for the fist 20uS a negative swing ... which I would say is the time needed for the OpAmp to "wake up and start to work", and I assume this is what I you can find in the spec. as the "setting time".

I will buy a couple of those OpAmps and start -as you suggested- to build up circuits on the breadboard.
Again. Thanks for your support!