[SOLVED] Chaining op amps for increased loop gain?

[jasonc2]

Is it possible to chain op amps together to increase the loop gain?

I observed that in two simple simulators the gain is increased to the product of the op amp gains:



However in PSpice the gain increase, at least for both the TL081 and LM358 models, was present but marginal and 3 op amps in PSpice showed no change over 2.

In reality, is it possible to approach the product of the op amp gains by chaining them together? I don't have any tools to measure voltages with that precision to test.

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I tried biasing the first op-amp output in pspice because I thought maybe it had to do with the small output voltage swing but that had no significant effect (the resistors increased the output from uV to 100mV range):


(I didn't realize I hid the pin names -- the +'s are on top)

 

[jiripolivka]

Is it possible to chain op amps together to increase the loop gain?

I observed that in two simple simulators the gain is increased to the product of the op amp gains:



However in PSpice the gain increase, at least for both the TL081 and LM358 models, was present but marginal and 3 op amps in PSpice showed no change over 2.

In reality, is it possible to approach the product of the op amp gains by chaining them together? I don't have any tools to measure voltages with that precision to test.

- - - Updated - - -

I tried biasing the first op-amp output in pspice because I thought maybe it had to do with the small output voltage swing but that had no significant effect (the resistors increased the output from uV to 100mV range):


(I didn't realize I hid the pin names -- the +'s are on top)

From your request I do not see what gain you need and at what frequency?
Typical opamps have up to 90 dB gain at ~DC, slowly falling with frequency. If you need a higher gain at a low frequency, it may be possible to use cascaded opamps but then noise is significant.

In your schematic, the second stage has a very low gain as the input series resistor is 10 Megaohms while the feedback resistor is 10 kOhms. For a high gain those resistors should change places.

 

[LvW]

Is it possible to chain op amps together to increase the loop gain?

In principle - yes, it is possible. However, not as shown in your diagrams.
When you have a series connection of two opamps each feedback would cause dynamic instability because each unit has a -20 dB slope of the frequency-dependent open-loop gain.
This means: 180 deg additional phase shift for larger frequencies.
Therefore, in the classical combination (called "composite" amplifier) the second opamp has reduced gain of 20...40 dB (internal feedback) - thus increasing the total loop gain by 20...40 db.
More than that, both opamps are NOT of the same type.
Then, this combination can be equipped with an overall feedback path. This combination combines some beneficial properties of both opamps (e.g. good offset from opamp 1 and good slew rate from opamp 2).

 

[jasonc2]

From your request I do not see what gain you need and at what frequency?
Typical opamps have up to 90 dB gain at ~DC, slowly falling with frequency. If you need a higher gain at a low frequency, it may be possible to use cascaded opamps but then noise is significant.

Thanks. I'm interested in this for very low frequency, almost constant DC (< 1Hz).

The goal would be to improve the accuracy of e.g. a voltage follower or differential amp. For example an op amp with 100dB DC gain would theoretically only be able to follow within 50µV of a 5V input. If I cascaded two together could I obtain a follow accuracy approaching that of a 200dB DC gain amp at around 0.5nV?

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In principle - yes, it is possible. However, not as shown in your diagrams.
When you have a series connection of two opamps each feedback would cause dynamic instability because each unit has a -20 dB slope of the frequency-dependent open-loop gain.
This means: 180 deg additional phase shift for larger frequencies.
Therefore, in the classical combination (called "composite" amplifier) the second opamp has reduced gain of 20...40 dB (internal feedback) - thus increasing the total loop gain by 20...40 db.
More than that, both opamps are NOT of the same type.
Then, this combination can be equipped with an overall feedback path. This combination combines some beneficial properties of both opamps (e.g. good offset from opamp 1 and good slew rate from opamp 2).

I see; so even for ~DC input, it seems I'm generally better off just using a single precision op-amp then trying to improve by composite (thanks for the keyword btw). Interesting point about combining op amps of different types.

Thanks guys!

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Do chopper-stabilized op amps generally have any significant chopper frequency ripple carried through to the output? I'm looking at the TLC2652 datasheet but I can't seem to find a related spec.

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I found this really interesting document about composite amps ("found" as in first Google result :lol: http://cds.linear.com/docs/Application Note/an21f.pdf -- I did not expect it to be such a fascinating subject! I wish I owned a nice scope, though.

 

[FvM]

Apart from the problem of stable loop gain addressed by LvW, you should consider that's almost useless to increase amplifier gain above the practical limits set by input noise and offset drift.

Precision OPs are designed with DC gains of 120 to 160 dB, there's little chance to improve it further by designing cascading amplifiers.

Composite amplifiers have their main application for combining features of different amplifier types, e.g. 100 MHz bandwidth and µV DC accuracy. In see that the Linear applications notes is addressing the most popular cases.

Do chopper-stabilized op amps generally have any significant chopper frequency ripple carried through to the output? I'm looking at the TLC2652 datasheet but I can't seem to find a related spec.

They generally have. The TLC2652 datasheet voltage noise spectrum gives a glimpse on it, current noise would look worse, and their are less obvious properties like chopper frequent intermodulation.