Op amp gain and number of stages - Page 1
Forum section: electronics / beginners

author: ZeroResistance
author_rank: Frequent Contributor
timestamp: May 04, 2019, 05:51:30 am
content: Is there any general rule for max op-amp gain that a single stage should be set too. Is a gain of 100 for a single stage ok? or is it good design practice to have 2 op-amp stages with gain of 10 each ?

author: MarkF
author_rank: Super Contributor
timestamp: May 04, 2019, 06:10:34 am
content: Dave's video doesn't directly answer your question. However, it brings up interesting considerations.Pay particular attention to his passing statement at 3:00 which seems to address your question.

author: ZeroResistance
author_rank: Frequent Contributor
timestamp: May 04, 2019, 06:16:10 am
content: Quote from: MarkF on May 04, 2019, 06:10:34 am@ 3.00 he says "you should always try to do all of your gain in 1 op-amp". That's fair enough, I guess he is addressing signal to noise issues here, correct?

author: awallin
author_rank: Frequent Contributor
timestamp: May 04, 2019, 06:49:25 am
content: one reason for splitting the gain into two stages is bandwidth. If your chosen op-amp can't give you 20dB of gain with the bandwidth you want you can instead split it to 10+10 dB with ~twice the bandwidth.For SNR usually more gain at the start of the signalpath is better.

author: MrAl
author_rank: Super Contributor
timestamp: May 04, 2019, 05:48:00 pm
content: Hi,The slew rate will be affected too, and the slew rate of the final op amp stage will not improve no matter how many stages you use unless you make the last stage (and possibly previous stages) a faster responding op amp which is usually higher cost.

author: ejeffrey
author_rank: Super Contributor
timestamp: May 04, 2019, 06:16:16 pm
content: You use two stages when one can't do what you need. There are lots of reasons for that: bandwidth, voltage range, drive current, or large total gain. Open loop gain of many jellybean opamps is >10^5 so closed loop gain of 100 is no problem for low frequency circuts. I've done gain of 1000 in a single stage with no problem.

author: ZeroResistance
author_rank: Frequent Contributor
timestamp: May 04, 2019, 07:34:13 pm
content: Quote from: MrAl on May 04, 2019, 05:48:00 pmAre you hinting that with increased gain the slew rate will get affected? That is an amplifier with a gain of 10 would have a better slew rate than one with a gain of 100 for the same op-amp?

author: ZeroResistance
author_rank: Frequent Contributor
timestamp: May 04, 2019, 07:36:37 pm
content: Quote from: ejeffrey on May 04, 2019, 06:16:16 pmA gain of 1000!! thats awesome! what kind of op-amp did you use? Was it a special instrument amp?

author: ejeffrey
author_rank: Super Contributor
timestamp: May 04, 2019, 08:59:58 pm
content: No, that was just with a standard opamp. As long as you only needs 100s of Hz of bandwidth it isn't a big deal.You do have to worry about the amplification of the offset voltage. An opamp with 100 uV offset voltage will have a 100 mV output offset. But that is an issue with any high gain DC coupled system, not specific to whether the gain is achieved in a single stage.Slew rate is only a problem because large gains tend to have high output swings, but a low gain amplifier trying to drive the same output swing will also have the problem.

author: Kleinstein
author_rank: Super Contributor
timestamp: May 04, 2019, 09:11:23 pm
content: Quote from: MrAl on May 04, 2019, 05:48:00 pmWith multiple stages one can choose the OPs depending on the needs:The first stage is important for the noise and input current. The last stage is important for the slew rate and the maximum output current and the output voltage range.There are mainly 2 limitation for how much gain can be used in a single stage: 1 is the GBW, as more gain reduces the bandwidth. The 2 nd limitation is the loop gain - this can be important for high accuracy. With higher gain it is harder to correct nonlinearity of the amplifier. This may limit the useful gain to something like a factor of 100 in some cases - often even a gain of 1000 is OK in 1 stage.

author: Zero999
author_rank: Super Contributor
timestamp: May 04, 2019, 09:35:07 pm
content: In an op-amp circuit, the overall gain is always very slightly less, than the calculated gain, because the op-amp has a finite gain. The higher the op-amp's gain, relative to the circuit's ideal gain, the closer it will be. The simplified op-amp gain equation, assumes the op-amp's open loop gain is so high, the error is small enough not to matter. The more accurate formula is below:G = GOL/(1+βGOL)Where:G = the closed loop gainGOL= the op-amp's open loop gainβ = the negative feedback through the resistive dividerTake a simple inverting amplifier.Normally we just say AV = RF/RIN = 100k/1k = 100, but let's work out the exact gain, taking into account the op-amp's open loop gain.β = RIN/RF = 1k/100k = 0.01According to the data sheet, the op-amp has a gain of 100dBGOL= 100 000G = GOL/(1+βGOL) = 100 000/(1+0.01*100 000) = 100 000/(1+1000) = 100 000/1001 = 99.9If 1% resistors were used to build the circuit, then they would contribute more error, than the op-amp's open loop gain.The open loop gain is lower at higher frequencies, say at 1kHz, it's 60dB.GOL= 1000G = 1000/(1+1000*0.01) = 1000/11 = 90.9That's nearly 10% lower than the target, which could be unacceptable in some applications.Exercise for the reader: what would G be, at 1kHz, if two amplifiers, each with a gain of 31.62 used in series, rather than one amplifier. Now take it further and try three amplifiers, each with a gain of 10.

author: David Hess
author_rank: Super Contributor
timestamp: May 04, 2019, 10:44:06 pm
content: Quote from: ZeroResistance on May 04, 2019, 05:51:30 am1. Dividing the gain up in proportion to the gain-bandwidth product of each operational amplifier will result in maximum bandwidth which is a good place to start.2. Slew rate (full power bandwidth) requirements are higher in later stages so there may be reason to use high slew rate (full power bandwidth) parts there. This is especially the case for the last stage which might have special requirements for driving the load.3. Noise is predominantly determined by the early stages up through the first gain stage so low noise parts might be used there.

author: StillTrying
author_rank: Super Contributor
timestamp: May 05, 2019, 01:03:39 am
content: For a gain of 100 from 2 op amps I'd try to make the first one's gain up to as much as X20 and the second as low as X5.

author: MrAl
author_rank: Super Contributor
timestamp: May 05, 2019, 02:23:05 pm
content: Quote from: Kleinstein on May 04, 2019, 09:11:23 pmHello,The first stage can alter the slew rate too because for example with a step input to the first op amp section the second op amp section does not get a step anymore it gets a ramp, and a ramp integrates into a quadratic which means even lower slew rate to start off with.

author: Zero999
author_rank: Super Contributor
timestamp: May 05, 2019, 05:25:21 pm
content: LTSpice's universal op-amp model can be used to model this. Here's a plot showing the gain of the inverting amplifier. For clarity, I've used a logarithmic scale for G_OL and plotted -V(out)/V(in), so the number is positive, even though the gain is inverting.

author: David Hess
author_rank: Super Contributor
timestamp: May 06, 2019, 03:18:07 am
content: Quote from: Kleinstein on May 04, 2019, 09:11:23 pmThere is a third limit.Over wide bandwidths, which can be 10s of MHz for operational amplifiers and sometimes less, too much gain can result in oscillation from parasitic feedback from the output to the input. Multiple stages help here because each stage can be more readily physically isolated from adjacent stages. Neutralization is sometimes used.This limit also applies to radio receivers and one of the reasons for the superhetrodyne topology which divides the gain up into different intermediate frequencies.