Electronics > Beginners

Op amp gain and number of stages

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Zero999:
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 gain
GOL = the op-amp's open loop gain
β = the negative feedback through the resistive divider

Take 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 = 0.01

According to the data sheet, the op-amp has a gain of 100dB
GOL = 100 000


G = GOL/(1+βGOL) = 100 000/(1+0.01*100 000) = 100 000/(1+1000) = 100 000/1001 = 99.9

If 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 = 1000

G = 1000/(1+1000*0.01) = 1000/11 = 90.9

That'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.

David Hess:

--- Quote from: ZeroResistance on May 04, 2019, 05:51:30 am ---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 ?
--- End quote ---

1. 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.

StillTrying:
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.

MrAl:

--- Quote from: Kleinstein on May 04, 2019, 09:11:23 pm ---
--- Quote from: MrAl on May 04, 2019, 05:48:00 pm ---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.

--- End quote ---
With 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.

--- End quote ---

Hello,

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.

Zero999:
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.

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