Single vs cascading op amp

A single opamp will have a finite gain-bandwidth. And you generally don't want to use all of it, because that will increase distortion.

So if the voltage gain times required bw is well below the opamp's specified GBW, one opamp is usually enough.

There are other special cases, like not wanting a precision front-end stage to dissipate a lot of power driving a load. Or wanting to use, say, a zero-drift low-voltage amp, followed by something bipolar that can swing lots of voltage.

John

Your question is not very clear. But, in general, each gain stage adds and amplifies noise plus each stage has a finite bandwidth. Cascaded stages reduce overall band width and increase noise Therfore you should use as few stages as possible for a given situation.

Secondly if the stages are within a feedbagck structure like in an op-amp the collective phase shift of the stages will add giving a high overall phase shift. Since each stage produces 90 of phase degrees shift at the limits of it's band width, two such stages will produce 180 degrees. If the gain is above unity when the phase shift becomes 180 degrees, the amplifier will oscillate or become unstable. For this reason most amplifiers and op-amps are rarely designed with more than two internal gain stages. Three or more gain stages are very difficult to stabilixe and keep from oscillating.

If the first stage has significant gain, the noise of downstream stages don't matter.

And more opamps increase available gain-bandwidth, not decrease it.

John

Or a low-noise first amp.

Etc.

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www.wescottdesign.com

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The total gain would be the product of the individual gains and the GBWP at the lowest frequency would be larger than one. But depending on how you look at it you are either increasing the GBWP or decreasing it.

For example, suppose you have two op amps with GBWP at 1Mhz and the other at 10Mhz. The "total" GBWP would be somewhere inbetween 1Mhz and

10Mhz. But since the total GBWP is the product of the two we have reduced the GBWP of the 2nd amp or increased that of the 1st amp.

or GBWP1

I was looking at using a number of identical opamps, running closed-loop, to achieve some non-trivial target overall gain.

Suppose we need a gain of 100 overall, and we have a lot of 1 MHz opamps around.

A single-stage design would have 100x all in one opamp, net bandwidth

10 KHz.

A two-amp cascade needs a gain of 10 per stage. Each stage is down 3 dB at 100 KHz, so the overall bandwidth is a bit less, 80K or something like that.

Four opamps need gain per stage of 3.16, which is 316 KHz bw per stage...

There's some derivation somewhere that figures out the maximum GBW you can get from cascading identical amp stages. The gain per stage turns out to be sqrt(e).

John

Cascading N identical stages of bandwidth W yields a net bandwidth of...

Wnet = W*sqrt(2^(1/N)-1)

It is left as an exercise for the student to calculate net gain-bandwidth ;-)

And input-referred noise (to satisfy Hobbs ;-)

...Jim Thompson

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George Herold

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Thanks Jim, I didn't realize it dropped off so fast. 5 cascaded gain stages and the BW is down by almost 1/3! This merits more study!

George Herold

John makes a good point - in multiple gain stages, it is advisable to have the first stage with lots of gain (without running into your GBW limitations). Getting the signal up as early as possible improves the signal to noise ratio of the amplifier chain

--
Bill Naylor
www.electronworks.co.uk
Electronic Kits for Education and Fun

Noise added by the second stage is normally insignificant; added amount is divided by gain of first stage.

Noise adds trig-wise (root of sum of squares) so if the first stage has a gain of 10, the second stage only adds about 1% to the total noise.

John

Squared.

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Yup, Unless the second stage has a higher bandwidth than the first stage. (which I think might be a good idea), I've been building amps with 5 or 6 x10 gain stages (to get thermal noise up to the 10V level) and I think the only reason that this hasn't 'bitten' me yet is that my bandwidth has been either limited by the first stage, or the slew rate of the final stage.

George H.

Are you building a noise generator?

An 8 or 10 volt zener, 1n751-series maybe, run at maybe 1 mA, makes about 300 nv/rthz wideband noise, which is easier to amplify than resistor noise. And it swamps most opamp noise, which can be very non-ideal.

John

John:

Surely this is talking about noise referred back to the input, not the actual noise itself....

Or do I need another coffee?

--
Bill Naylor
www.electronworks.co.uk
Electronic Kits for Education and Fun

I'm talking about the total noise that you see at the output. Divide by the overall gain to get input-referred noise. What usually matters in an amplifier is the s/n ratio at the output.

John

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"> Are you building a noise generator?" Nope. I want to measure kT and e by measuring noise.

I've done the Zener trick in the past. I found that I got the largest noise out of the highest voltage zeners (not surprising I assume higher voltage zeners have larger electron avalanches.) A single zener has a bit of an asymmetrical voltage waveform. But there are circuits using two zeners in series and then summing the current. (I=92ve never tried those.)

George H.

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Oh, right, slipped my mind.

How about paralleling a bunch of BF862's? Or did I suggest that already?

Yup, I've noticed the small asymmetry. It gets progressively worse at lower dc bias currents, and many (all?) zeners eventually break up onto raggedy sawtooth oscillations.

Subtracting the noise from two zeners should cancel the asymmetry. Better yet, use 2*N zeners.

John