EEVblog #572 - Cascading Opamps For Increased Bandwidth

Fundamentals Friday.
Dave explains Gain Bandwith Product and how it's possible to increase your system bandwidth by cascading opamps in series. Also, a discussion on the associated noise issues.
A breadboard example shows how variable GBWP can be, and how it can relate to distortion.

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[apino]

I'm taking Advanced Analog Electronic Circuit Design at Johns Hopkins for a Master's and this video was EXACTLY what I needed to help me with my assignment. You're always so thorough and helpful, Dave. I really appreciate all of your videos and love that this video was on the money for me.

[BelperFlyer]

I'm old enough to remember when 702 op amps cost a week's wages and suffered from 'purple plague' corrosion failure.  Been retired a while but you videos stir up my old brain cells a treat.

For the odd gain requirements the hardest thing is getting the right resistor values without resorting to pre-sat pots.

Clear, concise and not too theoretical. For me no longer any practical use but it's good to know I haven't forgotten everything :)

[emcgon]

I have missed Fundamentals Friday...its my favourite of the things that you do. This one was great...thanks.

[eddyfontaineyoutu]

Analog electronics, that the real thing !!!

[PsiQ]

You wont believe how much i currently learn from your videos :-)
Thanks for doing these !!

[scowell]

With a 2-stage setup, using inverting config allows easier resistor choices.  Same for all even-numbered stage configs.  Using even numbered stages as well as inverting config allows negative gain as well.

[omegacsblog]

You mentioned the challenge of getting an E96 resistor set to handle the 3-stage form.  I'm very analog-challenged, but if I'm reading things right you want a gain of 4.6414, so a resistor ratio of 3.6414.  I have a Python script I wrote a while ago that trial-and-error's all the available resistor values, and it gets 1300 / 357, which is 0.0085% off across all 3 stages.  4-stage isn't as close, 1370 / 634 gives 0.176% off 100x.

An interesting question would be what happens statistically with the tolerances of the 6+ resistors.  I calculate worst-case with all resistors pegged the wrong direction for a 3-stage setup using 1% resistors at 6.15%, but what happens when you take the tolerance *binning* (bell curve) and run the math?

[RobertSzasz]

"All things being equal" always makes me think of spherical cows.

Thanks for the great video.

[Laogeodritt]

Adding more stages has diminishing returns as mentioned, and at some point actually reduces the total system bandwidth (eventually an extra stage does not add enough bandwidth to compensate the next stage's additional attenuation of higher frequencies).

With that in mind I figured I'd make a few pencil scratches on the back of a napkin and figure out what the optimal number of stages is (yielding maximum bandwidth):

n = 1/lg(2 lg A / (2 lg A - 1))

This yields a maximum bandwidth of:

GBW (2 lg A / (2 lg A - 1))^(lg A) * sqrt(2 lg A / (2 lg A - 1) - 1)

Given:
- lg is the logarithm of base 2
- A is the desired system gain
- GBW is the gain-bandwidth of the op-amps
- It is assumed that each stage has the same gain and uses the same op-amp
- It is assumed that BW is perfectly linear wrt effective gain

Obviously, n must be a whole number, so round up/down, whichever gives the best result. Likewise, the maximum bandwidth formula is theoretical for a potentially real-valued n.

This is rarely worth the effort in practice, I was just bored and don't feel like working on my Capstone project =P As Dave mentioned in the video, there is a diminishing returns effect---so in the video's example, 9 stages might give the best bandwidth (something like 170kHz effectively), but 8 stages only gives you 500Hz less bandwidth (not even 0.5% difference!), 7 stages costs you 2kHz or so (around 1%), and so on - those last few stages aren't worth the extra design and production cost!

[gamccoy]

Great topic, Dave.  I love these fundamental tutorials. 

[tubical]

Nice to be back in class, 1st row as usual;)

Thanx Prof. D. Jones, great lesson!

[raguaviva]

Excellent video! Time to revisit an old project that didn't work just because I killed its gain by using a huge gain :) Thanks, and keep posting videos like this one! 

[Kezat]

Love it Dave, great white board theory to practical demonstration transition, really tied it together.

[magzire]

One smart guy, he knows his shizzle

[tubical]

At 15:30 you may add that: -3dB is as well as 45 degree phaseshift, as we all see clearly in your beautiful waveform display! Just to mention;)

[AttilaAsztalos]

Quite instructive and fun to watch - the minor quibble I have is that there's some mental gymnastics left unexplained: seasoned pros might not even understand what the difficulty is but it can really bog down someone trying to wrap their head around the math for the first time that the GBWP mentioned is not the frequency where you still _get_ your nominal unity gain (as some like me may have assumed) but the point at which you have _lost_ 3db of it (the source of the 0.7 figure).

Yes, I know (now...) that that _is_ the definition of bandwidth, but the finer point that your theoretical "1MHz" setup is not expected at all to really do x10 at 100KHz but an actual x7 instead is not a straightforward one at all for someone just trying to follow the experiment...

[jeremygrotte]

I don't even bother waiting for the video to end before giving it a big 'Thumbs Up' anymore.  They've all been great.

[Pulsar]

Glad to see you upgraded Dave CAD to gold version :D 

[MINUX]

With ONE LM311 or any comparator and apply X100 directly, it's works very well and you have the bandwidth. No need to cascading Opamps. Bold cowboys do that.

[RexxSchneider]

The only thing missing is the point that as we deal with larger signals, the slew rate can become the limiting factor, not the GBWP. For the TS912, with a supply voltage of 10V you can expect a slew rate as little as 0.8 V/μs, so for example, a 2Vrms (i.e. 5.6Vp-p) output will be limited to rather less than 100KHz, regardless of gain.