# Histogram of the crossover frequency. ADA4898-2

Dear Colleagues from Analog Devices,

My current scientific interest is related to determination of crossover frequency of operational amplifiers; and especially ADA4898-2, which we often use in our University. The search in the literature revealed that the crossover frequency is poorly described. Actually in some textbooks some methods for determination of this important parameter are described but in newer specifications of commercial operational amplifiers we do not find histograms of the crossover frequency of operational amplifiers. We have even submitted to a journal the following article uploaded in the Cornell University library https://arxiv.org/abs/1802.09342 (version 2, which will become visible tomorrow), but since the engineering science is concentrated on the industry, we do not expect any reliable response from the referees of the journal. Journals become tools for career instead of forums for exchange of scientific information. That is why I took the liberty to address Analog Devices.

As a university teacher I will appreciate a report from Analog Devices concerning our method for determination of the crossover frequency of ADA4898-2 and Probability Distribution Function (PDF) determined using 200 double amplifiers. This is already a reliable statistics and the result, which we have obtained is that PDF corresponds to Gaussian distribution of the crossover frequency. We are kindly asking Analog Devices whether our method and results looks acceptable. Still we have hundred ADA4898-2 and can make additional measurements using a digital lock-in voltmeter. It will be nice if in future some tutorial article in Analog Dialog can give clarity on the problem for determination of crossover frequency of operational amplifiers. Now for example, in the specification of ADA4817 are given some theoretical formulas for the frequency response of the main circuits (equations (4) and (7) in Rev. F) but without reference to any textbook or monograph in electronics. The relation between time dependent output and input voltages has also never been published.

In short, I am suggesting an Analog Dialog concerning the problem of method of determination and statistical properties of crossover frequency of Analog Devices operational amplifiers.

Truly yours,

Todor Mishonov

Professor in Physics,

University of Sofia, Bulgaria

mishonov@bgphysics.eu

• Dear Prof. Mishonov,

First let me state some definitions so we are talking about the same quantities:
1) -3dB bandwidth/frequency: This is the frequency where the closed-loop gain of the amplifier system reaches -3dB. Normally this is specified in a non-inverting gain of 1 (unity feedback) configuration. The -3dB bandwidth typically results in the highest bandwidth specification and is often used for high-speed amplifiers. -3dB bandwidth will depend on loading (especially capacitive loading).

2) Unity-gain bandwidth/frequency (UGF): This the frequency where the open-loop gain of the amplifier reaches 0dB (gain of 1). Being an open-loop measurement, the feedback configuration should not affect the number when done properly. Again, the frequency will be dependent on loading.

3) Gain-bandwidth Product (GBWP): This the product of the open-loop gain and frequency measured at a specified frequency (normally listed in the conditions). This number gives the frequency at which the amplifier's open-loop response would cross unity when extrapolated out. This number is often useful for applications where an amplifier is used in a higher gain configuration. It will be less dependent on loading conditions.

Now that the definitions are out of the way, let's talk about your work.

First, it is generally best to familiarize oneself with the open-loop gain and phase plots provided in a datasheet. For the ADA4898-2, this is provided in Figure 19. Looking at the open-loop gain and phase allows a discerning eye to see a number of non-idealities. These non-idealities will often introduce performance limitations. For example, looking at the ADA4898-2, you will see the phase dip around 20MHz and then come back up again. You will see a similar behavior with the magnitude, but the phase behavior is generally more pronounced. This dip indicates that a zero has been introduced into the compensation to increase the phase margin while maintaining a high unity-gain crossover point. This is acceptable in some applications and not in others. For filter applications, like you suggest in your arXiv paper, these phase and gain ripples can have significant effects.

This gets to a general comment on trying to pinpoint the statistics of the crossover. I would not approach the problem that way. I would select an amplifier that has more than enough bandwidth and the appropriate gain/phase behavior to meet your desired system specifications. If you are sensitive to percent-level variations of the component, you are probably not leaving enough engineering margin. I would recommend +/- 20% margin on your bandwidth specification (more or less depending on your sensitivity to the bandwidth).

With respect to collecting statistics, your method seems fine for collecting GBWP. If you want statistics on the UGF, you will need to measure the point where the gain crosses unity; there is no substitute. Similarly, the -3dB point needs to be measured where the gain crosses -3dB. Although your method seems acceptable to measure GBWP, it appears there may be a factor of 2 missing in your final result?

In your paper, you need to specify your measurement setup in more detail. It is hard to reconstruct precisely how you are measuring the quantity as well as all the feedback and loading conditions (including board parasitics). A schematic would help greatly.

Your paper also discusses the master equation for an operational amplifier. This is well known to the majority of electrical engineers. This is usually covered in courses on signals & systems, control theory, and circuit design. A good introduction can be found in Siebert's "Circuits, Signals, and Systems." The s-domain (Laplace) equivalent is just a much easier form to work with - and it is more compact.  In reality, the single-pole equation is inadequate for most system design. Of critical importance are the non-dominant poles and zeros. Specifically, all operational amplifiers have a non-dominant pole that limits the bandwidth. This introduces a phase shift before the unity-gain crossover frequency. I would hazard a guess that the non-dominant pole is much more important to the performance of your filters than the exact crossover frequency. Additionally, the other gain/phase wiggles can drastically impact circuit performance. Specifically, low frequency zeros in the open-loop transfer function tend to introduce long-tail settling effects (doublets).

Regards,

Art Kalb

Principal Design Engineer / Design Manager

Linear Product Systems

• Dear Art Kalb,

We appreciate this Analog Dialog.

Thank you very much for your clarifying questions.

In reply to your comment we have uploaded in the server of the library of Cornell university the next version of our compuscript which become visible in Monday 29 April 2019, arXiv:1802.09342v3,

“Probability distribution function of crossover frequency of operational amplifiers in the framework of Manhattan equation for the operational amplifier”.

Let us clarify the terminology. We are following the specification of ADA4817-1_4817-2.

We have re-derived given there equation 4. Our parameter f0 exactly corresponds with the parameter in this article denoted by fCROSSOVER. In our approach we use the well-known for the majority of the electrical engineers master equation for the operational amplifiers. This approximation is an adequate tool when RF/RG >> 1. In the schematic, we have added taking into account your suggestion RF/RG=100 and the influence of non-dominant poles and zeros is less than 1%. The schematic is very simple a voltage divider and a signal restored by a non-inverting amplifier. Using this method we determined f0 fop 200 ADA4898-2 and presented Probability Distribution Function (PDF) for this important for the operational amplifiers parameter. We are not going to produce any commercial system, we investigate operation amplifiers as physical devices. We found that 1% dispersion for ADA4898-2 is a very good and small dispersion.

We arrive at the problem for determination of f0 designing an educational set-up for measurements of electron charge by Schottky noise Eur. J. Phys. 39, 065202 (2018).

In short our questions are: Do you know histograms of ADA fCROSSOVER ?

Do you consider that this simple problem deserves further attention for physics education?

Yours sincerely,

Todor Mishonov

• Dear Prof. Mishonov,

Reading your paper, it is not clear to me what two ways you calculated the bandwidth. Specifically, it is not clear where equation 11 comes from (especially the sqrt(3)).

You seem to be arguing there are two methods to measure the bandwidth, but it is not clear to me what those two ways are. To be frank, the paper could use some editing for clarity.

With regard to jargon, a "master equation" is not really what is being written down. Master equations have to do with the evolution of the state in a probabilistic system (stochastic process). There is no state evolution in a probabilistic sense here; the system is deterministic (especially without addition of a noise source). You could call the description a state-space description, but that use of terminology is uncommon for a system with only one state variable.

Regards,

Art

• Dear Art Kalb,

We wish to thank you again for your clarification discussion
of 25 April and 20 May 2019 concerning crossover frequency of ADA4898-2.

First off all let us clarify the terminology.
For crossover frequency we suppose the parameter fCROSSOVER
which is used in Eqs.4-9 of the data-sheet of ADA4817.
These equations are exact if the crossover frequency fCROSSOVER is determined by the
linear extrapolation of the low frequency behavior as is
explained in Fig. 54 of ADA4817 data-sheet.
If the closed loop -3dB frequency is much smaller than
crossover frequency the later determines exactly the frequency dependence of the system irresponsibly how wigging is the frequency dependence of the logarithm of open loop gain
as function of logarithm of the frequency.

We tried to absorb completely with appropriate citation your clarification discussion in the amended version of our study
arXiv:1802.09342v5,
“Probability distribution function of crossover frequency of operational amplifiers"
which is published in the arXiv server; the library of the Cornell University.

Our question is:
do you know other study of statistical properties of crossover frequency for some OpAmp?
We wish to cite previous researches on the subject of our experimental study.

Our final goal is histograms for crossover frequencies
to become standard ingredient of data-sheets of OpAmps
just like the histograms for input bias current and input offset voltage.

In order to reach this aim we have submitted our compuscript
to Measurement journal and handling Editor
Prof.~Aime' Lay-Ekuakille could address you for support
of the evaluation of the manuscript.

We will appreciate if you can be go-between an academic journal and Analog Devices engineers developed ADA4898 and ADA4817.
The anonymous reports actually are the best tool to accelerate progress in our understanding
of some fundamental problem.

For further research in this direction,
what Analog Device OpAmp you can recommend us for measurement of the second pole?

Concerning the terminology we use
``master equation'' in sense of ruling equation (nothing related to stochastic theory) or ``main equation'' for operational amplifiers.
In the text of the article we suggested this equation to be called Manhattan equation remarking
that John Ragazzini used it for the first time working for the Manhattan project.
You are correct this equation is completely deterministic.

Returning back to the terminology, it is established by the many
data-sheets of Analog Devices and fixed by significant number of
users of operational amplifiers to whom is addressed the readership of our study.
If in the formulas is given notation fCROSSOVER
this means that authors of the data-sheet for ADA4817
suppose such a definition for the crossover frequency for which the formulas Eqs. (4-9) of the data-sheet are correct.
In our study we use these well-known formulas
just to measure the crossover frequency fCROSSOVER

The new result in our study is synthesized in Fig. 4
-- the histogram of the crossover frequency of 200 ADA4898-2 operational amplifiers.

We will appreciate every comment or suggestion you might have.

On behalf of authors,

Todor Mishonov