The most useful application note I’ve ever read

I have read that we humans have to see or read some information many times until it sinks in, and we remember it. That’s probably true for information that you may casually need to know. Then there are moments of serendipity when you stumble over the solution to a problem that has been plaguing you. These you remember right away because they are so immediately useful to some problem that has been bothering you.

That’s the story of the most useful application note that I have ever read.


In college I learned how to analyze circuits in many different ways and also learned many analysis tricks. These were mostly based on some sort of “voltage transfer function” analysis.

That was all good, but on that first paying job, I had to design PCBs full of op-amps, DACs, comparators, and logic gates. We only used 2-layer boards back in the stone age, and placement was always tight, so it was a struggle to figure out how to wire up all the different parts.

It was always somewhat of a cut-and-try approach to get systems working correctly, as even in this stone age the circuits I was designing and working with were accurate (14- to16-bit resolutions), and fast (greater than 20 MHz bandwidths). These things were difficult to get working on a breadboard, much less get crammed onto a much smaller production PCB.

It all seemed like a lost art, and I didn’t have the proper mental tools to analyze or visualize what was going on. But somehow boards were getting designed and working with a lot of trial and error. I remember looking at the senior engineer’s designs and seeing what they had done made sense, but exactly how they knew to do what they did was a mystery to me. I still seemed to be spending far too much time slapping capacitors here and there, trying to get my circuits to behave.

That Aha Moment

One day, I stumbled upon an Analog Devices data book that had the answer! Application Note AN-202, that seminal paper by Paul Brokaw titled: “An IC Amplifier User’s Guide to Decoupling, Grounding, and Making Things Go Right for a Change” [1] (Figure 1). Not only was the title catchy, I mean who can’t relate to “making things go right for a change”, but it was full of immediately useful information.

Figure 1 If you haven’t read this many decades-old application note, go download it now. Things will “go right for a change” after you absorb the knowledge presented there.

There it was, a clear explanation of what matters to analog circuits, it is not what the voltages do that matters, it’s what the return currents are doing to your circuit that matters (Figure 2)!

Figure 2 Mr. Brokaw’s clear description and wonderfully done illustrations stand out as easy-to-understand explanations of the currents that you need to worry about in any design. Source: Analog Devices Reference AN-202

 Yes, it is true that we measure the voltages with our oscilloscopes, but the current paths interacting with parasitic resistance and inductance and forming ground loops are what influence those last bits of resolution on our voltages.

Also clearly explained in this application note is the concept of where the op-amp’s internal integrator is grounded (Figure 3). All internally compensated op-amps have an integrator somewhere inside them to provide the dominant pole roll-off.

Figure 3 An op-amp’s internal integrator is typically connected to the negative power supply terminal since there is no ground terminal on the IC. As the red arrow shows, this is a ‘sneak’ input path directly to the output. Table 1 in AN-202, shows the actual connection point for many contemporary OPAMPs.

How the internal integrator is virtually grounded is very important in understanding the “fourth op-amp terminal” as Mr. Brokaw explained it. That fourth terminal is an input to the virtual ground reference point of the internal integrator as shown in Figure 3. Any voltage perturbations on that terminal will be directly coupled to the output. Decoupling badly at this terminal will, at best, add any signal or noise from the negative rail to the output; and at worst, with high-speed amplifiers, will cause instability.

Just about a year ago, I was asked to take a look at an oscillating linear power supply that was built with an op-amp as the error amplifier. I knew exactly what to look for. I immediately traced out the power connection on the op-amp’s negative power supply terminal. Sure enough, the decoupling capacitor for this terminal was some 2 inches away on the PCB. Slapping a decoupling capacitor right at the op-amp solved the problem. I gave the link for the AN-202 application note to the original designer of this circuit as a reference for future use.

I have to admit, without ever having seen this application note, I would have probably never had this insight into how this portion of an op-amp works. Sure, you can sometimes glean this information by looking at the power supply rejection ratio (PSRR) curves, and you can sometimes spot which power lead the internal integrator is tied to by the reduced PSRR on that lead, but that in and of itself does not lead you to this fundamental circuit cause and effect (Figure 4).

Figure 4 A typical PSRR plot for a negative supply connected integrator op-amp. The negative supply is seen to be more sensitive, by some 40 dB to power supply induced signal in this LF156 series op-amp. Source: LF156 Data Sheet, National Semiconductor / Texas Instruments

It should be noted that many modern op-amps have improved the connection of the internal integrator and maintain a more fully differential connection by buffering the integrator virtual ground connection from the power supply rails internally to the output to improve this aspect of the op-amp’s performance. It is still valuable to know what to look out for because there are still plenty of designs out there that have this possible issue.

Bonus Aha Moments

There are other notable aha moments in my learning “how to make things go right for a change”. One was the entire “National Semiconductor Linear Applications, Volume 1” [2] which Radio Shack stocked and published. This was the best $2.75 I ever spent! Still, half of what is in the book is applicable today.

The 1974 paper by James Solomon, “The Monolithic Op Amp: A Tutorial Study” [3], is still the single best, easy-to-read reference on how IC op-amps work. It should be a required reading for every analog engineer that uses op-amps. Much like Mr. Brokaw’s paper, Mr. Solomon’s work has plenty of simple circuit diagrams showing the signal flow in a manner unlike any other paper or textbook for that matter. Unlike most IEEE Journal of Semiconductor Circuits’ articles of the period, which described a particular design, this article describes the functioning of nearly all types of Monolithic op-amps.

At one time, I was tasked with implementing some hybrid amplifiers that had to settle quickly to 10-bit accuracy for a pipelined ADC design. I was having trouble understanding the settling time tails that I saw. While serendipitously browsing around through a senior engineer’s literature stack, I found an old Analog Dialog article from June 1970 by Robert I. Demrow titled: “Settling Time of Operational Amplifiers” [4]. Mr. Demrow clearly showed with calculations, measurements, and a clever demonstration circuit the hows and whys of settling time tails from a closed loop frequency response point of view. This article was published more than a decade and a half before I needed it, and if it hadn’t been for the senior engineers keeping that issue of Analog Dialogue, I would have never found it. I haven’t found any article that describes settling time as it relates to the closed loop frequency response this well since. I have to say, I have never looked at a closed loop frequency response curve of any system the same way again.

When the IBM PC became available and PC based SPICE programs started to appear at affordable prices (around 1985), the paper by Boyle, Cohn, Pederson, and Solomon titled: “Macromodeling of Integrated Circuit Operational Amplifiers” [5] caught my attention. This paper, although published some 10 years before I needed it, was invaluable information in teaching me how to simplify actual transistor circuits into behavioral models that could be speedily simulated on our 4 MHz PCs of the time. Macromodels like this are still used today because even in 2022 we don’t have the computing power on our desktops to simulate transistor-level models of even a single op-amp, much less a complete circuit design! Like all the others, there is still much to be learned from this paper today.


Looking back, it seems like an “aha moment” came along at every design obstacle I ever had. When that moment didn’t come, the project was just working by some luck, because I didn’t fully understand why it worked, or the circuit just outright failed to work properly.

Today, I browse the latest application notes, especially the ones that present “overview” tutorials on some subject, looking for tips, and always looking for perhaps that next “aha moment” that describes a solution to my latest design challenge.

What was the most useful application note you’ve ever read?


[1] Paul Brokaw, “An IC Amplifier User’s Guide to Decoupling, Grounding, and Making Things Go Right for a Change”, Analog Devices, AN-202

[2] “National Semiconductor Linear Applications”, Volume 1, Published by Radio Shack

[3] James E. Solomon, “The Monolithic Op Amp: A Tutorial Study”, IEEE Journal of Solid-State Circuits, Volume: 9, Issue: 6, December 1974

[4] Robert I Demrow, “Settling Time of Operational Amplifiers”, Analog Dialogue, Vol 4, No 1, June 1970.

[5] Boyle, GR, BM Cohn, DO Pederson, and JE Solomon, “Macromodeling of Integrated Circuit Operational Amplifiers,” IEEE Journal of Solid-State Circuits , December 1974.

Steve Hageman has been a confirmed “Analog-Crazy” since about the fifth grade. He has had the pleasure of designing op-amps, switched-mode power supplies, gigahertz-sampling oscilloscopes, Lock In Amplifiers, Radio Receivers, RF Circuits to 50 GHz and test equipment for digital wireless products. Steve knows that all modern designs can’t be done with Rs, Ls, and Cs, so he dabbles with programming PCs and embedded systems just enough to get the job done.

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