# Useful mental models for low-frequency analog circuit design?

While learning circuit analysis and design (from Introduction to Circuit Analysis and Design by Tildon H. Glisson ), I caught myself with a thought that experienced circuit designers should have a much clearer mental model to come up with circuits they design.

For example, digital logic circuit can be designed with a help of truth tables, Karnaugh maps and other almost algorithmically implementable techniques. (There are some design issues beyond that, like non-ideal signal/clock propagation, but those could be dealt with).

The question is, are there expressive tools, which help create low-frequency analog circuits given input/output conditions and other possible constraints? Is it kind of art, or is one required to memorize useful building blocks and just align those blocks to get the result? I am not speaking of simulation software, but human mental models, compressed most important body of knowledge serving as effective pathfinder in the realm.

I am not even sure if it is explainable at all (for example, if someone asked me how to program software I would have hard time to explain how to program in general), so I narrowed my question to low-frequency analog circuits, which more or less boil down to resistive circuits and dependent sources (am I right here?). (but I guess, transients is a challenge on its own, and maybe same mental maps help to design in frequency domain too).

I hope this question does not appear as too broad or vague. I believe, if there are answers, they could be as concrete as Karnaugh maps or have 4-6 sentences in their description.

• Well, there are whole bodies of theory surrounding transfer functions, and generally analysing circuits in the frequency domain; and also models and cookbook approaches for op-amps and transistors. Is that the sort of thing you mean? – pjc50 Oct 2 '13 at 21:13
• I really like this question however, I do worry that it isn't a good fit here but not because it isn't a great question. – Alfred Centauri Oct 2 '13 at 21:51
• Re " ... Is it kind of art ... memorize useful building blocks ..." Art and feel is a significant part of it. In part (only) a competent food cook is a good metaphor. They do not "just memorise" recipes but they know many. They do not "align" parts from different recipes related to a subject - ratherthey look at recipes and understand why they work as they do, how they are liable to interact with other recipes or combinations and they combine 'bits and pieces' because they are perhaps unconsciously 'cooking in their head'. Analog design is usually LESS complex than this as the ... – Russell McMahon Oct 3 '13 at 6:36
• ... interactions are better defined and understood than in food. There are "rules" and "tricks" which are really just 'laws of physics' reduced into shorthand. | eg almost nobody knows or accepts :-) that the max gain of a single bipolar transistor stage is ~= 38.4 x DC steady state voltage across the load resistor. This is because gain = R_collector cct / R_emitter circuit (= Rl/Re) and for a fully bypassed emitter resistor Re = Rbe of the transistor and this is linked to the dynamic resistance of the be junction which translates to ~ 26_Ohms/emitter_mA ie 13 Ohm at 2 mA or 52 Ohms at 0.5 mA. – Russell McMahon Oct 3 '13 at 6:42
• Plug those figures in and scratch you head a bit and you see that gain max = 1000/26 x Vload = 38.4 x Vload. | This assertion forms part of the deep magic and the less inaugurated howl in horror at the suggestion :-). | And so forth. | With time you get a feel for frequency response, noise levels, ... – Russell McMahon Oct 3 '13 at 8:45

## 4 Answers

The key to analog design is true understanding of what the available building blocks (transistors, opamps, etc) do. The rest is a creative thought process to come up with a way of connecting the building blocks to result in a circuit that achieves its goals. Experience helps to expedite this, but by itself doesn't enable it.

The basic problem is that the solution space is very very large. There are many different circuits that can achieve a set of goals for anything but the most trivial problems. Put another way, there is no single right answer in analog design.

Good analog design isn't done by plugging data into a set of formulas. Yes, you do some arithmetic to determine part values and the like. The real design part is not answering those questions but being creative in deciding what questions to ask in the first place. I don't know of any analog design aids equivalent to K-maps for combunatorial digital logic.

One thing that I believe is imperative for analog design is to be able to truly visualize what a circuit is doing. This is much more than being able to go thru a schematic and calculate voltages and currents as you do in homework assignments. That's just brute force much of the time, and isn't what I'm talking about. You have to be able to look at a schematic or otherwise think about a circuit and mentally see the voltages pushing and the currents flowing. You must be able to visualize how changes in these work on the components, which then cause changes elsewhere, etc.

I don't know how to teach this. In my experience, those that can do analog design started learning about voltages pushing and currents flowing at a early age, usually by late grade school. They just "get" it, probably from being exposed to enough cases at a early enough age so that this is now part of their intuition. Another factor may be that those that are truly interested in electronics will delve into it at a early age, so those that don't are the ones without the true passion.

You can teach someone all the theory you want, but it may well be too late to get the intuitive feeling required for real analog circuit design if you start in college. I remember a number of students in college that could do all the problems, got good grades, but still couldn't design circuits without lots of rote cranking and usually mostly copying existing designs. I'm not saying that looking at and even copying existing designs is necessarily a bad idea, but without the intuition and the ability to feel the voltages and see the currents that's all you're stuck with.

Leaning the theory is important and necessary, and experience helps you get to a good solution faster and avoid some pitfals, but these aren't what make a good analog designer a good analog designer. You need to feel the force, Luke to be a true Jedi.

• This is very nice answer indeed. Motivation is the key. It's pity there are not so many means to help Lukes. Visualization is a good hint. Starting early is a good hint too. – Roman Susi Oct 3 '13 at 13:32
• Whoever downvoted this, I'm interested to hear what you disagree with. – Olin Lathrop Jan 21 '17 at 15:23

Let me start by saying that your vision of an engineer drawing Karnaugh maps or truth tables when designing a digital circuit is a bit of... outdated.

Today, any digital design which is greater than few tens of gates is described using Hardware Description Language - a high level language which describes the overall functionality, not the exact implementation in terms of logic gates (there are exceptions, of course). Truth tables, Karnaugh maps, various optimization algorithms and etc. are left for automatic Synthesis Tools to handle.

Even digital designs written in HDLs are not "straightforward" - an engineer always has many alternatives, each having its advantages, disadvantages and pitfalls. It takes a lot of experience and thinking to write a good, reliable, readable and reusable HDL.

The things are much more complex in analog designs:

• There is more complex theory behind any analog component than is taught in undergrad and grad classes.
• The components interact in various fashions.
• The number of parameters for each component ranges from few to hundreds.
• There is always a bit of randomness associated with the complexity of the circuits
• Many more

I'm far from being an expert in analog design, but I guess the answer to your question is negative - there is no straightforward patterns/formulas/ideas which will always work even for low frequency design (low frequency can be high/low power, high tolerance, mechanically strong, etc.).

At work I see young engineers working in digital design groups and even younger programmers, but the heart of any analog design team are few "old oaks" - people with tremendous experience which can not be obtained by just reading books. I think that this age discrepancy is the best proof to my statement - nothing compares to experience in analog design.

Said all that, I don't want anyone to get an impression that reading books can't help in comprehending analog electronics, but one must understand that all the beautiful theories developed in, say Sedra&Smith, are very simplified. I like the Analog SEEKrets book (there is free PDF version on the site) - it is written in order to fill the gap between theories and real world components and applications. It is not an introductory level book though.

There is, however, one area of analog design where almost mathematical precision can be obtained: design of analog filters. There are many tools which can produce complete designs based on the specifications an engineer provides. But this is an exception (the only one I know).

• Good answer. This is what I actually feared is a situation. Is it like low level understanding is no more part of profession? Are those young engineers going to learn the foundations or it will be a sacred knowledge of few software companies, which develop synthesis software. I studied math and CS, and for me it sounds like solving ODE without understanding how to add two numbers without a machine... – Roman Susi Oct 3 '13 at 3:34
• @RomanSusi, the complexity of today's electronics designs makes it practically impossible to teach these topics at any professional level. Well, it is possible to teach, but without a lot of practice these topics will stay at least unclear to students. No, the knowledge isn't sacred (except for very fine details which are companies' trade secrets) - it is all over Internet nowadays. However, I don't believe it will do you any good if you only read materials, you must practice in order to learn. – Vasiliy Oct 3 '13 at 6:02
• @RomanSusi, I will be surprised to find an engineer with 10-15 years of experience in the field who can solve ODEs (except for the simplest ones), let alone PDEs. It is a bit of exaggeration (there are very "rigorous" engineers), but it demonstrates the point. – Vasiliy Oct 3 '13 at 6:06
• @RomanSusi, I also added a link to my favorite book on analog design in the answer. This book shows the electronics as it is - complicated and full of tradeoffs. It is not beginner's cookbook though. – Vasiliy Oct 3 '13 at 6:17
• Sure. Practice is a king. And those better mental models comes with practice. Brain compacts the knowledge even if books or lectures present material in much longer format. But is doing cookbook circuits (say, from 200 transistor projects book) really build up the knowledge? I guess not. To make any difference the practice should be about designing my own circuit from simple to more comples. I guess ODEs/PDEs are rarely part of everyday engineering. – Roman Susi Oct 3 '13 at 6:18

Converted from comment as requested - BUT this is much the same as others are saying.

Re " ... Is it kind of art ... memorize useful building blocks ..."


Art and feel is a significant part of it.
In part (only) a competent food cook is a good metaphor.

• They do not "just memorise" recipes but they know many.

• They do not "align" parts from different recipes related to a subject - rather they look at recipes and understand why they work as they do, how they are liable to interact with other recipes or combinations and they combine 'bits and pieces' because they are perhaps unconsciously 'cooking in their head'.

Analog design is usually LESS complex than cooking as the interactions are better defined and understood than in food. There are "rules" and "tricks" which are really just 'laws of physics' reduced into shorthand.

eg almost nobody knows or accepts :-) that

• the max gain of a single bipolar transistor stage is
~= 38.4 x DC steady state voltage across the load resistor.

This is because gain = R_collector cct / R_emitter circuit (= Rl/Re)
and for a fully bypassed emitter resistor
Re = Rbe of the transistor
and this is linked to the dynamic resistance of the be junction
which translates to ~ 26_Ohms/emitter_mA
ie 13 Ohm at 2 mA or 52 Ohms at 0.5 mA.

Plug those figures in and scratch your head a bit and you see that
gain max = 1000/26 x Vload = 38.4 x Vload.

This assertion forms part of the deep magic and the less inaugurated howl in horror at the suggestion :-). And so forth. With time you get a feel for frequency response, noise levels, ...

• I have not understood why do you measure gain in Volts (38.4 x Vload), but your cooking example is very nice. Thanks! – Roman Susi Oct 4 '13 at 19:56
• Hah, Your max gain example is right out of AoE. (Art of Electronics.) @RomanSusi, if you don't have AoE3, then buy it! (I'm not saying you didn't derive it on your own.) – George Herold Feb 6 '17 at 20:13
• @GeorgeHerold I'm pleased to hear that AoE know the deep magic too :-). I was introduced to that concept and similar in (AFAIR) either 1973 or 1978 by a Doctor Holbrook - a large and barrel shaped (more so than anyone else I;ve met AFAIR) lecturer who taught at Auckland Unoversity as a visiting lecturer. He was less than useful in some areas and brilliant in others and some of his good stuck wedged in my brain forever. The 38.4 x Vl is completely conventionally derived but still foreign to many very capable EEs – Russell McMahon Feb 7 '17 at 7:49

A K-map is a statement of what you want or what something is logically. It doesn't imply a circuit logic design. To do this you need skills and other information such as signal speed and the required voltage levels of the logic.

Similarly a bode-plot doesn't take you to a circuit design but skill helps you choose the correct op-mps based on speed requirements and what voltage levels you might have to deal with.

• logic circuit core... logic can be obtained quite thought-economically and with understanding. Of course, other considerations and related skills are needed, but if I am right getting the core (and manipulating it's constituents) is well over half of the solution. Thanks for mentioning Bode-plot. – Roman Susi Oct 3 '13 at 3:40