My thoughts extracted from a discussion with LvW

Ten days ago, my favorite question about the role of the op-amp in the inverting integrator was asked. I could not remain indifferent and with great pleasure I wrote my answer. Then I wrote comments under the other questions. LvW answered me and a discussion started between us which grew into a chat.

We have known each other for a long time and have discussed various issues many times ... but now there was some change in us.  We had become more tolerant of each other and this was clearly the key to success. I have extracted and written below my thoughts from the chat.

My chat

1. The main problem of the RC integrating circuit is its nonlinear (exponential) curve through time when a constant input voltage is applied.
2. The op-amp integrator is something qualitatively different from the ordinary RC integrating circuit; its curve is thousands of times more linear than the exponential curve of the RC circuit... so we can consider it as a straight line. Talking about circuit imperfections at the stage of understanding kills the understanding of the fundamental idea. This is a basic principle in inventive (creative) thinking.
3. There is a significant difference between the passive RC integrating circuit and the active op-amp inverting integrator. This difference is not only quantitative, it is qualitative. In the former, the voltage drop across the capacitor is subtracted from the input voltage; as a result, the current gradually decreases and the voltage slows down. In the latter, the op-amp copies the voltage drop across the capacitor and adds it to the input voltage. As a result, the "current-creating" voltage and accordingly the current, stays constant so the voltage across the capacitor linearly changes.
4. I did not expect that professors from technical universities with long experience would have to argue in what order circuits should be explained since it is clear to everyone that this has to be done from the simple to the complex... and that the simple is ideal (idealized), and the complex is real... Simple here means to apply a constant input voltage and to think of the op-amp as an amplifier (proportional device) ... and in this way to reveal the fundamental idea behind ​​the circuit. OK, ask what OP has found out from your last comment above; the answer will be "nothing".
5. The difference is qualitative... and there are a few qualitative differences. In the op-amp version: 1) the input resistance is constant = R; 2) the input current is constant = VIN/R; 3) the output resistance is zero; 4) the output voltage VOUT has the opposite polarity of VIN; 5) the graph is linear. However, the question arises what is "qualitative" and what is "quantitative" for you. I think we need to set some threshold and so we get two "qualities"... but we usually do it intuitively... E.g., we say the RC circuit is bad (imperfect) and the op-amp circuit is good (perfect)...
6. The qualitative difference also consists in the different structure of the two circuits…
7. I will consider your last comment here and I will answer but maybe tomorrow because now I feel very emotionally exhausted (today I took a lot of time to compose my comprehensive answer)... It is really very inconvenient to write here in the chat because the text cannot be corrected. That is why I always copy it at least in the clipboard... but it is still unpleasant if a mistake is made.
8. I have noticed that our arguments and discussions start well but end badly-:) Maybe this is because they gradually deepen and sharpen. Anyway, it is not so important... End results are most important…
9. I agree that in both cases (passive and active) we have the same two passive elements in series (the same RC network)... and the current passes through them. This is because the active circuit contains inside the passive circuit... or the active circuit is an improved passive circuit. The only difference is in the addition of another but active element - the op-amp, in series. But this drastically changes the circuit - as if removing the capacitor and replacing it with a piece of wire.
10. I agree that in both cases (passive and active) we have the same two passive elements in series (the same RC network)... and the current passes through them. This is because the active circuit contains inside the passive circuit... or the active circuit is an improved passive circuit. The only difference is in the addition of another but active element - the op-amp, in series. But this drastically changes the circuit - as if removing the capacitor and replacing it with a piece of wire.
11. You have correctly noticed that there is a problem with the use of the word "quality". I use it in its philosophical and dialectical meaning. When I say "qualitatively different", I mean "very different" ... so much that it has become something else. As in life, quantitative changes lead to qualitative changes (encyclopedia2.thefreedictiona…)
12. My remark was that your participation is counterproductive to me, not so much to the OP... because there is no encouragement to my idea but rather a hint that all this is well known. This is the big problem of everyone here on this site - do not encourage colleagues. From this everyone loses... and from the opposite everyone wins. It is like the simplest greeting, a kind word and elementary kindness in life. But maybe the reason is in the different cultures of different nationalities... I personally always admire and encourage originality, deep philosophical thinking...
13. At times, I get a little abrupt because over the years of non-recognition (against the backdrop of a massive creative mediocrity) I feel like I'm starting to get angry. Sorry if I offended you, I did it unknowingly. You don't deserve this because you have a unique thinking and philosophy for circuits… But let's leave this…
14. You made me think about the problem in what order to present and explain circuits … In fact, I also use different sequences and even alternate them in "straight" and "reverse" direction, "bottom up" and "top down", etc. My favorite approach is to build and even (re)invent circuits step-by-step. Thus students can see the logic of circuit solutions.
15. I have already said it, I will develop this thesis now… When we argue, we must be aware of the fact that we are different. I understand and explain circuits from the position of an inventor and creative teacher; you do it from the position of a (very good) engineer and a conventional teacher.
16. I do not take circuits for granted but I build and invent them at the moment in order for the students to show the logic of their evolution. I do it by using my imagination, intuition and emotions; you use your (precise) logic and formal thinking. For you, circuits exist and all that remains is to analyze them logically... for me, they should be invented, step-by-step, at the moment…
17. You can get a very good idea about me from my creative bio. For this very purpose I have written and am writing at the moment it - to avoid misunderstandings in my communication with other people. Look at the years 1973-74 in my bio. Then for the first time I learned what "invention" means and especially, "theory of invention"... and so far I look at circuits through this point of view…
18. You have not got me right, as I thought; that is not what I meant. You are a great specialist and you have achievements… and inventions too. I am just an amateur compared to you.
19. I just wanted to say that we achieve our goals (inventions, new ideas ...) in a different way and you cannot deny that. I think visually, use analogies, associations, thought experiments with equivalent elements ("rheostats", op-amp and transistor "men")... I express emotions and feelings and I communicate freely with the OP and colleagues. Another issue is that they do not behave adequately and I do not find people like me since relations here are rigid, at times even hostile and selfish…
20. Regarding voltage-current causality, I think there is no problem. You are absolutely right that voltage causes current. You know that I use a simple mechanical analogy to explain this phenomenon - a transmission. In this analogy, the motor is the voltage source and the current is the transmission that transfers the power from the motor to the load. It is obvious to everyone that the input quantity here is the motor force (voltage); the transmission (current) is not an input; it is only a mediator that conveys the voltage to the load.
21. As I have noted many times, there is only one case when the transmission can be an input quantity - if it is inert enough. Then it has accumulated kinetic energy and it can drive the load without a motor… In electrical form, this means current that circulates itself in a circuit of a superconductor.
22. But I have said many times that we can reverse this causal relationship by applying negative feedback thus turning the current into an input quantity and the voltage as an output quantity. For this purpose, we can change the voltage so that a current with the desired value is obtained. In the collection of circuit principles, which I created in 2000, and later published in Circuit idea wikibook, I have shown this as a separate principle. Only to add that this technique is artificial - it seems the current varies as an "input quantity" but "physically" the voltage is the input quantity that causes the current…
23. Here is the difference between us - I am looking for the most general (non-electrical) phenomenon; you are looking for the most specific, exact electrical model. There is no need for accurate (quantitative) models at the understanding stage; only the most general, fundamental resemblance to the phenomenon being explained is needed… a (qualitative) model…
24. So, what is the most general model here? There are three elements in this conceptual block diagram - power source (voltage), carrier (current) and load (resistance). It is obvious for everyone that the first element is the input (voltage) source... and it produces the input quantity (voltage)... What is the role of the second element? It can be anything else... just not an input quantity… It is obvious to everyone that this is a "carrying"... "transporting" quantity… which "moves" the input voltage to the load…
25. Thinking in this generalizing way, we can see this phenomenon (the concept "carrier") all around us... even here, at the moment... I am the input quantity, SE EE chat is the carrier and you, when appeared, will be the load-:) This is the way real inventors think…
26. I have nothing against talking about models. I was just afraid of getting upset in the end... but we really should not because we have a lasting relationship and nothing can overshadow it.
27. Do you remember analog computers of the 60's? I have mentioned another time that I started working in such a laboratory in the late 70's. They contained such integrating blocks, summing amplifiers, attenuators, comparators, nonlinear functional converters... and with their help differential equations were solved. They modeled processes and these models had to be accurate (because they were "qualitative", as I often say, correct or not)... But for the (qualitative) purposes of understanding and explaining the basic ideas behind circuits, there is a need for not so precise but "qualitative" models. I mean them in my explanations…
28. Do you remember the belt drives of agricultural and other machines? They transmitted the motor rotation at a distance to machines… Or metal chains in old car engines? For me, these are very good "qualitative" analogues of electric current because they perform the same function - they transmit, or if you want to call it "copy", the power (voltage) at a distance and apply it to the machine (load). This gives an initial idea of the elementary electrical circuit... which is useful and necessary for pupils, students and people...
29. Having this powerful notion, none of them will imagine that the belt or chain are "input sources"... and their motion (current) is the input quantity… My last sentence was not ironic since our discussions always are very interesting for me, I hope for you and for web readers…
30. But it is interesting for me to know whether you reject the analogies at all or only the mechanical one? Is there another analogy you like?
31. I can understand you but you also should understand me. You are talking about exact models needed for analyzing and designing circuits. That is why you consider mechanical analogies useless. But before these stages there is another very important stage - understanding and explaining the fundamental idea (concept) behind circuits. This means to answer the question, "Why is this circuit made this way?"
32. These stages do not need perfect analogies; they need simple life analogies that are based on the same most general idea. Their role is to transfer the well-known notions of life (the simpler thing) to the unknown circuit (something more complex). They are not a means of analysis, calculation or design; they are a means of "understanding." To avoid misunderstandings, I would like to state that I deal with circuits only at this first stage.
33. I have said that you need a "perfect" (exact, precise...) analogy or "model" for the purposes of analysis and design. I do not need a "perfect" analogy for the purposes of understanding (figuring out, grasping, realizing...) the fundamental idea behind the unknown circuit. As a rule, I use analogies to explain the basic idea behind circuits. Here is only one but favorite (for both us) example - any op-amp inverting circuit. I name the most general principle behind it "removing a disturbance by an equivalent anti disturbance". Here is an excerpt from a wikibook dedicated to this idea: "What do we do in real life when we solve some problem but a disturbance has stood in our way? First, we may brace our energy to overcome the disturbance. But there is another solution - someone can help us by adding as much effort as it is needed to overcome the disturbance (to remove the disturbance by an equivalent "anti disturbance"). Here are some funny examples.
34. If someone has broken our window in winter, we may turn on a heater or turn on an air-conditioner in summer. If the windows become dirty, we switch on additional lamps inside the room to "help" the sun. When a car has come into collision with our car, the insurance company compensates the damages caused by the else's car. If someone is spending money from our account, we begin depositing money into the account to restore the sum:) When we go to a mountain, we stock up on food, water, medicine, etc. to use them if a problem appears."
35. Note that in all these cases we do not increase the power of the main source to compensate for the losses; instead, we add energy by an additional "helping" power source to "help" the main source and, as a result, to compensate for the losses. And here is the circuit application of this general idea:
36. "Op-amp inverting circuits consist of three components connected in series: Element 1 (e.g., R1), Element 2 (R2) and a "helping" voltage source (op-amp). Element 1 converts the exciting (input) voltage V into a current I and Element 2 converts back the current into a voltage drop VE2. We need this voltage drop... but it disturbs the current. So the "helping" voltage source VH compensates the "disturbing" voltage drop VE2 by adding the same voltage to the exciting voltage source V. As a result, Element 2 is "neutralized"; it has disappeared and the current depends only on the exciting voltage and the Element 1… The voltage of the "helping" voltage source (op-amp output) is used as an output voltage.
37. Oh, Lutz ... could it be more fun for a teacher to have a student like you? I will be happy to conduct an "educational brainstorming" although I have such in many places on the web... Let's try... I will try to present it as an imaginary conversation between us:
38. 1. THE PROBLEM. Imagine we want to make an electrical integrator...
39. 2. LOOKING FOR A SOLUTION. We begin to look around for a suitable element... Yeah, here is a capacitor. How do we make an integrator with it?
40. 3. CURRENT INTEGRATOR. We begin to "fill" it with potential energy (charge) by passing a constant current through it. The voltage drop across it grows linearly and we use it as an output quantity. That is why we need this voltage drop - as an output...
41. 4. RC VOLTAGE INTEGRATOR. Only, for some reason (interesting what), we prefer to use voltage as an input quantity rather than a current. So, we want to connect an input voltage source to this capacitor integrator… but the capacitor needs a current. What do we do? So far I have answered your Question 1... Let's continue...
42. The idea. Obviously, we need to convert the input voltage into current. Here Mr. Ohm helps us by helpfully offering us his law - I = V/R. How do we put his idea in practice?
43. The implementation. Aha, it is so simple - we just connect a resistor with a resistance R in series acting as a simple "voltage-to-current" converter…
44. 5. UNDISTURBED RC INTEGRATOR." At first everything is fine. The current is exactly V/R and the voltage drop VC across the capacitor starts to grow linearly over time… we are happy…
45. 6. DISTURBED RC INTEGRATOR. However, our joy is soon overshadowed because we notice that the voltage slows down its rate of change and its trajectory becomes nonlinear (as if it looks like an exponent, doesn't it?)
46. 7. LOOKING FOR THE CAUSE OF DISTURBANCE. Obviously, some problem appeared… and we have to find out what it is to eliminate it. Let's begin thinking… Here, however, we see that there is a hidden "trap" and we must be very careful when we say that the voltage drop across the capacitor disturbs what...?
47. This is a very logical (methodical) question... which I myself frequently thought about when I invented these stories... If you really were my student, I would give you the highest grade-:) But since you are my colleague (older in rank than me), I shake your hand and thank you! Of course, I know that you understand these circuit ideas very well and you are only interested from a methodological point of view about the meaning of such a sequence of presentations… Okay, I will be happy to explain everything and I know you will understand me. By the way, this is a unique conversation that I have been constantly looking for and keep looking for... but I can't find it... Obviously this requires prepared minds…
48. I have fabricated this inventive scenario not so much for the purposes of op-amp inverting amplifiers but rather for op-amp converters as voltage-to-current, current-to-voltage (transimpedance amplifier), integrators, differentiators, active ammeters, active sensors, etc. I use it also as another way of "inventing" the inverting amplifier (as cascaded voltage-to-current and current-to-voltage converters).
49. An even more exotic way of presenting the inverting amplifier is as an "inverting -R2/R1 voltage divider" as opposed to the classic "non-inverting R2/(R1 + R2) voltage divider". I explain that the "small" difference between the two expressions is because, in the active inverting version, R2 is destroyed so the current flowing through the two resistors in series is VIN/R1 while, in the classic passive version, the current is less - VIN/(R1 + R2). But let's temporarily stop considering the integrator and return to the two most typical circuits that are most suitable for presenting in this way - current-to-voltage and voltage-to-current op-amp converter…
50. In principle, all inverting circuits operate with input current; the only difference is how this current is obtained in the input part of the circuit (on the left of the virtual ground). In some cases this is done through an "ideal" current source and in others - through a real source (voltage source and resistor in series). So, the main function of the input part is to produce current; it is a current source.
51. Once there is current, it must flow somewhere, best in a closed circuit (short circuited current source). So, the right part of the circuit should be just a piece of wire. It has zero resistance so there is no voltage drop across it… there is no voltage loss and the current is entirely determined by the input part.
52. But we need this current; we have created it to use it for some purpose - to measure it, to convert it to a proportional voltage or to a voltage that changes over time. So we break the circuit and insert something there (ammeter, resistor, capacitor)... As a result, a voltage drop appears across this element… and we have come to your Question 1: "Why (for which purpose) do we "need this voltage drop"?"
53. We need it since this is the output quantity - voltage, of the whole circuit. Even in the case of an ammeter, we need some voltage to be applied across it. In the case of an integrator, we need the increasing voltage drop across the capacitor to use it for some purpose (e.g., to make a ramp generator).
54. So, this voltage drop is desired by the next stage (the load). However, it decreases the input current since it is subtracted from the input (or internal) voltage... it is a "disturbing" voltage for the input voltage and, accordingly, for the input current. And so we come to your Question 2: "What do you mean with "disturb the current?"
55. In short: we have created a current, we want to consume it, we insert a consumer... but a voltage drop appears across it... which reduces the effect of the input voltage... and the current decreases… This was what I meant with "disturb the current"...
56. Let's now see how this idea is implemented in the two converters…
57. What is common between them? In the two configurations, a compensating voltage source is connected in series. It produces voltage that is equivalent to the voltage drop across Element 2 and adds it to the input voltage. As a result, Element 2 is "destroyed" and as though "disappeared". Thus the current is determined only by VIN and Element 1. As I usually figuratively say in this case, the compensating voltage source (op-amp output) acts as a "negative Element 2.
58. What is different between them? This is how the compensating source (op-amp output) is grouped with the other elements of the circuit.
59. In the current-to-voltage converter, this auxiliary source is attached to Element 2 (the output resistor on the right of the virtual ground); so the circuit consists of two elements - resistor + op-amp (output). It can be considered as a "neutralized resistor R2"... or, figuratively speaking, the transimpedance amplifier is "nothing"... just a piece of wire. The philosophy of this grouping can be explained as follows:
60. There is current flowing in a circuit... and we want to measure it. For this purpose, we insert a resistor to convert it into voltage... but because we know that this will cause an unwanted voltage drop, at the same time, we include a compensating source with the same voltage. A similar situation in life is when we decide to do something "bad"... but because we have remorse, at the same time, we do something "good". A typical example is a criminal who is also involved in charity.
61. In the voltage-to-current converter (I mean the circuit where a floating current load is connected in the place of Element 2), the auxiliary source is attached to Element 1 (the input resistor on the left of the virtual ground). So, the circuit consists again of two elements - resistor + op-amp (output). It can be considered as a "helped resistor R1" (more precisely, the input voltage source is helped). The philosophy of this grouping can be explained as follows:
62. We want to pass a current through a load. For this purpose, we made a current source by a voltage source and a resistor in series… but because we know that an unwanted voltage drop will be lost across the load, at the same time, we include a "helping" voltage source with the same voltage.
63. A similar situation in life is when we expect someone to do something "bad"... but because we are predictable enough, at the same time, we begin doing something "good". Maybe my behavior in SE EE is a typical example of this phenomenon-:)
64. By comparison, passive (current-to-voltage and voltage-to-current) converters do not contain an "auxiliary" source but only a resistor.
65. As you have noticed, when it comes to a voltage amplifier, my approach is more difficult to understand than the others because (here I agree with you) it is not clear for beginners the need to compensate for the voltage drop VR2.
66. That is why, in this case, I use the other scenario where I consider the combination of the two resistors R1 and R2 as a passive voltage summer. Later, when I start looking at other op-amp converter circuits, I pay attention to this phenomenon and use it as another point of view.
67. The trick to noticing this phenomenon is to see that in the output loop the voltage drop VR2 and the output voltage VOUT are subtracted according to KVL, and the result is zero. This is because the op-amp adjusts its output voltage equal to the voltage drop, ie, copies it. Here this equality is achieved by the mechanism of the negative feedback but this is not mandatory; it can be achieved, for example, by simply copying VR2 via a voltage follower (with floating power supply). That is why I do not speak about a gain or an amplifier but about a following voltage source VOUT = VR2.
68. This idea (I have named it voltage compensation) is more general than the negative feedback idea… although it can be implemented… and it is usually implemented this way. But, I repeat it again, this is not mandatory. For example, it can be implemented by an "op-amp man" that moves a potentiometer wiper to make its voltage equal to VR2. (At the time, I was able to explain the operation of the op-amp in negative feedback circuits only when I imagined it as a "servo").
69. Here I want to make an important remark - I deliberately do not use the concepts of "ground" and "virtual ground" and I am not talking about "voltage at a point" but about "voltage between two points". This allows you to better understand, by the help of KVL, what is going on in the circuit.
70. Now I would like to say something important about the so-called "virtual ground"... By definition, this is a point with artificially maintained zero voltage relative to the real ground. Working with "voltage at a point" instead of "voltage between two points" is convenient but hides the basic idea in this case. It turns out that with respect to ground, the input and output voltages are of opposite polarity… and this gives an impression they are subtracted… while, in fact, they are summed. "Virtual ground" is an abstract concept that does not show where the current flows. It gives an impression of a short circuit between the op-amp inputs… but this short is not inside the op-amp. It is outside of the op-amp like a shunt in parallel to the op-amp differential input. But what kind of shunt is it? We can name it with figurative names like "virtual shunt"... or "virtual short"... or "virtual piece of wire"... or "virtual conductor"... or "artificial superconductor"... or "virtual zero resistance"...
71. I see that I have time to write a line about my heuristic approach to explaining circuits. Yes, it is difficult for beginners… but not for everyone. Those who have an innate technical sense quickly grasp circuit ideas... but unfortunately they are few. For them I am a very good teacher but for others not so much... they would prefer a more "conventional" teacher.
72. I am grateful to fate that I had the opportunity to apply my approach in my work with students. If I have to be honest, my approach is best for discussions like this where designers, inventors, teachers who love circuits share their achievements in unraveling their secrets and encourage each other.
73. CONCLUSION: If I have to say in one sentence what all that I have written, I will do it in one sentence only: This is the well-known MILLER EFFECT in its perfect form (extremely high gain) ... described in a human intuitive way by showing its various applications in electronic circuits. Shortly, this was a fairy tale about Miller effect.
74. What you have said for the last time confirms my finding that although we manage to exchange valuable thoughts, we are still very different. More precisely, I am very different as I can't find a like-minded person to fully share my ideas. But I do not despair and maybe I will meet him in another world- :)
75. I will only comment on your sentence about "immediate and direct application to non-inverting OPV applications".
76. I have such a heuristic explanation of non-inverting circuits as well. Moreover, I have such explanations for all types of circuits (with and without negative feedback). This is my big idea - to create a system of most general circuit principles for understanding, teaching and inventing circuits (something like "circuit philosophy"). I presented it for the first time in 1998, at Electronics'98 conference in Sozopol. Then I dedicated to this idea the site circuit-fantasia.com (2002), Circuit Idea wikibook (2007) and my dissertation (2013). And to be more specific, I will show how I have classified the principles on which basic negative feedback circuits are built into three groups figuratively called DELETE, MOVE and COPY.
77. In circuits based on DELETE principle, the op-amp output voltage only compensates (removes, neutralizes, "deletes") the undesired voltage drop across the Element 2 (the load) with equivalent voltage… and this voltage is not used. An example of circuit based on this principle, is the op-amp ammeter.
78. In circuits based on MOVE principle, the op-amp output voltage compensates the "undesired" voltage drop across the Element 2 (especially inserted resistor, capacitor, diode, whatever…) with equivalent voltage and this voltage is used as an output to drive the load. As a result, Element 2 does not disturb the input source and the load does not disturb the circuit. Circuits based on this principle are all op-amp inverting circuits.
79. In circuits based on COPY principle, the op-amp output voltage only copies the desired voltage drop across the Element 2 (e.g., capacitor) without compensating it… and this voltage is used as an output to drive the load. As a result, Element 2 disturbs the input source but this is desired "disturburbance"; the load does not disturb the circuit since it is buffered. An example of circuit based on this principle, can be an RC circuit buffered by an op-amp follower. It can be used to produce a voltage with exponential form.
80. Another example of circuit based on this principle can be a voltage divider buffered by an op-amp follower. In contrast to the inverting amplifier, in this configuration, the voltage drop across R2 (the grounded resistor) is not neutralized by the op-amp; it is only copied on the load. As a result, its transfer ratio is R2/(R1 + R2) instead simply R2/R1.
81. You have probably noted that actually the COPY configuration is not a full negative feedback circuit; in fact, it consists of two cascaded circuits (without and with negative feedback). Then I added it a bit mechanically to complete the classification.
82. DELETE and MOVE show the property of circuits with parallel negative feedback (inverting circuits) to influence the input circuit. MOVE shows that circuits with series negative feedback (non-inverting circuits) do not influence the input circuit. This is because in inverting circuits there is connection (through R1-R2 network) between the input source and the op-amp output while in non-inverting circuits there is no such connection.
83. This book is on the shelf next to me, but busy with my own ideas, I now realize that I haven't opened it in years … Now I open it and remember what impressed me years ago: Dan Sheingold. Op Amps and Their Characteristics - gives a philosophy about negative feedback circuits… very interesting
    Tom Hornak. True Analog Circuit Design - shows how to visualize circuit operation (resistors as springs)
    A. Paul Brokaw. Building Blocks for the Linear IC Designer - a collection of basic circuits
    
    In fact, I just glanced at them ... but it would be good to read them in more depth. This is probably some mental deviation - I prefer to think instead of reading-:) My benevolent thoughts are more valuable than others'.
84. By the way, I think these great designers are a big exception. In my observations, as a rule, circuit designers are very limited in terms of "philosophical" thinking and explaining abilities. They make circuits but they can't explain well what they have done. And when you try to explain it to them, they get offended. Quite a strange paradox.
85. Thanks for the support. We had a very interesting dialogue which I think I will retell in my blog. I feel obliged to do the same but with your idea... as long as it is not very abstract for me... We have known each other for a long time and have discussed various issues many times... but now there is some change in us. We have become more tolerant of each other and this is clearly the key to success.
86. Today is a very nice sunny day with a more normal temperature and I managed to do my first sunbathing for this summer in the university park. I am very happy because yesterday I was able to find (after exactly one year) my "thought recorder" with which I recorded many of my ideas while walking or cycling in the university park (so it is something symbolic for me). I took the book to read some of these interesting materials ... but I was tempted first to share something about my students with you related to our conversation.
87. As I have shared, especially in recent years, I have been conducting my lectures and laboratory exercises quite freely (like brainstorming sessions or like our conversations here). But since last year, a new opportunity has opened up - online learning. In the beginning (spring 2020) it created problems for me, especially with the laboratory exercises. But I quickly realized that it provides many new opportunities thanks to my web resources accumulated over the years and the vast web. So, this semester, I did amazing classes with my students walking freely on the web resources with the help of Google. We typed each new term, typed it in English in the Google window, and checked how many web pages (usually millions) were dedicated to it. With this I wanted to show them how important these things are.
88. I also used another explanation technique: I used the pen of ZOOM to draw voltage bars, current paths, etc. on web schematics and so I enriched and enlivened them.
89. Also, I often shared with my students the questions we discuss in the forums and even asked them as assignments… In a word, as they say, I made lemonade from a lemon-:)