Certainly you are not alone, Cyril, because I belong to those who can arrive at exact results in an abstract way but their creative thinking is mainly based on pictures.

I couldn't rest until I found a way to model a diode and a Z-diode so that it works for voltages resp. differences of water levels in both directions. The main idea is that the weight of a sliding partition can be suspended by a floating body submerged by half (diode) resp. by 1.5 submerged floating bodies (Z-diode). Please see the attached rough sketch.

Hi Cyril, I think the possibilities are only limited by the skill of one's fantasy. If by "resistor" we understand exclusively sinks of energy, we have to remain inside the first and the third quadrant. I like, for example:

I = erf(U) + sin(k * U) * exp(-abs(U) / tau)

with k = pi / 2 and tau = 3 pi.

While it might be a hard task to design the interior of such a device, you could easily simulate it at the blackboard.

But (sorry for departing from your original question) for me, something to "remember for a lifetime" would be some kind of physical analogon, easy to visualize. And even if we limit the search for an analogon to the nearly constant voltage at diodes, I think finding something convincing isn't an easy task.

Something that works but does not immediately convey the picture of flowing current is: If the electrical potentials within a circuit are represented by heights within our gravitational field, we can fix the supply "rails" at constant heights, control the height of the inputs externally, and have all other points in the circuit "floating". Then linear resistors can be represented by rubber bands (very very short when not stretched, the higher the resistance the weaker the rubber). Diodes could be represented by an inelastic rope (e. g. of length 0,7 V) parallel to a rubber band but the tricky part is that the rope is only effective if the anode is higher than the cathode (rope fixed to the anode with an open hook at the other end which catches the cathode if the cathode is below the anode).

A usual picture for the constant resistor is a water pipe, voltage = difference of pressure between the ends of the pipe, and current = water flowing through the pipe. Apart from the intricacies of fluid dynamics, it is obvious that the amount of water flowing through the pipe per time unit is roughly proportional to the difference of pressure.

Tying in on this picture, how could a diode look like? The pressure difference had to remain nearly constant, independent of the strength of the flow. The only thing which comes to mind if we vaguely connect difference of pressure with difference of height is a barrier in a river bed, i. e. an (open) waterfall: If water is flowing down at all, the height difference is nearly independent of the amount of water per time.

Oh, Joerg... how nice you wrote it... as though I have written it. I thought I was alone in this black-and-white world with my colorful analogies. Now I know I am not alone...

Certainly you are not alone, Cyril, because I belong to those who can arrive at exact results in an abstract way but their creative thinking is mainly based on pictures.

I couldn't rest until I found a way to model a diode and a Z-diode so that it works for voltages resp. differences of water levels in both directions. The main idea is that the weight of a sliding partition can be suspended by a floating body submerged by half (diode) resp. by 1.5 submerged floating bodies (Z-diode). Please see the attached rough sketch.

Dear Cyril,

CM: Last Wednesday, after the lecture on diode circuits, an interesting discussion with some of my best students happened on the blackboard. They just wanted to know how actually all kind of diodes (ordinary, Zener, LED...) maintain constant voltage across their terminals.

The first thing I would point out is that ordinary diodes and LEDs produce a relatively stable voltage in the forward conduction regime whereas voltage reference diodes generally operate in the reverse breakdown mode. You could discuss how the forward voltage of LEDs is related to the bandgap and hence the wavelength of the light produced, i.e. why does a blue LED need a higher voltage than a red one.

The second point is that below about 5.6V for breakdown diodes, the mechanism is the Zener effect whereas above that it is avalanche breakdown:

https://en.wikipedia.org/wiki/Zener_effect

You might also consider mentioning bandgap references which use the difference between two forward conducting diodes:

https://en.wikipedia.org/wiki/Bandgap_voltage_reference#Operation

There's lots there for the students to investigate on their own and they could look into the principle of a Schottky Diode for comparison.

Today, I celebrated the Labor Day on May 1, doing garden work around the building where I live... and thinking about the interesting issues posed by the wonderful Joerg's comments above. I was excited about the similarity of his and my approach to circuitry, and while I was working, I was thinking about what new discussions to start in this direction...

Tonight, however, I read the written in depth George's comment, and it also moved me... Now it is approaching midnight here... I poured myself a glass of red wine and went into deep reflection on the essence of my nature...

George's explanations are perfect, detailed and professional... but I still prefer the Joerg's non-electrical analogies. Why? So I came to the conclusion that I am not really interested in the specific electronics phenomena. I am rather interested in the philosophy of these phenomena... and it is non-electronic... even non-electrical... it is nobody's... it is something above the concrete implementation...

For example, in this topic I realize that in fact I am not interested in the specific electronic elements diodes and transistors. I am interested in the nature of general non-linear elements that maintain constant voltage and current. And I explain their behavior using elementary electrical circuits or various non-electrical analogies like the Joerg's examples above. This is what causes problems in communicating with specialists because I talk about principles, ideas... but they talk about specific implementations.

The questions that I am concerned about are, "Does it make sense my philosophical approach to electronics? Or is it just a waste of time? Do we have to extract (with so much work) the most general principles in circuitry... or to be satisfied with their concrete implementations?"

Dear Cyril,

I too like Joerg Fricke's analogies, my contribution was really to say that there are distinct differences between types of diode and hence extending the analogy or providing variants to highlight and contrast those differences would add to the students' understanding. Joerg has covered two of those.

CM: Do we have to extract (with so much work) the most general principles in circuitry... or to be satisfied with their concrete implementations?"

I think the answer must be both. Ultimately the aim must be to prepare the students for their intended career. I am a Senior Principal Engineer and as such regularly mentor new graduates as they go from education to industrial life. I would expect a graduate to have an appreciation of the differences between the types of device but not necessarily be up to date with the latest specific implementations. They only need to know what type is required for a specific task, looking for a concrete device then often comes down to what parts are stocked by distributors. Most sites can be searched parametrically as long as they know what those parameters mean.

Of course the level of detail required depends on the specific focus of the student's course, someone majoring in Electrical Engineering needs much more detail than someone doing electronics as a background aspect of a Computer Science course.

I would add two versions of the Nikolai's "trivial cases" above:

*superconducting virtual short circuit (virtual ground)

*virtually open circuit (bootstrapping)

Resistor with inertial non-linearity (incandescent filament)

A kind of memristor?

No, usual incandescent lamp - it will change the reistance almost by factor x10 when heated, but heating creates inertial non-linearity

Such effect is used to create sinusoidal oscillators:

https://en.wikipedia.org/wiki/Wien_bridge_oscillator

Also: https://www.sciencedirect.com/topics/engineering/filament-lamp

You can also add Gunn diode which is low-ohmic near zero volts but then non-linear

Highly fluctuating impedances (Zener diode at microcurrent)

Illuminated photodiode

There is also interesting question: given just arbitrary amount, any value of resistors plus Zener diodes - can you assemble a circuit connected to battery and having some pushbutton such that closing of that pushbutton decreases current ?

It is impossible with resistors alone, trivial if using transistors.

It seems impossible with Zeners.. Then, the question what max ratio of current reduction is possible?

Very interesting thoughts, Nikolay...

Gunn diode has an N-shaped IV curve like the tunnel diode.

Generally speaking, by pushing a NO button you decrease the resistance and accordingly, increase the current.

If the pushbutton is connected in parallel to some part of a circuit, you can divert current from this part thus decreasing the current flowing through it.

Another way to decrease the current by closing a path is to connect in series an N-shaped differential negative resistor (e.g., tunnel or Gun diode)... but Zener diode?!?

Here is some example with 12V Zener diodes and 13V source

Nice trick:)

sorry it must be 6.8 Zeners (just above 13V/2 =6.5V)

Many times I have wondered why devices with dynamic resistance are so interesting to me... but not so for other people... For me, they have always been mysterious with their behavior that resembles the behavior of living beings... and allows us to understand them by putting ourselves in their place (empathy).

This has always been a favorite technique for me when I explain and demonstrate in the lab the operation of such bizarre devices to young people. I am deeply convinced that there is no better way of understanding a "thing" than putting yourself in its place and performing its functions. That is why I propose to take a closer look at how, with the help of just one variable resistor, we can model the behavior of any non-linear element...

The arrangement was extremely simple - two variable resistors in series to the power supply. One of them (RST) is connected to "minus" (ground) and acts as a "nonlinear resistor"; the other (RL) is connected to "plus" and acts as a load. I control the former and you control the latter; I and the rheostat combine to form a "man-controlled" dynamic resistor and you drive it.

To present graphically the circuit operation of this simple electrical circuit, we can think of it as consisted of two elements - a real source (with constant voltage V and variable internal resistance RL) connected to a variable resistor with static (instant) resistance RST. In this configuration, the voltages across and currents through elements are the same; so, we can superimpose their IV curves on the same coordinate system. The IV curve of the variable resistor RST is a straight line beginning from the coordinate origin, inclined to the right and having a slope depending on the instant resistance. The IV curve of the real source is a straight line beginning from the intersection point with X-coordinate, inclined to the left and having a slope depending on the instant load resistance RL. The intersection point of the two lines (alias operating point) represents the instant magnitudes of the current and voltage.

"A picture is worth a thousand words"... so let's illustrate this arrangement...

1. Linear resistor with high ohmic resistance.

In the beginning, I set the rheostat's slider in the end position (highest resistance RST) and you begin decreasing continuously the resistance RL. The whole circuit obeys Ohm's law and the current is a function of the decreasing RL - ↑I = V/(RST + ↓RL).

The RL IV curve rotates clockwise and the intersection (operating) point moves to the right thus drawing the IV curve of the constant resistor RST. Its slope represents graphically the value of the resistance. It is static, constant, steady, ohmic resistance as it does not depend on the location of the operating point.

2. Non-linear resistor with decreased differential resistance.

As above, when you decrease the resistance RL, its IV curve rotates clockwise. But now, from a certain point onwards, I decide to apply the clever "dynamizing trick" to decrease virtually the static resistance RST. For this purpose, I begin moderately decreasing the resistance RST. Its IV curve begins rotating counterclockwise; the intersection (operating) point moves more vigorously to the right (up) and draws more upright IV curve of a dynamic resistor with decreased differential resistance Rd < RST.

This is really a simple but clever trick - to make the current in Ohm's law depend on both resistances RST and RL... to make it a function of two simultaneosly decreasing variables - ↑↑I = V/(↓RST + ↓RL). As though, by decreasing RST, I help you in your desire to change more significantly the current by decreasing RL. You have the illusion that my resistance RST has permanently decreased but actually, it is continuously decreasing and you see new, lower dynamic (differential) resistance Rd < RST. As though, the "static" resistance is converted into a smaller differential resistance.

"Bad" Zener and ordinary diodes have such property...

3. Non-linear resistor with zero differential resistance (a diode in the role of voltage stabilizer).

If I strengthen the "dynamizing trick" above, I can virtually zero the resistance RST. For this purpose, from the same point, I begin more vigorously decreasing the resistance RST. Its IV curve rotates rapidly enough contraclockwise; the intersection (operating) point moves up and draws the vertical IV curve of a dynamic resistor with zero differential resistance Rd = 0.

In Ohm's law, the current significantly increases because of the RST rapid decrease - ↑↑↑I = V/(↓↓RST + ↓RL). You have the illusion that my resistance RST has zeroed but actually, it is vigorously decreasing and you see new, zero dynamic (differential) resistance Rd = 0. You have the feeling that my "static" resistor acts as a piece of wire.

Another viewpoint is to think of the RST-RL network as a dynamic voltage divider with a constant transfer ratio = ↓↓RST/(↓↓RST + ↓RL).

All kinds of diodes (zener, LEDs, etc.), varistors and some circuits with parallel negative feedback (active diodes, active zeners, etc.) act in this way.

4. S-shaped negative differential resistor (thyristor).

If I go too far and enormously strengthen the "dynamizing trick", I can convert the ordinary "positive" resistance RST into negative differential resistance. Practically, this means to make the voltage-stabilizing nonlinear resistor above overact... to go too far when decreasing its resistance.

For this purpose, from the same point, I begin extremely vigorously decreasing the resistance RST when RL decreases. Its IV curve rotates extremely rapidly contraclockwise; the intersection (operating) point moves to the left (up) and draws an inclined to the left IV curve of a dynamic resistor with negative differential resistance Rd < 0.

In Ohm's law, the current extremely increases because of the RST enormous decrease - ↑↑↑↑I = V/(↓↓↓RST + ↓RL).

If we look at the RST-RL network from the dynamic voltage divider viewpoint, you can see an extremely interesting situation - you decrease the resistance RL, the current increases... but the voltage decreases!?! What a magic!

--------------------

Let's summarize the last three situations in a figurative way. Two resistors - the pull-up RL and pull-down RST, "fight" each other striving to change in opposite directions the output voltage (across RST). There are three situations:

In other words:

In electronics, thyristors and neon bulbs act in this way (in certain parts of their S-shaped IV curves).

5. Linear resistor with low ohmic resistance.

Now, I set the rheostat's slider in the starting position (lowest resistance RST) and you again begin decreasing continuously the resistance RL. The whole circuit obeys Ohm's law and the current is a function of the decreasing RL - ↑I = V/(RST + ↓RL).

The RL IV curve rotates clockwise and the intersection (operating) point moves to the right thus drawing the IV curve of the constant resistor RST. Its slope represents graphically the value of the resistance but now it is more steep. As above, it is static, constant, steady, but low ohmic resistance as it does not depend on the location of the operating point.

6. Non-linear resistor with increased differential resistance.

As usual, when you decrease the resistance RL, its IV curve rotates clockwise. But now, from a certain point onwards, I decide to "dynamize" the static resistance RST in an opposite manner. For this purpose, I begin moderately increasing the resistance RST. Its IV curve begins rotating clockwise; the intersection (operating) point moves more vigorously to the right (slightly up) and draws an IV curve with a smaller slope of a dynamic resistor with increased differential resistance Rd > RST.

This is the same clever trick as before - to make the current in Ohm's law depend on both resistances RST and RL... to make it a function of two simultaneosly changing (but now in opposite directions) variables - ↑↑I = V/(↑RST + ↓RL). As though, by decreasing RST, I impede you in your desire to change the current by decreasing RL. Now you have the illusion that my resistance RST has permanently increased but actually, it is continuously increasing and you see new, higher dynamic (differential) resistance Rd > RST. As though, the "static" resistance is converted into a higher differential resistance.

Incandescent light bulbs have such property in certain part of their IV curves...

7. Non-linear resistor with infinite differential resistance (a transistor in the role of current stabilizer).

If I strengthen the "dynamizing trick" above, I can virtually increase the resistance RST up to infinite. For this purpose, from the same point, I begin more vigorously increasing the resistance RST. Its IV curve rotates rapidly enough clockwise; the intersection (operating) point moves up and draws the horizontal IV curve of a dynamic resistor with infinite differential resistance Rd = 0.

It is interesting to see what happens with Ohm's law. Now, the current does not change at all because when RL decreases, RST increases with the same rate - I = V/(↑↑RST + ↓RL). You have the illusion that my resistance RST is infinite but actually, it is vigorously decreasing and you see new, infinite dynamic (differential) resistance acting as a current-stabilizing nonlinear resistor. You have the feeling that my "static" resistor acts like an open circuit.

The output parts (collector-emitter, drain-source) of all kinds of transistors (bipolar, FET, MOS, etc.), tubes and resettable fuses act in this way.

8. N-shaped negative differential resistor (tunnel diode).

Again, if I go too far and enormously strengthen the "dynamizing trick", I can convert the ordinary "positive" resistance RST into negative differential resistance. Practically, this means to make the current-stabilizing nonlinear resistor above overact... to go too far when increasing its resistance.

For this purpose, from the same point, I begin extremely vigorously increasing the resistance RST when RL decreases. Its IV curve rotates extremely rapidly clockwise; the intersection (operating) point moves to the right (down) and draws an inclined to down IV curve of a dynamic resistor with negative differential resistance Rd < 0.

In Ohm's law, the current decreases because of the RST enormous increase - ↓↓↓↓I = V/(↑↑↑RST + ↓RL). It is interesting that you decrease the resistance RL, the voltage increases... but the current decreases!?!

--------------------

Let's again summarize the last three situations in a figurative way. Two resistors - the pull-up RL and pull-down RST, "fight" each other striving to change in opposite directions the common current through them. There are three situations:

In other words:

In electronics, tunnel diode, Gunn diode and lambda diode act in this way (in certain parts of their IV curves).

Before I continue to develop the idea of the experiment, I would like to make one, seemingly out of the question, commentary.

This is not my first question by which, as a teacher, I try to draw the students' attention to our discussions... to awaken their curiosity and interest in circuit phenomena. And not for the first time I do not get support from my colleagues - lecturers in technical schools, in particular from the institution where I work. This surprises me once again... and I try to imagine what this teacher is, who is not touched by the attempts of a colleague to awaken the interest of young people with the help of such a noble and completely selfless initiative... and beleive me, I cannot...

The teacher at a technical school is not just an engineer... he/she is more than an engineer because he works with living people and not with dead machinery... And if this profession is not his vocation, he will not see the necessity of such endeavors... they will simply be unnecessary and even annoying to him. Then his students will be his exact copies - maybe good professionals but cold, insensitive and terrible people... who would gladly develop perfect weapons to kill innocent people... but not to cure hopelessly ill...

Aparna,

Do you agree that the T resistive network can be thought as a voltage-to-current converter with scaled input... and the PI resistive network - as a current-to-voltage converter with a scaled output?

So the T resistive network consists of cascaded voltage divider and voltage-to-current converter... and the PI resistive network - of cascaded current-to-voltage converter and voltage divider?