Cyril,

All this is fundamental for building  clear comminication with students. 

We have agreed, for ages : 

(1)  X is the horizontal axis,

(2)  Y is the Vertical axis,

(3)  Z is the other.  

As you observed,

We have not agreed on any naming scheme

for Cyril's  "graphical-analytical-diagram".  

Our custom has been for energy/data to travel left-to-right,

so I suggest : 

(1)  left 'entering' line to be  'generator' ,

(2)  right 'exiting' line to be the 'load'.

(3)  other 'auxillary' to be the 'aux' line.   

The 'generator' could have the left margin value labels, and visa-verse.

The caveat is

that the generator line might not always appear to be 'entering',

and the load might not always be 'exiting',

...  so  we make ad-hoc adjustments.  

'X' and 'Y' and 'Z' would be confusing 

in Cyril's  'Graphical-Alalytic-Diagram'. 

because

(1) the Load Line concepts are not horizontal v. vertical, 

(2) they are already claimed in the analytical geometry world.

The DIDALAB system.

It was a typical data acquisition board having 8 analog inputs and 2 analog outputs.

The interfacing modul.

It consisted of various converters - V-to-I, I-to-V, etc., with buffered inputs/outputs to work with low resistive loads.

The main circuit was an inverting amplifier with buffered input and output like the described in the RG question below. 

https://www.researchgate.net/post/How_do_we_investigate_the_IV_curve_of_a_forward_biased_diode-by_a_current_voltage_or_real_source

The experimental setup for investigating "living" superimposed IV curves of a voltage divider.

It was a circuit consisting of three varying elements - the voltage source E, the upper resistor (rheostat) R1 and the lower resistor R2 (rheostat), connected in series. Also real (movement) voltmeters were connected in parallel to each of elements and an ammeter - in series. Finally, two single-ended analog voltage inputs (AI1 and AI2) were connected to the two intermediate points and a third current input AI3 of DIDALAB - in series, to give a chance to the computer to "see" the potentials and current... and then to draw the graphical representation on the screen (under the control of a program).

When I (or any of my students) was changing some (or a combination) of these attributes (E, R1 or R2), the real meters showed the values in the conventional "movement" form, while the computer was moving or rotating the IV curves (lines) on the screen. The one line was scanning and the other - scanned... and their intersection (operating) point was moving along the scanned line...

Thus the real circuit, meters and the image on the screen synchronously were operating.  This was the same arrangement as in the Wikibooks story about the Ohm's experiment (the attached link below).

https://en.wikibooks.org/wiki/Circuit_Idea/Walking_along_the_Resistive_Film#How_to_visualize_the_voltage_diagram_on_the_screen

Step 1 - a lonely operating point on the screen.

Actually, the operation of this circuit at a given instant should be represented by only one (operating) point on the screen with coordinates X (V) and Y(I). When the something (E, R1 or R2) changes, this point should move and draw a curve (line) on the screen.

Note that this point is real-time measured.

Step 2 - R2 IV curve.

But the operating point actually is the intersection point between two IV curves (lines). To show this, they should be drawn and superimposed on the screen.

Note that, for our educational purposes, these two curves are not real-measured... they are preliminary prepared... In this simple experiment (voltage divider), the two curves are two lines simply drawn by the computer on the screen (sorry for the little scam, but there was no way:)

The first of them is the IV curve of the varying ohmic resistor R2; it passes through the coordinate origin...

Step 3 - R1 IV curve.

But what is the second line? It is not so simple as the first line... since it represents a network of two elements in series - E and R1. So it should be a composed curve assembled by summing (subtracting) their IV curves...

More precisely, the R1 IV curve (similar to the R2's curve) should be subtracted from the E IV curve (a vertical line)... so the composed E-R1 IV curve is sloped to left...

Step 4 - the operating point presented as an intersection point of the two IV curves.

Thus both lines are superimposed on the same coordinate system on the screen... and the operating point is the intersection point between them.

Now we are ready to start various experiments where we will move (rotate) real knobs and sliders... while the computer will draw and move imaginery lines on the screen. This will allow us to "feel" the circuit operation... to create psychomotor models in our brains...

Step 5 - varying the voltage E.

We may begin with changing the voltage E of the only source in this resistive circuit. When we vary E, the composed E-R1 IV curve moves horizontally remaining parallel to itself (i.e., it translates). As a result, the operating point slides along the R2 IV curve of the resistor R2. So, the composed E-R1 IV curve is a scanning line while R2 is a scanned line.

Step 6 - varying the resistance R1.

Then we may change the resistance R1 by moving the slider of the upper resistor. Now the composed E-R1 IV curve rotates around the point E on the X coordinate... and the operating point slides again along the R2 IV curve. Again the composed E-R1 IV curve is a scanning line and R2 - scanned line.

Step 7 - varying the resistance R2.

With the same success we can change the resistance R2 by moving the slider of the lower resistor. Now its R2 IV curve rotates around the origin of the coordinate system... and the operating point now slides along the composed E-R1 IV curve. Now, the R2 curve is a scanning line while the composed E-R1 IV curve - scanned line.

Step 8 - visualizing the power of R1.

Many other basic electrical quantities can be visualized by this real-time "simulation" (only our imagination can limit them)... For example, the power applied to R1 can be visualized by a rectangle with a corresponding area...

Step 9 - visualizing the power of R2.

... or the power applied to R2 - by another rectangle...

Step 10 - visualizing both powers.

... or both powers - by two rectangles... where the total area shows the total power applied to this voltage divider...

Step 11 - adding another source E2... and continue the experiments.

We can make this experiment even more sophisticated by inserting another voltage source E2 between the resistor R2 and ground... and, in addition to the experiments above, we can change its voltage...

Unfortunately, I have not kept hard copies of the screen from this part of the experiment... though that was 25 years ago... But fortunately, there is a picture (from 1997) illustrating this situation in the operation of the ubiquitous inverting amplifier.

Here the input voltage EIN "moves" the input composed IV curve EINR1 while the op-amp output voltage VA "moves" the output composed IV curve EAR2 so that to keep the intersection (operating) point on the Y coordinate. Y coordianate is always zero and this represents the virtual ground ohenomenon.

The same circuit can be visualized by means of "living potential diagram" (see the attached picture and link).

https://en.wikibooks.org/wiki/Circuit_Idea/Walking_along_the_Resistive_Film#An_op-amp_inverting_amplifier

Hi Cyrill, nice to salute you.

1) For some unexplained reason, each time I tap any of your images, only schematic diagram (step 0) appears on my screen. Do you get zoomed each of all of your images?

2) I will review your interesting way to present the "load line".

3) But, in advance, how much (micro) economy does know your students?.  Because, conceptually, this line is identical to the Demand line (x-quantity, y-price), (how much quantity you are allowed to buy given certain price). And the equilibrium point is given by the intersection with the Offer line (how much producers are interested to sell at certain price). In my poor opinion, the analogy is almost perfect.... But, if your students do not know economy, certainly useless.... Indeed. 

Hi Sergio,

It is so nice when you meet any support in some of your brittle, timid and vulnerable to attacks ventures... As you can see, I have just briefly outlined the rough idea of such a "living (real-time) simulation"... and I was ready to depict in detail it... if only anyone was interested... and that is what happened... Thanks for the encouregement!

Regarding the overlapping images... it seems it is a problem of the RG software. I hope they will correct it. For now, I use such a remedy - first I refresh the page, and then click on the image.

Interesting observations about the usage of analogies... BTW I have found the picture about the microeconomics equilibrium in Wikipedia. But is the intersection point named "operating point"?:)

@ all

This seems to be an RG "feature". It happens from time to time. I could not yet find out under which exact conditions. But it seems that when I open an image in one of the answers, the images of the original question get stuck. It seems not to happen if you open the images in a new window...

For me, refreshing the page helps reset the problem.

Regards

The load line is the locus of the possible operating points "defined mostly by linear part of an electrical circuit".

Interaction of load line with the characteristics of "active elements" (non-linear elements) allows us graphics solution of the electrical circuit which is very visible. We are able to do linearization, etc.

It is advisable to show the students that analytical solution may be more difficult and laborious.

Dear Prof Mechkov,

"load line" represents the components that come into play (load) when  DC/AC voltages are applied and characterizes the device operation (until then quiescent,Q-point)

So Josef, the load line is not something "material"... but it is just the locus of the operating points... the trajectory of the moving operating point... and thus it is a kind of illusion? 

May be an illusion , that is why separate AC -DC load line Prof Mechkov !!!

Maybe:)

Hi Cyril

No illusion, another quiescent points are no possible.

That's just the essence of the graphical solutions.

"Intersect with the description of the nonlinear element."

Sorry , not so graphical , more of analytical as the dependencies change with applied signals ... Are we back :(

Josef,

"Intersect with the description of the nonlinear element." Well, but with what do we intersect the characteristic of the nonlinear element? What is this "thing" that will intersect it? Does it represent something material?

(Sorry for the insistence, but I want to completely clarify the matter)

Cyril

"Intersect with the graphical description of the nonlinear element."

I honestly admit that I do not understand the query:

Does it represent something material?

It is perhaps axiomatic that the "description" is based on the specific characteristics of the implemented circuit element (from measurement).

Cyril,

To you, is the intersection a "balance Point" 

specific to the context/circuit for which you draw a Load-Line diagram

and related to the conceptual point you are making ? 

That would be the purpose and manner in which I would draw a Load-Line. 

Josef and Glen,

I mean that in many cases the load line represents the IV curve of some "material" element, e.g. a real voltage source (a network of an ideal voltage source E1 and resistance R1 in series). The attached picture shows the graphical solution of a voltage divider.

Maybe I should expose my philosophy about the graphoanalytical solution...

By means of equivalent transformations, we can reduce any electric circuit to an equivalent network of two parts (composed "elements") connected in series - an upper "pull-up" part (E1) and a lower "pull-down" part (E2). They can contain whatever elements - linear, nonlinear, passive, active... This network is supplied by an equivalent voltage source that is combined with the upper part.

To present graphically the circuit operation of this elementary electrical circuit , we can use the fact that the voltage across both parts and the current  through them are the same. So, we can superimpose their IV curves on the same coordinate system - the IV curve of the upper part that is shifted from the origin with V and the IV curve of the lower part that begins from the origin. Depending on the corresponding elements, these characteristics can be lines or any other curves. The intersection (operating) point represents the instant magnitudes of the current and voltage (the equilibrium)... and is the solution...

Now we can change whatever in this arrangement... in the upper, in the lower or in both parts... and will see how the one, other or both IV curves move, rotate or both... When change something in one of the parts, its IV (scanning) curve moves/rotates and the intersection point slides along the other (scanned) curve... thus drawing it...

The question is, "What is the load line in this arrangement?"

Maybe we should first to answer, "What is the load here?"

Dear Cyril,

With reference to your voltage divider:

May the two 2-terminals E1 and E2 contain operational amplifiers ?

Sincerely

ERIK

An interesting question, Erik... which make me think more about the nature of these two elements...

At first glance, I think these two elements should be passive... and any voltage sources, (pull-up, pull-down or both) be out of them... as in the attached picture... where the op-amp "pulls" up or down the output through R2 (acting as E1)...

So Erik, I have noted that, for the purposes of such a graphoanalytical interpretation, we group (divide) all the elements of this "mess" of elements into two groups (E1 and E2)... Thus we have two IV curves superimposed on the same coordinate system. But we can ask ourselves why not to divide the "mess", for example, in three groups?

A possible answer can be because both the voltages and currents have to be the same... or because this 2-coordinate system requires only two curves to intersect in one point...

It is still interesting how can we visualize a circuit with another element E3... maybe by using a 3-coordinate system?

Cyril,

Please see this figure

Well, I have seen it... and what?

I see two voltage sources (EIN and EA) "pulling" through resistors (R1 and R2) the same common point in opposite directions... like in the game of "tug of war"...

More precisely speaking, by considering the causality, the input source VIN begins "pulling" the point... the point tries to "move"... but the second opposing voltage source VA immediately reacts to this "intervention"... and returns the point back in its initial place (zero)...

Hi Cyril

and so what nonlinear divider?

An impressing picture, Josef! It remains only to clarify what is the input variable here...

They may be different values of the UBE - or base current? (:-0) - for example. Or an another parameter of the nonlinear resistance element generally.

OK... As I can see, you have prepared a good introductory picture to transistor amp stages:)

It still would be a good idea to show the input, e.g. naming the lower element "controlled nonlinear resistor"... or, more precisely, "controlled constant-current nonlinear resistor":)

It would be useful to make a dual picture with a "controlled constant-voltage nonlinear resistor"... The only problem would be to find an example of such a nonlinear element...

BTW during the first semester, my favorites were able to make such "heat-driven elements" in the laboratory, almost baking diodes and transistors:)

Cyril,

concerning:

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

Well, I have seen it... and what?

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

I have added the ground (reference node)

to the op.amp. in your figure.

Questions:

Are the E1 and E2 two-terminal circuits (elements) proper two-terminals ?

Is the current in these circuits the same ?

Erik... thank you... but if you want to do it more real, better add the non-inverting input and connect it to ground... I have not done it because I wanted to show that inverting circuits generally do not need an opamp with a differential input...

Your last question is very relevant... In my opinion, E1 and E2 should be true 2-terminal "elements"... "floating" elements which are "suspended" between the supply rails... so the same current flows through them...

Have you realized how ubiquitous this "voltage divider" configuration is? Maybe more than 80% of modern integrated circuits have voltage outputs... and maybe 100% of these outputs are implemented in this way!

All they are controlled voltage dividers consisting of E1 and E2... which are nothing else than some kind of "resistors"... and the upper (PMOS, p-n-p...), lower (NMOS, n-p-n...) or both resistances (CMOS, totem pole, push-pull...) are controlled by the previous stage... 

Cyril,

concerning:

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

Thanks Erik... thank you... but if you want to do it more real, better add the non-inverting input and connect it to ground... I have not done it because I wanted to show that inverting circuits generally do not need an opamp with a differential input...

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

When you only show the inverting input it is assumed that the noninverting input is grounded.

The op.amp. is a 6-terminal circuit: + input, - input, pos. rail, neg. rail, output, ground.

concerning:

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

Your last question is very relevant... In my opinion, E1 and E2 should be true 2-terminal "elements"... "floating" elements which are "suspended" between the supply rails...

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

Question:

You introduce a coupling between E1 and E2 so that the power supply current in the two circuits become the same ?

eg. you have a 4-terminal circuit where the input signal comes from E1 and the output signal goes to E2 (controls E2).

Erik,

If we are talking about real op-amps, they are essentially 5-terminal devices (excluding adjustments, frequency corrections, etc.)... they do not need a ground terminal... they only need their inputs to be galvanically connected to some points having potentials between a little over V- and V+...

Look at the 741 internal structure. Where do you see a ground terminal inside it?

Cyril,

output signal is measured with respect to ground !   (Single ended)

And what about this

Erik, we can measure the op-amp output voltage with respect to any other reference point having voltage between supply rails... The reference point is not an op-amp's problem... it is our problem... and a load's problem...

The op-amp does not care whether and where we have connected the lower end of the voltmeter (load)... it simply "moves" its upper end. If we have connected them to a stable reference point ("hard" ground), current will flow through the load... and it will successfully do its job.

But op-amp inputs are other thing... The op-amp needs they to be connected somewhere... since the biasing currents need somewhere to flow...  the biasing loops should be closed via the op-amp inputs. This can be seen in the nice Josef's picture.

Josef, congratulations for the impressive drawing! It is a real pleasure for me to examine your colorful picture! I have only two suggestions for its improvement so that it shines with all its splendor.

First, turn down VCC- and move the biasing current mirror below the ground rail. Thus the circuit will become more intuitive (the positive voltages are above the ground, negative voltages - below the ground, and the ground - between them). See as an example, the attached picture.

Second, draw whole closed current loops instead of those little arrows. This will enormously increase the understanding. Here you can rely on the Cyril's golden rule about currents:)

Each current returns back to where it has started.

I formulated this topological rule in the early 90's to complement the quantitative Kirchhoff's Current Law:)))

(I hope that your sense of humor will not mislead you now... and you will forgive me this joke:)))

https://en.wikibooks.org/wiki/Circuit_Idea/Op-amp_Inverting_Current-to-Voltage_Converter_Visualized

Hi Cyril

The main task of the illustration is to show that the itself OPA has no ground outlet - it is "totally floating" :-))

And that, in my opinion, succeeded.

Josef

 Maybe... But in 2007, when I created this story, my purpose obviously was more ambitious - to transform the hackneyed textbook circuit diagram of an I-toV converter to a colorful "geometrical" circuit diagram.

Here is a more sophisticated application of Cyril's law:)

Cyril,

I was just looking over "Walking along the resistive film" with interest. 

And there is so much more.  

Glen

Thanks, Glen! Note this was a collaborative (wiki) work with my students...

(Pay attention to the comments of Mike Zielinski at the bottom of the talk page ... he is a very interesting and distinctive person, which I was fortunate to meet in Web a decade ago.)

https://en.wikibooks.org/wiki/Talk:Circuit_Idea/Walking_along_the_Resistive_Film

Cyril,

concerning:

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

Erik, we can measure the op-amp output voltage with respect to any other reference point having voltage between supply rails... The reference point is not an op-amp's problem... it is our problem... and a load's problem...

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

You are right. I just referred to our normal macro-models for op.amps.

Normally we choose the node with maximum number of branches

connected to other nodes as the reference node in order

to minimize the number of coefficients in the equation system.

Erik,

I see, there are theoretical considerations specific for the circuit analysis...

But I still have not understood which of the two lines is the "load line"... and what exactly is the so-called "load line":)

Cyril,

I suggest that the "Load Line" is a method for determining "Balance" 

between several 'sets' of values. 

So Glen, sometimes "load line" means just a "single line" while in other cases - a "set of two superimposed lines"?

It seems these viewpoints are interchangeably used... but IMO they are different...

In terms of analytical geometry, the "load line" represents geometrically the right part of the equation ("balance) ... the "other line" represents the left part.... and the set of both lines represents the whole equation.

In terms of circuitry, the "load line" represents the upper element E1 (the load) and the "other line" - the lower (varying) element E2.

So I suggest to name the method "grapho-analytical solution", "grapho-analytical representation", "superimposed IV curves" or something similar...

So far we were talking only about the one of the lines... naming it "load line". But there is also another line... and we should somehow name it...

As in this arrangement two elements - a generator and a load, are connected to each other, maybe we should name the "other line" with the name of a "generator line"?

So the questions are, "What is what in this arrangement... what is a load line and what - a generator line? Are they related, and if so, how?"

https://www.researchgate.net/post/What_is_a_generator_line_and_how_it_is_related_to_the_load_line

Cyril,

All this is fundamental for building  clear comminication with students. 

We have agreed, for ages : 

(1)  X is the horizontal axis,

(2)  Y is the Vertical axis,

(3)  Z is the other.  

As you observed,

We have not agreed on any naming scheme

for Cyril's  "graphical-analytical-diagram".  

Our custom has been for energy/data to travel left-to-right,

so I suggest : 

(1)  left 'entering' line to be  'generator' ,

(2)  right 'exiting' line to be the 'load'.

(3)  other 'auxillary' to be the 'aux' line.   

The 'generator' could have the left margin value labels, and visa-verse.

The caveat is

that the generator line might not always appear to be 'entering',

and the load might not always be 'exiting',

...  so  we make ad-hoc adjustments.  

'X' and 'Y' and 'Z' would be confusing 

in Cyril's  'Graphical-Alalytic-Diagram'. 

because

(1) the Load Line concepts are not horizontal v. vertical, 

(2) they are already claimed in the analytical geometry world.

"Generator line" (and load line) is just another name for the replacement of certain parts (linear) circuit using Thevenin's theorem; we work with the concepts of open circuit voltage and short circuit current.

Glen, very interesting ideas... Only I do not think the two lines are equal....

According to me, at some point the left can be а "generator line" and the right - a "load line", and v.v., at other point  the left can be a "load line" and the right - а "generator line"... and we just have to decide what is what at a given instant...

In my opinion, the line representing the input variable part, is a "generator line"... and the other line is a "load line".

To present the grapho-analytical solution by a 3-coordinate system is a new idea to me... I need time to realize it...

Yes Josef, I think in a similar way...

The "generator line" represents the input variable part of the circuit while the "load line" represents the other (usually constant) part...

Well Glen, Josef and Erik,

Let's generalize the problem...

There are three elements in series represented by two intersecting lines. Each of quantites assosiated with the corresponding element, can be varied... as well the place of the ground.

The questions are: "What is the generator and what - the load here? Accordingly, what is the generator line and what - the load line?"

Cyril,

* I never saw the Generator Line as equal to the Load Line,

ie, these are two different concepts. 

* I saw the "Aux" or "Z" line is just a logical possibility

... ie, for future development. 

* I see the 'generator device' as NOT part of 'this' discussion. 

* I see the 'load device' as NOT part of 'this' discussion. 

* I see the 'Graphical Analytic Diagram' as a Black Box  

... if possible, else (ad hoc) defined for the specific instance.

Along that thought, If the Graphical Analytic Diagram 

is concerned with the "Generator"  reflected in the "Load" 

then the Black Box would be defined for that specific scenario.  

And, lastly,  

* the  'generator Line' and 'load line'  need NOT be linear,

( which I expect Josef or Erik would have pointed out very soon. )  

"""at the instant""" refers to an "ad hoc" description, right ? 

ie,   Latin meaning "For This" instance only. 

All this seems so mundaine or trivial,

but it can provide a clearly defined platform for student discussion.    

I do recall a electrical course  in the1970's where I stopped the discussion by pointing out that an important concept was described by three authors of the text , wherein each used distinctly different or shared definitions.  

Apparently the 1/3 book sections were extracted from one of their own publications, and each came with their own peculiar notation. 

The students that were studying only to answer questions for one set of chapters, were not concerned with concepts, were not bothered.  

The professor was concerned, thankfully,

and we were instructed to write notes in the text book at certain places , which reflected  the standard definition and terms

( exactly as used in the first part of the text-book ).  

So,

clearly defined terms are mundain to develop, but can be beneficial.  

Glen, thanks for all this wisdom. You are a very good story teller...

Maybe you have seen that I gradually began to consider the both dual concepts (load and generator line) in parallel. To help the discussion, I have considered some examples in the other question:

https://www.researchgate.net/post/What_is_a_generator_line_and_how_it_is_related_to_the_load_line

Hi Glen,

"which I expect Josef or Erik would have pointed out very soon."

I agree with You - it all may be nonlinear :-)), but the problem is then more complicated. We can not siply use "the open voltage" and "short current" - we must know "the all nonlinear lines".

Josef

Note that here we are talking about non-linear elements with IV curves approximated by two lines - the first is ohmic and the second is either constant-voltage or constant-current... and they operate at their second part... that is also a line... So in this region the non-linear element is linear with exremely high/low differential resistance...

Dear Cyril,

The "signals" in our electrical and electronic

circuits are electromagnetic field patterns.

So far Maxwells equations are our "best model".

All the "single" components in our circuits "couple"

with the surroundings inside and outside the circuit.

It is a matter of energy transfer and energy storage.

Often we are interested in the "balance" of energy

between different "parts" of our circuits e.g.

the "coupling" between flux and charge in a LC-circuit.

The students must be aware of the assumptions we make

when we set-up models for our systems.

The students must be aware of the limitations of our

"measurements" and our "models".

Best regards

ERIK

Erik, it is hard for me to see the connection between your comment and the topic... 

Cyril,

Please explain your load line ideas by means of this circuit:

Hmmm... when talking about "load lines" we usually do not take into account impedances... we make an asumption that XC = 0 (considering capacitors as short connections)...

Erik

but it is not an amplifier.

Josef

Josef,

By the way, the voltage divider is also not an amplifier but is presented in this way:)

Prof Mechkov,

may be I am a bit lost , load line is meant to fix the effect of load for (performance) stability of the circuitry that is sourcing hence "load"

Cyril

but this circuit has not DC quiescent current.

Josef,

The point A (IA, VR2) is its quiescent point...

I am afraid it will be more complicated here.

Dear Cyril, Good basic question and lots of excellent answers already. My understanding and way of teaching the load line is as follows. Load line is a special type of I-V curve showing the characteristics of load (Linear load in most cases) applied to a circuit (Non-linear circuit in most cases), i.e., it represents the response of a linear circuit connected to the nonlinear device (such as diode, transistor, ...). For simplicity let's look at the diode case. Here, the load line contains every possible operating point for the circuit. The purpose for plotting a load line is to determine the operating point (called Q-point) and range for a non-linear characteristic. Here, we need the characteristic curve for the diode. A load line is drawn by two exterem points: 1) Finding the open circuit voltage, usually Thevinen voltage (Vth), on the voltage axis (horizontal). 2) Finding the maximum current, usually Thevenin voltage divided by the Thevenin resistor (Vth/Rth), on the current axis (vertical). The load line is the straight line drawn between those two points. Now, combine (superimpose) the load line and the I-V graph of diode. The load line intersects the diode I-V characteristic curve at a point (Q-point), which represents the the operating point of the circuit. This is in essence a load-line analysis.

An excellent answer, Mahmoud! Thanks for the support!

I just keep wondering what is the load here and what - the generator...

The problem is that a diode, unlike a transistor, is not a controlled element... and it is not what changes the current through and the voltage across the load...

It turns out that in this "static" circuit, both elements (IV curves) are on equal footing... either the diode or resistor can serve as a load... and we should not call them with such specific names ("load line" and "generator line")...

For example, if we vary the voltage, the diode can be considered as a (non-linear) load... and v.v., if we somehow vary the diode VF (e.g., by heating it), the resistor can be considered as a load. In the first case, the resistor will be represented by a moving generator line and the diode - by a static load "line"; in the second case, the  resistor will be represented by a static load line and the diode - by a moving generator "line".

And finally, if we vary the resistance, the diode will act again as a load with a static load "line"... and the resistor - as a "generator" with a rotating load line...

Interesting reincarnations of the elements...

Josef,

What can be complicated in the humble voltage divider circuit? There are two equal elements (resistors) with equal IV curves (lines)... Each of them can act either as a "generator" or a load...

Load line can used for any nonlinear device (not necessarily electronic devices). It brings the constraint from other parts of the circuit (e.g., Thevenin equivalent for simplicity) in a lumped fashion which exert on the non-linear device. In my previous answer, I was explaining the basic DC (static) load line of diode which is the load line of the Thevenin DC equivalent circuit, Current and voltage still follow the Kirchhoff's voltage law applied to the resistor and voltage source (Rth and Vth). For a series circuit (Vth, Rth and Diode), current is the same through the circuit, and the voltage at diode's terminals must be the same. This can only be true if the operating point (Q-point) of the circuit will be at the intersection of diode I-V characteristic curve with the load line. 

You objected "...we should not call them with such specific names." what you suggest?

Impressive explanations, Mahmoud... this is exactly what I think, "feel" and imagine! And you are a remarkable person because you somehow managed to activate my creative thinking.

There is some kindness in your comments... something as a constructive rather than destructive opposition... that makes me develop my ideas... аnd not to fall into despondency, despair, and depression... reaching out to the thought of the futility of what I do... So thank you again!

I hope you understand my goal - it is not the very term (load or generator line) оr the equation, but rather the physical nature of what lies behind this representation.To do it, I try to break the conventional "textbook" presentation and take a look at the problem from a different perspective. 

Incidentally, I began to think on it in the early 90's. Here is my first article dedicated to this problem. I photographed it by my phone a few minutes ago, especially for you (the only problem is that it is written in Bulgarian).

Well, let's try again to summarize the problem as go deep even deeper in it...

There are three elements connected in series - two "resistors" and one voltage source (if I had time, I would draw them in a form of a circle as in the attached picture). For the purposes of the equation, we must equate the momentary characteristics (voltage and current) of only two elements... but unfortunately, for some reasons, they are three:( So we have to reduce them to two by combaining two of them into one composed element. What can be this element?

1. First, we can combain the resistor (RC in my picture) and the voltage source (E) into a real voltage source ERC (with internal ohmic resistance RC). The other element - the transistor T, will act as a non-linear load.

So, in this "conventional arrangement", a real voltage source with linear internal resistance drives a load with non-linear resistance...

2. Then, we can combain the transistor T and the voltage source E into a real voltage source ET with internal non-linear resistance RCE. The other element - the resistor RC, will act as a linear load.

In this "unusual arrangement", a real voltage source with non-linear internal resistance drives a load with linear resistance...

3. Finally, we can combain the resistor RC and the transistor T into a composed "resistor" RCT. The other element will be the ideal voltage source E (with zero internal resistance).

So, in this most "unconventional arrangement":), an ideal voltage source with zero internal resistance drives again a load with (mixed) non-linear resistance.

That was the factual aspect of things seen by the side of circuitry. But for the purposes of the graphical presentation, we should accordingly groupe the IV curves of the elements... and somehow situate them in the coordinate system. Let's imagine it...

The first and second case are the same but mirrored. The third case should be quite different - the vertical IV curve of the ideal voltage source will intersect a composed IV curve (a sum of a linear and non-linear curve) of the non-linear load...

Josef,

This drawing is a gift from my students especially for you:) It remained yesterday on the blackboard after my last discussion (aka "lecture":) with them about the secrets of the famous long-tailed pair...

As you can see, it combines "three in one" (voltages, currents and circuit). Maybe I had to beautifully redraw it after the lecture (or at least, to clean better the blackboard)... but I chose to show it in its natural looks... I think that, in this raw form, it is even more impressive...

It would be very interesting to guess how many aspects of the circuit operation are imposed on this picture...

Cyril

Yes very nice, we can see a lot of work there :-))

Josef

Another picture shows a possible application of the Cyril's Current Rule (CCR) - any electrical current returns to where it left (a humor:)

And here is another more sophisticated version of the same idea...

Circuit building blocks (elementary passive "circuits") from the library below are used in these pictures. I gathered them a month ago, together with my students, during the first lectures on Basic electronics...