Talk:Circuit Idea/Voltage Compensation

The great idea of voltage compensation (a generalized circuit diagram).

Revealing the secret of circuits with voltage compensation (op-amp inverting circuits with negative feedback) is my first great achievement in teaching analog electronics. I would like to dedicate all my insights about this legendary idea that I will expose in this story to my love who inspires me to continue revealing the secrets of electronic circuits. Circuit-fantasist (talk) 06:26, 2 December 2008 (UTC)

History

Fig. 1. The first meeting with the inverting amplifier, 1976.

In the beginning of our discussion I would like to tell how I have managed to reveal the truth about these legendary electronic circuits as my story is quite indicative for education. This was not one-act process; I needed many years (from 70's to 90's) to think about these so popular circuits before to grasp the fundamental idea behind this great phenomenon. By presenting the evolution of my thinking about this great idea through time I would like to show how hard and even painfully is to reveal great circuit ideas. Maybe, this is the reason why nobody does this thankless job and why lecturers continue trying to "explain" circuits with formal methods. Imagine I published the truth about these circuits 12 years ago but I haven't still seen it somewhere on the web or in electronics books! Regretfully, circuits with parallel negative feedback remain still unexplained! If you don't believe me, write op-amp inverting circuits or some similar key words in Google window and try to find what the basic idea is behind them. Please, let me know if you have found even some rudiments of the basic idea; I'm eager to get familiar with the author! Well, here is my story...

Fig. 2. Beginning to reveal the secret of circuits with parallel negative feedback, 1989.

Learning without understanding

In 1976, as a student in Technical university of Sofia, I was working in a research laboratory where I had to design an electronic instrument for measuring mechanical vibrations. Then, for the first time, I struck the circuit of op-amp inverting amplifier and the concept of virtual ground in the book Emploi Rationnel Des Circuits Integres by Oehmichen J.P. (Fig. 1). I remember it looked quite strange for me; I didn't understand what the concept of virtual ground was, what it meant and how it arose. Two years later I began studying analog electronics; then I was trying without success to grasp the great idea behind this class of op-amp circuits with parallel negative feedback (op-amp inverting circuits). I remember I stayed after lections and asked the lecturer what was hidden behind all these formulas on the black board...but she can't answer me. I passed this examination perfectly and yet I didn't understand what the great idea was; I knew these circuits but actually I didn't understand them...

Teaching without knowing

In 1986, when I began teaching analog electronics to my students, I continued trying to reveal the secret of circuits with parallel negative feedback. The paradox was that I was accurately teaching them to pure students but...actually I didn't still understand them:) Now, I don't feel worried about this "educational phenomenon" as thousands of lecturers continue teaching their students in this manner - teaching without actually knowing the ideas behind circuits. What is more, thousands of electronic designers create well-working circuits without knowing the ideas behind them as well. So, I have finally stopped wondering at these paradoxes nowadays...

Gradually, I began sensing some rudiments of the great idea. In the circuit of op-amp inverting amplifier (Fig. 2a), I discerned the humble but so useful and elegant circuit of passive parallel voltage summer R1-R2 acting as "electrical scales" (Fig. 2b). Then, I understood how important is to show where currents flow in these circuits (Fig. 2c) and showed these insights in the student manual for laboratory exercises. Finally, I understood that the essence of the great voltage compensation idea is hidden in the two elements: the very op-amp and the element connected between the op-amp's output and its inverting input. In the case of op-amp inverting amplifier, they constitute the famous op-amp inverting current-to-voltage converter (transimpedance amplifier).

I remember, it was maybe in 1988, I showed to students that the two voltage sources in the op-amp inverting amplifier (the input voltage source and the op-amp output acting as another voltage source) are connected in series with opposite polarities. Then, a curious student that was looking at Fig. 2b cried out, "But the two voltages are summed!" I was deeply impressed by his insight and began thinking about this strange fact.

Fig. 3. Realizing the great idea of voltage compensation, 1992.

Realizing the great idea

It looked strange but although the two voltages had opposite polarities they were summed; the output voltage was added to the input one! "What did it mean?", I began thinking with feverish haste. Thus, in the end of 80s, I began realizing the great "input voltage helping" idea:

In all the op-amp circuits with parallel negative feedback (op-amp inverting circuits) the op-amp is connected with the purpose to "help" the input voltage source. The op-amp adds as much voltage to the input voltage as it loses across the "disturbing" element connected between the op-amp's output and its inverting input.

This was the truth about these legendary circuits! Imagine I needed as many as 15 years to reveal it! I suppose this insight into the great idea conceived in my mind in the early 1990s. Then I was writing down all the ideas arising in my mind on squared sheets of A5 paper. I have scanned especially for you the yellowed record (Fig. 3) that I made on May 14, 1992 at my home. As you can see, I have written there the same 3 stages of building the circuit of a current-to-voltage converter that I have showed in the present story about this legendary circuit (see also another story).

Fig. 4. The first paper about the voltage compensation idea, 1997.

Generalizing the "helping" idea

In the middle 90's, I realized how great the "helping" idea was; I had the feeling that I had managed to reveal a great natural phenomenon that was widely used in analog electronics. I began seeing it everywhere around me where people overcome various disturbances by injecting additional energy; that was the ubiquitous "removing a disturbance by an antidisturbance" idea. Thus I gradually managed to build my own philosophy about how to transform any passive circuit into an inverting op-amp one, the relation between passive and active versions.

In the end of 90's, I had the good fortune to buy the Hayes's student manual where I saw some interesting thoughts about these op-amp circuits. Then I was impressed by his insights about passive circuits (page 185 - ...the circuit of passive RC integrator failed to the extent that Vout moved away from ground but the output had to move away from ground, in order to give an output signal...) although he hadn't revealed the secret of the corresponding active versions (page 185 - ...the op amp integrator solves the problem elegantly, by letting us tie the cap's charging point to 0 volts, while allowing us to get a signal out; "virtual ground" lets us have it both ways...) and he hadn't showed the relation between the passive and active versions. Nevertheless, I had the feeling that I had finally met an adherent and I sent my work to him. Alas, Mr. Hayes had lost an interest in revealing the basic circuit ideas...

Fig. 5. Investigating a circuit with negative feedback, 2008.

Disseminating the great idea

In 1997, I began propagating the "helping" idea. First, I decided to show my philosophy (Fig. 4) to my colleagues at ELECTRONICS'2007 conference but I hadn't their approval. Nevertheless, I continued presenting these circuits to students in this way...

During 2000-2001, I created two animated Flash tutorials about this phenomenon and a year later I uploaded them on my site of circuit-fantasia.com. In the first tutorial, I showed how to combine the elementary voltage-to-current converter, current-to-voltage converter and current summer, in order to build a compound passive voltage summer and then how to transmute it to the famous op-amp inverting summer. The second was an interactive Flash tutorial that showed how to transform any passive circuit into an inverting op-amp one.

In the beginning of 2006, I started Circuit stories on the whiteboard where I placed seven stories about this great phenomenon .

In 2006, I joined Wikipedia and created three stories dedicated to this idea and its applications.

In 2007, I started Circuit idea and created three similar but more informal stories in Circuit Idea.

In 2008, I joined my students to Circuit idea and we were studying this phenomenon during the laboratory excercises .

Basic implementation

The purpose of this story

Fig. 6. Creating the story about voltage compensation.

Here, I would like finally to generalize all these 20 specific stories into one great "philosophical" story about the voltage compensation idea; that is why I have started this discussion. In this story we have to extract the essence of the phenomenon and to present it in the most general way. Here, as usual, I will use my favorite hand-drawn pictures, in order to visualize the evolution of the idea. I draw them only by using color fiber pens (Fig. 6).

In the beginning, we might say that there are a great number of op-amp circuits that are grouped in various classifications. Usually, they are divided according to formal attributes e.g., according to their applications (amplifying, generating, converting, etc.) or according to their implementations (tube, transistor, op-amp, etc.) However, in Circuit idea we look for general principles behind circuits; so, we have to classify circuits according to these ideas. This classification is more meaningful than the formal classifications above.

What are these circuits based on the voltage compensation idea? These are all the op-amp circuits with parallel negative feedback or, in other words, all kinds of op-amp inverting circuits with negative feedback. In the first place, we might mention here the famous transimpedance amplifier, inverting amplifier, integrator and differentiator, logarithmic and antilogarithmic converter. It would be appropriate to place a list of the most popular circuits based on this idea.

What the problem is

If we scrutinize and generalize the operation of all these circuits, we will realize that they produce a current depending on a voltage in some definite way - constant, linear, non-linear, time-dependent, quantity-dependent. The first of them - "creating a constant current" is the most popular task. So, we might think of this module as a story about the famous constant current source. Well, let's begin building, step-by-step, a generalized circuit with voltage compensation.

Converting voltage to current

Fig.7. Converting voltage to current by a current-setting element.

What do we have? We have a voltage source. What do we want? We want to produce a current. So, in order to make a current flow, we have to close the circuit in some way. But we mustn't simply short the voltage source by a pice of wire as the current will be infinite and unpredicted. We want to obtain a current depending in some completely definite way on the voltage; we need some functional relation between the output current and the input voltage.

For this purpose, we have to close the circuit by an Element 1 setting the desired finctional relation (Fig. 7) so that it will set, form, shape the current as we want. Depending on the nature of this current-setting element we can obtain various devices acting as voltage-to-current converters: linear - a classic voltage-to-current converter (a resistor), a non-linear - an antilogarithmic converter (a diode), a time-dependent - an integrator (an inductor) and a differentiator (a capacitor), etc. We may also keep the voltage constant and to vary the magnitude of the element's attribute - a resistive sensor (a variable resistor). Finally, we may vary both the input voltage and the element's attribute - an "analog-digital multiplier" (a DAC with R-2R ladder).

Converting current to voltage

Fig.8. Converting current to voltage by a voltage-setting element.

By connecting the Element 1 (Fig. 7) we have already obtained a current I as a function of the input voltage V and the Element 1's attribute. But we need this current; we would like to consume it. In the simplest case, we connect the Element 2 acting as a current load that consumes directly the current I (an active ammeter). More frequently, we want to obtain now a voltage depending in a definite way on the current; we need some functional relation between the output voltage and the input current.

For this purpose, we have to insert another Element (2) setting the desired finctional relation (Fig. 8) so that it will set, form, shape the output voltage as we want. Again, depending on the nature of this voltage-setting element we can obtain various devices acting now as the inverse current-to-voltage converters: linear - a classic current-to-voltage converter (a resistor), a non-linear - a logarithmic converter (a diode), a time-dependent - a differentiator (an inductor) and an integrator (a capacitor), etc. We may also keep the voltage constant and to vary the magnitude of the element's attribute - a resistive sensor (a variable resistor). Finally, we may vary both the input current and the element's attribute - an "analog-digital multiplier" (a DAC with R-2R ladder).

Solving the problem

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(a copy from a Wikipedia talk page): Circuit-fantasist (talk) 06:40, 17 March 2009 (UTC)

Here, we solve the well-known problem - how to obtain a constant current. There isn't any problem, if we drive the imperfect current load by a perfect current source or, if we drive a perfect current load (shorted output) by an imperfect current source. There is a problem in our situation as we drive the imperfect current load by an imperfect current source. How to solve the problem?

You say, "A current source is a current source, the voltage required to create the current is continuously varying (if necessary) to produce the desired current." Right, this is one of the possible ways of creating a constant current source - by simple varying the excitation voltage or by negative feedback (the best solution). In this arrangement, the excitation voltage source (as a part of a constant current source), increasing additionally its voltage, compensates the losses into the imperfect current load (and not only them). It is wonderful! Unfortunately:(, in the most cases, we can't do that trick as we just can't reach (can't drive) the excitation voltage source! An analogy: can we control the sun, in order to adjust the light or the temperature inside the room:)?

That is why, we apply more frequently the other trick - we connect an additional voltage source, which compensates (only the local) losses into the imperfect current load. An analogy: we connect additional light or thermal sources inside the room, in order to "help" the sun (instead to control directly it): In this way, we actually convert the imperfect current load into a perfect one with zero resistance (a kind of an active "superconductor":) You probably guest that using this technique, we can make almost ideal diodes without VF, "botomless" capacitors with infinite capacitance, perfect ammeters with zero resistance etc. Another advantage of this trick is using the compensating "anti-voltage" as an output voltage; so that we can connect as much low resistance load as we want - see the explanations below. --Circuit-fantasist 10:30, 29 July 2006 (UTC)

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Connecting an additional "helping" voltage source...

Fig.9. Where do we connect the "helping" voltage source?

...under the input voltage source? NO!...

Fig.10. ...under the input voltage source? NO!

...above the input voltage source? NO!...

Fig.11. ...above the input voltage source? NO!

...above the Element 2? NO!...

Fig.12. ...above the Element 2? NO!

...under the Element 2? YES!

Fig.13. ...under the Element 2? YES!

Generalization

Circuits with voltage compensation consist of three components connected in series: a passive Element 1, a passive Element 2 and a "helping" voltage source V_H(Fig. 13). The Element 1 converts the exciting (input) voltage V into a current I and the Element 2 converts back the current into a voltage drop V_E2; we need it... but it disturbs the current. So, the "helping" voltage source V_H compensates the "disturbing" voltage drop V_E2 by adding the same voltage to the exciting voltage source V; as a result, the Element 2 is "neutralized" and the current depends only on the exciting voltage and the Element 1. If we need a current output, we connect the current load in the place of the Element 2; if we need a voltage output, the compensating voltage V_H can serve as a perfect "mirror" output voltage - powerful, grounded and inverting.

Real op-amp implementation...

...by using negative feedback.

An implementation of the voltage compensation idea.

Generalization

Most of the circuits with voltage compensation are implemented as op-amp circuits with parallel negative feedback where the op-amp (including the power supply) serves as a "helping" voltage source. It compensates the "disturbing" voltage drop across the Element 2 by adding the same voltage V_H = V_E2 to the exciting voltage source V. The compensating voltage is negative with respect to the ground; so, all these op-amp circuits are inverting.

A negative impedance viewpoint at the voltage compensation idea

A generalized electrical circuit

Fig. 14. Great insight - the "helping" voltage source acts actually as a negative impedance element!

Yesterday morning, strolling along the park, thinking aloud and recording my thoughts about the voltage compensation idea, I gained suddenly a new insight into this great phenomenon. I realized that the "helping" voltage source in this arrangement acts actually as an element with negative impedance! I am deeply moved by my new insight and would like to share it with you! Circuit-fantasist (talk) 10:35, 1 January 2009 (UTC)

Look again at the right part of the generalized circuit showing the voltage compensation idea (Fig. 14). It consists of two series connected elements: the Element 2 and the "helping" voltage source V_H. The same current flows through the two elements and the same voltage appears across them; so, they process the same energy and they have the same impedance. But while the first of them is a passive element that consumes energy from the input voltage source, the second is an active element that adds the same energy to the input voltage source! Then, if the first element has "positive" impedance Z, the second one has negative impedance -Z. The negative impedance element neutralizes the positive impedance element; the result is zero impedance and a virtual ground appears between Element 1 and Element 2!

Eureka! I have finally realized the simplest technique for creating negative impedance:

Copy the voltage drop across an "original" passive element by a voltage follower and "insert" the "copy" voltage into the circuit to obtain negative impedance.

Imagine how powerful this negative impedance viewpoint is! Now we may draw important conclusions:

In electronic circuits with voltage compensation, the compensating voltage source acts as a negative impedance element. More particularly, in op-amp circuits with parallel negative feedback (op-amp inverting circuits), the combination of the op-amp and the power supply acts as a negative impedance element.

How simple it is! I wonder how I have not never yet realized this simple truth about op-amp invertin ciruits! Well, let's consider some examples.

Implementation

Fig. 15a. How to create the simplest current-driven negative resistor without using a negative feedback.

Fig. 15b. Creating the simplest current-driven negative resistor by applying a negative feedback.

A negative resistor

Fig. 16. An op-amp acting as a negative resistor.

In a transimpedance amplifier containing a resistor with "positive" resistance R, the combination of the op-amp and the power supply acts as a negative resistor with negative resistance -R;

A negative diode

Fig. 17. An op-amp acting as a negative diode.

In a logarithmic converter containing a diode with "positive" non-liner resistance R_D, the combination of the op-amp and the power supply acts as a negative diode with negative resistance -R_D.

A negative capacitor

Fig. 18. An op-amp acting as a negative capacitor.

In an op-amp inverting integrator containing a capacitor with capacitive reactance X_C - as a negative capacitor with negative capacitive reactance -X_C.

A negative inductor

Fig. 19. An op-amp acting as a negative inductor.

In an op-amp inverting differentiator containing an inductor with inductive reactance X_L - as a negative inductor with negative inductive reactance -X_L, etc.

List of the most popular op-amp circuits based on this idea

Linear: active ammeter, voltage-to-current converter, current-to-voltage converter (transimpedance amplifier), resistance-to-current converter, resistance-to-voltage converter, analog amplifier, inverting amplifier, summing amplifier, DAC with R-2R ladder.

Non-linear: RD logarithmic converter, DR antilogarithmic converter.

Time-dependent: C integrator, RC integrator, charge amplifier, CR differentiator, LR integrator, L differentiator, RL differentiator.