Talk:Circuit Idea/Revealing the Mystery of Negative Impedance

Starting the page
I have placed a great amount of text from the related Wikipedia page about negative impedance to start the page. Circuit-fantasist (talk) 06:23, 5 February 2009 (UTC)

I have written the text below in the old Wikipedia talk page about negative resistance. Circuit-fantasist (talk) 16:13, 3 March 2009 (UTC)

New insights into the great phenomenon
(A copy from an old Wikipedia talk page about negative resistance)

The great voltage compensation idea
(see also the discussion about the relevant Circuit idea story)





I think revealing the secret of circuits with voltage compensation is my first great achievement in teaching analog electronics (saying circuits with voltage compensation I mean op-amp circuits with parallel negative feedback or, in other words, all these popular op-amp inverting circuits with parallel negative feedback - an inverting amolifier, an integrator, a differentiator, a logarithmic converter, etc.) I grasped this powerful, intuitive  and extremely simple idea in the end of 80s and from then I have been creating a great many various materials, in order to popularize it. Finally, I decided to generalize all my insights about the great idea into one "philosophical" story and started a discussion in Circuit idea wikibook a month ago. Well, here is the secret of these legendary circuits:

General idea. Circuits with voltage compensation consist of three components connected in series: a passive Element 1, a passive Element 2 and a "helping" voltage source VH. 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 VE2; we need it... 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, 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 VH can serve as a perfect "mirror" output voltage - powerful, grounded and inverting.

Implementation. 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 VH = VE2 to the exciting voltage source V. The compensating voltage is negative with respect to the ground; so, all these op-amp circuits are inverting. Circuit-fantasist (talk) 15:14, 11 January 2009 (UTC)



Another great idea: negative impedance
I have finally realized how to expose the great idea of negative impedance by using lucid explanations based on human common sense and intuition. IMO, in the beginning, we have to show in the most general way what the ordinary "positive" resistance is and what the odd negative resistance is by comparing the two electrical attributes. For this purpose, we may reason as folows.

What a "positive" impedance is...
In electrical circuits, passive elements (resistors, capacitors and inductors) impede current by their inherent resistance, capacitance and inductance (impedance is the combination of them). As a result, voltage drops appear across the passive elements that represent the energy losses in them. Passive elements absorb this energy from the exciting electrical source: resistors dissipate energy from them to outside environment while capacitors and inductors accumulate energy into themselves. For the purposes of this article it is no matter if passive elements dissipate or accumulate energy; it is only important they absorb energy.









''I cannot stop using a funny analogy to picture these properties (don't worry, I will not place it in the main article:) You know, in every society, there are such bad people that steal. Some of them spend immediately what they have stolen while others steal up the swag. But for us (the victims) it is no matter if they spend or store the swag; for us it is only important that we have lost our property:(''

In circuitry, we may connect elements in series or in parallel or mixed. For example, if we connect a resistor R in series with a load (Fig. 3a), a voltage drop VR = R.I that is proportional to the current appears across the resistor. If we connect a capacitor or an inductor, voltage drops changing through time appear across them.

Conversely, if we connect the resistor R in parallel with the load (Fig. 3b), a current IR = VL/R that is proportional to the voltage flows through the resistor. If we connect a capacitor or an inductor, currents changing through time flow through them. Circuit-fantasist (talk) 15:14, 11 January 2009 (UTC)

Let's see the graphoanalytical interpretation of the circuit operation by superimposed IV curves on Fig. 4. When the input current/voltage varies, the crossing operating point slides over an IV curve representing the "positive" resistance. It is a real IV curve having a positive slope and passing through the origin of the coordinate system.



...and what a "negative" impedance is
Elements with "negative" impedance do the opposite - they inject energy into electrical circuits. While passive elements with "positive" impedance absorb energy from the input source (they are loads), the elements with "negative" impedance add energy to the input source (they are sources). While voltage drops appear across "positive" elements, negative elements produce voltage; while "positive" elements sink current, negative elements produce current. Only, they are not ordinary, steady sources; they are varying sources (voltage sources whose voltage across them depends on the current through them or current sources whose current depends on the voltage across them).









Above (Fig. 3), we connected the "positive" resistor R in series with the load; so, a voltage drop VR = R.I that is proportional to the current appeared across the resistor. Let's now connect a negative resistor -R in series with the load (Fig. 5a). As a result, a voltage VH = VR = R.I that is proportional to the current appears across the negative resistor. Only, while above the resistor R detracts the voltage V from the input voltage (V is a voltage drop), here the negative resistor -R adds the same voltage V to the input voltage (here V is a voltage). The element named "resistor" is really a resistor while the "negative resistor" here is actually a voltage source, whose voltage is proportional to the current passing through it. If we connect a negative capacitor or a negative inductor, voltages changing through time appear across them (the negative elements generate these voltages).

''A negative resistor can be a voltage source, whose voltage is proportional to the current passing through it (a two-terminal current-controlled voltage source). This is a current-driven negative resistor.''

Contrary, if we connect the negative resistor in parallel with the load (Fig. 5b), the same current as above IR = VL/R that is proportional to the voltage drop across the load flows through the negative resistor. However, while above the resistor R sinks the current from the input current (diverts it from the load current), here the negative resistor -R ads the same current to the input current (injects an additional current into the load). If we connect a capacitor or an inductor, currents changing through time flow through them.

'' A negative resistor can be also a current source, whose current is proportional to the voltage across it (a two-terminal voltage-controlled current source). This is a voltage-driven negative resistor.''

Let's see the graphoanalytical interpretation of the circuit operation by superimposed IV curves on Fig. 6. When the input current/voltage varies, the voltage/current source representing the negative "resistor" changes its voltage/current. As a result, its IV curve moves and the crossing operating point slides over a new dynamic IV curve representing the negative resistance. It is not a real IV curve; it is an artificial, imaginary IV curve having a negative slope and passing through the origin of the coordinate system.

Circuit-fantasist (talk) 10:55, 24 January 2009 (UTC)



How to create the simplest current-driven negative impedance element...
Negative impedance elements are wonderful... but there is only a little problem:) with them - there are not such elements in nature; there are only ordinary, passive elements with "positive" impedance. So, we have to make them... and this is the most interesting part of this discussion. Well, how do we create negative impedance elements?

The idea is extremely simple, clear and intuitive; it is so plain that it is even... invidious:) Only, I don't know why I needed years of time to realize it as all we need to grasp it is only our human common sense! I began thinking about negative resistance phemomenon in the early 90s... and realize this simple truth only in the end of 2008! Why the simplest things in this world are the most unintelligible and ununderstandable? But let's begin thinking!

Well, we have an element with "positive" impedance (a resistor, a capacitor or an inductor) but we need an element with negative impedance (a negative resistor, a negative capacitor or a negative inductor). A voltage drop appears across the "positive" element that depends on the current passing through it in a some definite way (linear, non-linear or time-dependent); the same voltage (depending in the same way on the current) has to appear across the negative element. What do we have to do then?

...without using a negative feedback...
''I cannot stop relying again on the funny analogy above to extract the solution (don't worry, I will not place it in the main article:) Imagine there are bad people that steal but we need good people with the opposite behavior (to grant instead to steal), in order to "neutralize" the wickedness of the bad people. But imagine there are not such people; so, we have to create them. For this purpose, we take some bad person as an "original" and make an inverse "copy" of his/her behavior. The paradox is that, in order to make goodness, we need wickedness! But what do we do if there are not good people:)?''



Of course, we have only to "copy" the voltage drop across the "positive" element and to "insert" this voltage into the circuit so that to "help" the input voltage source! All we need to do this donkey work is only a bare voltage follower (including its power supply) - Fig. 5! In this arrangement, the voltage drop across the "positive" element PE2 is the "original"; the voltage across the negative element NE2 is the "mirror copy".

Eureka! We have invented the simplest technique for creating a negative impedance; we know already what the simplest negative impedance element contains:

The simplest element with negative impedance consists only of two components: an element with "positive" impedance and a voltage follower that is the actual negative impedance element.

Note the "positive" impedance element is necessary but it does not belong to the negative impedance element in this arrangement (compare with the 2-terminal negative impedance element below):

Let's look at this idea from another viewpoint. The current-driven negative impedance element is actually a current-controlled voltage source with a specific relation between the voltage and current (linear, non-linear or time-dependent). So, it has to measure in some way the current flowing through it and to convert it to a voltage according to the desired function. For this purpose, the negative impedance element needs a functional current-to-voltage converter and the positive impedance element serves exactly as such an exotic converter.

The simplest negative impedance element exploits the available "positive" impedance element as a functional current-to-voltage converter.

Is there a feedback in this arrangement? There is only a slight positive feedback as we have not a large amplification. Let's consider it. When we increase the input voltage V, the current increases and the voltage drop VPE begins increasing as well. The voltage follower copies and adds it to the input voltage. As a result, the current increases thus incrasing the voltage drop.

We just need a bare voltage follower; it might be a poor transistor amplifier with amplification 1... but it has to amplify exactly 1 time. The only way of doing that is the ubiquitous negative feedback... Circuit-fantasist (talk) 07:12, 13 January 2009 (UTC)





...by using a negative feedback.
Of course, negative feedback is the most perfect technique for making voltage followers. In this arrangement (Fig. 6), we have made an op-amp compare its output voltage VNE (by subtracting) with the voltage drop VPE2 across the positive element and change it so that the difference between them is always (almost) zero. As a result, the op-amp output voltage is a copy of the voltage drop across the positive element. Note the op-amp may have a bare single-ended input as its input voltage - the difference VPE2 - VNE, is measured regarding to the ground.



Putting into practice the simplest negative impedance element
The amazing feature of this arrangement is that negative impedance "neutralizes" the same positive one; as a result, the whole combination of the two elements has zero total impedance. This is the most important use of the negative impedance phenomenon - to destroy, remove, annihilate, neutralize the ordinary positive impedance by an equivalent negative one. For example, all the circuits with voltage compensation (op-amp inverting circuits) exploit this technique (see below). Accordingly, there is zero voltage drop across this zero impedance element and the famous virtual ground (great circuit phenomenon) appears above the positive element 2. The virtual ground represents the result of the "neutralization".



In order to see the benefits of using the simplest negative impedance element, let's discover a well-known problem from circuitry - how to make perfect voltage sources with zero internal resistance. Real voltage sources have some internal resistance; in addition, there is some line resistance between the source and the line. As a result, the load voltage droops when the source is loaded as disturbing voltage drops appear across the internal and line resistances. That is why, in electronics, we frequently need voltage sources and conductors having zero internal "positive" resistance.

The classical solution is to buffer the imperfect voltage source by a powerful voltage follower. But we have to place the buffer at the end of the line, near the load; frequently, this is just impossible. What do we do then?

The more exotic and sometimes, more useful solution is to compensate the internal resistance by an equivalent negative resistance. For this purpose, we might use the simplest negative resistor that we have created above, i.e., a transimpedance amplifier with resistor Ri (the internal resistance). In this arrangement (Fig. 7), the op-amp compensates the voltage drop across the "positive" resistance Ri by adding the same voltage in series to the input voltage source.



Comparing the general ideas...
A month ago, I started a discussion about the great voltage compensation idea in Circuit idea wikibook. I used Christmas holidays to rationalize all I have known and collected about this great phenomenon through years. On December 31, at the top of the New Year, 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 and more particularly, in all the 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!





Look again t Fig. 1 and Fig. 8 to compare the two great ideas and to convince yourself that they are absolutely identical.

Voltage compensation (see the copy of Fig. 1 on the left) means to compensate the "disturbing" voltage drop VE2 across the passive Element 2 by adding the same voltage to the exciting voltage source V by a "helping" voltage source. As a result, the Element 2 is "neutralized" and the current depends only on the exciting voltage and the Element 1.

Negative impedance (Fig. 8) means to compensate the "disturbing" voltage drop VE2 across the Element 2 with "positive" impedance by adding the same voltage to the exciting voltage source V by a "mirror" element with negative impedance. As a result, the "positive" impedance Element 2 is "neutralized" again and the current depends only on the exciting voltage and the Element 1. Now, don't you think negative impedance is voltage compensation and v.v., voltage compensation is negative impedance?

In electronic circuits with voltage compensation, the compensating voltage source acts as a negative impedance element and v.v., in electronic circuits with negative impedance, the negative impedance element acts as a compensating voltage source.

'In all the circuits with voltage compensation, there are two elements connected in series: one with "positive" impedance and other with the same but negative one. The total impedance of this combination is zero.'



...and the specific op-amp implementations




Now, should I convince you very much that in all these popular op-amp inverting circuits the op-amp, in combination with the power supply, acts actually as a negative impedance element? See for example the legendary circuits of transimpedance amplifier, inverting amplifier, diode antilogarithmic converter, capacitive differentiator and inductive integrator (Fig. 9). All they contain various elements (a resistor, a diode, a capacitor and an inductor) acting as Element 1 from the generalized voltage compensation circuit (Fig. 1), an ordinary "positive" resistor R acting as Element 2, an op-amp and a power supply. Here, the combination of the op-amp and the power supply acts as a negative resistor with negative resistance -R that "neutralizes" the "positive" resistance R (the negative resistor -R adds as much voltage as it loses across the positive resistor R).





Or see another legendary circuit - the capacitive op-amp inverting integrator (Fig. 10). Here, the combination of the op-amp and the power supply acts as a negative capacitor with negative capacitive reactance that "neutralizes" the "positive" capacitive reactance (the negative capacitor adds as much voltage as it accumulates in the positive capacitor).

Similarly, in the circuit of the op-amp inverting logarithmic converter (Fig. 11), the op-amp acts as a negative diode; it adds a forward voltage VF to the input voltage instead to subtract a voltage drop from the input voltage. In the circuit of the op-amp inverting inductive differentiator (Fig. 12) the op-amp acts as a negative inductor, etc. So, we may generalize this great insight into op-amp inverting circuits with negative feedback as a final conclusion:

'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. It is a "mirror" copy of the positive impedance element connected between the op-amp's output and the inverting input. The two elements (the "positive" and the negative one) are connected in series so that the total impedance of this combination is zero.'



What does this viewpoint mean?
Just imagine what this negative impedance viewpoint at op-amp inverting circuits means! Now, negative impedance does not look already as a "black magic"; it is not already that mystic, odd, strange, exotic and ununderstandable circuit phenomenon! No one can already take unfair advantage of it as it is an everyday phenomenon that we may see in every circuit with parallel negative feedback! We have unveiled the mystery of negative impedance; we are just the boy from Andersen's story who says, "The King is naked!":)



What the problem is
Finally, we have arrived at the most interesting part of our discussion. Here, we will unveil the mystery of the conventional negative impedance elements - the so called negative impedance converters (NIC). IMO, they are the most interesting, odd, strange and even "mystic" electronic circuits, which are still unexplained; they are real nightmares for students and for their teachers:) I have not still met some "human-friendly" explanations of this legendary circuit on the web or in the books (if you have found, let me know). Even the famous Mr. Horovitz has not explained (although mentioned) it in his bestseller The Art of Electronics (see page 251). Instead, he has afforded this opportunity to his students; maybe, he had hoped they would help him:)?

Well, what the problem is? We have already made the simplest element with negative impedance (Fig. 5). Then, why do we need another negative impedance element?

See again Fig. 7 where we have used a transimpedance amplifier to make a perfect voltage source with zero internal resistance. Thes solution seems perfect but it has one great disadvantage: the op-amp needs a third wire to measure the internal voltage drop; sometime this is impossible (in the case of compensating the internal resistance) or inconvenient (in the case of compensating the line resistance). What do we do then?

The general idea
Obviously, we have to create a more sophisticated 2-terminal negative impedance element so that we can insert it at any place along the line. How do we make it? Maybe, the funny analogy above will give a hint to us?

'' Well, imagine the bad person acting as an "original" is far away and we cannot observe his/her behavior, in order to make an inverse "copy". What do we do then? Of course, we may take another bad person that is near at hand as an "original" and make again an inverse "copy" of his/her behavior. But now it has to be 2 times bigger "copy", in order to "neutralize" the wickedness of the two bad persons!



Let's use this clever trick to create a true 2-terminal negative impedance element for the same purpose - to make a perfect voltage source with zero internal resistance. Now, we need two components (Fig. 13): an additional near resistor with "positive" resistance R = Ri and a voltage amplifier with amplification K = 2 (including its power supply). The amplifier produces two times higher voltage; half the voltage compensates the voltage drop across the near resistor R = Ri; the other half the voltage compensates the voltage drop across the remote resistor Ri. As a result, the total internal resistance is zero.

Eureka again! We have invented another clever technique for creating a negative impedance; we have already known what the negative impedance element contains:

The element with negative impedance consists of two components: an element with "positive" impedance and a doubling voltage amplifier.

It is a paradox but it is true: Every element with negative impedance contains an element with the same "positive" impedance.

As above, this current-driven negative impedance element is actually a current-controlled voltage source with a specific relation between the voltage and current (linear, non-linear or time-dependent). It needs a functional current-to-voltage converter to measure the current flowing through it. Above, we used the accessible "positive" impedance element as such an exotic converter. Here, we have not such an element; so, we connect another identical "positive" impedance element (a duplicate) acting as such a converter.



The implementation


We have to make the op-amp produce two times higher output voltage than the "mirror" voltage drop across the "copy" resistor R = Ri. The op-amp will do this "magic", if we make it compare 1/2 of its output voltage with the "mirror" voltage drop across the "copy" resistor. For this purpose, let's connect a voltage divider consisting of two equal resistors R between the op-amp output and the non-inverting input (Fig. 14).



General idea






Implementation






A copy from the Wikipedia talk page about negative resistance
I have written the text below from Archive_4 talk page about negative resistance. Circuit-fantasist (talk) 19:00, 4 March 2009 (UTC)

The most typical properties of the negative impedance phenomenon as follows:


 * Negative impedance element is an electronic circuit, not an element (a component). There are not true negative impedance elements; there are only negative differential resistance elements.


 * Negative impedance element is a two terminal (1-port) electronic circuit


 * Negative impedance elements are sources that inject energy into circuits while the according passive elements (resistors, capacitors and inductors) absorb energy from circuits


 * Negative impedance element is not an ordinary, steady source; it is a dynamic source:
 * it may be a dynamic voltage source that produces voltage depending on the current passed through it in the same way as the voltage across the resistors, capacitors or inductors depends on the current passed through them;
 * it may be also a dynamic current source that produces a current depending in the same way on the voltage applied across it as the current passed through the resistors, capacitors or inductors depends on the voltage applied across them.


 * Negative linear resistance is a special but the most popular case of the negative impedance phenomenon


 * There are also non-linear negative resistors (e.g., "negative diodes")


 * Also, we have to mention the most typical applications:
 * Elements with negative impedance are used mainly to compensate the losses in elements having the same "positive" impedance

Please, comment my insertion. Circuit-fantasist (talk) 09:15, 28 January 2009 (UTC)

What negative impedance is
(a copy from the Wikipedia talk page about negative resistance) Circuit-fantasist (talk) 17:35, 4 March 2009 (UTC)

Thank you for your reaction to my work. I appreciate your efforts to improve the page about negative impedance and invite more Wikipedians to join this discussion. All we have the same goal - to show the truth about negative impedance (resistance) phenomenon. I will first comment thoroughly your contentions (in bold and italic) and then I will draw general conclusions. I have also saved below your insertion from the article. Circuit-fantasist (talk) 17:36, 7 February 2009 (UTC)

"Negative Impedance is an alternative description of an electronic effect called Negative Resistance. Impedance, however refers to the frequency dependent resistance of a component.   Components and materials that display a negative resistance effect may have frequency dependent properties as well.   There is no contemporary research in this area and so it might be assumed that the term is a holdover from the 19th Century."

...The impedances of capacitors and inductors have opposite signs when circuits are analyzed incrementally... Maybe, the main problem here is that you think in terms of classical electricity while I think in terms of electronic circuitry. In the area of negative impedance phenomena, it is the custom to say that all natural passive components (resistors, capacitors and inductors) absorbing energy from the input source have "positive" impedance (or just impedance in the wide sense of the word, not only as an opposition to a sinusoidal alternating current); so, from this viewpoint, the impedances of capacitors and inductors have the same positive signs. Conversely, the artificial electronic circuits (negative "resistors", negative "capacitors" and negative "inductors") behaving in an opposite way (adding energy to the input source in the same manner as the according passive components) have a true "negative" impedance.

This classification regards to the way of processing energy - "positive impedance" means consuming while "negative impedance" means producing energy. From this viewpoint, "positive impedance" means "ordinary impedance" while "negative impedance" means something opposite as "inverse impedance", "opposite impedance" or "anti-impedance". Then "capacitor" and "inductor" mean elements that absorb energy from the input source and accumulate it into themselves.

This concept is extremely simple, clear and intuitive if we think in terms of voltages when we apply a constant input voltage to the elementary RC and RL circuit. Then, voltage drops appear across capacitors and inductors; they change in a different (opposite) way through time but both they are voltage drops. Conversely, voltages appear across negative capacitors and inductors; they also change in a different (opposite) way through time but now both they are voltages, not voltage drops.

Well, I would like to ask you what a negative impedance converter does. What does it convert? Does it make a capacitor behave as an inductor and v.v., an inductor as a capacitor? No, it doesn't. A gyrator can do this magic. A negative impedance converter can make capacitors and inductors behave as sources (negative impedance elements) instead as passive elements having positive impedance. I hope all these pages listed by Google will persuade you what negative impedance means in this area.

...This is why resonant circuits work - the inductive and capacitive impedance cancel each other out at their resonant frequency... This is a formal explanation of the unique resonance phenomenon that does not explain anything... But let's leave this discussion or move to the according talk page where Wjbeaty has tried to explain the great phenomenon in such an intuitive manner (...a paired coil/capacitor acts as a passive oscillator which essentially sends out an inverse copy of the incoming signal...) as I try to explain here the no less great negative impedance phenomenon. Although there is some resemblance between them the negative impedance phenomenon is quite different from the resonance phenomenon: negative impedance is a process of injecting additional energy (by an additional outer source) while resonance is a process of using a treasured energy (it is drawn by the input source, not by another source). If you want to say something about resonance here, say that negative impedance is extremely useful for resonant circuits as LC generators are based on the combination resonator + negative resistor.

...An Ohmic device always has a positive impedance... Of course, I second this assertion; who has said the opposite? Only electrical sources can possess true negative impedance.

...There is no way of creating a resonant circuit with resistive devices... Who has said the opposite? There is no such assertion in the article.

...Previously this was extremely overdone,... What do you want to say? Negative impedance (resistance) phenomenon is very, very important. For example, all the op-amp inverting circuits (1,020,000 pages showed by Google) based on the presence of virtual ground (have I to list them?) exploit this powerful idea (of course, if you can see it), the legendary Howland current source (pump) (46,000 pages) and Deboo integrator (4,000 pages) are negative impedance circuits (again, if you are able to discern the great idea), telephony line reperitors are negative "resistors" connected in series...negative impedance converters (120,000 pages), gyrators...have I to continue? The ubiquitous virtual ground phenomenon (448,000 pages!!!) is based on the negative impedance phenomenon; it is a result of "neutralization" between opposite impedances - "positive" and "negative". However, negative impedance (especially true negative impedance) is not explained in a satisfactory way somewhere on the web; there are only particular speculations mainly about differential negative resistance. As a rule, the authors don't distinguish the two kinds of resistances although they are completely different by their nature. See in forums how many people (425,000 pages!!!) want to know what a negative impedance (resistance) is! All they ask, What is a negative resistance?, Does the resistance can be negative?, Have you heard about negative resistance?, etc. So, negative impedance phenomenon deserves to be explained satisfactory. Circuit-fantasist

Negative resistance versus negative impedance
(a copy from the Wikipedia talk page about negative resistance) Circuit-fantasist (talk) 18:45, 4 March 2009 (UTC)

It is obvious there are two concepts - general (negative impedance) and more particular (negative resistance); negative impedance comprises negative resistance. Obviously, there are two possible ways of exposing the topic - deductive (moving from top to down) and inductive (moving from down to top). The first means to present negative impedance as a main (more general) idea and negative resistance as a special case; the second (your suggestion) means to present the specific negative resistance as a main (more used) idea and to generalize it into negative impedance. I chose the first when I moved and redirected the negative resistance to negative impedance page a month ago. But, in the course of time, I have been gradually realizing that the second viewpoint is more acceptable. Really, negative resistance is more widespread concept than negative impedance and the term is in general currency. So, I agree with you and will reword my edits.


 * Finally, don't you think it's time to consider the main problems - how to distribute the content between the three existing pages about negative resistance phenomena (negative resistance, negative differential resistance and negative impedance converter) and how to structure these articles? Circuit-fantasist (talk) 23:11, 21 February 2009 (UTC)

What does "to understand circuits" mean?
It is more than obvious that, in order to create this part of the article, we (Wikipedia editors, responsible for it) have to understand all these op-amp circuits. Otherwise, it would be very confusing if we "explain" these circuits to people but the very we do not know what the basic ideas behind them are. But what does "to understand circuits" mean?

Generally speaking, it means to find out all about each of the components constituting the circuit: why it is added to the circuit, what its function is, what it does, how it does it, what its value has to be, etc. Then we have to discern groups of components constituting familiar sub-circuits and to clarify its role. Especially for the present op-amp circuits we have to know the role of the positive impedance element connected between the op-amp output and the non-inverting input,  the role of the voltage divider connected between op-amp output and the inverting input and, of course, the role of the very op-amp. Please, answer the concrete questions below and suggest possible circuit explanations. Circuit-fantasist (talk) 15:37, 22 February 2009 (UTC)



Basic initial circuit
What does the resistor R do? What does the op-amp do? How does the circuit behave when connected in parallel to a load load with resistance R driven by a real input voltage source?





Negative resistor
What does the resistor R do? What do the resistors R1 do? What does the op-amp do? How does the circuit behave when connected in parallel to a load load with resistance R driven by a real input voltage source?





Negative capacitor
What does the capacitor C do? What do the resistors R1 do? What does the op-amp do? How does the circuit behave when connected in parallel to a load with capacitance C driven by a real input voltage source?





Generalized negative impedance circuit
What do positive impedance element Z do? What do the resistors R1 do? What does the op-amp do? How does the circuit behave when connected in parallel to a load with impedance Z driven by a real input voltage source?

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Negative "inductor"
What does the resistor R1 do? What do the resistor R1 do? What do the capacitor C do? What do the combination R1-C do? What does the op-amp do? How has the inductance achieved? How does the circuit behave when connected in parallel to a load with inductance L driven by a real input voltage source?

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Interesting thoughts about the negative impedance phenomenon
(Negative Impedance: What It Is and How It Works by Tom Bearden)

I have extracted these interesting thoughts about the negative impedance phenomenon from the Tom Bearden's article. Please, discuss. Circuit-fantasist (discuss • contribs) 20:15, 23 July 2012 (UTC)

"...Positive energy EM energy flow is a flow of “naturally divergent” EM energy. The energy is always trying to diverge out away from its direction or path of flow, and escape back to the environment. What we call “conductivity” is the ability of the path or conductor to hold that divergence effort in check along that conductor or path. So along a perfect conductor, one will have the same amount of positive energy flow out of a conducting section, as one had going into that section.

What we call “impedance” is a priori a lowering of the conductance. So if the positive energy flow meets an impedance in its path, in that impedance the conductance is lowered, and so in the impedance section the flow is not totally held in along the line of flow. Hence part of the positive energy flow will be diverged out of the impedance and away from the intended path, back to the external environment. Hence the positive energy flow exiting the impedance and along the original path of flow, will be less than the amount of positive energy flow entering the impedance region.

Negative energy EM energy flow is a flow of “naturally convergent” energy. Excess negative energy flow is always trying to converge – from the external environment – into that line or path or conductor of negative energy flow. What we call “conductivity” is – in this case – the ability of the path or conductor to hold back that excess environmental negative energy that is trying to converge into the flow along the path and thus enlarge that flow. In a perfect conductor or path, that “holding back” the excess convergent negative energy is 100% successful. So from any section of a 100% conductive path, the negative energy flow exiting that section along the original line of flow will be equal to the negative energy flow entering that section along the path.

But when the negative energy flow path contains an impedance, that impedance again is a “reduction” in the normal holding action of the conductive path. Hence for a negative energy flow, in that “standard impedance” region the “hold-back the extra in-converging action” is reduced. So excess negative energy flow-in from the external environment will be added to the original negative energy flow through that impedance region. Hence the negative energy flow exiting the impedance section along the original flow path and direction, will be greater than the negative energy flow entering the impedance section along the original flow path and direction. In short, the ordinary impedance (of an ordinary resistance, capacitance, or inductance) will act as a “true negative impedance”, with an automatic gain in the throughput of negative energy across it. The excess negative energy of course is furnished freely by the surrounding vacuum environment.

And that action produces a “true negative resistor”. Actually the impedance (e.g., a resistor) is totally normal; it is the particular type of EM energy flow – along with its fundamentally particular behavior – that has changed.

With positive energy flow, impedance “feeds energy away from the path and back to the active environment”, decreasing the flow of positive energy proceeding further in the circuits. This is known and evidenced as “losses” in the energy flow of the operating system, or just “system losses” for short.

With negative energy flow, impedance “feeds excess energy flow from the active environment into the ongoing flow”, increasing the flow of negative energy occurring in the circuit. This is known and evidenced as “free gains” in the energy flow of the system..."