# Why are there no practical applications of negative impedance?

It is easy to design a circuit, using operational amplifiers, for example, which produce either negative resistance, negative capacitance, or negative inductance. This is often taught in undergraduate level electronics courses. However, can anyone name one commercial or practical electronic product that actually exploits negative impedance? If there are none, why is that?

## Popular Answers

Amin Gorji· Iowa State University## All Answers (28)

Erik Lindberg· Technical University of DenmarkDerek Abbott· University of AdelaideCarlos Ignacio Sarmiento· Metropolitan Autonomous UniversityAmin Gorji· Iowa State UniversityErik Lindberg· Technical University of DenmarkG. Chris Pappas· Lawrence Berkeley National LaboratoryJacques B Sombrin· Telecommunications for Space and Aeronautics- in oscillators,

- in filters to improve the quality factor by decreasing filer resistance

- as amplifiers such as Gunn diode and parametric amplifiers.

A negative resistance is a 2-port device and much more difficult to use than a transistor:

- it as generally lower bandwidth,

- a lot of manual tuning is necessary,

- a circulator is needed to separate input and output,

- its negative value must be quite close to the opposite of the positive value of the resistance it negates for usable effect,

- if its negative value becomes higher, the device oscillates or becomes unstable.

So, as soon as a correct transistor technology exists at a given frequency, negative resistance devices are replaced by their equivalent 4-port devices.

That is why negative resistances are not generally used in consumer equipment.

Pisupati Sadasiva Subramanyam· Vignana Bharathi Institute of TechnologyThe concept of negative Impedance is not prevalent.But negative reactance is comprehensible. As Inductive reactance is expressed as

+jX we say -jx is capacitive reactance. Impedance Z=Sqrt ( R^2+X^2) and it can never be negative.

But the concept of negative resistance is well established. Electrical arc has negative resistance.

In Electronic Devices characteristics like Tunnel Diode,Gunn Diode etc. etc.we have negative Resistance region and only in negative resistance region it can act as Oscillator.

In addition to the feedback oscillators, which use two-port amplifying active elements such as transistors and op amps, linear oscillators can also be built using one-port (two terminal) devices with negative resistance such as magnetron tubes, tunnel diodes and Gunn diodes. Negative resistance oscillators are often used at high frequencies in the microwave range and above, since at these frequencies feedback oscillators perform poorly due to excessive phase shift in the feedback path.

Dr.P.S.

Erik Lindberg· Technical University of DenmarkIn the negative resistance region the small signal model is unstable. The bias point of an oscillator vary with time. Oscillators are nonlinear circuits which may be investigated as time varying linear circuits.

Pisupati Sadasiva Subramanyam· Vignana Bharathi Institute of TechnologyYou are absolutely correct in that Oscillators should operate in the negative resistance characteristic region of these devices.

In the case of negative resistance of the arc, as the current increases resistance decreases and current increase and so on.

By negative impedance we mean the impedance phase shifted by 180 degrees and the current also gets phase shifted likewise by 180 degrees but does not change in magnitude.

I am happy that the question by Mr.Abbot and the answers by you are quite interesting.

This has led to discussions on Circuit parameters and Electronic Devices,

particularly micro wave generation.,

Dr.P.S.

Erik Lindberg· Technical University of DenmarkReal world linear oscillators are damped circuits. The nonlinearities do not bring the poles to the imaginary axis. The Barkhausen criterion is based on the assumption of a linear circuit. A steady state linear oscillator with poles on the

imaginary axis is mathematical fiction. You cannot balance on a razor's edge. For a real world steady state oscillator the poles of the time-varying small-signal model moves between the right and the left half-plane and an energy balance is obtained.

Lutz von Wangenheim· Hochschule BremenMore than that, the well-known GIC topology, which is used in many high-performance filter circuits, is based on the combination of two NIC stages (NIC=Negative Impedance Convertor).

Erik Lindberg· Technical University of DenmarkSoumen Mandal· Central Mechanical Engineering Research InstituteGo through this link. It gives an explanation of reactive power and its practical implications which is due to negative impedence.

Pisupati Sadasiva Subramanyam· Vignana Bharathi Institute of TechnologyHowever the inductance has some small resistance of the material and the capacitance has some small loss due to lossy dielectric which is represented by a pure capacitance in parallel with a large resistance.

The real Power Loss calculated in Load flow studies take int account the losses in the resistances of the lines and such practical losses in the distributed capacitances(which are not loss-less) .

Dr.P.S.

Pisupati Sadasiva Subramanyam· Vignana Bharathi Institute of TechnologyJust introduction of the application of Gyrator Networks in Network Realization and corresponding links are given below. This comes under Network Synthesis.

http://en.wikipedia.org/wiki/Gyrator

A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer.[1] Unlike the four conventional elements, the gyrator is non-reciprocal. Gyrators permit network realizations of two-(or-more)-port devices which cannot be realized with just the conventional four elements. In particular, gyrators make possible network realizations of isolators and circulators.[2] Gyrators do not however change the range of one-port devices that can be realized. Although the gyrator was conceived as a fifth linear element, its adoption makes both the ideal transformer and either the capacitor or inductor redundant. Thus the number of necessary linear elements is in fact reduced to three. Circuits that function as gyrators can be built with transistors and op amps using feedback.

http://www.beigebag.com/case_gyrator.htm

The gyrator is a two port network that is designed to transform a load impedance into an input impedance where the input impedance is proportional to the inverse of the load impedance. The gyrator network can be used to transform a load capacitance into an inductance. This feature is extremely useful in integrated circuit technology where it is difficult to realize physical inductors. The gyrator circuit can be created with just two dependent sources. The model in Figure 1 following displays the schematic of the gyrator macro:

For further details kindly refer to the links.

Dr.P.S.

Orin Laney· Atwood ResearchCyril Mechkov· Technical University of SofiaThe question is excellent and natural, and it deserves a well-founded answer. I will try to give here my modest contribution to this undertaking.

(True) negative impedance is a fundamental circuit concept (like positive feedback, virtual ground, bootstrapping, etc.) and variety of circuits are based on this phenomenon... but people usually are unaware of its existence. A typical example of this wide-spread situation is the comprehensive TI material below dedicated to the legendary Howland current pump:

http://www.ti.com/lit/an/snoa474/snoa474.pdf

Browsing through the well-written TI material, you will not find even a gentle hint at existing of some negative resistance subcircuit. Instead, the circuit is considered as consisting of four resistors and an op-amp, and then is thoroughly analyzed and “explained” on half a page (as they say, “the authors have not seen the forest for the trees”:). If they saw the negative “resistor” (NIC) inside the Howland pump, they could consider the circuit as consisting only of two components (negative and positive) and analyze it in a few lines... So, negative impedance helps us to build convenient current sources that “can be used to force currents into sensors or other materials. They can be used in experiments, or in production test. They can bias up diodes or transistors, or set test conditions.”

So, the negative impedance exists and we have only to discern it in its various circuit implementations. For this purpose, we have first to realize what the negative impedance actually is.

We may think of the (true) negative impedance element as of a "mirror copy" of the equivalent "positive" impedance element (resistor, capacitor or inductor) since the negative element adds the energy (voltage, current) that the corresponding positive element would consume. The negative impedance is not used independently but together with a portion of "positive" impedance. Depending on the proportion between the two ingredients of this "mixture", the result of this neutralization can be positive, zero, infinite or negative impedance. Most frequently, two equivalent (positive and negative) impedances are mixed to obtain virtual zero or infinite impedance.

If a current-controlled negative impedance element (voltage-inversion NIC) is connected in series with an equivalent positive impedance element, the result is zero impedance. This arrangement is used in line repeaters to compensate (zero) the line resistance or in real voltage sources to compensate (zero) their internal resistance:

http://www.lucent.com/bstj/vol10-1931/articles/bstj10-3-485.pdf

If a voltage-controlled negative impedance element (current-inversion NIC) is connected in parallel to an equivalent positive impedance element, the result is infinite impedance. This configuration is used for topological reasons (the grounded load) in the Howland current source mentioned above. Another famous application of this circuit is the Deboo integrator (it is invented independently by Gordon Deboo in the 60’s when working for NASA) what is nothing else than a Howland current source driving a grounded capacitor. In these circuits, the negative resistance neutralizes (in the sense that makes infinite) the internal resistance of the imperfect current source (MAXIM specialists have managed “to see the forest for the trees “:)

http://www.maximintegrated.com/app-notes/index.mvp/id/1155

Similarly, in the exotic circuit of a load canceller, the negative resistance neutralizes (makes infinite) the load resistance:

http://pdfserv.maximintegrated.com/en/an/AN815.pdf

And finally, in the similar exotic circuit of the capacitance neutralizer invented in the distant 60’s, the negative capacitance neutralizes the “positive” stray capacitance:

http://www.philbrickarchive.org/1964-1_v12_no1_the_lightning_empiricist.htm

I have considered in detail the negative impedance (resistance) and its implementations in a series of materials uploaded on my profile. I recommend to see at least the two Wikibooks stories about the true and differential negative resistance:

http://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_Impedance

http://en.wikibooks.org/wiki/Circuit_Idea/Negative_Differential_Resistance

Andreas Tanda· O.K. + Partner GmbHLutz von Wangenheim· Hochschule BremenCyril Mechkov· Technical University of SofiaLutz von Wangenheim· Hochschule BremenAndreas Tanda· O.K. + Partner GmbHLutz von Wangenheim· Hochschule Bremenfor my opinion, the question has been answered already (NIC applicatins).

However, I am afraid the link as provided by you does not help too much because it shows how a commercial unit (OTA) can be used as an active device to realize an NIC. That means - it is not an example how and where the NIC is used.

Or am I wrong?

Sudhanshu Mathur· Jagannath UniversitySuggest me whether i am wright or wrong

Pisupati Sadasiva Subramanyam· Vignana Bharathi Institute of TechnologyIn Gunn Diode ( Gunn Oscillator) as you said only A.C.Resitance (in the negative Region ) is used.

Dr.P.S.

Cyril Mechkov· Technical University of SofiaEmil Matus· Technische Universität DresdenCan you help by adding an answer?