en>Ktr101: /* Spin density */clean up, replaced: http://www.iupac.org/ → http://goldbook.iupac.org/, 4.pdf → 4.html using AWB

2014-04-08T02:20:08Z

Spin density: clean up, replaced: http://www.iupac.org/ → http://goldbook.iupac.org/, 4.pdf → 4.html using AWB

en>Peertje55 at 12:56, 3 February 2014

2014-02-03T12:56:24Z

New page

[[File:Rtd seq v3.gif|thumb|350px|right|Figure 1: A working mechanism of a resonant tunneling diode device and negative differential resistance in output characteristic. Notice the negative resistance characteristic after the first current peak due to reduction of first energy level below source fermi level with gate bias.]]

'''Negative resistance''' is a property of some [[Electrical network|electric circuit]]s where an increase in the [[Electric current|current]] entering a port results in a decreased [[voltage]] across the same port. This is in contrast to a simple ohmic [[resistor]], which exhibits an increase in voltage under the same conditions. Negative resistors are theoretical and do not exist as a discrete component. However, some types of [[diode]]s (e.g., [[tunnel diode]]s) can be built that exhibit negative resistance in some part of their operating range. Such a differential negative resistance is illustrated in Figure 1 with a [[resonant-tunneling diode]]. Electric [[Gas discharge|discharges]] through gases exhibit negative resistance, and some [[chalcogenide]] glasses,<ref>{{cite journal
|title=DC electric-field effect in bulk and thin-film Ge5As38Te57 chalcogenide glass | last1 = Abdel-All | first1 = A. | last2 = Elshafieb | first2 = A. | last3 = Elhawaryb
| first3 = M.M. | journal = Vacuum | year = 2000 |volume = 59 | issue = 4 | pages = 845–853 | doi=10.1016/S0042-207X(00)00378-X}}</ref> [[organic semiconductors]], and [[conductive polymers]] exhibit a similar region of negative resistance as a bulk property. In [[electronics]], negative resistance devices are used to make bistable switching circuits and [[electronic oscillator]]s, particularly at [[microwave]] [[frequency|frequencies]].

==Entropy consideration==
Any ''passive'' component with a time-invariant I-V characteristic will have a graph in the first and third quadrants. That is, current will always flow from higher voltage to lower voltage, and (at least with I≠0 and V≠0) the quantity V/I will be positive. So some "reverse" of a simple resistor is impossible, since it will be supplying power out of nowhere. What is often meant is a negative ''marginal'' resistance. That is, current always will flow from high to low voltage, but less current will flow with more voltage difference. This is found in many cases.

It is possible to construct circuit blocks using ''active'' components which have an I-V curve in the second and fourth quadrants. In this way an equivalent circuit of a negative simple resistor can be simulated. The power flowing out of this "negative resistor" is supplied from the power rails of the active device.

==Properties==
[[Image:Current-driven neg resistor graph.svg|right|thumb|300px|Figure 2: The IV curve of a theoretical negative resistor]]

Figure 2 shows a graph of a negative resistor, showing the negative slope. In contrast to this, a resistor will have a positive slope. [[Tunnel diode]]s and [[Gunn diode]]s<ref name="GunnDiode">W. Alan Davis, ''Microwave Semiconductor Circuit Design'', p. 329, Van Nostrand Reinhold ISBN 0-442-27211-1</ref> exhibit a negative resistance region in their IV (current – voltage) curve. They have two terminals like a resistor; but are not linear devices. [[Unijunction transistor]]s also have negative resistance properties when a circuit is built using other components.

For negative resistance to be present there must be active components in the circuit providing a source of energy. This is because current through a negative resistance implies a source of energy just as current through positive resistance implies that energy is being dissipated. A resistor produces voltage that is proportional to the current through it according to [[Ohm's law]]. The IV curve of a true negative resistor has a negative slope and passes through the origin of the coordinate system (the curve can only enter the 2nd and 4th quadrants if energy is being supplied). This is to be compared with devices such as the tunnel diode where there is no source of energy within the device. The negative slope portion of the curve is entirely in the first quadrant and the curve passes through the origin into the third quadrant, never entering the second or fourth quadrants.<ref>N. Balkan, B. K. Ridley, A. J. Vickers, ''Negative Differential Resistance and Instabilities in 2-D Semiconductors'', p. 2, Springer, 1993 ISBN 0-306-44490-9.</ref>
{{Clear}}

== History ==

In early research it was noticed that [[electric arc|arc discharge]] devices and some [[vacuum tube]] devices such as the [[dynatron]] exhibit negative differential resistance effects.<ref>For instance G Crisson, [http://www.alcatel-lucent.com/bstj/vol10-1931/articles/bstj10-3-485.pdf "Negative Impedances and the Twin 21-Type Repeater"], ''The Bell System Technical Journal'', p. 492, January 1931.</ref> If the [[screen grid]] is at a higher potential than the [[plate electrode]] the secondary emission from the plate will result in large numbers of electrons being attracted to the screen grid. If the plate voltage is reduced further the plate current to the screen grid will increase. This effect is a negative resistance and when a screen grid tube is operated in this negative resistance region it is called a dynatron. <ref>Electronics and Radio Engineering, pp 196-197, Frederick E. Terman, 1955</ref> Small-signal transit-time effects in vacuum tube diodes can result in alternating positive and negative conductance. This occurs when the transit time of the electrons is slightly over one cycle of the AC signal. <ref>Electronics and Radio Engineering, pp 212-215, Frederick E. Terman, 1955</ref> Practical and economic devices only became available with [[Solid state (electronics)|solid state technology]]. The typical true negative impedance circuit—the [[negative impedance converter]] – is due to [[John G. Linvill]] (1953)<ref>{{cite journal|author=Linvill, J.G.|title=Transistor Negative-Impedance Converters|journal=[[Proceedings of the IRE]]|pages=725–729|year=1953|doi=10.1109/JRPROC.1953.274251|volume=41|issue=6}}</ref> and the popular element with negative differential resistance—the [[tunnel diode]] – is due to [[Leo Esaki]] (1958).<ref>{{cite journal|authorlink=Vitold Belevitch|author=Belevitch, V|title=Summary of the history of circuit theory|journal=Proceedings of the IRE|volume=50|issue=5|page=853|year=1962|doi=10.1109/JRPROC.1962.288301}}</ref>

== Implementations ==
[[File:Negative resistance by positive feedback.svg|thumb|Figure 3: Amplifier exhibiting negative resistance through positive feedback]]

Any amplifier with sufficient positive feedback will present a negative resistance at its input. Referring to figure 3,

:<math> i = \frac{v - Av}{R_1} + {v \over R_{\mathrm {in}}} </math>

and,

:<math> {1 \over R} \triangleq {i \over v} = \frac {1-A}{R_1} + {1 \over R_{in}} </math>

If ''R''in is large,

:<math> R \simeq \frac {R_1}{1-A} </math>

=== Operational amplifiers ===
[[File:Practical negative resistance op amp.svg|200px|thumb|right|Figure 4: Negative resistance circuit
]]
{{Main|Negative impedance converter}}

The negative resistance circuit shown in Figure 4 is an opamp implementation of the negative impedance converter. The two resistors R1 and the op amp constitute a negative feedback non-inverting amplifier with gain A = 2. The input resistance (for an ideal opamp) is given by;

:<math> R_\text{in} \triangleq {v \over i} = -R \,\!</math>

The input port of the circuit can be connected into another network as if it were a negative resistance component.

In the general case <math>Z</math> can be selected to produce any value of negative impedance. Negative capacitances and negative inductances can both be simulated by these means.

===Components exhibiting negative differential resistance===
[[Tunnel diode]]s are heavily doped<ref name="TunnelDiode">RCA Tunnel Diode Manual</ref> semiconductor junctions that have an "N" shaped transfer curve. A [[vacuum tube]] can also be made to exhibit negative resistance.<ref>{{cite journal|title=A New Electron Tube Having Negative Resistance |author=J. Groszkowski|journal= Proceedings of the IRE |year=1936|doi=10.1109/JRPROC.1936.228352|volume=24 |issue=7|page=1041 }}</ref> Other negative resistance diodes have been built that have an "S" shaped transfer curve.<ref>Nyle Steiner [http://www.sparkbangbuzz.com/els/zincosc-el.htm Zinc Negative Resistance Oscillator] 22 March 2001</ref> When biased so that the operating point is in the negative resistance region, these devices can be used as an [[Amplifier]]. These devices can also be biased so that they will switch between two states very quickly, as the applied voltage changes.<ref name="TunnelDiode" />
{{clear}}

===Neuronal models===
Some instances of neurons display regions of negative slope conductances (RNSC) in voltage-clamp experiments.<ref>MacLean and Schmidt, [http://jn.physiology.org/content/86/3/1131.full "Voltage-sensitivity of motoneuron NMDA receptor channels is modulated by serotonin in the neonatal rat spinal cord"], ''Journal of Neurophysiology'', vol. 86, no. 3, 1 September 2001.</ref> The negative resistance here is implied were one to consider the neuron a typical [[Hodgkin-Huxley model|Hodgkin-Huxley]] style circuit model.

== Applications ==
=== Oscillators ===
Many [[electronic oscillator]] circuits use [[Two-port network|one-port]] [[negative resistance]] devices, such as [[magnetron]] tubes, [[tunnel diode]]s and [[Gunn diode]]s. In these circuits, a [[resonator]], such as an [[LC circuit]], [[Crystal oscillator|quartz crystal]], or [[cavity resonator]], is connected across the negative resistance device, and a DC bias voltage applied. The negative resistance of the active device can be thought of as cancelling the (positive) effective loss resistance of the resonator, creating sustained oscillations. These circuits are frequently used for oscillators at [[microwave]] frequencies. Oscillators have also been built using the negative resistance region of amplifying devices like [[vacuum tube]]s, as in the [[dynatron oscillator]].

===Amplifiers===

[[File:Negative resistance amp.svg|thumb|300px|Figure 5: Negative resistance microwave amplifier using a circulator]]
[[File:10Gig Tunnel Amp M.jpg|thumb|300px|Figure 6: 8–12 GHz tunnel diode amplifier, circa 1970]]
A device exhibiting negative resistance can be used to amplify a signal and this is an especially useful technique at [[microwave]] frequencies. Such devices do not present as pure negative resistance at these frequencies (in the case of the tunnel diode a large parallel capacitance is also present) and a matching filter is usually required. The reactive components of the device's equivalent circuit can be absorbed into the filter design so the circuit can be represented as a pure resistance followed by a bandpass filter. The output of this arrangement is fed into one [[two-port network|port]] of a three-port [[circulator]]. The other two ports constitute the input and output of the amplifier with the direction of circulation as shown in the diagram. Treating ''R''0 as being positive, the [[reflection coefficient]]s at the two ends of the filter are given by;

:<math>\Gamma_1 = \frac{Z_1 - R_0}{Z_1 + R_0}</math> and, <math>\Gamma_2 = \frac{Z_2 - R_1}{Z_2 + R_1}</math>

Since the filter has no resistive elements, there is no dissipation and the magnitudes of the two reflection coefficients must be equal,

:<math>\left| \Gamma_1 \right| = \left| \Gamma_2 \right| </math>

The input power entering the circulator is directed at the matching filter, is reflected at both the input and output of the filter and a portion finally arrives at the load. This portion is given by;

:<math>\frac{P_\mbox{out}}{P_\mbox{in}} = \left| \Gamma_1 \right|^2</math>

For a well matched filter, the reflection coefficients will be very small in the passband and very little power will reach the load. On the other hand if ''R''0 is replaced by a negative resistance such that,

:<math>R_0' = - R_0 \,\!</math> then,

:<math>\Gamma_1' = \frac{Z_1 + R_0}{Z_1 - R_0}</math> and,

:<math>\left| \Gamma_1' \right| = \left| \Gamma_2' \right| = \frac{1}{\left| \Gamma_1 \right|}</math>

Now the reflection coefficients are very large and more power is reaching the load than was injected in the input port. The net result of terminating one port in a negative resistance is amplification between the remaining two ports.<ref>Matthaei, Young, Jones ''Microwave Filters, Impedance-Matching Networks, and Coupling Structures'', pp. 4–9, McGraw-Hill 1964.</ref>

=== Mixers and frequency converters ===

The highly non-linear characteristics of tunnel diodes makes them useful as frequency mixers. The conversion gain of a tunnel diode mixer can be as high as 20 dB if it is biased to operate in the negative resistance region.<ref>[http://www.tpub.com/neets/book11/45j.htm Solid-state microwave devices]. tpub.com</ref>

=== Antenna design ===
Another concept of negative resistance exists in the domain of radio frequency antenna design. This is also known as negative impedance. It is not uncommon for an antenna containing multiple driven elements to exhibit apparent negative impedance in one or more of the driven elements.<ref>Roger L. Freeman, ''Radio System Design for Telecommunication'', page 805, John Wiley & Sons, 2006
ISBN 0470050438.</ref><ref>J. Belrose, "VLF, LF and MF antennas", in: Alan W. Rudge (ed), ''The Handbook of Antenna Design, Volume 2'', page 612, [[Institution of Electrical Engineers|IEE]], 1983 ISBN 0906048877.</ref> This situation is different from the meaning of negative resistance in this article: the ratio of V/I is indeed negative but the slope of the IV curve remains positive at all points. The same is true of any source of electric energy For instance a battery has a negative V/I ratio (positive I defined as going into the positive terminal) but a positive slope equal to its internal resistance.

===Impedance cancellation===
Negative impedances can be used to cancel the effects of positive impedances, for example, by eliminating the internal resistance of a voltage source or making the internal resistance of a current source infinite.
This property is used in telephony line repeaters<ref>Neil J. Boucher, ''The Paging Technology Handbook'', p. 143, John Wiley and Sons, 1995 ISBN 0-930633-17-2</ref> and in circuits such as the Howland current source,<ref>[http://www.philbrickarchive.org/1964-1_v12_no1_the_lightning_empiricist.htm Impedance and admittance transformations using operational amplifiers]</ref> Deboo integrator<ref>[http://electronicdesign.com/Articles/Index.cfm?AD=1&ArticleID=1633 Consider The "Deboo" Integrator For Unipolar Noninverting Designs]</ref> and load cancellers.<ref>Wang, W. et al., "A Comprehensive Study on Current Source Circuits", ''IFMBE Proceedings'', '''Vol 17''', pp. 213–216, Springer, 2007 ISBN 3-540-73840-1 {{DOI|10.1007/978-3-540-73841-1_57}}.</ref><ref>[http://www.elecdesign.com/Articles/Index.cfm?AD=1&ArticleID=4128 Negative-Resistance Load Canceller Helps Drive Heavy Loads]</ref>

== See also ==
*[[Negative impedance converter]]

==References==
{{Reflist|3}}

==Further reading==
{{Refbegin}}
*Negatron yields real natural frequency, Aleksandr Belousov, USA, EDN, 08/1993 (practical application of the equivalent Negatron circuit related to Instrumentation and Measurement knowledge domain)
*E.W. Herold, "Negative Resistance and Devices for Obtaining It," Proceedings of the Institute of Radio Engineers, Volume 23, Number 10, October 1935.
{{Refend}}

== External links ==
{{External links|date=August 2010}}
{{Commons category|Negative resistance}}
*[http://users.tpg.com.au/ldbutler/NegativeResistance.htm Negative Resistance Revived] – condensed version of article originally published in ''Amateur Radio'', November 1995
*[http://www.answers.com/topic/negative-resistance-circuits Negative-resistance circuits] – nice material from Answers.com
*[http://focus.ti.com/lit/an/sboa093a/sboa093a.pdf Handbook Of Operational Amplifier Active RC Networks] – a formal but well-written electronic book
*[http://www.edn.com/archives/1994/072194/15di1.htm Negatrons enrich filter, oscillator designs, Aleksandr Belousov, USA, EDN, July 21, 1994]
*[http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/RadCom/part5/page1.html Negative resistance as it applies to microwave oscillators]
*[http://www.sparkbangbuzz.com/els/zincosc-el.htm Negative resistance oscillators using Zinc plated steel]
*[http://www.zen22142.zen.co.uk/Theory/neg_resistance/negres.htm Oscillations and Regenerative Amplification using Negative Resistance Devices]
*[http://nanohub.org/tools/rtdnegf Resonant Tunneling Diode Simulation Tool] on [[Nanohub]] enables the simulation of resonant tunneling diodes under realistic bias conditions for realistically extended devices.
*[http://www.km5kg.com/negative.htm Negative resistance antenna elements] An analysis of power transfer between driven elements of an antenna.

{{DEFAULTSORT:Negative Resistance}}
[[Category:Electronics]]
[[Category:Organic semiconductors]]
[[Category:Molecular electronics]]
[[Category:Conductive polymers]]

[[de:Elektrischer Widerstand#Negativer differentieller Widerstand]]

Electron density - Revision history

en>Ktr101: /* Spin density */clean up, replaced: http://www.iupac.org/ → http://goldbook.iupac.org/, 4.pdf → 4.html using AWB

en>Peertje55 at 12:56, 3 February 2014