Negative resistance
From Wikipedia, the free encyclopedia
[edit] Overview
Image:Negative differential resistance.pngNegative resistance or negative differential resistance is a property of electrical circuit elements composed of certain materials in which, over certain voltage ranges, current is a decreasing function of voltage. This range of voltages is known as a negative resistance region.
Some writers prefer to reserve the term negative resistance for situations in which the negatively-sloping portion of the load line passes through the origin, so that a positive absolute value of voltage is associated with a negative absolute value of current. Such a circuit must contain an energy source, and can be used as a form of amplifier. However, the use of the term negative resistance to encompass negative differential resistance is more common.
Absolute negative resistances without an external energy source cannot exist as they would violate the law of conservation of energy.
[edit] The basic idea behind negative resistance
[edit] Non-electrical domain: "over-helping" and "over-impeding" ideas
The negative resistance phenomenon may be observed in many well-known everyday situations where something (a being, a device etc.) containing an additional power source affects (as a proportional reaction of some disturbance) something else containing the main power source [1]. The additional source may help or impede the main one in three degrees (under-, exact- or over-). Negative resistance represents the last degree when the additional source "over-helps" or "over-impedes" the main one. Examples: human (parents that over-help their children, husbands that over-help their wives and v.v.), fluid (a pneumatic amplifier over-helps the driver when he presses the brake pedal), mechanical ("clicking" mechanisms) etc.
Negative resistance phenomenon is a process of injecting an additional excessive power to an existing power source proportionally to some disturbance. A negative resistor acts as a proportional additional power source.
[edit] Electrical domain: "positive" versus negative resistance
[edit] Voltage source acting as a negative resistor
The nature of electrical negative resistance is clarified below (Fig. 1) by comparing an ordinary "positive" resistor R with a negative resistor -R (click on the pictures to view full-size images). For this purpose, two equivalent electrical circuits are used, in which the two components are connected in series with the loads so that the same current passes through them.
| Image:Ser pos resistor 1000.jpg | Image:Ser help volt source 1000.jpg | Image:Ser imp volt source 1000.jpg |
As a result, a voltage drop VR = R.I appears across the "positive" resistor R (Fig. 1a) and the same voltage VH = VR = R.I appears across the negative resistor -R (Fig. 1b). However, the resistor R sucks the voltage V from the circuit (it is a voltage drop) while the negative resistor -R adds the voltage V into the circuit. Therefore, a resistor acts as a current-to-voltage drop converter while a negative resistor acts as a current-to-voltage converter. The element named "resistor" is really a resistor while the "negative resistor" is actually a voltage source, whose voltage is proportional to the current passing through it. If the additional voltage source is connected in the opposite direction to the input voltage source (Fig. 1c), it will act as an "over-impeding" voltage source.
A negative resistor can be a voltage source, whose voltage is proportional to the current passing through it (a current-controlled voltage source).
[edit] Current source acting as a negative resistor
Dual circuits may be assembled (Fig. 2) where the components are connected in parallel to the loads so that the same voltage is applied across them (click on the pictures to view full-size images).
| Image:Par pos resistor 1000.jpg | Image:Par help current source 1000.jpg | Image:Par imp current source 1000.jpg |
As a result, a current IR = VL/R passes through the resistor R (Fig. 2a) and the same current IH/ = VL/R passes through the negative resistor -R (Fig. 2b). Only, the resistor R sucks the current from the circuit while the negative resistor -R injects the current into the circuit. The element named "resistor" is really a resistor while here the "negative resistor" is actually a current source, whose current is proportional to the voltage across it. If the additional current source is connected in the opposite direction (Fig. 2c) versus the input current source, it will act as an "over-impeding" current source.
A negative resistor can be also a current source, whose current is proportional to the voltage across it (a voltage-controlled current source).
[edit] How to make negative resistors
The IV curve of an ohmic (static) resistor is sloped from left to right. The only way to slope it from right to left in a limited region is to "dynamize" sufficiently the ohmic resistor in this region. In this way, the problem of obtaining a negative resistance is reduced to the problem of creating a dynamic resistance [2].
In electrical circuits, static resistance is the ratio of the voltage across a circuit element to the current through it. However, the ratio of the voltage to the current may vary with either voltage or current. The ratio of the change in voltage to the change in current is known as dynamic resistance.It is more correct to say that a circuit element has a negative differential resistance region than to say that it exhibits negative resistance because even in this region the static resistance of the circuit element is positive, while it is the slope of the resistance curve which is negative.
There are two techniques for obtaining dynamic (negative) resistance - by varying the resistance [3] and by varying the voltage [4]. The first produces negative differential resistance, while the second gives absolute negative resistance.
[edit] Creating negative differential resistors by varying the resistance
This is historically first and more natural way of creating negative resistance. In electronics, there are a few two-terminal electronic components having negative differential resistance. Some of them have an S-shaped IV curve while other components have an N-shaped IV curve. Electronically-active conductive polymers such as Melanin can also show marked negative differential resistance.
[edit] S-shaped negative differential resistors (based on constant-voltage dynamic resistors)
By dynamically decreasing the resistance of an ordinary ohmic resistor [5], three degrees of dynamic resistance may be obtained (Fig. 3a): decreased (section 1-2), zeroed (section 2-3) and S-negative differential resistance (section 3-4). As the section 2-3 represents a voltage-stable dynamic resistor (for example, a zener diode), a conclusion may be derived:
An S-shaped negative differential resistor is actually an "over-acting" voltage-stable dynamic resistor.
An example of an electronic component exhibiting a negative differential resistance region is the medium within a gas discharge lamp which, as current increases, ionizes to a greater extent, thereby carrying more current. If such a lamp were allowed to draw power without limit, it would instantly burn itself out. Limiting the possible current is one of the roles of the ballast in a fluorescent lamp.
[edit] N-shaped negative differential resistors (based on constant-current dynamic resistors)
Dually, by dynamically increasing the resistance of an ordinary ohmic resistor (fig. 3b), three other degrees of dynamic resistance may be obtained: increased (section 1-2), infinite (section 2-3) and N-negative differential resistance (section 3-4). As the section 2-3 represents a current-stable dynamic resistor (for example, a barreter or the collector-emitter part of a transistor), another conclusion may be derived:
An N-shaped negative differential resistor is actually an "over-acting" current-stable dynamic resistor.
An example of an electronic component exhibiting an N-shaped negative differential resistance region is the tunnel diode. Such a device, when biased into its negative differential resistance region, acts as an amplifier. See also Gunn diode.
Negative differential resistor is an "over-acting" dynamic resistor (a dynamic resistor with extremely varying resistance).
In compliance with the law of conservation of energy, a plot of the negative differential resistance region of a passive component cannot pass through the origin.
[edit] Absolute negative resistors based on negative differential resistor
The negative differential resistor is not a true negative resistor as it does not contain a source; it is just a part of a true negative resistor. In order to get an absolute negative resistor, an additional constant voltage source has to be connected in series:
Actually, the combination of the two components constitutes the varying voltage source needed. By applying this approach, a tunnel diode amplifier is built (see applications).
[edit] Creating absolute negative resistors by including a varying voltage source
In op-amp circuitry, there are perfect voltage-controlled voltage sources - operational amplifiers. That is why, it is preferred to make dynamic resistors rather by varying the voltage [6] than by varying the resistance. Following this approach, excellent "circuit" true negative resistors are built by connecting in series two circuit elements (Fig. 4): a steady "positive" (ohmic) resistor and an "over-acting" varying voltage source (an amplifier):
It is a paradox that a negative resistor -R contains a "positive" resistor R. However, this idea is used in many cases of human routine where, in order to begin creating something positive (-R), they first need something negative (R). Then, they produce two (or many) times more positive quantity (-2R) in order not only to compensate the negative quantity (R) but also to get the desired positive quantity (-2R + R = -R).
According to this idea, the current-sensing resistor R converts the current into proportional voltage drop VR = R.I (Fig. 4a); then, the "over-helping" varying voltage source VH (the amplifier) doubles this voltage drop thus producing an additional voltage VH = 2R.I. Half the voltage (VR) compensates the voltage drop VR; the rest half (VR) adds to the voltage of the excitation input voltage source VIN. As a result, the whole circuit acts as a current-controlled voltage source producing a voltage -VR. Since the "positive" resistance R is converted into negative one -R, these kinds of circuits are named negative impedance converters (NIC).
If the additional voltage source is reversed (Fig. 4b), it subtracts its voltage from the voltage of the input voltage source VIN. In this case, VI "over-impedes" VIN.
[edit] Operation modes of negative resistance circuits
Negative resistors are two-terminal elements, which inputs and outputs are the same - the voltage applied across (or the current passed through) the two terminals of the negative resistor controls the resistance/current/voltage between the same two terminals. Therefore, a feedback exists naturally in the negative resistance circuits. The kind of this feedback (negative or positive) determines the circuit behavior.
[edit] Linear (analog) operation mode
Applying a dominating negative feedback. By applying only a negative feedback, at the best case two kinds of dynamical resistances can be obtained: a dynamical zero resistance (having a vertical IV curve - [7]) and an infinite resistance (having a horizontal IV curve). Further, in order to get a negative resistance (to slope the IV curves), an additional positive feedback has to be added. In order to ensure a linear mode (a stability), the negative feedback has to dominate over the positive one. An example of a linear negative resistance device: Negative impedance converter.
Applying a depressed positive feedback. The same effect might be achieved by using only a small enough positive feedback (e.g., by using a non-inverting amplifier with small gain A or a feedback attenuator with large ratio B). In these cases, the loop gain is kept A.B < 1.
Many circuit topologies are capable of producing absolute negative resistance (which requires that an energy source be included). The simplest case requires a non-inverting amplifier with voltage gain greater than one. If a resistor R is connected from input to output, the input current, <math>i_i</math>, for a given input voltage <math>v_i</math> is:
<math>i_i = \frac{v_i - v_o}{R}</math>
Where <math>v_o</math> is the output voltage. This assumes an ideal amplifier with infinite input impedance and zero output impedance. If the voltage gain, <math>A_v</math>, of the amplifier is defined as:
<math>A_v = \frac{v_o}{v_i}</math>
The input resistance, <math>R_i</math> is:
<math>R_i = \frac{v_i}{i_i} = \frac{R}{1-A_v}</math>
The input resistance is negative for values of <math>A_v > 1</math>.
In the case of a non-ideal amplifier, negative resistance is still possible as long as the amplifier input impedance is sufficiently high. The net resistance is reduced to:
<math>R_i = \frac{1}{\frac{1}{Z_{i}} + \frac{1-A_v}{R + Z_{o}}}</math>
where <math>Z_i</math> is the amplifier input impedance and <math>Z_o</math> is the amplifier output impedance.
[edit] Bi-stable (discrete) operation mode
[edit] Negative resistance applications
[edit] Linear applications
[edit] Compensating resistive losses
Using series connected negative resistor. If a voltage source drives a distant low-resistive load through a long line (a thin wire) having significant resistance Rl, a problem arises - a voltage drop VRl = I.Rl appears across the line resistance Rl. In other words, the line and the load resistance constitute a voltage divider with ratio K = RL/(Rl + RL). As a result, the output voltage VOUT drops (VOUT = VIN - VRl). The problem may be solved by connecting in series a negative resistor with resistance -Rl (Fig. 5). In this arrangement, the "copy" resistor R converts the flowing current I into proportional "mirror" voltage drop VR = Rl.I, which drives the compensating voltage source BH (an amplifier with K = 2). As a result, the doubling voltage source BH produces an additional "helping" voltage BH= -2.Rl.I. A portion of this voltage compensates the voltage drop across the "copy" resistor R; the rest part compensates the voltage drops across the line resistance Rl. As a result, the output voltage is equal to the input voltage - VOUT = VIN.This idea may be implemented by an op-amp circuit of a negative impedance converter [8] (NIC). In this arrangement, the op-amp compares its output voltage with the "mirror" voltage drop across the "copy" resistance instead with the "original" line resistance (it "supposes" that the two resistances are equal). If the "original" resistance varies, the op-amp will be misled and an error will appear. Only, a negative resistance solution has an advantage - it has only two terminals; therefore, it needs only two wires (it is a 1-port amplifier).
In contrast to this circuit solution, the op-amp of a transimpedance amplifier compares its output voltage directly with the "original" voltage drop across the "harmful" resistance [9]. In this way, it compensates exactly the resistance even when it varies (for example, because of temperature or length variations). However, for this purpose the op-amp needs an additional voltage sense wire, in order to "observe" the virtual ground by its inverting input. Unfortunately, in many cases, this point is inaccessible.
Using parallel connected negative resistor. Electrical negative resistance is often used to design oscillators. Many topologies are possible, such as the Dynatron oscillator, Colpitts oscillator, Hartley oscillator, Wien bridge oscillator, and some types of relaxation oscillators. Negative resistance characteristics of Gunn diodes are often used in microwave frequencies as well.
[edit] Amplification
Tunnel diode amplifier.
[edit] Applying negative impedance in the domain of RF 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.
[edit] Bi-stable applications
[edit] Non-electrical examples
There are many mechanical systems that exhibit ranges of negative differential resistance. In fact, this is a common design element in systems that are designed to have "detents" or a "positive action" or a "click." A popular example is the well-known pen clicker. Good examples are also the keys on a computer keyboard and on a computer mouse, taking the key position and upward force to be analogous to voltage and current, respectively. As the key is pressed downward, it initially presents a firm and increasing upward force. Beyond a critical point, a zone is entered in which the upward force decreases, which feels like a "sudden" yielding. This is often referred to as a "collapse action" mechanism. A general characteristic of negative resistance systems is that by driving them "firmly" it is possible to traverse the negative resistance region continuously, but bistable switching action occurs if the system is driven "loosely."
[edit] Electrical examples
Switching circuits. Negative resistance is also useful in certain switching and comparator circuits, such as the Schmitt trigger. Specialized diodes, such as the step recovery diode also exhibit negative resistance. In this case, a very sharp pulse can be generated that produces a broad spectrum of harmonics. This can be used as a frequency multiplier at gigahertz frequencies. This is sometimes used in certain frequency synthesiser designs.
Memory circuits.
[edit] Historical facts
Interesting examples of the use of negative resistances in analogue computing can be found in the works of Gabriel Kron. While a scientist for General Electric, [10] Kron used negative resistors (circuits like those described above) for the US Navy's "Network Analyser" in the 1930s. [11] For example, this paper refers to the use of active negative resistances with network analysers, and also shows how these can be replaced by inductors and capacitors in AC simulations.
[edit] Scientific sensations: Deborah Chung's 'apparent negative resistance'
In July 1998, Deborah Chung and Shoukai Wang of the University of Buffalo presented the results of an experiment that showed an apparent absolute negative resistance in bare carbon fibers held together by pressure.<ref name="apparent negative">Apparent negative electrical resistance in carbon fiber composites — Shoukai Wang, D.D.L. Chung — Composite Materials Research Laboratory, State University of New York at Buffalo — Received 8 April 1998; accepted 31 March 1999</ref>
In the experiment, two bundles of carbon fibers are arranged in a cross shape, with the ends of each bundle shorted with copper foil and silver paint (at A, B, C, and D in the image). A current is driven through one branch, and a voltage is measured across the other branch. In the paper, the voltage divided by current is referred to as an "apparent resistance". (A real electrical resistance requires both the current and voltage to be measured at the same points.)
The paper describes how the apparent contact resistance of the interface changes from positive to negative when the fibers are compressed. The current-voltage characteristic of the measured "negative resistance" is then a straight line of negative slope through the origin. The apparent negative resistance was also observed in metal wires (silver-coated copper), but was not observed for a single fiber crossing another single fiber. The paper claims that this phenomenon is useful because the forward flow and backflow of electrons in the same piece of material can be reproducibly controlled by external forces.
It was initially reported on July 9, 1998 by the University as a breakthrough in room temperature superconductor research, in the press release Superconduction At Room Temperature: Negative Electrical Resistance Seen In Carbon Composites, claiming that the discoveries "have enabled carbon-fiber materials to superconduct at room temperature", because of measurements of "zero apparent resistance" at certain pressures.<ref>Copy of the original press release available from Zero Point Technologies article The Zero Point Interaction</ref> This was quickly seized upon by the free energy community as a working example of a device that supplies energy with no apparent source, claiming it to be a true, absolute negative resistance<ref>Dr. Deborah Chung's Negative Resistor — The Tom Bearden website — "There is no question at all about it being a true negative resistor."</ref><ref>On Extracting Electromagnetic Energy From The Vacuum — Thomas E. Bearden</ref><ref>The Chung's Negative Resistance experiment — JLN Labs</ref>, and was reported in the popular press as a breakthrough.<ref> 'Negative resistance' surprises material scientists — PhysicsWeb, 10 July 1998</ref> The original press release was later pulled from UB's website, on July 16, 1998, and replaced with one which stated "her findings do not indicate that the combination is itself a superconductor."<ref>Editor's note from UB Professor Looking To Identify Mechanism Behind Observation Of Negative Electrical Resistance</ref><ref>Research Focusing On Mechanism Behind Observation of Negative Electrical Resistance — University of Buffalo news — latest revision of the press release</ref>
Chung's paper itself says:
True negative resistance in the former sense is not possible due to energy consideration. However, apparent negative resistance in the former sense is reported here. ... Although the negative resistance reported here is apparent rather than true, its mechanism resembles that of true negative resistance (which actually does not occur due to energetics) in that the electrons flow in the unexpected direction relative to the applied current/voltage.—Wang, Chung
It never claims that the device is a source of energy.
[edit] References
<references/>
- Peter D. Hooper, G. McHale, and M. I. Newton, "Negative differential resistance in MIM devices from vacuum to atmospheric pressure", Proc. SPIE Int. Soc. Opt. Eng., 2780, 38 (1996)
- Negative impedance converter - is dedicated to INIC.
[edit] External links
- A heuristic approach to teaching negative resistance phenomenon
- How to Compensate Resistive Losses by Series Connected Negative Resistor
- How do we create dynamic resistance?
- How do we make decreased, zero and negative differential resistance?
- How do we make decreased, zero and negative resistance?
- Understanding negative impedance converter (VNIC) - reveals in three consecutive steps the basic idea behind VNIC.
- Negative-resistance circuits
- The mysterious "Negistor" shows how a transistor may act as a negative resistorda:Negativ differentiel modstand
de:Elektrischer_Widerstand#Differenzieller_Widerstand fr:Resistance negative nl:negatieve weerstand
