Negative resistance
In
This is in contrast to an ordinary
Negative resistance is an uncommon property which occurs in a few nonlinear electronic components. In a nonlinear device, two types of resistance can be defined: 'static' or 'absolute resistance', the ratio of voltage to current , and differential resistance, the ratio of a change in voltage to the resulting change in current . The term negative resistance means negative differential resistance (NDR), . In general, a negative differential resistance is a two-terminal component which can
Because they are nonlinear, negative resistance devices have a more complicated behavior than the positive "ohmic" resistances usually encountered in
Definitions
The
Negative resistance occurs in a few nonlinear (nonohmic) devices.[19] In a nonlinear component the I–V curve is not a straight line,[6][20] so it does not obey Ohm's law.[19] Resistance can still be defined, but the resistance is not constant; it varies with the voltage or current through the device.[3][19] The resistance of such a nonlinear device can be defined in two ways,[20][21][22] which are equal for ohmic resistances:[23]
- Static resistance (also called chordal resistance, absolute resistance or just resistance) – This is the common definition of resistance; the voltage divided by the current:[3][18][23] It is the inverse slope of the line (battery or electric generator, positive current flows out of the positive voltage terminal,[26] opposite to the direction of current in a resistor, so from the passive sign conventionand have opposite signs, representing points lying in the 2nd or 4th quadrant of the I–V plane (diagram right). Thus power sources formally have negative static resistance ([23][27][28] However this term is never used in practice, because the term "resistance" is only applied to passive components.[29][30][31] Static resistance determines the power dissipation in a component.[25][30] Passive devices, which consume electric power, have positive static resistance; while active devices, which produce electric power, do not.[23][27][32]
- Differential resistance (also called dynamic,derivative of the voltage with respect to the current; the ratio of a small change in voltage to the corresponding change in current,[9] the inverse slopeof the I–V curve at a point:Differential resistance is only relevant to time-varying currents.[9] Points on the curve where the slope is negative (declining to the right), meaning an increase in voltage causes a decrease in current, have negative differential resistance ().[3][9][20] Devices of this type can amplify signals,[3][11][13] and are what is usually meant by the term "negative resistance".[3][20]
Negative resistance, like positive resistance, is measured in ohms.
- Static conductance
- Differential conductance
It can be seen that the conductance has the same sign as its corresponding resistance: a negative resistance will have a negative conductance[note 1] while a positive resistance will have a positive conductance.[28][34]
Operation
One way in which the different types of resistance can be distinguished is in the directions of current and electric power between a circuit and an electronic component. The illustrations below, with a rectangle representing the component attached to a circuit, summarize how the different types work:
The voltage v and current i variables in an electrical component must be defined according to the This applies to both DC and AC current. The diagram shows the directions for positive values of the variables. | |
In a positive static resistance, , so v and i have the same sign.[24] Therefore, from the passive sign convention above, conventional current (flow of positive charge) is through the device from the positive to the negative terminal, in the direction of the electric field E (decreasing potential).[25] so the charges lose potential energy doing work on the device, and electric power flows from the circuit into the device,[24][29] where it is converted to heat or some other form of energy (yellow). If AC voltage is applied, and periodically reverse direction, but the instantaneous always flows from the higher potential to the lower potential. | |
In a power source, ,[23] so and have opposite signs.[24] This means current is forced to flow from the negative to the positive terminal.[23] The charges gain potential energy, so power flows out of the device into the circuit:[23][24] . Work (yellow) must be done on the charges by some power source in the device to make them move in this direction against the force of the electric field. | |
In a passive negative differential resistance, , only the AC component of the current flows in the reverse direction. The static resistance is positive[6][9][21] so the current flows from positive to negative: . But the current (rate of charge flow) decreases as the voltage increases. So when a time-varying (AC) voltage is applied in addition to a DC voltage (right), the time-varying current and voltage components have opposite signs, so .[37] This means the instantaneous AC current flows through the device in the direction of increasing AC voltage , so AC power flows out of the device into the circuit. The device consumes DC power, some of which is converted to AC signal power which can be delivered to a load in the external circuit,[7][37] enabling the device to amplify the AC signal applied to it.[11] |
Types and terminology
rdiff > 0 Positive differential resistance |
rdiff < 0 Negative differential resistance | |
---|---|---|
Rstatic > 0 Passive: Consumes net power |
Positive resistances:
|
Passive negative differential resistances:
|
Rstatic < 0 Active: Produces net power |
Power sources:
|
"Active resistors" Positive feedback amplifiers used in:
|
In an electronic device, the differential resistance , the static resistance , or both, can be negative,[24] so there are three categories of devices (fig. 2–4 above, and table) which could be called "negative resistances".
The term "negative resistance" almost always means negative differential resistance .
- Passive negative differential resistance devices (fig. 2 above): These are the most well-known type of "negative resistances"; passive two-terminal components whose intrinsic I–V curve has a downward "kink", causing the current to decrease with increasing voltage over a limited range.gas-discharge tubes, tunnel diodes, and Gunn diodes.[43] These devices have no internal power source and in general work by converting external DC power from their port to time varying (AC) power,[7] so they require a DC bias current applied to the port in addition to the signal.[37][39] To add to the confusion, some authors[17][43][39] call these "active" devices, since they can amplify. This category also includes a few three-terminal devices, such as the unijunction transistor.[43] They are covered in the Negative differential resistancesection below.
- Active negative differential resistance devices (fig. 4): Circuits can be designed in which a positive voltage applied to the terminals will cause a proportional "negative" current; a current out of the positive terminal, the opposite of an ordinary resistor, over a limited range,circuit theory this is called an "active resistor".[24][28][48][49] Although this type is sometimes referred to as "linear",[24][50] "absolute",[3] "ideal", or "pure" negative resistance[3][46] to distinguish it from "passive" negative differential resistances, in electronics it is more often simply called positive feedback or regeneration. These are covered in the Active resistorssection below.
Occasionally ordinary power sources are referred to as "negative resistances"[20][27][32][51] (fig. 3 above). Although the "static" or "absolute" resistance of active devices (power sources) can be considered negative (see Therefore, these devices cannot function as one-port amplifiers or have the other capabilities of negative differential resistances.
List of negative resistance devices
Electronic components with negative differential resistance include these devices:
- Gunn diode[57] and other diodes using the transferred electron mechanism[56]
- IMPATT diode,[43][57] TRAPATT diode and other diodes using the impact ionization mechanism[56]
- Some NPN transistors with E-C reverse biased, known as negistor[58]
- unijunction transistor (UJT)[54][43]
- thyristors[54][43]
- triode and tetrode vacuum tubes operating in the dynatron mode[9][59]
- Some magnetron tubes and other microwave vacuum tubes[60]
- maser[61]
- parametric amplifier[62]
Electric
including these devices- electric arc[65]
- thyratron tubes[66]
- neon lamp[6]
- fluorescent lamp[2]
- other
In addition,
Negative static or "absolute" resistance
A point of some confusion is whether ordinary resistance ("static" or "absolute" resistance, ) can be negative.[68][72] In electronics, the term "resistance" is customarily applied only to passive materials and components[30] – such as wires, resistors and diodes. These cannot have as shown by
However it is easily shown that the ratio of voltage to current v/i at the terminals of any power source (AC or DC) is negative.
Eventual passivity
A circuit cannot have negative static resistance (be active) over an infinite voltage or current range, because it would have to be able to produce infinite power.[10] Any active circuit or device with a finite power source is "eventually passive".[49][74][75] This property means if a large enough external voltage or current of either polarity is applied to it, its static resistance becomes positive and it consumes power[74]
Therefore, the ends of the I–V curve will eventually turn and enter the 1st and 3rd quadrants.[75] Thus the range of the curve having negative static resistance is limited,[10] confined to a region around the origin. For example, applying a voltage to a generator or battery (graph, above) greater than its open-circuit voltage[76] will reverse the direction of current flow, making its static resistance positive so it consumes power. Similarly, applying a voltage to the negative impedance converter below greater than its power supply voltage Vs will cause the amplifier to saturate, also making its resistance positive.
Negative differential resistance
In a device or circuit with negative differential resistance (NDR), in some part of the I–V curve the current decreases as the voltage increases:[21]
Passive negative differential resistances have positive static resistance;[3][6][21] they consume net power. Therefore, the I–V curve is confined to the 1st and 3rd quadrants of the graph,[15] and passes through the origin. This requirement means (excluding some asymptotic cases) that the region(s) of negative resistance must be limited,[17][77] and surrounded by regions of positive resistance, and cannot include the origin.[3][10]
Types
Negative differential resistances can be classified into two types:[16][77]
- Voltage controlled negative resistance (VCNR, short-circuit stable,
- Current controlled negative resistance (CCNR, open-circuit stable,gas discharge tubes .[43]
Most devices have a single negative resistance region. However devices with multiple separate negative resistance regions can also be fabricated.
An intrinsic parameter used to compare different devices is the peak-to-valley current ratio (PVR),[67] the ratio of the current at the top of the negative resistance region to the current at the bottom (see graphs, above):
Amplification
A negative differential resistance device can amplify an AC signal applied to it[11][13] if the signal is biased with a DC voltage or current to lie within the negative resistance region of its I–V curve.[7][12]
The tunnel diode circuit (see diagram) is an example.[82] The tunnel diode TD has voltage controlled negative differential resistance.[54] The battery adds a constant voltage (bias) across the diode so it operates in its negative resistance range, and provides power to amplify the signal. Suppose the negative resistance at the bias point is . For stability must be less than .[36] Using the formula for a voltage divider, the AC output voltage is[82]
Explanation of power gain
The diagrams illustrate how a biased negative differential resistance device can increase the power of a signal applied to it, amplifying it, although it only has two terminals. Due to the superposition principle the voltage and current at the device's terminals can be divided into a DC bias component () and an AC component ().
In a passive device, the AC power produced comes from the input DC bias current,[21] the device absorbs DC power, some of which is converted to AC power by the nonlinearity of the device, amplifying the applied signal. Therefore, the output power is limited by the bias power[21]
The device may also have reactance and therefore the phase difference between current and voltage may differ from 180° and may vary with frequency.[8][42][87] As long as the real component of the impedance is negative (phase angle between 90° and 270°),[84] the device will have negative resistance and can amplify.[87][88]
The maximum AC output power is limited by size of the negative resistance region ( in graphs above)[21][89]
Reflection coefficient
The reason that the output signal can leave a negative resistance through the same port that the input signal enters is that from transmission line theory, the AC voltage or current at the terminals of a component can be divided into two oppositely moving waves, the incident wave , which travels toward the device, and the reflected wave , which travels away from the device.[90] A negative differential resistance in a circuit can amplify if the magnitude of its reflection coefficient , the ratio of the reflected wave to the incident wave, is greater than one.[17][85]
Stability conditions
Because it is nonlinear, a circuit with negative differential resistance can have multiple
- In a CCNR (S-type) negative resistance, the resistance function is single-valued. Therefore, stability is determined by the poles of the circuit's impedance equation:.[98][99]
- For nonreactive circuits () a sufficient condition for stability is that the total resistance is positive[100] so the CCNR is stable for[16][77][97]
- Since CCNRs are stable with no load at all, they are called "open circuit stable".[77][78][86][101][note 2]
- In a VCNR (N-type) negative resistance, the conductancefunction is single-valued. Therefore, stability is determined by the poles of the admittance equation .conductance in the circuit is positive[100]so the VCNR is stable for[16][97]
- Since VCNRs are even stable with a short-circuited output, they are called "short circuit stable".[77][78][101][note 2]
For general negative resistance circuits with reactance, the stability must be determined by standard tests like the Nyquist stability criterion.[102] Alternatively, in high frequency circuit design, the values of for which the circuit is stable are determined by a graphical technique using "stability circles" on a Smith chart.[17]
Operating regions and applications
For simple nonreactive negative resistance devices with and the different operating regions of the device can be illustrated by load lines on the I–V curve[77] (see graphs).
The DC load line (DCL) is a straight line determined by the DC bias circuit, with equation
- VCNRs require a low impedance bias (), such as a voltage source.
- CCNRs require a high impedance bias () such as a current source, or voltage source in series with a high resistance.
The AC load line (L1 − L3) is a straight line through the Q point whose slope is the differential (AC) resistance facing the device. Increasing rotates the load line counterclockwise. The circuit operates in one of three possible regions (see diagrams), depending on .[77]
- Stable region (green) (illustrated by line L1): When the load line lies in this region, it intersects the I–V curve at one point Q1.monostable multivibrator.[104]
- VCNRs are stable when .
- CCNRs are stable when .
- Unstable point (Line L2): When the load line is tangent to the I–V curve. The total differential (AC) resistance of the circuit is zero (poles on the jω axis), so it is unstable and with a tuned circuit can oscillate. Linear oscillators operate at this point. Practical oscillators actually start in the unstable region below, with poles in the RHP, but as the amplitude increases the oscillations become nonlinear, and due to eventual passivity the negative resistance r decreases with increasing amplitude, so the oscillations stabilize at an amplitude where[105].
- Bistable region (red) (illustrated by line L3): In this region the load line can intersect the I–V curve at three points.bistable multivibrators) and Schmitt triggersoperate in this region.
- VCNRs can be bistable when
- CCNRs can be bistable when
Active resistors – negative resistance from feedback
In addition to the passive devices with intrinsic negative differential resistance above, circuits with amplifying devices like transistors or op amps can have negative resistance at their ports.[3][37] The input or output impedance of an amplifier with enough positive feedback applied to it can be negative.[47][38][107][108] If is the input resistance of the amplifier without feedback, is the
In circuit theory these are called "active resistors".[24][28][48][49] Applying a voltage across the terminals causes a proportional current out of the positive terminal, the opposite of an ordinary resistor.[26][45][46] For example, connecting a battery to the terminals would cause the battery to charge rather than discharge.[44]
Considered as one-port devices, these circuits function similarly to the passive negative differential resistance components above, and like them can be used to make one-port amplifiers and oscillators[3][11] with the advantages that:
- because they are active devices they do not require an external DC bias to provide power, and can be DC coupled,
- the amount of negative resistance can be varied by adjusting the loop gain,
- they can be linear circuit elements;harmonic distortion.
The I–V curve can have voltage-controlled ("N" type) or current-controlled ("S" type) negative resistance, depending on whether the feedback loop is connected in "shunt" or "series".[26]
Negative
Feedback oscillators
If an LC circuit is connected across the input of a positive feedback amplifier like that above, the negative differential input resistance can cancel the positive loss resistance inherent in the tuned circuit.[114] If this will create in effect a tuned circuit with zero AC resistance (
Q enhancement
A tuned circuit connected to a negative resistance which cancels some but not all of its parasitic loss resistance (so ) will not oscillate, but the negative resistance will decrease the
Chaotic circuits
Circuits which exhibit chaotic behavior can be considered quasi-periodic or nonperiodic oscillators, and like all oscillators require a negative resistance in the circuit to provide power.[124] Chua's circuit, a simple nonlinear circuit widely used as the standard example of a chaotic system, requires a nonlinear active resistor component, sometimes called Chua's diode.[124] This is usually synthesized using a negative impedance converter circuit.[124]
Negative impedance converter
A common example of an "active resistance" circuit is the negative impedance converter (NIC)[45][46][115][125] shown in the diagram. The two resistors and the op amp constitute a negative feedback non-inverting amplifier with gain of 2.[115] The output voltage of the op-amp is
Negative capacitance and inductance
By replacing in the above circuit with a capacitor () or inductor (), negative capacitances and inductances can also be synthesized.[37][46] A negative capacitance will have an I–V relation and an impedance of
There is also another way of looking at them. In a negative capacitance the current will be 180° opposite in phase to the current in a positive capacitance. Instead of leading the voltage by 90° it will lag the voltage by 90°, as in an inductor.
Oscillators
Negative differential resistance devices are widely used to make
Uses
Negative resistance oscillators are mainly used at high
The negative resistance oscillator model is not limited to one-port devices like diodes but can also be applied to feedback oscillator circuits with
Gunn diode oscillator
The common Gunn diode oscillator (circuit diagrams)[21] illustrates how negative resistance oscillators work. The diode D has voltage controlled ("N" type) negative resistance and the voltage source biases it into its negative resistance region where its differential resistance is . The choke RFC prevents AC current from flowing through the bias source.[21] is the equivalent resistance due to damping and losses in the series tuned circuit , plus any load resistance. Analyzing the AC circuit with Kirchhoff's Voltage Law gives a differential equation for , the AC current[21]
- : (polesin left half plane) If the diode's negative resistance is less than the positive resistance of the tuned circuit, the damping is positive. Any oscillations in the circuit will lose energy as heat in the resistance and die away exponentially to zero, as in an ordinary tuned circuit.[39] So the circuit does not oscillate.
- : (poles on jω axis) If the positive and negative resistances are equal, the net resistance is zero, so the damping is zero. The diode adds just enough energy to compensate for energy lost in the tuned circuit and load, so oscillations in the circuit, once started, will continue at a constant amplitude.[39] This is the condition during steady-state operation of the oscillator.
- : (poles in right half plane) If the negative resistance is greater than the positive resistance, damping is negative, so oscillations will grow exponentially in energy and amplitude.[39] This is the condition during startup.
Practical oscillators are designed in region (3) above, with net negative resistance, to get oscillations started.[118] A widely used rule of thumb is to make .
At large amplitudes the circuit is nonlinear, so the linear analysis above does not strictly apply and differential resistance is undefined; but the circuit can be understood by considering to be the "average" resistance over the cycle. As the amplitude of the sine wave exceeds the width of the negative resistance region and the voltage swing extends into regions of the curve with positive differential resistance, the average negative differential resistance becomes smaller, and thus the total resistance and the damping becomes less negative and eventually turns positive. Therefore, the oscillations will stabilize at the amplitude at which the damping becomes zero, which is when .[21]
Gunn diodes have negative resistance in the range −5 to −25 ohms.[135] In oscillators where is close to ; just small enough to allow the oscillator to start, the voltage swing will be mostly limited to the linear portion of the I–V curve, the output waveform will be nearly sinusoidal and the frequency will be most stable. In circuits in which is far below , the swing extends further into the nonlinear part of the curve, the clipping distortion of the output sine wave is more severe,[134] and the frequency will be increasingly dependent on the supply voltage.
Types of circuit
Negative resistance oscillator circuits can be divided into two types, which are used with the two types of negative differential resistance – voltage controlled (VCNR), and current controlled (CCNR)[91][103]
- Negative resistance (voltage controlled) oscillator: Since VCNR ("N" type) devices require a low impedance bias and are stable for load impedances less than r,[103] the ideal oscillator circuit for this device has the form shown at top right, with a voltage source Vbias to bias the device into its negative resistance region, and parallel resonant circuit load LC. The resonant circuit has high impedance only at its resonant frequency, so the circuit will be unstable and oscillate only at that frequency.
- Negative conductance (current controlled) oscillator: CCNR ("S" type) devices, in contrast, require a high impedance bias and are stable for load impedances greater than r.[103] The ideal oscillator circuit is like that at bottom right, with a current source bias Ibias (which may consist of a voltage source in series with a large resistor) and series resonant circuit LC. The series LC circuit has low impedance only at its resonant frequency and so will only oscillate there.
Conditions for oscillation
Most oscillators are more complicated than the Gunn diode example, since both the active device and the load may have reactance (X) as well as resistance (R). Modern negative resistance oscillators are designed by a
Alternately, the condition for oscillation can be expressed using the reflection coefficient.[85] The voltage waveform at the reference plane can be divided into a component V1 travelling toward the negative resistance device and a component V2 travelling in the opposite direction, toward the resonator part. The reflection coefficient of the active device is greater than one, while that of the resonator part is less than one. During operation the waves are reflected back and forth in a round trip so the circuit will oscillate only if[85][117][137]
Amplifiers
Negative differential resistance devices such as Gunn and IMPATT diodes are also used to make
Reflection amplifier
One widely used circuit is the reflection amplifier in which the separation is accomplished by a
The filter has only reactive components and so does not absorb any power itself, so power is passed between the diode and the ports without loss. The input signal power to the diode is
Switching circuits
Negative differential resistance devices are also used in
- Astable multivibrator – a circuit with two unstable states, in which the output periodically switches back and forth between the states. The time it remains in each state is determined by the time constant of an RC circuit. Therefore, it is a relaxation oscillator, and can produce square waves or triangle waves.
- Monostable multivibrator– is a circuit with one unstable state and one stable state. When in its stable state a pulse is applied to the input, the output switches to its other state and remains in it for a period of time dependent on the time constant of the RC circuit, then switches back to the stable state. Thus the monostable can be used as a timer or delay element.
- digital counters.
Other applications
Neuronal models
Some instances of neurons display regions of negative slope conductances (RNSC) in voltage-clamp experiments.[142] The negative resistance here is implied were one to consider the neuron a typical Hodgkin–Huxley style circuit model.
History
Negative resistance was first recognized during investigations of
Arc transmitters
Vacuum tubes
By the early 20th century, although the physical causes of negative resistance were not understood, engineers knew it could generate oscillations and had begun to apply it.
In 1918 Albert Hull at
The negative impedance converter originated from work by Marius Latour around 1920.[153][154] He was also one of the first to report negative capacitance and inductance.[153] A decade later, vacuum tube NICs were developed as telephone line repeaters at Bell Labs by George Crisson and others,[26][127] which made transcontinental telephone service possible.[127] Transistor NICs, pioneered by Linvill in 1953, initiated a great increase in interest in NICs and many new circuits and applications developed.[125][127]
Solid state devices
Negative differential resistance in
The first person to exploit negative resistance diodes practically was Russian radio researcher
The first widely used solid-state negative resistance device was the tunnel diode, invented in 1957 by Japanese physicist Leo Esaki.[67][163] Because they have lower parasitic capacitance than vacuum tubes due to their small junction size, diodes can function at higher frequencies, and tunnel diode oscillators proved able to produce power at microwave frequencies, above the range of ordinary vacuum tube oscillators. Its invention set off a search for other negative resistance semiconductor devices for use as microwave oscillators,[164] resulting in the discovery of the IMPATT diode, Gunn diode, TRAPATT diode, and others. In 1969 Kurokawa derived conditions for stability in negative resistance circuits.[136] Currently negative differential resistance diode oscillators are the most widely used sources of microwave energy,[80] and many new negative resistance devices have been discovered in recent decades.[67]
Notes
- ^ Some microwave texts use this term in a more specialized sense: a voltage controlled negative resistance device (VCNR) such as a tunnel diode is called a "negative conductance" while a current controlled negative resistance device (CCNR) such as an IMPATT diode is called a "negative resistance". See the Stability conditions section
- ^ astable multivibrator, and the bistableregion is considered the "stable" one. This article uses the former "linear" definition, the earliest one, which is found in the Abraham, Bangert, Dorf, Golio, and Tellegen sources. The latter "switching circuit" definition is found in the Kumar and Taub sources.
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neon negative resistance glow discharge.
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Further reading
- Gottlieb, Irving M. (1997). Practical Oscillator Handbook. Elsevier. ISBN 978-0080539386. How negative differential resistance devices work in oscillators.
- Hong, Sungook (2001). Wireless: From Marconi's Black-Box to the Audion (PDF). USA: MIT Press. ISBN 978-0262082983., ch. 6 Account of discovery of negative resistance and its role in early radio.
- Snelgrove, Martin (2008). "Negative resistance circuits". AccessScience Online Encyclopedia. McGraw-Hill. . Retrieved May 17, 2012. Elementary one-page introduction to negative resistance.