Negative Resistance Oscillator Analysis Essay

In electronics, negative resistance (NR) is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it.[4][5]

This is in contrast to an ordinary resistor in which an increase of applied voltage causes a proportional increase in current due to Ohm's law, resulting in a positive resistance.[6] While a positive resistance consumes power from current passing through it, a negative resistance produces power.[7][8] Under certain conditions it can increase the power of an electrical signal, amplifying it.[3][9][10]

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 amplify,[3][11] converting DC power applied to its terminals to AC output power to amplify an AC signal applied to the same terminals.[7][12] They are used in electronic oscillators and amplifiers,[13] particularly at microwave frequencies. Most microwave energy is produced with negative differential resistance devices.[14] They can also have hysteresis[15] and be bistable, and so are used in switching and memory circuits.[16] Examples of devices with negative differential resistance are tunnel diodes, Gunn diodes, and gas discharge tubes such as neon lamps. In addition, circuits containing amplifying devices such as transistors and op amps with positive feedback can have negative differential resistance. These are used in oscillators and active filters.

Because they are nonlinear, negative resistance devices have a more complicated behavior than the positive "ohmic" resistances usually encountered in electric circuits. Unlike most positive resistances, negative resistance varies depending on the voltage or current applied to the device, and negative resistance devices can have negative resistance over only a limited portion of their voltage or current range.[10][17] Therefore, there is no real "negative resistor" analogous to a positive resistor, which has a constant negative resistance over an arbitrarily wide range of current.

Definitions[edit]

The resistance between two terminals of an electrical device or circuit is determined by its current–voltage (I–V) curve (characteristic curve), giving the current through it for any given voltage across it.[18] Most materials, including the ordinary (positive) resistances encountered in electrical circuits, obey Ohm's law; the current through them is proportional to the voltage over a wide range.[6] So the I–V curve of an ohmic resistance is a straight line through the origin with positive slope. The resistance is the ratio of voltage to current, the inverse slope of the line (in I–V graphs where the voltage is the independent variable) and is constant.

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 (chord) from the origin through the point on the I–V curve.[6] In a power source, like a 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 convention and 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,[3][22] or incremental[6] resistance) – This is the 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 slope of 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.

Conductance is the reciprocal of resistance.[33][34] It is measured in siemens (formerly mho) which is the conductance of a resistor with a resistance of one ohm.[33] Each type of resistance defined above has a corresponding conductance[34]

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[edit]

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 passive sign convention; positive conventional current is defined to enter the positive voltage terminal; this means power P flowing from the circuit into the component is defined to be positive, while power flowing from the component into the circuit is negative.[25][31] 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 fieldE (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[edit]

rdiff > 0
Positive differential resistance
rdiff < 0
Negative differential resistance
Rstatic > 0
Passive:
Consumes
net power
Positive resistances:
  • Resistors
  • Ordinary diodes
  • Most passive components
Passive negative differential resistances:
  • Tunnel diodes
  • Gunn diodes
  • Gas-discharge tubes
Rstatic < 0
Active:
Produces
net power
Power sources:
  • Batteries
  • Generators
  • Transistors
  • Most active components
"Active resistors"
Positive feedback amplifiers used in:
  • Feedback oscillators
  • Negative impedance converters
  • Active filters

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 .[3][17][20] Negative differential resistance devices have unique capabilities: they can act as one-port amplifiers,[3][11][13][38] increasing the power of a time-varying signal applied to their port (terminals), or excite oscillations in a tuned circuit to make an oscillator.[37][38][39] They can also have hysteresis.[15][16] It is not possible for a device to have negative differential resistance without a power source,[40] and these devices can be divided into two categories depending on whether they get their power from an internal source or from their port:[16][37][39][41][42]

  • 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.[41][42] The I–V curve, including the negative resistance region, lies in the 1st and 3rd quadrant of the plane[15] so the device has positive static resistance.[21] Examples are 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 resistance section 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,[3][26][44][45][46] Unlike in the above devices, the downward-sloping region of the I–V curve passes through the origin, so it lies in the 2nd and 4th quadrants of the plane, meaning the device sources power.[24] Amplifying devices like transistors and op-amps with positive feedback can have this type of negative resistance,[37][47][26][42] and are used in feedback oscillators and active filters.[42][46] Since these circuits produce net power from their port, they must have an internal DC power source, or else a separate connection to an external power supply.[24][26][44] In 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 resistors section below.

Occasionally ordinary power sources are referred to as "negative resistances"[20][27][32][51] (fig. 3 above). Although the "static" or "absolute" resistance

Fluorescent lamp, a device with negative differential resistance.[1][2] In operation, an increase in current through the fluorescent tube causes a drop in voltage across it. If the tube were connected directly to the power line, the falling tube voltage would cause more and more current to flow, causing it to arc flash and destroy itself.[1][3] To prevent this, fluorescent tubes are connected to the power line through a ballast. The ballast adds positive impedance (AC resistance) to the circuit to counteract the negative resistance of the tube, limiting the current.[1]
An I–V curve, showing the difference between static resistance (inverse slope of line B) and differential resistance (inverse slope of line C) at a point (A).
The quadrants of the I–V plane,[24][25] showing regions representing passive devices (white) and active devices (red)
Fig. 1: I–V curve of linear or "ohmic" resistance, the common type of resistance encountered in electrical circuits. The current is proportional to the voltage, so both the static and differential resistance is positive
Fig. 4: I–V curve of a negative linear[8] or "active" resistance[24][35][36](AR, red). It has negative differential resistance and negative static resistance (is active):
A battery has negative static resistance[20][23][32] (red) over its normal operating range, but positive differential resistance.

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