Dual of Miller's Theorem Consider an arbitrary network (shown in Fig. The transformations suggested in Miller's Theorem and its dual are useful in. current drawn from node 2 in fig – 2 is same as current drawn from node 2 in fig ,This is known as Miller's theorem. MILLER'S THEOREM Miller's theorem states that if an impedance is connected between the input and output nodes in an amplifier, having a reference node.


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They are used in oscillators and amplifiers, particularly at microwave frequencies. Most microwave energy is produced with negative resistance devices.

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They can also have hysteresis and be bistable, and so are used in switching, 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 and these are used in oscillators and active filters.

Millers theorem and its dual they are nonlinear, negative resistance devices have a complicated behavior than the positive ohmic resistances usually encountered in electric circuits. Therefore, there is no real negative resistor analogous to a positive resistor, the resistance between two terminals of an electrical device or circuit is determined by its current—voltage curve, giving the current i through it for any given voltage v across it.

Most materials, including the ordinary resistances encountered in electrical circuits, obey Ohms law, so the I—V curve of an ohmic resistance is a straight line through the origin with positive slope.

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The resistance is the ratio of voltage to current, the slope of the line and is constant. Negative millers theorem and its dual occurs in a few nonlinear devices, in a nonlinear component the I—V curve is not a straight line, so it does not obey Ohms law. Resistance can still be defined, but the resistance millers theorem and its dual not constant and it is the inverse slope of the line from the origin through the point on the I—V curve.

Thus power sources formally have negative static resistance, however this term is never used in practice, because the term resistance is only applied to passive components.

Miller theorem

Static resistance determines the power dissipation in a component, passive devices, which consume electric power, have positive static resistance, while active devices, which produce electric power, do not. Differential resistance is only relevant to time-varying currents, points on the curve where the slope is negative, meaning an increase in voltage causes a decrease millers theorem and its dual current, have negative differential resistance.

Devices of this type can amplify signals, and are what is meant by the term negative resistance 6. Potentiometer — A potentiometer, informally a pot, is a three-terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider.

Miller theorem - Wikipedia

If only two terminals are used, one end and the wiper, it acts as a resistor or rheostat. The measuring instrument called millers theorem and its dual potentiometer is essentially a voltage divider used for measuring electric potential, potentiometers are commonly used to control electrical devices such as volume controls on audio equipment.

Potentiometers operated by a mechanism can be used as transducers, for example. Potentiometers are rarely used to control significant power, since the power dissipated in the potentiometer would be comparable to the power in the controlled load.


The resistive element can be flat or angled, each end of the resistive element is connected to millers theorem and its dual terminal on the case. The wiper is connected to a terminal, usually between the other two. On panel potentiometers, the wiper is usually the terminal of three.

For single-turn potentiometers, this wiper typically travels just under one revolution around the contact, the only point of ingress for contamination is millers theorem and its dual narrow space between the shaft and the housing it rotates in. Another type is the slider potentiometer, which has a wiper which slides along a linear element instead of rotating.

Contamination can potentially enter anywhere along the slot the slider moves in, making effective sealing more difficult, an advantage of the slider potentiometer is that the slider position gives a visual indication of its setting.

Others are enclosed within the equipment and are intended to be millers theorem and its dual to calibrate equipment during manufacture or repair and they are usually physically much smaller than user-accessible potentiometers, and may need to be operated by a screwdriver rather than having a knob.

Miller theorem

They are usually called preset potentiometers or trim pots, some presets are accessible by a small screwdriver poked through a hole in the case to allow servicing without dismantling.

Multiturn potentiometers are also operated by rotating a shaft, but by several turns rather than less than a full turn, a string potentiometer is a multi-turn potentiometer operated by an attached reel of wire turning against a spring, enabling it to convert linear position to a variable resistance.

User-accessible rotary potentiometers can be fitted with a switch millers theorem and its dual operates usually at the extreme of rotation.


Multiple resistance elements can be ganged together with their contacts on the same shaft, for example. The relationship between position and resistance, known as the taper or law, is controlled by the manufacturer 7.

Miller’s theorem & its Dual

Potentiometer measuring instrument — A potentiometer is an instrument for variable potential in a circuit. Before the introduction of the coil and digital volt meters, potentiometers were used in measuring voltage.

The method was described by Johann Christian Poggendorff around and became millers theorem and its dual standard measuring technique.

In this arrangement, a fraction of a voltage from a resistive slide wire is compared with an unknown voltage by means of a galvanometer.