CZ:Featured article/Current: Difference between revisions

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In electronics, the '''[[Miller effect]]''' is the increase in the equivalent input capacitance of an inverting voltage amplifier due to a capacitance connected between two gain-related nodes, one on the input side of an amplifier and the other the output side. The amplified input capacitance due to the Miller effect, called the '''Miller capacitance''' ''C<sub>M</sub>'', is given by
{{Image|Two diode structures.PNG|right|200px|Mesa diode structure (top) and planar diode structure with guard-ring (bottom).}}
:<math>C_{M}=C (1-A)\ ,</math>
where ''A''  is the voltage gain between the two nodes at either end of the coupling capacitance, which is a negative number because the amplifier is ''inverting'', and ''C'' is the coupling capacitance.


Although the term ''Miller effect'' normally refers to capacitance, the Miller effect applies to any impedance connected between two nodes exhibiting gain. These properties of the Miller effect are generalized in '''Miller's theorem'''.
A '''[[semiconductor diode]]''' is a two-terminal device that conducts current in only one direction, made of two or more layers of which at least one is a semiconductor. An example is the ''pn''-diode, made by joining a ''p''-type semiconducting layer to an ''n''-type semiconducting layer. For a discussion of dopant impurities and the terminology ''p-'' and ''n-''type. see [[Semiconductor#Dopant_impurities|dopant impurities]].


The Miller effect is named after John Milton Miller.When Miller published his work in 1920, he was working on vacuum tube triodes, however the same theory applies to more modern devices such as bipolar transistors and MOSFETs.
The figure shows two of the many possible structures used for ''pn-''semiconductor diodes, both adapted to increase the voltage the devices can withstand in reverse bias. The top structure uses a mesa to avoid a sharp curvature of the ''p<sup>+</sup>-''region next to the adjoining ''n-''layer. The bottom structure uses a lightly doped ''p-''guard-ring at the edge of the sharp corner of the ''p<sup>+</sup>-''layer to spread the voltage out over a larger distance and reduce the electric field. (Superscripts like ''n<sup>+</sup>'' or ''n<sup>−</sup>'' refer to heavier or lighter impurity doping levels.)
==Types==
Semiconductor diodes come in a large variety of types:
*''pn''-diode: The ''pn'' junction diode consists of an ''n''-type semiconductor joined to a ''p''-type semiconductor.
*Zener diode: The Zener diode is a special type of ''pn''-diode made to operate in the reverse breakdown region, and used often as a voltage regulator. The breakdown voltage in these diodes is sometimes called the ''Zener voltage''. Depending upon the voltage range designed for, the diode may break down by either Zener breakdown, an electron tunneling behavior, or by avalanche breakdown.
*Schottky diode: The Schottky diode is made using a metal such as aluminum or platinum, on a lightly doped semiconductor substrate.
*Tunnel diode: Like the Zener diode, the tunnel diode (or Esaki diode) is made up of heavily doped ''n-'' and ''p''-type layers with a very abrupt transition between the two types. Conduction takes place by electron tunneling.
*Light-emitting diode: The light-emitting diode is designed to convert electrical current into light.
*Photodiode: The photodiode is the inverse of the light-emitting diode, acting as a photodetector, converting incident light to a detectable electric current.
*''pin''-diode: The ''pin''-diode is made of three layers: an intrinsic (undoped) layer between the ''p''- and ''n''-type layers. Because of its rapid switching characteristics it is used in microwave and radio-frequency applications.
*Gunn diode: The Gunn diode is a ''transferred electron device''  based upon the Gunn effect in III-V semiconductors, and is used to generate microwave oscillations.
*Varactor: a ''pn''-junction used in reverse bias as a voltage-variable capacitor for tuning radio receivers. The term ''varactor'' also is used for devices that behave like back-to-back Zener diodes.


=== Derivation ===
[[semiconductor diode|...]]
{{Image|Miller effect.PNG|center|350px|These two circuits are equivalent. Arrows indicate current flow. Notice the polarity of the dependent voltage source is flipped, to correspond with an ''inverting'' amplifier.}}
Consider a voltage amplifier of gain −''A'' with an impedance ''Z<sub>&mu;</sub>'' connected between its input and output stages. The input signal is provided by a Thévenin voltage source representing the driving stage. The voltage at the input end (node 1) of the coupling impedance is ''v<sub>1</sub>'', and at the output end  −''Av<sub>1</sub>''.  The current through ''Z<sub>&mu;</sub>'' according to Ohm's law is given by:
 
:<math>i_Z =  \frac{v_1 - (- A)v_1}{Z_\mu} = \frac{v_1}{ Z_\mu / (1+A)}</math>.
 
The input current is:
 
:<math>i_1 = i_Z+\frac{v_1}{Z_{11}} \ . </math>
 
The impedance of the circuit at node 1 is:
 
:<math>\frac {1}{Z_{1}} = \frac {i_1} {v_1} = \frac {1+A}{Z_\mu} +\frac{1}{Z_{11}} .</math>
 
This same input impedance is found if the input stage simply is decoupled from the output stage, and the reduced impedance ''{{nowrap|Z<sub>&mu;</sub> / (1+A)}}'' is substituted in parallel with ''Z<sub>11</sub>''. Of course, if the input stage is decoupled, no current reaches the output stage. To fix that problem, a dependent current source is attached to the second stage to provide the correct current to the output circuit, as shown in the lower figure. This decoupling scenario is the basis for ''Miller's theorem'', which replaces the current source on the output side by addition of a shunt impedance in the output circuit that draws the same current. The striking prediction that a coupling impedance ''Z<sub>&mu;</sub>'' reduces input impedance by an amount equivalent to shunting the input with the reduced impedance ''{{nowrap|Z<sub>&mu;</sub> / (1+A)}}'' is called the ''Miller effect''.
 
[[Miller effect|...]]

Revision as of 13:24, 17 June 2011

(PD) Image: John R. Brews
Mesa diode structure (top) and planar diode structure with guard-ring (bottom).

A semiconductor diode is a two-terminal device that conducts current in only one direction, made of two or more layers of which at least one is a semiconductor. An example is the pn-diode, made by joining a p-type semiconducting layer to an n-type semiconducting layer. For a discussion of dopant impurities and the terminology p- and n-type. see dopant impurities.

The figure shows two of the many possible structures used for pn-semiconductor diodes, both adapted to increase the voltage the devices can withstand in reverse bias. The top structure uses a mesa to avoid a sharp curvature of the p+-region next to the adjoining n-layer. The bottom structure uses a lightly doped p-guard-ring at the edge of the sharp corner of the p+-layer to spread the voltage out over a larger distance and reduce the electric field. (Superscripts like n+ or n− refer to heavier or lighter impurity doping levels.)

Types

Semiconductor diodes come in a large variety of types:

  • pn-diode: The pn junction diode consists of an n-type semiconductor joined to a p-type semiconductor.
  • Zener diode: The Zener diode is a special type of pn-diode made to operate in the reverse breakdown region, and used often as a voltage regulator. The breakdown voltage in these diodes is sometimes called the Zener voltage. Depending upon the voltage range designed for, the diode may break down by either Zener breakdown, an electron tunneling behavior, or by avalanche breakdown.
  • Schottky diode: The Schottky diode is made using a metal such as aluminum or platinum, on a lightly doped semiconductor substrate.
  • Tunnel diode: Like the Zener diode, the tunnel diode (or Esaki diode) is made up of heavily doped n- and p-type layers with a very abrupt transition between the two types. Conduction takes place by electron tunneling.
  • Light-emitting diode: The light-emitting diode is designed to convert electrical current into light.
  • Photodiode: The photodiode is the inverse of the light-emitting diode, acting as a photodetector, converting incident light to a detectable electric current.
  • pin-diode: The pin-diode is made of three layers: an intrinsic (undoped) layer between the p- and n-type layers. Because of its rapid switching characteristics it is used in microwave and radio-frequency applications.
  • Gunn diode: The Gunn diode is a transferred electron device based upon the Gunn effect in III-V semiconductors, and is used to generate microwave oscillations.
  • Varactor: a pn-junction used in reverse bias as a voltage-variable capacitor for tuning radio receivers. The term varactor also is used for devices that behave like back-to-back Zener diodes.

...

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