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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
{{:{{FeaturedArticleTitle}}}}
:<math>C_{M}=C (1-A)\ ,</math>
<small>
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.
==Footnotes==
 
{{reflist|2}}
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'''.
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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.
 
=== Derivation ===
{{Image|Miller effect.PNG|right|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''.
 
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Latest revision as of 10:19, 11 September 2020

The Irvin pin. The eyes have always been red, but there are urban legends about the meanings of other colors.
A pin from another company, possibly Switlik or Standard Parachute. This style is common in catalogs and auctions of military memorabilia.

The Caterpillar Club is an informal association of people who have successfully used a parachute to bail out of a disabled aircraft. After authentication by the parachute maker, applicants receive a membership certificate and a distinctive lapel pin.

History

Before April 28, 1919 there was no way for a pilot to jump out of a plane and then to deploy a parachute. Parachutes were stored in a canister attached to the aircraft, and if the plane was spinning, the parachute could not deploy. Film industry stuntman Leslie Irvin developed a parachute that the pilot could deploy at will from a back pack using a ripcord. He joined the Army Air Corps parachute research team, and in April 1919 he successfully tested his design, though he broke his ankle during the test. Irvin was the first person to make a premeditated free fall jump from an airplane. He went on to form the Irving Airchute Company, which became a large supplier of parachutes. (A clerical error resulted in the addition of the "g" to Irvin and this was left in place until 1970, when the company was unified under the title Irvin Industries Incorporated.) The Irvin brand is now a part of Airborne Systems, a company with operations in Canada, the U.S. and the U.K.[1].

An early brochure [2] of the Irvin Parachute Company credits William O'Connor 24 August 1920 at McCook Field near Dayton, Ohio as the first person to be saved by an Irvin parachute, but this feat was unrecognised. On 20 October 1922 Lieutenant Harold R. Harris, chief of the McCook Field Flying Station, jumped from a disabled Loening W-2A monoplane fighter. Shortly after, two reporters from the Dayton Herald, realising that there would be more jumps in future, suggested that a club should be formed. 'Caterpillar Club' was suggested because the parachute canopy was made of silk, and because caterpillars have to climb out of their cocoons and fly away. Harris became the first member, and from that time forward any person who jumped from a disabled aircraft with a parachute became a member of the Caterpillar Club. Other famous members include General James Doolittle, Charles Lindbergh and (retired) astronaut John Glenn.

In 1922 Leslie Irvin agreed to give a gold pin to every person whose life was saved by one of his parachutes. By 1945 the number of members with the Irvin pins had grown to over 34,000. In addition to the Irvin Air Chute Company and its successors, other parachute manufacturers have also issued caterpillar pins for successful jumps. Irvin/Irving's successor, Airborne Systems Canada, still provides pins to people who made their jump long ago and are just now applying for membership. Another of these is Switlik Parachute Company, which though it no longer makes parachutes, still issues pins.

Footnotes