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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'''.
</small>
 
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|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|...]]

Latest revision as of 10:19, 11 September 2020

1901 photograph of a stentor (announcer) at the Budapest Telefon Hirmondó.

Telephone newspaper is a general term for the telephone-based news and entertainment services which were introduced beginning in the 1890s, and primarily located in large European cities. These systems were the first example of electronic broadcasting, and offered a wide variety of programming, however, only a relative few were ever established. Although these systems predated the invention of radio, they were supplanted by radio broadcasting stations beginning in the 1920s, primarily because radio signals were able to cover much wider areas with higher quality audio.

History

After the electric telephone was introduced in the mid-1870s, it was mainly used for personal communication. But the idea of distributing entertainment and news appeared soon thereafter, and many early demonstrations included the transmission of musical concerts. In one particularly advanced example, Clément Ader, at the 1881 Paris Electrical Exhibition, prepared a listening room where participants could hear, in stereo, performances from the Paris Grand Opera. Also, in 1888, Edward Bellamy's influential novel Looking Backward: 2000-1887 foresaw the establishment of entertainment transmitted by telephone lines to individual homes.

The scattered demonstrations were eventually followed by the establishment of more organized services, which were generally called Telephone Newspapers, although all of these systems also included entertainment programming. However, the technical capabilities of the time meant that there were limited means for amplifying and transmitting telephone signals over long distances, so listeners had to wear headphones to receive the programs, and service areas were generally limited to a single city. While some of the systems, including the Telefon Hirmondó, built their own one-way transmission lines, others, including the Electrophone, used standard commercial telephone lines, which allowed subscribers to talk to operators in order to select programming. The Telephone Newspapers drew upon a mixture of outside sources for their programs, including local live theaters and church services, whose programs were picked up by special telephone lines, and then retransmitted to the subscribers. Other programs were transmitted directly from the system's own studios. In later years, retransmitted radio programs were added.

During this era telephones were expensive luxury items, so the subscribers tended to be the wealthy elite of society. Financing was normally done by charging fees, including monthly subscriptions for home users, and, in locations such as hotel lobbies, through the use of coin-operated receivers, which provided short periods of listening for a set payment. Some systems also accepted paid advertising.

Footnotes