CZ:Featured article/Current: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Chunbum Park
m (longer)
imported>John Stephenson
(template)
 
(231 intermediate revisions by 8 users not shown)
Line 1: Line 1:
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|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''.
 
...

Latest revision as of 09:19, 11 September 2020

Paramhansa Yogananda circa 1920.

Paramhansa Yogananda (5 Jan 1893–7 Mar 1952) was one of the first Indian teachers from the Hindu spiritual tradition to reside permanently in the West, and in particular, he was the first to teach yoga to Americans. He emphasized the universality of the great religions, and ceaselessly taught that all religions, especially Hinduism and Christianity, were essentially the same in their essence. The primary message of Yogananda was to practice the scientific technique of kriya yoga to be released from all human suffering.

He emigrated from India to the United States in 1920 and eventually founded the Self-Realization Fellowship there in Los Angeles, California. He published his own life story in a book called Autobiography of a Yogi, first published in 1946. In the book, Yogananda provided some details of his personal life, an introduction to yoga, meditation, and philosophy, and accounts of his world travels and encounters with a wide variety of saints and colorful personalities, including Therese Neumann, Mohandas K. Gandhi, Luther Burbank, and Jagadis C. Bose.

Paramhamsa, also spelled Paramahamsa, is a Sanskrit title used for Hindu spiritual teachers who have become enlightened. The title of Paramhansa originates from the legend of the swan. The swan (hansa) is said to have a mythical ability to sip only the milk from a water-and-milk mixture, separating out the more watery part. The spiritual master is likewise said to be able to live in a world like a supreme (param) swan, and only see the divine, instead of all the evil mixed in there too, which the worldly person sees.

Yogananda is considered by his followers and many religious scholars to be a modern avatar.

In 1946, Yogananda published his Autobiography of a Yogi. It has since been translated into 45 languages, and in 1999 was designated one of the "100 Most Important Spiritual Books of the 20th Century" by a panel of spiritual authors convened by Philip Zaleski and HarperCollins publishers.

Awake: The Life of Yogananda is a 2014 documentary about Paramhansa Yogananda, in English with subtitles in seventeen languages. The documentary includes commentary by George Harrison and Ravi Shankar, among others.[1][2]

Footnotes
  1. ↑ Wikipedia has an article about the 2014 documentary film.
  2. ↑ The IMBd filmography database has a full cast list and other details about the 2014 documentary film.

Retrieved from "https://citizendium.org/wiki/index.php?title=CZ:Featured_article/Current&oldid=759442"