Borel's lemma: Difference between revisions

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By the point you progress in, you can be amazed at how accessible and effectively-connected to the remainder of Singapore you're.<br><br>A number of buses are available near J Gateway along with purchasing facilities and eating places. J Gateway is also near to Jurong Lake Park and The Japanese Garden. Leisure in your loved ones and buddies is due to this fact at your fingertips with the total rental facilities as well as the amenities close to J Gateway. Considerable of Amenities – New Rental is simply next door to Northpoint Purchasing Centre which offers a big selection of retail, consuming joints and leisure amenities. Effectively Connected – New Condo is easily related to SLE which makes island wide traveling a breeze. Potential Rental Return – With its conveniences, New Condominium is sure to draw a huge pool of tenants. Hallmark Residences @ District 10 Mon Jervois @ District 10 pending on the market licence Approval
[[File:Common Gate.svg|thumbnail|200px| Figure 1: Basic N-channel common-gate circuit (neglecting [[biasing]] details); current source ''I<sub>D</sub>'' represents an [[active load]]; signal is applied at node ''V<sub>in</sub>'' and output is taken from node ''V<sub>out</sub>''; output can be current or voltage]]
 
In [[electronics]], a '''common-gate''' [[electronic amplifier|amplifier]] is one of three basic single-stage [[field-effect transistor]] (FET) amplifier topologies, typically used as a [[Electric current|current]] [[buffer amplifier|buffer]] or [[voltage]] [[amplifier]]. In this circuit the source terminal of the transistor serves as the input, the drain is the output and the gate is connected to ground, or "common," hence its name.
The analogous [[bipolar junction transistor]] circuit is the [[common base|common-base amplifier]].
 
==Applications==
 
This configuration is used less often than the [[common source]] or [[source follower]]. It is useful in, for example, CMOS RF receivers, especially when operating near the frequency limitations of the FETs; it is desirable because of the ease of [[impedance matching]] and potentially has lower [[Electronic noise|noise]]. Gray and Meyer<ref name=Gray-Meyer>
  {{cite book
|author=Paul R. Gray, Paul J. Hurst, Stephen H. Lewis, Robert G. Meyer
|title=Analysis and Design of Analog Integrated Circuits
|year= 2001
|edition=4th
|publisher=Wiley
|location=New York
|isbn=0-471-32168-0
|pages=186–191}}
</ref> provide a general reference for this circuit.
 
==Low-frequency characteristics==
 
[[File:Common gate hybrid pi.PNG|thumbnail|200px| Figure 2: Small-signal low-frequency [[hybrid-pi model]] for amplifier driven by a [[Norton's theorem|Norton signal source]]]]
 
At low frequencies and under [[small-signal]] conditions, the circuit in Figure 1 can be represented by that in Figure 2, where the [[hybrid-pi model]] for the MOSFET has been employed.
 
[[File:Common gate output resistance.PNG|thumbnail|200px| Figure 3: Hybrid pi model with test source ''i<sub>x</sub>'' at output to find [[output resistance]]]]
The amplifier characteristics are summarized below in Table 1. The approximate expressions use the assumptions (usually accurate) ''r<sub>O</sub>'' >> ''R<sub>L</sub>'' and ''g<sub>m</sub>r<sub>O</sub>'' >> 1.
 
{| class="wikitable" style="background:white;text-align:center;margin:  1em auto 1em auto 1em auto 1em auto"
!Table 1 !! Definition !! Expression !! Approximate expression
|-valign="center"
! '''[[gain|Short-circuit current gain]]'''
|<math> {A_{i}} = {i_\mathrm{out} \over i_\mathrm{S}} \Big|_{R_{L}=0} </math>
|<math>\ 1 </math>
|<math>\ 1</math>
|-valign="center"
! '''[[gain|Open-circuit voltage gain]]'''
|<math> {A_{v}} = {v_\mathrm{out} \over v_\mathrm{S}} \Big|_{R_{L}=\infty}</math>
|<math>\begin{matrix} ((g_m+g_{mb}) r_\mathrm{O}+1) \frac {R_L} {r_O + R_L} \end{matrix}</math> 
|<math>\ g_m  R_L </math>
|-valign="center"
! '''[[Input resistance]]'''
|<math> R_\mathrm{in} = \frac{v_{S}}{i_{S}}</math>
|<math> {{R_L+r_O} \over {(g_m+g_{mb}) r_O +1}} </math>
|<math>\begin{matrix} \frac {1} {g_m} \end{matrix}</math>
|-valign="center"
! '''[[Output resistance]]'''
|<math> R_\mathrm{out} =\frac{v_{x}}{i_{x}}</math>
|<math>\ (1+(g_m+g_{mb})r_O)R_S + r_O </math>
| <math>r_O</math>
|}
 
:'''Note:''' Parallel lines (||) indicate [[Series_and_parallel_circuits#Parallel_circuits|components in parallel]].  
 
In general the overall voltage/current gain may be substantially less than the open/short circuit gains listed above (depending on the source and load resistances) due to the [[loading effect]].
 
===Closed circuit voltage gain===
 
Taking input and output loading into consideration, the closed circuit voltage gain (that is, the gain with load ''R<sub>L</sub>'' and source with resistance ''R<sub>S</sub>'' both attached) of the common gate can be written as:
: <math>
{A_\mathrm{v}} \approx \begin{matrix} \frac {g_m R_\mathrm{L}} {1+g_mR_S} \end{matrix}</math> ,
which has the simple limiting forms
: <math>A_\mathrm{v} = \begin{matrix} \frac {R_L}{R_S}\end{matrix} \ \ \mathrm{ or } \ \ A_\mathrm{v} = g_m R_L </math>,
depending upon whether ''g<sub>m</sub>R<sub>S</sub>'' is much larger or much smaller than one.  
 
In the first case the circuit acts as a current follower, as understood as follows: for ''R<sub>S</sub>'' >> 1/''g<sub>m</sub>'' the voltage source can be replaced by its [[Norton's theorem|Norton equivalent]] with Norton current ''v<sub>Thév</sub> / R<sub>S</sub>'' and parallel Norton resistance ''R<sub>S</sub>''. Because the amplifier input resistance is small, the driver delivers by [[current division]] a current ''v<sub>Thév</sub> / R<sub>S</sub>'' to the amplifier. The current gain is unity, so the same current is delivered to the output load ''R<sub>L</sub>'', producing by Ohm's law an output voltage ''v<sub>out</sub> = v<sub>Thév</sub>R<sub>L</sub> / R<sub>S</sub>'', that is, the first form of the voltage gain above.
 
In the second case ''R<sub>S</sub>'' << 1/''g<sub>m</sub>'' and the Thévenin representation of the source is useful, producing the second form for the gain, typical of voltage amplifiers.
 
Because the input impedance of the common-gate amplifier is very low, the [[cascode]] amplifier often is used instead. The cascode places a [[common-source]] amplifier between the voltage driver and the common-gate circuit to permit voltage amplification using a driver with ''R<sub>S</sub> >> 1/g<sub>m</sub>''.
 
==References==
{{reflist|30em}}
 
== See also ==
 
*[[Electronic amplifier#Input and output variables|Electronic amplifier variables]]
*[[Two-port_network#Example:_common_base_amplifier|Two-port network]]s
*[[Common drain]]
*[[Common source]]
*[[Common base]]
*[[Common emitter]]
*[[Common collector]]
 
==External links==
* [http://www.chic.caltech.edu/Publications/ESSCIRC_Guan.pdf A 24GHz CMOS Front-end]
 
{{Transistor amplifiers}}
 
[[Category:Single-stage transistor amplifiers]]

Latest revision as of 12:53, 10 July 2014

If you are looking for affordable propertycondominiumhouse for sale in Singapore, You'll, can't help to really feel that you is likely to be lacking out on the best offers, someplace, one way or the other. The Singapore property market is very risky and fast paced; especially relating to the extraordinarily good bargain ones.

Posted by Edison Foo November 17, 2013 Open for booking NOW !!! Posted by Edison Foo November 7, 2013 Open for booking NOW !!! Posted by Edison Foo September 28, 2013 Posted by Edison Foo September 12, 2013 Posted by Edison Foo September 10, 2013 Posted by Edison Foo August 19, 2013 Posted by Edison Foo August 15, 2013 Posted by Edison Foo August eleven, 2013 Posted by Edison Foo July 25, 2013 Posted by Edison Foo July three, 2013 J Gateway will be accessible through Jurong East MRT. Commuting to the Bukit Timah Area in addition to the town area is subsequently very handy. It is usually right beside J Cube, Westgate and Jem. IMM Jurong as well as Jurong Country Club are also within a short walk.

Riverbank at Fernvale is nicely linked to many different locations and there are a lot of bus amenities you'll discover along the buying facilities & restaurants. Seletar Mall which shall be come full with a Cineplex, restaurants and lots of retails retailers, might be solely strolling distance away. The Waterway Level – referred to as the hub for buying, dining & entertainment, which is anticipated to open up in next 2 years' time, is also close to The Skywoods calculator the Riverbank at Fernvale. The Punggol Waterfront is only a quick drive away from Riverbank at Fernvale. With your entire range of condominium services and the neighbourhood, the entertainment and fun awaits your loved ones and pals, all at the call of your fingertips. Riverbank at Fernvale condo - Accesibility

Leisure and dining options are also easily obtainable with Guillemard Suites just a stone's throw away from the City Plaza Purchasing Mall, Guillemard Village, Tanjong Katong Advanced and the famous Outdated Airport Highway Meals Centre. Along with this, Guillemard Suites ' residents could have a wider choice with the upcoming Pavilion Sq. at Kallang area, the place sports lovers would enjoy facilities at the new Sports Hub Mall and other recreational and entertainment actions at Kallang Leisure Park.

_____________________________________________________________________________________________________________________________________ New Rental Web site Plan and Services __________________________________________________________________________________________________________________________________________ Highlights of New Condominium __________________________________________________________________________________________________________________________________________ New Condominium Factsheet Scott Disick attended the 2014 FIFA World Cup McDonald's launch get together at Pillars 38 on June 5 in New York Metropolis. At launch in Apr 2012, revenue margin was estimated at 27% (estimated breakeven at $1300 per sq ft and average promoting worth at $1650 psf) Select - Condominium / Apt Landed

So why wait, register your curiosity with us now and be informed when the Waterfront @ Faber is open. On the similar-time, we will ship you all the newest updates and announcements of Waterfront @ Faber, the Faber Walk Rental. Benefit from the finest things that life has to supply, enjoy a pristine way of life that's filled with convenience and tons of entertainment. Contact us for more information about Waterfront @ Faber at present. The Hillford can be accessible through the upcoming Magnificence World MRT station on the Downtown Line. Commuting to the Bukit Timah Space in addition to town space is subsequently very handy. It is usually close to to Ten Mile Junction, Rail Mall, Beauty World, King Albert's Park, West Mall, Bukit Panjang, Chilly Storage, and many extra.

Echelon Towering forty three storeys excessive on the sting of the town centre, Echelon ascends as the peak of luxurious in Alexandra property. Conveniently positioned within a minute walk to Redhill MRT station, Echelon offers its residences the final word ease of accessibility to all elements of Singapore. Ocean View Ave. Rye, NH. This property is listed as Brown's second home with an asset worth greater than $a hundred,000. Skypark Residences, one of the crucial anticipated EC in the North, is only a few minutes stroll away from Sembawang MRT. In the 2015 Undertaking Expressway, four new flyovers and five new road connections to improve connectivity might be created. By the point you progress in, you can be amazed at how accessible and effectively-connected to the remainder of Singapore you're.

A number of buses are available near J Gateway along with purchasing facilities and eating places. J Gateway is also near to Jurong Lake Park and The Japanese Garden. Leisure in your loved ones and buddies is due to this fact at your fingertips with the total rental facilities as well as the amenities close to J Gateway. Considerable of Amenities – New Rental is simply next door to Northpoint Purchasing Centre which offers a big selection of retail, consuming joints and leisure amenities. Effectively Connected – New Condo is easily related to SLE which makes island wide traveling a breeze. Potential Rental Return – With its conveniences, New Condominium is sure to draw a huge pool of tenants. Hallmark Residences @ District 10 Mon Jervois @ District 10 pending on the market licence Approval

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