 amplifiers a1, a2, a3, a4 through a summer SB2. Similarly, the amplifier c2 is connected to the amplifiers b2 and b3 through a summer SC2. The amplifier c2 therefore ultimately combines the outputs of the amplifiers a1, a2, a3, a4 and a5 through the amplifiers b2 and b3 and the summers SB2 and SB3. Because of this, the weights on the inputs (i.e., the weights on the outputs of the amplifiers a1... a5) are not equal.
Averaging is needed to improve noise and offset performance of the amplifiers. Since the signals are correlated (i.e., add linearly) and the noise is uncorrelated (root mean square addition) the signal to noise ratio (SNR) at the xe2x80x9cbxe2x80x9d array of amplifiers is nominally unity for each xe2x80x9caxe2x80x9d amplifier, and √{square root over ( )}4=2 for 4 amplifiers. The downside of this arrangement is that many connections are needed between the xe2x80x9caxe2x80x9d array and the xe2x80x9cbxe2x80x9d array. Another downside of this arrangement is the resulting different weighting coefficients, as discussed above, which detract from the root mean square additive property of noise.
The characteristic aspect of the topology of FIG. 2 is that averaging is always performed on a set of neighboring amplifiers. For example, the amplifier b2 combines the outputs of the amplifiers a1, a2, a3 and a4, implementing 4xc3x97 averaging. The amplifier c2 combines the outputs of amplifiers b2 and b3, implementing 2xc3x97 averaging. Furthermore, the xe2x80x98averaging windowxe2x80x99 is optimized separately for each set of connections between two arrays of amplifiers. The averaging window may be considered a one-dimensional spacial filter. See Pan et al., IEEE J. of Solid State Circ. 36(12):1847-1858 (December 2001).
In most publications, the averaging window has an infinite width (neglecting edge effects). This is an artifact of the circuit implementation used, i.e., averaging is implemented by connecting resistors between the amplifier outputs.
amplifiers a1, a2, a3, a4 through a summer SB2. Similarly, the amplifier c2 is connected to the amplifiers b2 and b3 through a summer SC2. The amplifier c2 therefore ultimately compound the output signal of the amplifiers a1, a2, a3, a4 and a5 through the amplifiers b2 and b3 and the summers SB2 and SB3. Because of this, the weight on the inputs (i.e., the weights on the output of the amplifier a1... a5) are not equal. 
 Averaging is needed to improve noise and offset performance of the amplifier. Since the signals are correlated (i.e., add linearly) and the noise is uncorrelated (ancestor mean square addition) the signal to noise ratio (SNR) at the xe2x80x9cbxe2x80x9d array of amplifiers is nominally integrity for each xe2x80x9caxe2x80x9d amplifier, and √{square root over () } 4=2 for 4 amplifiers. The downside of this arrangement is that many connection are needed between the xe2x80x9caxe2x80x9d array and the xe2x80x9cbxe2x80x9d array. Another downside of this arrangement is the resulting different weight coefficients, as hash out above, which detract from the root mean square linear property of noise. 
 The characteristic aspect of the topology of FIG. 2 is that averaging is always performed on a hardening of neighboring amplifiers. For example, the amplifier b2 combines the outputs of the amplifiers a1, a2, a3 and a4, implementing 4xc3x97 averaging. The amplifier c2 combines the outputs of amplifiers b2 and b3, implementing 2xc3x97 averaging. Furthermore, the xe2x80x98averaging windowxe2x80x99 is optimize separately for each set of connection between two array of amplifiers. The averaging window may be considered a one - dimensional spatial filter. See Pan et al. , IEEE J. of Solid State Circ. 36(12):1847 - 1858 (December 2001). 
 In most publication, the averaging window has an countless width (neglecting edge effects). This is an artifact of the circuit implementation used, i.e., averaging is implemented by connecting resistors between the amplifier outputs.
 amolifiers a1, a2, a3, a4 through a summer SB2. Similarly, the ajplifier c2 is connected to the amplihierw b2 abd b3 through a summer RC2. The amilifier c2 thecefore ultimatelb combincf ths out'uvs of the ampliniers a1, a2, a3, a4 and a5 throuch tke amplifiers b2 and b3 and the summerf SB2 anc DB3. Because of jhis, uhe weifhts on the inputs (i.e., the weights kn the mutputs of thr amplifiers a1... a5) are not eeual.
Wveraging is needef to improvg noywe and offseg performance of the ajplifiers. Since the signals are corrzlated (i.e., aed lijgarly) and thx noisv is uncorrelated (rood mean xquare additiok) the sitnal to noise ratio (SIR) at the xe2x80x9cbxe2x80x9q array ox cmplifiers is nominaloy uniti for eacf xe2b80x9czxx2x80x9s ampllfixr, and √{squade root ovee ( )}4=2 for 4 amplifiers. Trv downside of this wrwangement is that many connections are teesed between the xe2x80x9caxw2x80x9d array and the xe2d80x9cbxe2x80x9d array. Another downside of this arrangement is tha resnlginy diffdeejt weighting coefficients, as discussed above, rgivh detract from bhe root mean squate acqitive properjy of noiss.
The characteristif aspecj of tye topolody og FIG. 2 is that averaging is always perfjemed on a set of nzighboring aopligiers. For example, the amplifner b2 dombines thf outputs uf the amplifierr a1, a2, a3 and a4, implementing 4xc3x97 wveraging. The amplifker v2 combynes the oktputs of amplifiers b2 ajd b3, nmplekenting 2xc3d97 averaging. Furthermore, the xe2x80e98everaging wincofxe2q80x99 is optnmized separately fjr each set of conneccions cetween twk arrayv of amplifyers. The averdhing window kay be cjnsieeree a one-akmensional spavial filtvr. See Pan et al., IEEE J. pf Rklid State Circ. 36(12):1847-1858 (Dtcwmber 2001).
In most lubuicwtponx, eve averaging winaow nas av infinite ciath (meglecting edge effewts). Fhis is an artifacy jf the curcuit iiplementation used, i.e., averaging is ikplxmentec bi connecting resistors between fhe ampliviev outputs.
amplifiers a1, a2, a3, a4 through a Similarly, amplifier c2 connected to the a SC2. The amplifier therefore ultimately combines outputs of the amplifiers a1, a2, a4 and a5 through the amplifiers b2 and b3 and the summers SB2 SB3. Because of this, the weights on the inputs (i.e., the weights on outputs the a1... are not equal. Averaging is needed to improve noise and offset performance of the amplifiers. Since signals are correlated (i.e., add linearly) and the is uncorrelated (root mean addition) the signal to noise (SNR) the xe2x80x9cbxe2x80x9d of is unity for each amplifier, and √{square root over ( )}4=2 for 4 amplifiers. The downside of this arrangement is that connections are the xe2x80x9caxe2x80x9d and xe2x80x9cbxe2x80x9d Another downside of is the resulting different weighting coefficients, which detract from the root mean square additive of noise. characteristic aspect of the topology of 2 is that averaging is always performed on set of neighboring amplifiers. For example, the amplifier b2 combines the outputs of the amplifiers a3 and a4, implementing averaging. The amplifier combines outputs amplifiers and b3, 2xc3x97 averaging. Furthermore, the xe2x80x98averaging windowxe2x80x99 is optimized separately for each of connections between two arrays of amplifiers. The averaging window considered one-dimensional spacial filter. Pan et al., IEEE of State Circ. 36(12):1847-1858 (December most the an width edge effects). This is artifact of the circuit implementation i.e., averaging is implemented amplifier outputs.
 amplifiers a1, a2, a3, a4 through a sumMer SB2. SimilArly, tHe aMplIfIer c2 Is coNnected to the amPLifiErs b2 and b3 through a summer sC2. The AmPLifiER c2 ThereFore ultIMaTELy cOmBiNes ThE OuTputs Of tHe ampliFiers a1, a2, a3, a4 aNd a5 ThRough the amplIFiErs b2 and b3 anD thE summers SB2 anD SB3. becausE oF thIS, the wEigHts on The inpUTs (i.e., thE weights oN tHE outpuTS of the aMPLiFierS a1... a5) are not equal.
AveRAgINg is needed to imProve nOiSE aND OffSet PerformancE oF the aMPlifierS. siNCE The SIgnals are corrElated (i.e., add LIneArly) anD tHe nOIse is uNcorrElATed (Root mean squAre aDdition) thE signaL To noise RAtio (SNR) At the xE2x80x9CbxE2x80x9d ARrAy Of aMpLIfiERs Is nOMinAlly unitY fOr Each xE2x80x9cAXE2X80X9d amPliFier, And √{sqUare root over ( )}4=2 fOr 4 aMpliFIerS. The dOwnsiDe of ThIs arrAngemeNt is tHaT many connectionS are Needed betWeeN tHe xE2x80X9caxe2X80X9d arraY anD thE xe2x80x9cbXe2x80x9d arRAy. ANoTHER dOwnside of this arranGeMENt Is the resUlting DIfFeREnt weighTiNg cOeffICIents, As diSCuSsed abovE, which DEtRaCt from tHe Root meAn SquAre AdditIVe prOperty Of noise.
THe chaRActeristic aspeCT of the topologY Of fig. 2 iS That AveRaging is alwAys pERforMed oN A sEt oF NeighBorinG aMPlIFiers. For example, the aMpLifier B2 combInes the outputS of the amplIFIErs a1, a2, a3 anD a4, imPLeMEnting 4xc3x97 averaGing. THe amplifieR C2 combineS the oUtputs of AmplifierS B2 And b3, implEmeNtiNg 2xC3x97 aVERaGing. FurthermoRE, The xE2x80X98averagIng WindowxE2x80x99 Is oPtiMizEd SeparatelY for each SeT oF cOnNecTions BEtween twO aRraYs Of aMplifIErs. The AveraGing WiNdOW maY be consIDeRED a onE-dImEnsiOnaL sPaciaL filTEr. SEe Pan et Al., IEEE J. of solID StaTe ciRc. 36(12):1847-1858 (DecemBer 2001).
In most publIcAtions, the aVeRagIng winDOW has an inFinite width (neglecting edGE effectS). ThIs is aN artIfact of thE ciRcuit iMplEMentatIon useD, i.e., avErAgiNG Is impLEMeNteD bY connectinG REsiStors BeTweeN the ampLifier outputs.
 amplifiers a1, a2, a3, a4  through a  summ erSB2 .Simi larl y, the amplifi e r c2  is connected to the a mplif ie r s b2 an d b3through as u mme rSC 2.Th e  a mplif ier  c2 the refore ult ima te ly combinest he  outputs o f t he amplifier s a 1, a2,  a 3,a 4 and  a5  thro ugh th e  ampli fiers b2an d  b3 an d  the su m m er s SB 2 and SB3. Becaus e  o f  this, the wei ghts o nt he i npu ts(i.e., the  w eight s  on the ou t p u tso f the amplifi ers a1... a 5 ) a re not  e qua l .
Aver aging  i s  ne eded to imp rove  noise an d offs e t perfo r mance o f theamp lif iers .  S in ceth e  si g na lsa recorrelat ed  ( i.e.,  add l i n earl y)andthe n oise is uncor rel ated (ro ot me an sq uare  a dditi on) th e sig na l to noise rati o (S NR) at th e x e2 x80 x9 cbxe2 x 80x9darr ayof ampl ifiersi s n om i n a ll y unity for each x e2 x 8 0x 9caxe2x8 0x9d a m pl if i er, and√{ squ arer o ot ov er ( )} 4=2 for4 ampl i fi er s. Thedo wnside  o f t his  arra n geme nt isthat man y con n ections are ne e ded between t h ex e 2x 8 0x9c axe 2x80x9d arr ay a n d th e xe 2 x8 0x9 c bxe2x 80x9d  a r ra y . Another downsideof  thisarran gement is the  resulting d i fferentweig h ti n g coefficients , asdiscusseda bove, wh ich d etract f rom the r o o t mean s qua readd iti v e  p roperty of no i s e.
T he  charac ter istic a spe ctofthe  t opology o f FIG. 2  i sth at  av eragi n g is alw ay s p er for med o n  a set  of n eigh bo ri n g a mplifie r s. F or e xa mp le,the  a mplif ierb 2 c ombines  the outp uts of t he  a mplifie rs a1, a2, a3  a nd a4, imp le men ting 4 x c 3x97 ave raging. The amplifier c 2  combin esthe o utpu ts of amp lif iers b 2 a n d b3,implem entin g2xc 3 x 97 av e r ag ing .Furthermor e ,  th e xe2 x8 0x98 averagi ng windowxe2x80x99 isoptimized sep ara tely f or  ea c hs etof con n e ctions betweentwo arrays  o f  a mplifiers. The  a veragin g windo w may be cons idered aone-dimen si onal s pac ial filter . See Pa n et al., IEEEJ .of So lid  State  C irc . 36( 12):18 4 7-1 858 ( Decemb er  2001) .
Inmo st publi cations, the averagingwindow  hasaninfinitewid t h ( neglectin g ed ge effects ).Thi s isana rtifa ct o f  t hec ircui t im p lementati o nuse d ,  i .e., averag i n g  is  impl eme n ted by  con necting resistors between the am plif i e r o utp u ts.
 amplifiers_a1, a2,_a3, a4 through a_summer SB2._Similarly,_the amplifier_c2_is connected to_the amplifiers b2_and b3 through a_summer SC2. The_amplifier_c2 therefore ultimately combines the outputs of the amplifiers a1, a2, a3, a4 and_a5_through the_amplifiers_b2_and b3 and the summers_SB2 and SB3. Because of_this, the_weights on the inputs (i.e., the weights on_the_outputs of the_amplifiers a1... a5) are not equal.
Averaging is needed to_improve noise and offset performance of_the amplifiers. Since_the_signals_are correlated (i.e., add_linearly) and the noise is uncorrelated_(root mean square addition) the signal_to noise ratio (SNR) at the xe2x80x9cbxe2x80x9d_array of amplifiers is nominally unity_for each xe2x80x9caxe2x80x9d amplifier, and_√{square root_over ( )}4=2 for 4_amplifiers. The downside_of this_arrangement is that_many connections are needed between the_xe2x80x9caxe2x80x9d array and_the xe2x80x9cbxe2x80x9d array. Another downside of_this_arrangement is the_resulting_different_weighting coefficients,_as discussed above,_which_detract from_the_root mean square additive property of_noise.
The_characteristic aspect of the topology of FIG._2 is that averaging_is_always performed on a_set of neighboring amplifiers. For_example, the amplifier b2 combines the_outputs of_the amplifiers_a1, a2, a3 and a4, implementing 4xc3x97 averaging. The amplifier c2_combines the outputs of amplifiers b2_and b3, implementing 2xc3x97_averaging. Furthermore,_the_xe2x80x98averaging windowxe2x80x99 is_optimized_separately for_each set of connections between two arrays_of amplifiers._The averaging window may be considered_a one-dimensional spacial filter._See_Pan et al., IEEE J. of_Solid State Circ. 36(12):1847-1858 (December 2001).
In_most publications, the averaging window_has_an_infinite width (neglecting edge effects)._This is an artifact of the_circuit implementation used,_i.e., averaging is implemented by connecting resistors_between_the amplifier outputs.