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Theory of Linear and nonlinear circuits - Engberg J.

Engberg J. Theory of Linear and nonlinear circuits - Wiley & sons , 1995. - 154 p.
ISBN 0-47-94825
Download (direct link): noisetheoryoflinearandnonlinear1995.pdf
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= {o^i.i, -.5t?s,b.Wi,i, -3^1,1, tfi.i. -<h,i} (8.51)
5,3 = {Щ,1. Фй,2, Фб,з, Фв,4. «6,3, «6.*, ««.r} , E6-l (8.52)
— {6i?i,i, -6i)i.i, 4i?i л. -4г): д. 2ъ>! д, - 2 i , 0} (8.53)
St = {«7.1, «’.2, *7,3, «7,4, «7,5, «7.6, «7,7, «7,8> • Ет = 8 (8.54)
= {701.1,—701,1.501,1» -501.1,301,1, -301.1, 01,1, ~ 01,i} (8.55)
and thus Е — 15, and
8.2. Example 2
195
{Ф1,...,'Ф15} = {0, 01Л. — t*!,!, 2-01Д, — 2i>iil: 31?1Л, -3()1Л. 4i)]
501Л, -5г)1Л, -601Л, 7iilib —7(#1Л}
Using Equations (7.57)47.59) and (8.36) leads to
ti(^) = [Cx, 0, 0, 0. 0, 0, 0. 0, 0, 0, 0, 0, 0, 0. of
The conversion vector ri,i(£p) can be determined using Equations (7 as
ti,i(4p) = [n,u?p-«i)----,ri,i(?p,,£'i5)|
where
n,i(fP,«i) = (#i)o.i(scp)
+ 2 (#1)2,1 (i?i,i, — 0i,i; Zp) *'i('0i,i) ^i( — 01.1)
+ 6 (#1)4,1(01,11 0i ,1, — 0i,i' — 0i,i; ip)
J1С01.1) A'i( 0i,i) si( — "0i,i.) ■ni -0i,1)
+ 20 (ffije,i(0i,i> 01,1. ^1,1» —^1,1- — ’01,1, — 01,ь (,?) •si(0i,i) £1 (0i,i) si(0i,i) si(- 0i,i) si(—'0i,1) (-
n,i(fp>«г) = {^i)i,i(0i,i;fp - 0i,i)«i(i?i,i)
+ 3 (#i).3,i(i'i.i, 0i.1,-l'i.i; чр - l’i.i)
+ 1О(ЯУЛ(0!Л, 01.1. 0i.i • -01.1- f;; - 01,1'
' 1 1 ; ) ' 1 ' '■ ' ; 1 ; : 01,1 ) ' 1 — ^ 1, i ) ■' ' '■ L.i j
+ 35 (#i)r i( ’Vi, 01 I. 0;,1- 01Д, -01л. -01.1,-01, ?i(0i,i) -41С?01,1) *’i( 01,1) ■5i(’0i.1)
?i( -’0i,i) Si( -^1,1) -0i ,i)
.1,-401,1.
(5.56)
(8.57) .98) and (7.96)
(8.08)
'01,1)
(S.59)
. ■ c _
i ‘ 4 D ** i
196
8. Noise in поп-linear systems: Examples and Conclusion
Пд(£р,Фз)
П.1(еР,Фв)
= (-^1 )i,i(—i^i.i; iP + tfi.i) '3i(~ ^i,i)
+ 3 (-ff 1)3,1 — $1,1, — ^1,1; sp + $1,1)
■5i(^i,i) ■3i(—^1,1) 5l(-^l,l)
4-10 ^1.1. -di.u-tiiX’tr + -i i)
■5i(^i,i) -si($i,i) ?i( — $1,1) 5ц — ^1,1) ?i( — t?i,i)
+ 35 (5i)7,i(l>i4, $1,1, -t?i,b -$1,1, -$1д',цр т Ч?гд)
M'Ki) *’1(^1,1) ■3i(i^i,i)
■s"i(—^1,1) si(_|?i,i) ?i(-^i,i) 5^i(— ^1,1) (8.61)
= (^1)2,1(^1,ь ^1,1; iP - 20i,1) «i(0i,i) ■-1 (^1,1)
+ 4 (H\(41 ($M, $1д. j?i,i, — i?i,i; tp ~ 2^i.i) '5l(^l,l)'sl(^l,l)'sl(^l,l)-'il(—^1,1)
+ 15 (Hi)e,i(&i,u t?i,i. $i,i: $1,1. —^i,i. -^i,i; ip — 2tfi,1)
si(^i,i) si(i?i,i) si(t)1|1) si(i3iti) si( — $1,1) 3i(— ^1д) (8.62)
= (#i)a,i(—tfi.i,-0i,i;£p + 2tfi,i) si(-tfi.i) si(-^i.i) т 4 (-//1)4,1($i,i, -^1,1, —^1,1. -$1,1; tp + 2г?1д)
■sl(f?lд) *’l(“^l,l) ?i( —$i,i) ?i( — $1,1)
+ 1-5 (-Й1)бд№,ъ ^1.1, - 1^1,1, — ^1,1, “ $1,1: — ^1,Ъ £p + 2^1д )
'Sl(^l.l) $l(Jh,l) Sl(— $1,1) -5l( —$1,1) -Sl( — ^1,1) •3l( — $1,1)
(8.63)
= №)зд№д, tfi.i, ^i,i;(p — 3$i,i) Si(i?i,i) ■si(t)i,i) si($i,i)
+ 5 (Hi)5,1 (i?i,i, 1^1,1, $1,1, $1,1, —$1,1; ip — Зйгд)
Sl($l,l) 3l(^l,l) S’U^l.l) Sli'^l.l) ■5l( — $l,l)
I- 21 (//1)7,1 ( $1,1, '$1д, $1д, 7$1д, $1д, — Ji,i, — $i,i; - 3^1д)
■si(t?iд) -si(iд) Ji($i,i) -Sii $1 д) -Si(i?i,1)
5i(~^1.1) S”i(—^1,1)
(8.61)
8.2. Example 2
197
rl,l(s;
'rl,l(fp-
П.1 (?р
rl,l(sp
Ф7) = (Ji)3,i(-i>i.i, -*u; Z? + Mi,i)
3l( —01,l) S[( —■5l( —^l,l)
+ 5 (,ffi)s.i(01Д, — i?i,i, -0i,i, -01,1, -0i.il ip + 301д)
•5H:'l,l) ■5H~l/5l,l) ei(-^l.l) Sl(-^l.l)
+ 21 (Я1)7д(*,.ь 01.1, -0i,i, -0],ь -01,1. -ihx, ip + 3i?i.i) s"i(0i,i) si(0i,i) si(-0i,i) si(-0i,i) *
Si(-"01,l) si(— i?i,i) *l(— 01,i)
(8.65)
, Фз) = ( ffl )4,1 ( 01,1 ■ 01,1. 01,1 , !, ip - Wl.l )
Si(0i,i) «Ц01,l) sii 0i,i) -si(0i.i)
+ 6(fl’l)s,;(0iil,>01.1, 01Д . 01,1, 01,1, —01,i;(p - 4 0 ! ,1 ) si(0i,i) *’i(. 01.l) *’i(0i.i) «i( ’01.1) ?i(0i,i) 51(-'01,1)
(8.66)
.«a) = (-ffi)4,i( — 0i,i, — 0i,i, —’01.1, - 01, Г, ip + 40i д)
,?1 f — l)i ,1 ) 5; ( — ’0, 1 ) Si f — д ) ( — 7?1 Д )
+ С (ffi)e,i(iJi,i> — 01,1, — 0i,l, -01Д, —’0i,i- — 0i,i j т 4t>i,i) *l(01,l) *"i( — 01.1) ^l(— 01,l) si( — 0i,i) Si( — 01 д) ?i(-0i,i)
(8.67)
*io) = (-^1)5,1 (01,17 0i,i, 01,1. 0i,i, 0i,1: ip - 50i,i)
si(’0i,i) ■‘’l (01,1) .51(01,1) ^ 1 (01,1) 3^1 ( 01,1)
+ 7 (Я1)7д(-01Д. 01,!, 01,1, 01,1. 01,1, 01,l,-0!,i;sCP - 501,1)
Sli 01 ,l) ?l(0’,,l) Si (01Д ) ,<i( 01Д ) 01 ( 01,1) .?1 (01.1 ) .Si (—'01,1 )
(8.68)
Ф. l) = ( Hi )g,i( — 01Д , - 01,1. -01,1 ■ -01,1, -01.1: ip + 50i,i)
^l( —01,l) Si( -01,1j Si(- 01,1) S1 ( -01,1) Si ( - 0i ,1)
+ n^i)7,i(0M. -01.1,-01.1,-01.1,-01.1,-01,:.-0i.b
f . 4- О
n( 01.U Sii - 01.1) Si I ~'J\ д t -’i ■ -0i ,1 ! •?,! - 0i ,i i j _,} ,) ( — ■-), ,
i 8.69)
Ф12) = (Hi )s,i(0i,i. 01,1, 01,1, 01,1-01,1, 0i,i! ip ~ 6'01 д )
Si(0i.i) si( 01Д ) si l'01Д ) si( 0i.i) si( 0i д).?! ( 0i,i ) (8.70)
198
8. Noise in non-linear systems: Examples and Conclusion
ri,i!sp, Ф13) — (#1)6,1 ( — $1.1, — $1,1. — $1,1» —^1,1 > ~$1,ь — $1,1; ip + 6^1,1)
'si(_$i,i) $i(-tfi,i) «i(-i?i,i) «i(—^1,1) *il-^i,i) si(-'>i,i) (8.71)
7i,i(fp. Фм) = (#1 )t,i($i,i , $1,1, $1,1 1 $i,i- $1,1. $1,11 $1,1; ip — 7$ 1,1)
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