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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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# Main
########################################################################### HI := volfunCvtf] ( [1] , [fi], 3, [1,1,1,[[1]]], (algf();
H2 := volfunCvtf] ([2] , [fl,f2], 3, [l,1,1,[Cl]]] , 'algf');
H3 := volfunCvtf]([3] , [fl.f2.f3], 3, [l,1,1,[Cl] ] ], falgff);
E.4 Program listing for example 2
# example 2 - Test of vtf procedure ###########################################################################
# Ref.; L. 0. Chua and C.-Y. Ng: "Frequency-domain analysis of nonlinear
# systems: formulation of transfer func'cions", IEE Journal on Electronic
# Circuits and Systems, November 1973, Vol.3. No. 6, pp. 257-269. #######################################£#####*#######*######■######£######## read 'volfun':
################################################
# Alcal - calculate the A inverse matrix ###########################################################################
Alcal := proc(s)
Е.4. Program listing for example 2
local D: global AI:
D : = s‘2*(Rp*gl + l) + s*(Rp*ll + cl*gl) + cl+11: AI [ 1,1] := -s*(s*gl + 11)/D:
AI [1,2] := s~2/D:
AI [2,l] := -s~2/D:
AI[2,2] := -s*(s*Rp + cl)/D end: # Alcal
######################################################################£####
# Beal - calculate the В matrix
Beal := proc(s) global B:
В [1,1] : - Rp:
B[2,1] := 0 end: # Beal
# acal - calculate the a vector
acal := proc(s) global a: a[l] := -Rp: a[2] := 0 end: # acal
########
# bcal - calculate the b vector #############
bcal := proc(s) global b: b[l] := Rp end: # bcal
# Gl - nonlinear Volterra transfer function for nonlinear element 1 ##################
Gl := proc(ordL, psiL)
i лга! orde-’- result: order := op(l, ordL): result := 0:
if order = 2 then result := c2/(op(l, psiL)*op(2, psiL' • fi:
288
E. Determination of Volterra transfer functions using Maple
if order s 3 then result := c3/(op(l, psiL)*op(2, psiL)*op(3, psiL)) fi:
result
end: # GI
#########################################################■¥#################
# G2 -* nonlinear Volterra transfer function for nonlinear element 2
G2 := proc(ordL, psiL) local order, result: order := op(l, ordL): result := 0:
if order = 2 then result := 12/(op(l, psiL)*op(2, psiL))+g2 fi:
if order = 3 then result :- 13/(op(l, psiL)*op(2, psiL)*op(3, psiL))+g3 fi:
Г9SUlt
end: # G2
#######################################^#######3###*########### ######£###
# Main
##################################################445#######^############ Hlprime := volfun[vtf]( [1], [si], 3, [l,2,2, [ [l], [2]]], *algfr):
H2priiue := volfun[vtf] ( [2] , [sl,s2], 3, [1,2,2, [ [1] , [2] ] ] , 'algf'):
H3prime := volfun[vtf]( [3] , [sl,32,s3], 3, [1,2,2, [ [1], [2]]], falgff):
HI := limit(Hlprime, Rp=infinity);
H2 := limit(H2prime, Rp=infinity);
H3 := limit (H3prime , Rp=mf inity ) ;
E.5 Program listing for example 3 ###########################################################################
# example 3 - Test of vtf procedure *######
# Ref.; T. Lar3en, "Cotermination of Multi-Port Volterra Transfer. fr 5’lTlC*: ions", Int. 1. cir. thsor. appl. . 1992.
###4######S444##4###44#######4#####44#####44#S#4##4###4####444444##Jt###4#4# read (volfunf:
###########################################################################
# Alcal - calculate the A inverse matrix ########################################################################-##
Е.5. Program listing for example 3
289
Alcal := proc(f) global AI:
AlEl.l] :=
AI [1, 2] := 0:
лтГо,!] : = ™l/(Yi(f)*Yc(f )): AI[2,2] := -l/Yo(f) end: # Alcal
# Bcal - calculate the В matrix
Bcal := proc(f) global B:
B[l,l] := Ys(f):
В [1,2] := Ri*Ys(f):
B[l,3] := 0:
В [2,1] := 0:
3 [2,2] := 0:
В [2,3] := -1 end: # Bcal
# acal - calculate the a vector
acal := proc(f) global a:
a [l] := 0: a[2] := 1 end: # acal
######*############*
# bcal - calculate the b vector ############################### bcal := proc(f)
global b:
bfll := 0: b [2] : = 0 : b[3] := 0 end: # ocal
###########################################################################
# Gl - nonlinear Volterra transfer function for nonlinear element 1 ######################################################?**###################
290
E. Determination of Volterra transfer functions using Maple
G1 := proc(ordL, psiL) local order, result: order : = op(ordL): result := 0:
if order = 2 then result := 7+2*P-i *C£^*(op( 1 . nsiT.)+op(2. psiL)) fi: if order = 3 then
result : = I*2*Pi*Cg3*(op(1, psiL)+op(2, psiL)+op(3, psiL)) fi:
result end: # G1
# G2 - nonlinear Volterra transfer function for nonlinear element 2
G2 := proc(ordL, psiL) local orderl, order2, result: orderl := op(l, ordL): order2 := op(2, ordL): result := 0:
if orderl = 0 and order2 = 2 then result := f i:
if orderl = 0 and order2 = 3 than result := go3 fi:
if orderl = 2 and order2 - 0 then result := gn2 fi:
if orderl = 3 and order2 = 0 then result := gm3 fi:
result end: # G2
################## #######################*#########:m#########£###########
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