Computer program for differential-input voltage- controlled voltage source effects in analysis of distributed lumped active network

Gentry, M. L.

Huelsman, L. P.

English

NASA Technical Reports Server

MODIFICATION OF THE DIGITAL COMPUTER PROGRAM DLANET 
TO INCLUDE THE EFFECTS OF DIFPERENTIAL-INPUT 
VOLTAGE-CONTROLLED VOLTAGE SOURCES 
Prepared under Grant NGL-03-002-136 for the 
Instrumentation Division of the Ames Research Center 
National Aeronautics and Space Administration 
https://ntrs.nasa.gov/search.jsp?R=19690017445 2020-03-12T03:30:53+00:00Z
VOLTAGE-CONTROLLED VOLTAGE 
Prepared under Grant NGL-03-002-136 f o r  t h e  
Nat ional  Aeronautics and Space Administration 
Instrumentat ion Divis ion of t he  A m e s  Research Center 
M.L. Gentry 
and 
L . P . Hue lsman 
Department of Electrical Engineering 
Universi ty  of Arizona 
Tucson, Arizona 
1 ABSTRACT: This r epor t  descr ibes  a modif icat ion of DLANET , a 
d i g i t a l  computer program f o r  t h e  ana lys i s  of distributed-lumped- 
a c t i v e  networks. 
t o  inc lude  a c t i v e  elements which are d i f f e ren t i a l - inpu t  voltage- 
con t ro l l ed  vol tage  sources  of f i n i t e  ga in .  
The modif icat ion extends DLANET's capab i l i t y  
March 1969 
This is one of a 
d i g i t a l  computational 
(Distributed-Lumped-Active) - - - networks. This class of ne 
of t h r e e  d i s t i n c t  classes of elements, namely, d i s t r i b u t e d  elem 
(modeled by p a r t i a l  d i f f e r e n t i a l  equat ions) ,  lumped elements (m 
by a lgeb ra i c  r e l a t i o n s  and ordinary d i f f e r e n t i a l  equat ions) ,  and 
a c t i v e  elements (modeled by a lgeb ra i c  r e l a t i o n s ) .  Such a charac te r iza-  
t i o n  is app l i cab le  t o  a broad class of c i r c u i t s ,  e spec ia l ly  including 
those usua l ly  r e f e r r e d  t o  as l i n e a r  i n t eg ra t ed  c i r c u i t s ,  s i n c e  the  
f a b r i c a t i o n  techniques f o r  such c i r c u i t s  r ead i ly  produce elements which 
may be modeled as d i s t r i b u t e d  and a c t i v e ,  as w e l l  as ones which may be  
considered as lumped. I n  a previous report '  t h e  use of a d i g i t a l  
computer program D U E T  ( f o r  - Distributed-Lumped-Active - - m o r k  ana lys i s )  
w a s  descr ibed which had the  c a p a b i l i t y  of providing a s i n u s o i d a l  
s teady-s ta te  ana lys i s  of a broad class of DLA networks over a 
prescr ibed frequency range, and d isp lay ing  the  r e s u l t s  i n  t abu la r  
and p l o t t e d  form. D U E T ' S  o r i g i n a l  capab i l i t y  included a c t i v e  
c i r c u i t  elements which were s ingle- input  vol tage-control led f i n i t e -  
ga in  vo l t age  sources ,  he re in  r e f e r r e d  t o  as VCVS's. Figure 1 i l l u s t r a t  
3 
7 
I1 
I 2  
n I 
d 
i l l u s t r a t e s  t h e  schematic and c i r c u i t  model f o r  a DI/VCVS. A 
DI/VCVS may be  r e f e r r e d  t o  as a f in i t e -ga in  d i f f e r e n t i a l  ampl i f i e r ,  
and may be  used t o  implement many i n t e r e s t i n g  DLA network configurat ions.  
DLANET employs matr ix  methods i n  its ana lys i s  of a DLA network. 
A network's admittance matrix is formed and then constrained by 8 
subrout ine of DLANET, c a l l e d  CONST, i n  such a way as t o  inc lude  the  
e f f e c t s  of t he  VCVS a c t i v e  elements using well-known techniques. 
2 
The modif icat ion of t h e  techniques f o r  D I / V C V S s  i s  discussed i n  t h e  
following sec t ion .  
11. Theory of Cons t ra in t  Operations 
For a gene ra l  n-terminal network, Kirchhoff ' s  Current Law y i e l d s  
n independent equat ions-descr ibed i n  matr ix  no ta t ion  as: 
P 
. .  y12 * 
Y22 - = 
. . .  
. . .  
. . .  
Yn2 - - 
The square matrix is ca l l ed  t h e  admittance matrix.  
Suppose a DI/VCVS of g a i n  K is connected such t h a t  nodes i (+) 
and j (-) are t h e  con t ro l l i ng  vol tages  and t h e  output  i s  connected t o  
node n. The s i t u a t i o n  i s  shown i n  Fig. 3. The e f f e c t  of each a c t i v e  
element is t o  reduce the  rank of t h e  admittance matrix by one. Because 
equat ions r e s u l t :  
yll 
Y i l  
. 
yJ 1 
-Ylj-KYln 
*Yij-KYin 
* *Y j j-KYjn 
. . .y 1,n-1 
"'i ,n- 1 
' Y j  ,n-1 
- 
v1 
vi 
. 
j 
V 
'n- 1, 
Thus, t h e  Y-matrix i s  reduced by one row and one column. Notice t h a t  
e i t h e r  column i o r  j could have been el iminated in s t ead  of column n 
with t h e  appropr ia te  column manipulation. There are, then, t h r e e  cases 
which can arise depending upon which node o r  Y-matrix column is t o  be 
5 
t h a t  t he  opera t ion  of adding K times column n t o  column i is exac t ly  
the  opera t ion  required f o r  a VCVS connected from node i t o  node n 
where again node n is t o  be el iminated.  
was already programmed i n t o  the  subrout ine  CONST i n  t he  o r i g i n a l  DLANET. 
CASE 2: Eliminate  the  p o s i t i v e  inpu t  re ference  node i. 
The l o g i c  for %his  opera t ion  
The cons t ra in ing  r e l a t i o n  can l e  wr i t ten :  Vi=Vn/K +V This 
e j' 
r equ i r e s  column i t o  be added t o  column j and a l s o  divided by the  source 
gain and added t o  column n. 
opera t ion  is also requi red  f o r  a VCVS from node i t o  node n i n  which 
node i w a s  t o  be el iminated.  
i n  CONST. 
CASE 3: El iminate  the  negat ive input  re ference  node j. 
The cons t ra in ing  r e l a t i o n  can be writ ten:V =V 
Again, t he  d iv ide  by K and add t o  column n 
This opera t ion  w a s  also already a v a i l a b l e  
- V /K. This  
requi res  column j to  be added to column i and column j divided by 
the  source g a i n  t o  be sub t r ac t ed  from column n. Neither of t hese  
operat ions was previously required i n  CONST. 
Tile modif icat ions necessary t o  permit the  subrout ine  CONST t o  handle 
the  t h r e e  cases  l i s t e d  above are descr ibed i n  the  following sec t ion .  
j i  n 
111. Modifications of t h e  Subrout ine CONST 
Fortunately,  DLANET's i npu t  d a t a  format included provis ion  f o r  
two a d d i t i o n a l  node va r i ab le s  f o r  each VCVS. One of these  (NG2) is 
employed as t h e  negative-input node f o r  DI/VCVS's. This read i n  I3 
format i n  columns 4-6 of Card 140. 3 i n  the  Input  Data Format s e c t i o n  
1 of the  r epor t  descr ibing DLANET. The correspondence of nodes and 
is unchanged with t h e  exce 
equal  t o  a node number ind ica t ing  t h a t  a DI/VCVS, n 
input  terminal  is connected t o  t h a t  node. 
The po r t ion  of CONST which el iminated rows an4columns from the  
admittance mat r ix  d id  not  need t o  be a l t e r e d .  T h e  rows el iminated 
correspond wi th  t h e  nodes a t  which t h e  source po r t ion  of t h e  V C V S ' s  
o r  DI/VCVS's is connected. The columns t h a t  are el iminated are those 
assoc ia ted  wi th  e i t h e r  t h e  con t ro l l i ng  node vo l t age ( s )  o r  t h e  node 
a t  which the  source is located.  Note t h a t  the  f l e x i b i l i t y  of elimina- 
t i n g  any node assoc ia ted  with a given a c t i v e  element is maintained. 
The po r t ion  of CONST t h a t  required modif icat ion w a s  t h e  s e c t i o n  
t h a t  performs the  column add i t ion  operat ions.  For a VCVS, t h e  con- 
s t r a i n i n g  opera t ion  is t o  add t h e  column t o  be el iminated t o  the  
column which is not  e l iminated a f t e r  f i r s t  mult iplying o r  d iv id ing  
its elements by t h e  ga in  of t he  source.  
cases as ou t l ined  i n  t h e  previous s e c t i o n  were implemented. 
shows t h e  flow cha r t  f o r  t he  s e c t i o n  of CONST which w a s  modified. 
For a DI/VCVS, t he  t h r e e  
Fig. 4 
7 
two column cons t ra in ing  opera t ions  per  node and column e l imina t ion  
whereas a VCVS r equ i r e s  only one column cons t ra in ing  opera t ion  pe r  
node and column el iminat ion.  
Some caut ions must be observed with regard t o  input  data .  The 
da ta  f o r  t h e  a c t i v e  elements i n  a network must no t  spec i fy  t h a t  a 
given node o r  column be  el iminated more than once. I n  add i t ion ,  t h e  
order  i n  which the  da t a  f o r  t he  sources  i s  read i n t o  the  program must 
be such t h a t  no operat ions are made on a column a f t e r  i t  has been 
el iminated.  For example, consider  t h e  cascade of sources  shown i n  
Fig. 5. For t h i s  connection, examples of permiss ib le  input  da t a  are:* 
Example 1 
C a a GAINA. 
d b b GAINB . 
e d e  C GAINC . 
Here, nodes a,  b,  and c are eliminated. 
Example 2 
e d c  e GAINC. 
C a C GAINA. 
d b d GAINB . 
Here, nodes e ,  c, and d are eliminated. 
Example 3 
d b b GAINB . 
e d c  e GAINC. 
C a C GAINA . 
Here, nodes b ,  c ,  and e are el iminated.  
*The f i v e  columns shown read t h e  v a r i a b l e s  NGl(I), NGZ(I), 
8 
Examples of improper input  da t a  are: 
Example 1 
C a C GAINA. 
d b d G A I h B  . 
e d c  e GAINC . 
Here, opera t ions  on columns c and d are requi red  a f t e r  they have 
been el iminated and thus v i o l a t e s  t h e  ru l e .  
Example 2 
e d c  C GAINC e 
C a a GAINA . 
d b d GAINB . 
Here, node c is  el iminated too soon. 
I V .  Example of Applicat ion 
A s  an example of t h e  app l i ca t ion  of t h e  modified DLANET program, 
consider t h e  c i r c u i t  shown i n  Fig. 6. T h i s  c i r c u i t  contains  two con- 
t r o l l e d  sources ,  a VCVS and a DI/VCVS.  Nominal values  of 4-4.0 f o r  t he  
DI/VCVS and 0.59 f o r  t he  VCVS give  a Q of approximately 40. Fig. 7 
shows t he  c i r c u i t ' s  response f o r  t h e s e  ga in  values  for a r e s t r i c t e d  
range of f requencies  i n  the  v i c i n i t y  of t h e  resonant pea ls .  
V.  Conclusion 
The modif icat ion t o  the  d i g i t a l  computer program DLANET descr ibed 
i n  t h i s  r epor t  provides a considerably broader range of c i r c u i t s .  
This r epor t  makes i t  poss ib l e  t o  apply t h e  program to a considerably 
broader range of c i r c u i t s .  Future  developments are planned t o  
inc rease  t h e  c a p a b i l i t i e s  of DLANET even fu r the r .  These w i l l  be 
descr ibed i n  forthcoming repor t s .  
A cknow ledg emen t 
9 
The research descr ibed i n  t h i s  repor t  w a s  supported i n  p a r t  
by t h e  Instrumentat ion Division of t he  Ames Research Center of 
t h e  Nat ional  Aeronautics and Space Administration under Grant 
NGL-03-002-136, The authors  wish t o  express t h e i r  apprec ia t ion  
t o  t h e  gran tee ,  and espec ia l ly  t o  D r ,  W. J.  Kerwin, Chief,  Elec- 
t r o n i c s  Research Branch, Instrumentat ion Divis ion,  NASA A m e s  
Researcji Center,  for t h e  encouragement given t o  t h i s  research  
p r o j e c t  e 
References 
1. L. P. Huelsman, "DLANET - A D i g i t a l  Computer Program f o r  the  
Analysis of D i s  tributed-lumped-Active Networks ," Report pre- 
pared under NASA Grant NGL-03-002-136, 46 pages, Nov. 1968. 
2. A Nathan, "Matrix Analysis of Constrained Networks," I n s t i t u -  
t i o n  of Electrical Engineers, Monograph No. 399E, Sept. 1960. 
N NG I 
( a  1 
Fig. 1. Voltage-controlled voltage source: (a) Behematic; 
(b) circuit model. 
( b )  
Fig. 2. Differential-input voltage-controlled voltage source: 
(a) schematic; (b) circuit model. 
i o  
on D I / V C V S  
jo 
CONSTRAINT:  
I I 
I 
I 
I 
1 
I 
I 
Fig. 5. An interconnection of sources. 
+ 
"OUT + 
"IN - 
12 
= .59 
= 4  
Fig. 6. A resonant circuit, 
35 
30 
15 
IO 


Modification of the digital computer program DLANET to include the effects of differential-input voltage-controlled voltage sources

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