(NASA-CR-128516) ADVANCED COMMUNICATION N72-30148

SYSTEM TIME DOMAIN MODELING TECHNIQUES

ASYSTD SOFTWARE DESCRIPTION. VOLUME 1:

PROGRAM USERS GUIDE (Systems Associates, Unclas

Inc.) Auq. 1972 168 p CSCL 17B G3/07 39624

SYSCTEMS ASSOCIATES Wr

SYSTEMS ASSOCIATES, INC.444 West Ocean Boulevard

Long Beach, California 90802

Cat, /42d51

ATTENTION REPRO:

.BEFORE PRINTING, CONTACT INPUT FOR PAGINATION.

PROCESSOR

NTIS-185 (3-72)

V/I-

Prepared for:

Space Electronics System DivisionNational Aeronautics Space Administration

Manned Spacecraft CenterHouston, Texas 77058

SYSTEMSASSOCIATES

444 West Ocean BoulevardLong Beach, California 90802

Telephone 213/435-8282

R72-001Contract No. NAS9-11743

ADVANCED COMMUNICATION SYSTEMTIME DOMAIN MODELING TECHNIQUES

ASYSTD SOFTWARE DESCRIPTION

VOLUME I

PROGRAM USER'S GUIDE

August 1972

VI~

TABLE OF CONTENTS

SECTION PAGE

PREFACE v

1. 0 PROGRAM DESCRIPTION . . . . 1-1

2. 0 DATA PREPARATION 2-1

3. 0 INPUT LANGUAGE 3-1

4. 0 PROBLEM SUBMISSION . 4-1

4. 1 Program Run Preparations 4-1

4. 2 Output Description 4-3

5. 0 FORTRAN INTERFACING . 5-1

5. 1 FORTRAN Library Model Procedures 5-1

5. 2 FORTRAN Post-Processing Routines 5-3

6. 0 EXAMPLES . 6-1

APPENDIX

A BIBLIOGRAPHY AND REFERENCES A-1

B ASYSTD LIBRARY DESCRIPTIONS . B-1

C DISTRIBUTION LIST . . C-1

ii

LIST OF ILLUSTRATIONS

FIGURE PAGE

2-1 Model Library 2-2

2-2 ASYSTD Phase 1 Output for Model NRZ . 2-14

4-1 Run Deck Setup for MSC 1108 Exec II System 4-2

4-2 ASYSTD First Phase Output 4-4

6-1 Apollo PCM/PM/PM Link Block Diagram 6-2

6-2 ASYSTD Example, Output . 6-3

6-3 ASYSTD Example 2 6-20

6-4 ASYSTD Example 3 Output . 6-23

6-5 Vary/Define Feature Example . 6-27

iii

LIST OF TABLES

TABLE PAGE

2-1 Intrinsic ASYSTD Parameters . 2-8

2-2 ASYSTD Identifiers 2-11

3-1 ASYSTD Identifier Hierarchy 3-6

iv

PREFACE

This document describes the computer program ASYSTD, which is

primarily designed to simulate the transient behavior of communications

systems.

The ASYSTD program is based in part on earlier work performed

for NASA MSC under Contract No. NAS9-10831, the development of the

SYSTID program. The program is written in FORTRAN V for the

UNIVAC 1108 computer operating under EXEC II.

The document is presented in two volumes - Volume I, Program

User's Guide, and Volume II, Program Support Documentation. Program

listings and detailed flow charts are under separate cover.

The analyses performed during the ASYSTD development contract

are published in a series of progress reports addressing the individual

tasks, which include:

· Parametric Analysis

· Optimization and Statistical Analysis

· Propagation Model Development

· Frequency to Time Domain Filter Transformations

· Orthogonal Transforms

· Bit Error Rate Measurements (EVT)

* SNR Measurements

* Distortion Measurements

v

SECTION 1.0

PROGRAM DESCRIPTION

ASYSTD is a system of computer routines which provides the analyst

with a powerful tool for the transient simulation and analysis of complex

systems - in particular, telecommunications systems, although other con-

tinuous and discrete systems can be simulated.

The unique characteristic of telecommunications systems is the

large ratio between the RF carrier and baseband frequencies. Simulation

of such systems would normally require prohibitive run times. However,

with the techniques utilized in ASYSTD, this problem is alleviated. In par-

ticular, the RF system elements can be translated to baseband with com-

plete retention of their RF characteristics.

The program accepts as input a topological "black box" description

of a system, automatically generates the appropriate algorithms, and then

proceeds to execute the simulation program. Thus the user is not neces-

sarily required to write the algorithms in a computer language nor possess

a great facility in computer programming. The system description, includ-

ing both topology and element information, is supplied to the program in a

free-form, user controlled engineering language which is easily learned.

ASYSTD offers the user enormous flexibility in the representation of

system elements, i. e., "black boxes". An element may be defined as:

1) An ASYSTD library model.

2) A user written, temporary ASYSTD model.

1-1

3) A FORTRAN arithmetic expression involving any intrinsic

ASYSTD parameter, constants, variables, FORTRAN

library functions, ASYSTD library functions, model

output nodes (TAP's), and user supplied FORTRAN

functions.

The ASYSTD model library consists of a set of computer routines,

either written in FORTRAN or ASYSTD, which have been stored on a library

file and cataloged in the ASYSTD directory. The user, at any time, can

modify or replace the library and directory as he may choose - thus every

user can easily create his own library. One unique characteristic of

ASYSTD is the capability of nesting models to a level of 100 - that is, any

model (or system) can reference up to 100 models, excluding itself. The

nesting feature provides the user with the tools necessary to build a model

library to suit his needs based upon a canonic set of models. An example

might be a receiver that is used in several systems - the receiver would be

a model consisting of a connection of othe'r models.

The basic, or canonic, ASYSTD library consists mainly of a group

of routines which aid in the simulation of continuous functions, that is G(s).

The technique applied is that of the bi-linear z-transform representation of

G(s). The transfer function may be defined in several ways - in terms of

its poles and zeros or as one of the classical functions such as BESSEL,

ELLIPTIC, etc. The sample data routines accomplish all the necessary

transformations in addition to the numerical processing such as integration

and differentiation. In addition, all of the FORTRAN arithmetic features

are an intrinsic part of the ASYSTD library - although they do not appear

in the directory.

The bi-linear transform rather than the standard z-transform is

used in the representation of continuous functions because it eliminates

aliasing errors, making possible the realization of commonly encountered

functions whose response does not approach zero at high frequencies. Note

that aliasing of the signals, however, is possible.

Another aspect of the ASYSTD model library is that it contains

FORTRAN subroutines - that is, when a model (or system) is processed by

1-2

il

ASYSTD, the result is a FORTRAN subroutine (or main program) which is

available to the user for any purpose, whether for ASYSTD or not. Thus,

ASYSTD can be viewed as a FORTRAN program generator which converts

a topological, non-procedural input into a procedural language-FORTRAN.

Although not unique to ASYSTD, this aspect allows one to evaluate mathe-

matical problems via ASYSTD with no concern for the Input/Output coding

necessary in FORTRAN programs. That is, ASYSTD may be used as a

shorthand FORTRAN system.

ASYSTD's flexibility is in part attained by designing the program to

execute as a multipass processor in a batch mode of operation. The first

phase reads the user input description of all models and/or a system and

proceeds to formulate the corresponding FORTRAN algorithms. In this

phase, the program checks for input errors such as erroneous model ref-

erences, dangling nodes, etc., in which case appropriate error messages

are issued. If the first phase terminates without fatal errors, the

FORTRAN routines are automatically compiled and collected with the

ASYSTD library to from the second phase, that of executing the simulation.

Output from the program includes plots as well as tabulated data.

Conventional output is any system node or 'TAP" which may be individually

selected, or any variable whether intrinsic or user defined. Plots can be

produced on the printer as well as a digital plotter. Printed data can be

formatted, under user control, for either 8-1/2 by 11 inch pages or the

full 11 by 14 inch page. Digital plotters are handled by the subroutine

TMPLT, which is installation dependent.

The additional flexibility of linking to a user defined post processing

routine is intrinsic to ASYSTD when utilizing the POST system identifier.

This feature allows the user to access the time histories of any node, tap,

or variable much the same way as the plot routines. As a matter of fact,

the plot routines are indeed intrinsically named post-processors. Utility

routines are available to perform any necessary input/output for the user.

The user, because of the two phase aspect, has available to him

several techniques for controlling his computer runs and ensuring that the

most effective use is made of the machine time. The primary means is

1-3

that of saving the results of the first phase, that is, the collected

simulation package for subsequent reruns with alternate input data. Rerun

would then simply entail a load-go operation. The alternate input data can

be provided at execution time by use of the "DATA' identifier in the first

phase.-

1-4

SECTION 2. 0

DATA PREPARATION

Given a description of a system or model in an engineering oriented

language, ASYSTD will automatically generate the FORTRAN code required

to simulate the system or model. The user, however, must reduce the

system or model to an equivalent block diagram form consisting of model

references, math expressions, etc., which can be interpreted by ASYSTD.

The transcription of the equivalent block diagram into the input language

is straightforward and easily mastered.

The initial step in using ASYSTD is to prepare the equivalent block

diagram utilizing the ASYSTD library directory and FORTRAN expressions

available. The model library directory currently available is given in

Figure 2-1. The usage of these internal models is explained in Appendix B.

The user is not in any way restricted or limited to this library - any par-

ticular function in the library can be replaced with one's own model. Thus

the user's model repertoire consists of:

1) The invoked ASYSTD library directory.

2) FORTRAN math functions, including user variables,

constants, etc.

3) Any ASYSTD model defined in the same run stream.

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There are three basic types of ASYSTD elements (black boxes) which

make up a model or system:

* Mono-node elemnents

K OUTPUT

for example, a source

* Bi-node elements

for example, a filter

· Multi-node elements

for example, a mixer

The mono-node and bi-node elements are certainly the most common

and most readily implemented. The multi-node element, however, may

pose some problems to the inexerpeinced user. All elements or models

have, by definition, one INPUT node and one OUTPUT node. Any other

connection, be it an input or an output, is considered a "TAP". A "TAP''

may be thought of in the conventional way - that is, as a point in the system

or model which can be externally accessed either for observation or for

insertion of a signal. There is no explicit distinction between the different

types of elements since all ASYSTD topological descriptions have one input

2-5

and one output. In the case of the mono-node device, the input node serves

only to satisfy the input syntax. The bi-node and multi-node distinction is

even less obvious since the only requirement is that all input TAP connec-

tions to a multi-node device must be specified.

Several rules and assumptions make up the formulation of the algo-

rithms for simulating a system or model, and impact on the user in the

following ways:

1) Every user defined model must have an input node

named "INPUT", and an output node named "OUTPUT''.

2) At least one path must be defined which relates OUTPUT

to INPUT.

3) All paths must terminate at OUTPUT or at a TAP.

4) The value of the signal at a node is the instantaneous

sum of the OUTPUT of all devices connected to the node.

5) The value of a TAP is the instantaneous OUTPUT of

the element to which it is attached (not the output node

of the element).

6) A TAP may be referenced external to the model in which

it is defined.

7) Model nodes are not externally available.

8) TAP's maintain the status of a unique variable name

and thus may be used in FORTRAN expressions, sub-

routine calls, output requests, etc.

9) Node names must be legal FORTRAN variables, i. e.,

no more than six alphanumeric characters, the first

of which must be a letter.

10) TAP names are defined as TAPXXX, where XXX is a

unique number less than 1000. Sequential numbering

is recommended.

Z-6

11) All variable names and expressions must be FORTRAN

compatible, including integer and floating point con-

ventions. Names beginning with the letters I through N

or the letter Z are typed as integers.

12) Intrinsic ASYSTD variables are defined in Table 2-1,

and are available to the user.

13) The user is cautioned against using variables which

begin with the letters V or Z, as a conflict with system

variables is possible.

14) Maximum number of continuation cards is four.

15) A node may not connect directly to itself.

16) A model name may be up to 36 characters long.

17) The distinctions between a model and a system are

the declaration and I/O identifiers. A system is exe-

cutable; a model is callable.

18) A TAP is externally referenced from the element field

by stating the model name and the tap number. The tap

number is positive for an input, negative for an output.

The RNF of the statement is the LNF of the model

reference.

In addition to the above, certain procedures and requirements exist

as to setting up the appropriate parameter values necessary to ensure an

efficient, yet cost effective simulation. These include the following:

1) Sampling rate should be at least 15 to 20 times that of

the highest frequency of interest - which is normally

the widest bandwidth, although relaxation of this approxi-

mation is certainly desirable when possible. Accuracies

of less than 1 percent are easily achieved for transfer

function representations with lower sampling rates.

One obvious problem, particularly for low order func-

tions, is aliasing of the input signals. Thus care must

2-7

Table 2-1. Intrinsic ASYSTD Parameters

Variable

TIME (or T)

TSTART

TSTOP

SETTLE

DT

$

Z+ 1

ZZ

V ( ) or VV (

VIN

VIN + 1

VOUT

VOUT + 1

PI

TWO PI

NPRINT

Usage

The time as kept by the SimulationClock (unrelated to actual computerrun time)

The simulation start time (i. e., atime bias for output labeling)

Simulation stop time

Setting time before outputting

Sample time

Used to denote the current signalat the input node

Absolute address of the first datacell available to the model (V(Z+1))

Absolute address of the last datacell used by the model (V(ZZ))

Dynamic storage array

Address of the current real input

Address of the current imaginaryinput

Address of the current output

Address of the current imaginaryoutput

3. 14159

6. 28318

Output print interval

2-8

be taken, and in some cases, the SWAG technique is

the only recourse.

2) All simulations require the specification of sampling

time (DT) and stop time (TSTOP): Unless parameters

are defined in a DATA or DEFAUL statement, ASYSTD

will abort the simulation phase.

3) Turn on transients can be eliminated from the output

by use of the intrinsic parameter SETTLE. A rule

of thumb is that turn on transients should die out at

approximately 5/BW, where BW is the approximate

system bandwidth.

Once the user has applied the above rules in specifying the block

diagram equivalent of his system, he may assign node names and tap names

where appropriate, and proceed to encode the system accordingly. The

input language is fully explained in the next section; its most important

aspects are introduced here. The basic problem is to represent the two-

dimensional block-diagram using a series of statements. This is accom-

plished using the following standard format for all ASYSTD input:

LEFT EXPRESSION RIGHT TAPNODE OR ELEMENT NODE FIELDFIELD FIELD FIELD (TF)(LNF) (EF) (RNF)

where O denotes any non-alphanumeric character delimiter (other than

(7-8) and (0-8-2) punches) which serve as field separators. The Tap Field

is not required.

A general element definition is exemplified by:

NODE1 < BLACK BOX > RIGHT 'TAP69

2-9

This statement says that model BLACK BOX processes the signal at

NODE1 and its output is at node RIGHT. The tap TAP69 also contains the

signal output by model BLACK BOX which may not be the signal at node

RIGHT.

The standard card format is used for inputting the various ASYSTD

identifiers and is given in Table 2-2. These identifiers are required to

define whether the descriptions are for a system or model. All but DEFINE,

SET, and END are illegal for a model description. The ASYSTD identifiers

occupy the LNF with the appropriate data in the EF. Recall that the dis-

tinction between a model and a system is the input/output and declaration

information.

An example of a model definition:

MODEL = EXAMPLE WITH TAPS, A, B

INPUT = SIN ($)/TAP1 = NODE1

NODE1 = DUMY MODEL (TAP2) = NODEZ 'TAP1

NODEZ = $ '$''A/B = OUTPUT

END

Although this example is physically meaningless, it serves to

illustrate one use of taps and is explained thusly: The signal at NODE1

equals the sine of the input signal (denoted by $) divided by the signal output

from model DUMY MODEL. (This follows from the definition of TAP1.

The signal at NODEZ is then equal to the output of DUMY MODEL, when

NODE1 and TAP2 are its inputs. Note that TAPZ is an input to EXAMPLE

WITH TAPS, since it was not defined in the model description. The output

of EXAMPLE WITH TAPS, OUTPUT, is the signal at NODE2 squared,

times A, divided by B. Here A and B are variables which must be speci-

fied by whatever model references the EXAMPLE WITH TAPS model. Also

note that TAP1 is externally available for any other model reference.

2-10

Table 2-2. ASYSTD Identifiers

Identifier

SYSTEM

MODEL - Name - arg 1, arg 2

END

DATA - Variable list

DEFAUL(T) - Variable list

PRINT - Node or tap names

PLOT - Node or tap names

PPLOT - Node or tap names

POST - Routine name, nodeor tap names

PAGE

DEFINE -Variable -expression

SET - Variable - expression

VARY - Variable -parameters

Use

Indicates that the deck followingdefines an ASYSTD system

Indicates that the deck which followsdefines an ASYSTD model

Used to indicate the end of a modelor system deck

Indicates that the following valuesare to be read in at execution timeby namelist (used only in a system)name ASYSTD

Indicates the default values forDATA parameters not input throughnamelist

Indicates a list follows specifyingoutput to the printer

Indicates a list follows specifyingoutput to be plotted on theCalComp plotter

Indicates a list follows specifyingoutput to be plotted on the printer

Indicates that the following post-processing routine is to be called

When present causes 8-1/2" x 11"compatible output

Generates a FORTRAN definestatement, which produces code toevaluate the expression

Generates a FORTRAN assignmentstatement, which gives the variablethe value of the expression

Indicates the value of the variableis to be varied over a specifiedrange

2-11

The external connection of taps between models is best illustrated

in the following example:

MODEL - EXTERNAL TAP CONNECT, FC

INPUT < SINE (TWOPI*:FC4,TIME) > NODE1

NODE < EXAMPLE WITH TAPS (1., 2.) > NODE2

NODEZ < $'$ >NODE3

NODE3 < EXAMPLE WITH TAPS +2 > NODE 1

NODE3 < 2. *$ > OUTPUT

NODE4 < EXAMPLE WITH TAPS -1 > NODE1

NODE4 < $ >DUMY 'TAP09

In this example the signal at NODE3 is connected to input tap number

two of the model named EXAMPLE WITH TAPS (as denoted in the EF and

RNF of the statement). In addition, tap one of the model was externally

connected to NODE4 and given the external name of TAP09, which in turn

makes it available to yet another level of models.

The instructions necessary to define a system are identical to those

for a model, except for the addition of the declarations and Input/Output

statements. These are fully described in the next section. The entire

input for similar problems is described in Section 6. 0.

Several advanced techniques are available to the user in modeling any

system. The principal technique is modeling directly in FORTRAN (or

other compatible language) and interfacing with ASYSTD generated models.

The lmost likely necessity for such a requirement is in RF element modeling,

in which case the signals become complex. ASYSTD maintains any complex

quantities but does not directly perform complex arithmetic operations. All

complex RF models are, or use, models written in FORTRAN. Such an

undertaking is not recommended to the novice user.

2-12

As noted above, the user may modify or replace the ASYSTD

library and directory at will. This task is accomplished within the com-

puter system executive, utilizing the file manipulation and updating features.

The library directory given earlier in Figure 2-1 contains the necessary

information for modifying the directory. Since each model is a subroutine,

any computer system file may be designated as a library to be searched, or

the EXEC temporary program file can be loaded with the desired subroutines

at allocation time.

In any event, the directory serves to:

1) Cross reference model names and subroutine entry points.

2) Flag the model as a subroutine or function.

3) Defines the number of arguments to the routine.

4) Defines the number and type of each tap.

5) Defines the use (presently ignored) of the model.

Whenever a model is processed by ASYSTD, an entry point name is

assigned to it, and any subsequent models in the same run. The assign-

ment is made by alphabetically incrementing the least significant character

of the directory entry at Line 23, i. e., if Line 23 is MODEL MODEL, then

the first temporary model would have entry MODELA, the second MODELB,

etc. If Line 23 was MODELX, then the first model would be MODELY,

the second MODELZ, the third MODEMA, etc. In addition, the appropriate

entries are temporarily made in the directory for defining the model for the

particular run only. An example is given in Figure 2-2 where the directory

entry is the first line of output. If it were desirable to add the model to the

permanent library, one of two paths is available:

1) Rename the entry point by recompiling and updating the

FORTRAN Subroutine and entering the appropriate data

into the directory.

2) Adding the ASYSTD generated directory card into the

directory and changing Line 23 to reflect the "highest"

model name in the library.

Certainly, the latter is much easier, but may lead to future confusion.

2-13

N RZ M OD EL AASYSTD PROCESSOR LEVEL IIVERSION DATED 01 NOV 71 FOR THE MSC U1108 SYSTEMTHIS DECK PROCESSED ON 28 APR 72 AT 19:17:05

SYS TI D MO DE LS REF EREN CE D

SO

1 I 0 00 00 00000 00 2

ENTRY POI NT

SQ

THIS MODEL ASSIGNED THE ENTRY POINT NAME MODELA

MOPELN RZ ,BRINPUT < S(BR/2, ) > N1N1 ( $ .5+. 5 > OUTPUT

END

Figure 2-2. ASYSTD Phase 1 Output for Model NRZ

2-14

0000010000020 00 00 3000004

SECTION 3.0

INPUT LANGUAGE

The ASYSTD input language consists of descriptive statements

constructed largely from user defined names and specifications. Several

key variables are used, as defined earlier in Table 2-Z, in addition to

names which reference defined library models. The statements for the

most part define some input and output node, along with an element specifi-

cation or expression relating the two. The statements can be punched in a

completely free-field data card (Columns 1 through 80). Since all state-

ments are scanned from both the left and right, field delimiters can be any

non-alphanumneric character other than (7-8) and (0-Z-8) punches. A

statement may have up to four continuation cards, which are defined by a

non-alphanumeric in Column 1. With the exception of the title on a SYSTEM

card, all blanks are ignored by the processor.

As discussed in Section 2. 0, the standard card format is utilized for

all ASYSTD input, including the identifiers given in Table 2-2. These

identifiers primarily concern themselves with initializing and controlling

the execution of a system simulation. The identifier occupies the LNF and

any data occupies the EF of the standard card format defined as follows:

LEFT ELEMENT RIGHTNODE OR NODE TAPFIELD EXPRESSION FIELD FIE(LNF) FIELD (RNF) (TF)

(EF)

3-1

The various identifiers are discussed below:

DATA: var1 , var2

, ... , varn

This identifier names a list of variables which can be

read in at simulation time under namelist SYSTID.

Whenever this statement appears, a namelist data card

must appear at execution time. The number of variables

is limited only by the number one can squeeze on 5 cards.

The variables must conform to FORTRAN requirements,

and may be any intrinsic ASYSTD variable, e. g.,

DATA = TSTOP, DT, NPRINT, MEDIA, SAM, A

The Phase II input data for this example would be, for

example:

$SYSTID DT = 1. 5 E-6, TSTOP = 10 ... $

which is standard FORTRAN namelist input.

DEFAUL: var1 = const, var2

=const, . ., var= const

This identifier serves to load default values for any

variable in the simulation, including any intrinsic

ASYSTD variable. The constant values must conform

to the FORTRAN rules of integer and Floating point

variables or errors may occur. The number of entries

is limited by the number one can squeeze on 5 cards,

e. g. ,

DEFAUL: DT = 1. 5 E-6, TSTOP = 2.0, A = 10.,

: IOU = 3

3-2

DEFINE: variable = FORTRAN expression

This identifier generates a FORTRAN 'DEFINE'

statement. 'Variable' must be a legal FORTRAN

name. Whenever this name appears in the generated

FORTRAN program, the FORTRAN expression is cal-

culated using current values of any variables which may

appear in the expression, and this result is used for the

value of 'variable'.

END: comment

Signifies the end of a model or system description.

MODEL: model external name, argl, arg2, .. ., arg

This identifier instructs ASYSTD to expect a model

definition only (i. e., topological information) and to

generate a subroutine.

The external name must be no more than 36 characters,

with no more than 99 arguments, e. g.,

MODEL: FM MODULATOR, BETA, FC

or

MODEL: UHF RECEIVER

PAGE: comment I

This identifier, merely by being present, causes all

printed output to be 8-1/2 by 11 inch compatible.

3-3

PLOT: namel, name, ., name

This identifier is similar to PPLOT, the exception being

that here the CalComp (or SC4060) plotter is utilized,

e. g. ,

PLOT: TAP69, X, NODE4, OUTPUT

POST: subroutine name, name, name2 name

This identifier causes a post-processing routine named

"subroutine name" to be called following the simulation.

This routine is called for each occurrence of name.,1

which may be nodes, taps, or variables. The call

sequence generated is similar to that of the plot request,

the only difference being the entry point. Utility routines

are available for interfacing a user post-processor with

the data time histories which are stored on drum.

PPLOT: name1 , na2 namen

This identifier defines the data to be plotted vs. TIME

following the simulation. The quantities may be nodes,

taps, and variables, e.g.,

PPLOT: NODE1, TAP69, B

PRINT: namel, name2 , name3 ... namen

This identifier defines the data

the simulation. The quantities

to be printed during

which may be printed

3-4

consist of nodes, taps, and variables. Note that TIME

is automatically printed - it need not be requested, e. g.,

PRINT: NODE1, TAP69, AVAR

SET: variable = FORTRAN expression

This identifier generates a FORTRAN assignment

statement which sets 'variable' equal to the value of

'FORTRAN expression'.

SYSTEM: title

This identifier instructs ASYSTD to expect other identi-

fiers dealing with input/output, etc., and to generate

a main program. The title serves to label all output

(36 characters), e. g.,

SYSTEM: TRY ME SOMETIME

VARY: variable = min, max, delta

This statement generates a FORTRAN DO-LOOP which

has within its range any VARY or SET statements

which follow it in the ASYSTD deck as well as the pro-

gram simulation. If the 'variable' name is type integer

(first letter is I through N or Z), the parameters are

expected to be of integer type, otherwise the variable

name and parameters can be real or integer. The

parameters (min, max, delta) must be constants,

DEFINE variable names, or variable names which have

appeared in a DATA or DEFAULT statement.

3-5

Any card which has an empty LNF (a non-alphanumeric in Column 2

or later as the first non-blank character) is treated as a comment. A

comment may appear anywhere except the middle of a continued statement.

Comments may be continued.

Topological input data fully utilizes the standard card format, that is:

Input node G expression or element output nodeO Tap

as signment

where Q is any valid delimiter as defined above. For example,

NODE1 = RF PHASE MODULATOR (BETA, FC) = NODEZ

= TAP8

represents a normal statement utilizing the four fields of a standard input

form.

Thus, with one format, ASYSTD input data is extremely straight-

forward and easily mastered.

Table 3-1 shows which statements are allowed and what order they

must be placed in Systems and Models respectively.

Table 3-1. ASYSTD Identifier Hierarchy

SYSTEM MODEL

DATADEFAULPAGEPLOTPOSTPPLOTPRINT

DEFINEVARYSET

TOPOLOGICALINFORLATION

END

DEFINESET

TOPOLOGICAL 1INFORMATION

END

3-6

The first card of a System is the SYSTEM card. This is followed

by DATA, DEFAUL, ... , PRINT statements as appropriate in any order.

Any DEFINE statements come next followed by any VARY or SET state-

ments which are required. Topological information cards describing the

System come next in any order, followed by the END card.

A MODEL card defines a Model. Any DEFINES followed by any

SET statements appear next. The topological information is again followed

by an END card.

3-7

SECTION 4. 0

PROBLEM SUBMISSION

4. 1 PROGRAM RUN PREPARATIONS

When executing the first phase of ASYSTD, the procedure

PROCS/SYSTID and the element LIBARY are required along with the

absolute element for the first phase (SYSTID). The LIBARY element is

the model library dictionary.

The second phase requires only the library file containing all the

ASYSTD library relocatable elements and the elements output to the PCF

by the first phase (MAIN316/SYSTID).

4. 1. 1 Deck Setup

The technique used by ASYSTD is to output the processed models to

the PCF as elements named MODELA/SYSTID, MODELB/SYSTID, etc., in

the same order as processed. When a system is processed, its element

name is MAIN1A6/SYSTID. Therefore, the user at MSC must provide the

FORTRAN control card for each of the elements. The models generated

in the following example are "temporary" models for this run only. That

is, any system description can reference model EXAMPLE 1 during this

run only. Models are permanent when the relocatable is available and an

entry is made in the LIBARY element used by the first pass. Figure 4-1

is the run deck setup for the MSC UNIVAC 1108 system.

4-1

@ XQT CUR

.--- LOAn THE pCF WITH SYSTID ABSOLUTE, PROCS/SYSTID, A4N LITrAY

@ XPT SYfTIDMODEL: EYAMPLE ONE

END IMODEL: ExAMPLE TWO

ENnMODEI: EYAMPLE THREE

END~SYSTEM. IISE EXAMPLES ONETWO,THRFE

END@I FOR#. ,MOOELA/SYSTIO@I FOR)* MODELB/SYSTID@I FfO),* MODELC/SYSTTD I@T FOR.* MAIN /SYSTID@ XPT MATN /SYSTID

$SYSTID ENAMELIST I/Ov IF SPECIFIEl)

MODELA /SYSTIDis generated in PCF

MODELB/SYSTID

MODELC /SYSTID

MAINOB/SYSTID

User suppliedcompiler cards

Execute the second passIN SIJUL AT IT Or'j

Figure 4-1. Run Deck Setup for MSC 1108 Exec II System

4-2

.

4. 1. 2 Required I/O Devices

The ASYSTD program contains two phases. The first phase

requires the Logical Unit assignments as follows:

Logical Unit Device

5 Card Reader

6 Line Printer

1 Scratch Drum

Phase two requires the following I/O devices:

Logical Unit Device

5 Card Reader

6 Line Printer

13 Drum

14 Drumn

4. 2 OUTPUT DESCRIPTION

4. 2. 1 Data Output

ASYSTD output consists of the first phase processing and the simu-

lation or second phase output. The first phase provides output similar to

the FORTRAN V compiler. Figure 4-2 is an example of the first phase

output for a particular model. Annotations on the output fully explain

their significance.

4-3

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4. 2. 2 Optional Output

The second phase output is completely optional under user control.

The two forms of output are printed and graphical presentations, whose

size is selectable as 8-1/2 by 11 inches or 11 by 14 inches (see Section 3. 1).

The current version provides printer plot (PTPLT), with the entry point

TMPLT reserved for CalComp or SC4020 graphical routines. Examples

of the output are contained in Section 6. 0.

4-5

SECTION 5. 0

FOR TRAN IN TERFACING

There are two instances in which the user may wish to write his

own FORTRAN subroutines to interface with the main ASYSTD simulation.

These are Models which, for some reason, are not easily or efficiently

written in the ASYSTD language and post-processing routines.

5. 1 FORTRAN LIBRARY MODEL PROCEDURES

An important feature of ASYSTD is its ability to reference any

FORTRAN subprogram (model). However, in order for a user's FORTRAN

subprogram to be re-entrant and interface correctly with any other model,

it must conform to certain procedures. The characteristics of such a sub-

program and then usage should be:

o Input arguments are never altered.

o Every reference to the subprogram is unique (independent).

* All local storage is considered scratch; permanent storage

is only available in a common storage pool named "V".

o If a subroutine-primary input is at V(VIN) and V(VIN + 1),

primary output goes to V(VOUT) and V(VOUT + 1).

e Numeric values of VIN and VOUT should be restored

prior to exit.

5-1

To properly interface with any routine processed by ASYSTD, the following

procedures should be followed, if applicable:

• A FORTRAN procedure named HEDFOR is available

to provide compatible definition of intrinsic ASYSTD

storage and variables. Use of the procedure is the

FORTRAN V statement:

INCLUDE HEDFOR, LIST

When writing FORTRAN models, a current listing of

this procedure is sometimes useful.

Defining local variable Z as the last cell in the "V"

pool used by the calling subroutine, and common vari-

able ZZ the last cell to be used by this routine, set:

Z = ZZ

and

ZZ = ZZ + n

where n is the number of locations required for per-

manent storage in the "V" pool.

A reservation of storage space for a particular ref-

erence to this model is made, reserving cells (V(Z + 1)

through V(Z + n) for storage.

* Local variable Z is used to address the V array in the

model. Common variable ZZ should not be utilized in

any statement other than above, unless no other models

are referenced.

o When referencing other models, VIN and VOUT should

be assigned to one of the reserved cells in the "V" pool.

5-2

If a user written model is to be referenced, the user must update

the ASYSTD library (element LIBRARY). This task is performed under the

system executive, external to ASYSTD. See Pages Z-2 and 2-13 for instruc-

tions on making a library entry.

5. 2 FORTRAN POST-PROCESSING ROUTINES

Linkage to any user post-processing routine is available through

use of the ASYSTD identifier "POST". When a reference to post is made

in any system description, a subroutine call is made to the user's program

for every specified variable in the form:

CALL NAME (LABEL, NPAGE)

where

LABEL is the hollerith name of the variable.

NPAGE conveys the output sizing, i. e., NPAGE = 4

is 8. 5 x 11 compatible output, NPAGE = 7 is standard

computer size output.

For example:

The ASYSTD statements

POST 0) SPECTM 0 NODE1, OUTPUT

would generate the following two lines in the main simulation

program:

CALL SPECTM ('NODEl', 7)

CALL SPECTM ('OUTPUT', 7)

5-3

The first line of the user written routine SPECTM would

generally be as follows:

SUBROUTINE SPECTM (LABEL, NPAGE)

Two input parameters are required, even if the user is not

concerned with output sizing.

Whenever a POST statement appears in an ASYSTD program,

MAIN/SYSTID contains the following common block (all variables which

begin with Z are integers):

COMMON/DRMHED/ZDATE(Z), ZTOD(Z), TSTART,TSTOP, VEQDT, SETTLE, ZEDIT, ZNPU, ZRESRV,ZUSED, ZNAMES, ZNAME (< ZNAMES >)

where

ZDATE

ZTOD

= BCD of DATE, left adjusted, blank filled

= BCD of TIME OF DAY, left adjusted,blank filled

TSTOP

Self explanatory, VEQDT = DT (whichappears in /COGENT/)

= Edit interval (if all values won't fit ondrum)

= Number of variables saved on eachlogical unit

= Number of words of storage reservedfor each variable to be saved

5-4

TSTART

VEQDT

SETTLE

ZEDIT

ZNPU

ZRESRV

ZUSED

ZNAMES

= Number of values for each variablestored on drum (in some routinesnamed NVAL)

= Number of different variables storedon drum

ZNAME(I),I = 1, < ZNAMES > = names of variablesstored on drum

Inclusion of this common block in a post-processing routine allows

the user access to several important variables, particularly NVAL (ZUSED),

the number of values available for any particular variable stored on drum.

All retrieval of information stored on drum should be accomplished

with the two subroutines DRMGET and DRMEDT.

DRMGET: Calling sequence:

CALL DRMGET (NAME, ARRAY, LENGTH, MSKIP)

where

NAME contains name of variable referenced (BCD).

ARRAY is array into which values are to be read(dimensioned at least by LENGTH).

LENGTH is number of values to be read.

MSKIP is number of words to skip before reading.

Continuing the example, the following lines of code retrieve

all values stored on drum for a particular variable, 1000 values

at a time.

5-5

Example 1:

SUBROUTINE SPECTM (LABEL, NPAGE)COMMON/DRMHED/DUMMY(11), NVALDIMENSION ARRAY (1000)

DO 100 MSKIP = 0, NVAL, 1000CALL DRMGET (LABEL, ARRAY, 1000, MSKIP)

Analysis of the 1000 valuesof the variable named in LABEL

100 CONTINUE

DRMEDT: Calling sequence:

CALL DRMEDT (NAME, NREQ, ARRAY)

where

NAME contains name of variable referenced (BCD).

NREQ equals number of values to be read off drum.

ARRAY is array into which values are placed(dimensioned at least by NREQ)

Let NVAL be the twelfth word of common block /DRMHED/.

NVAL equals the number of values stored on drum for each

variable. If NREQ > NVAL, then NVAL words (all that are

5-6

on the drunrk) will be read into ARRAY. If NREQ < NVAL,

the data on drum is edited and NREQ equally spaced values

are read into ARRAY.

Example 2:

SUBROUTINE SPECTM (LABEL, NPAGE)DIMENSION ARRAY (1000)

CALL DRMEDT (LABEL, 1000, ARRAY)

ARRAY now contains 1000 equally spaced valuesof the variable named in LABEL.

Values of TIME are not stored on drum but are computed by

DRMGET and DRMEDT when needed, saving drum I/O time.

In Example 1, assume the array TIME is dimensioned by 1000.

Then the statement:

CALL DRMGET ('TIME', TIME, 1000, MSKIP)

placed inside the DO LOOP will compute the 1000 values of time correspond-

ing to the values in ARRAY.

Similarly, in Example 2, the statement:

CALL DRMEDT ('TIME', 1000, TIME)

would produce 1000 values of time in the array TIME such that ARRAY(I)

was the value of the variable named in LABEL at time TIME(I).

5-7

SECTION 6. 0

EXAMPLES

Four example sets are presented in this section, namely:

1) ASYSTD simulation of an Apollo PCM/PM/PM

communications link whose characteristics are given

in Figure 6-1.

2) ASYSTD squaring loop model also defined in Figure 6-1.

3) ASYSTD model of sonar propagation through sea water.

This example serves to illustrate evaluation of a mathe-

matical function with ASYSTD.

4) ASYSTD model of FILTER response. This example

serves to illustrate the DEFINE, VARY, and SET

commands.

The first example consists of a temporary definition of model NRZ and use

of several library models, along with some math expressions. Figure 6-Z

illustrates the ASYSTD output for the run. The sequence numbers to the

left of the input statements correspond to the data card number. Thus,

model NRZ was defined with the first four cards of the input data deck.

Following the two pages of Phase I output are the FORTRAN compilations

of the resultant subroutine and main program. These two routines, along

with the ASYSTD library make up the Phase II simulation program. The

results of the simulation are evident following the FORTRAN routines.

A few remarks concerning this simulation are in order. Notice

that following the square wave phase modulator is an RF phase modulator.

At this point, we are representing the RF portion of the link at baseband.

6-1

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This process is actually implemented by assuming that the input signals

are analytic. This condition is met if the baseband signal spectrum is

essentially zero at the carrier frequency. If this assumption is not true,

a ripple in the simulation output at frequencies of approximately twice the

carrier is introduced - the case if the input is a step function, for instance.

In any event, the ripple is normally negligible due to the large ratio between

baseband and carrier.

The second example is to illustrate the definition of a model,

namely a squaring loop. Squaring loops have been utilized for deriving

subcarrier phase references for detection of phase modulated signals. The

topology is shown in Figure 6-1 since the elements making up the proposed

model were used in the Apollo link simulation. The model utilizes a single

tap for use by the multiplier. Figure 6-3 presents the Phase I ASYSTD

output and resulting FORTRAN subroutine.

The third example is a model representing a sonar system propaga-

tion function. The mathematical form of the model is given by:

Af f2a +2 Bf 2 dB/meterf2 + f2m

where

f Relaxation frequency (kHz) given in table belowm

f = Operating frequency (kHz)

A, B are curve fit coefficients for salt water given by thefollowing

Temperature f A Bm

5°C 60 kHz 6 x 1 0 - 4 3.2 x 10-

15 0 C 100 kHz 6 x 10 - 4 2.x 10- 7

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APPENDIX A

BIBLIOGRAPHY AND REFERENCES

(1) Golden, R. M. and Kaiser, J. F., "Design of WidebandSampled Data Filters", B.S. T. J., pp. 1533-1545, vol. 43,part 2, July 1964.

(2) Kaiser, J. F., "Design Methods for Sampled-Data Filters",Proc. First Allerton Conference on Circuit and System Theory,Nov., 1963, Monticello, Illinois, pp. 221-236.

(3) Golden, R. M., "Digital Computer Simulation of a Sampled-DataVoice-Excited Vocoder", J. Acoust. Soc. Am., 35, Sept., 1963,pp. 1358-1366.

(4) Wilts, C. H., Principles of Feedback Control, Addison-Wesley,1960, pp. 197-207.

(5) Hamming, R. W., Numerical Methods for Scientists and Engineers,McGraw-Hill, New York, 1962, pp. 277-280.

(6) Kelly, J. L., Jr., Lochbaum, C. and Vyssotsky, V. A. "a BlockDiagram Compiler", B. S. T. J., 40, May, 1961, pp. 669-676.

(7) Storer, J. E., Passive Network Synthesis, McGraw-Hill, New York,1957, pp. 293-296.

(8) Kuo, F. F. and Kaiser, J. F., System Analysis By DigitalComputer, J. Wiley & Sons, Inc., New York, 1966.

(9) D. C. Baxter, Digital Simulation Using Approximate Methods,National Research Council, Ottawa, Canada, Report MK-15,Division of Mechanical Engineering, July 1965.

(10) J. E. Gibson, Nonlinear Automatic Control, McGraw Hill, New York,1963, pp. 147-159.

(11) K. Steiglitz, The General Theory of Digital Filters with Applicationsto Spectral Analysis, AFOSIR Report No. 64-1664, New York Univer-sity, New York, May 1963.

A-1

(12) K. Steglitz, "The Equivalence of a Digital and Analog Signal Pro-cessing", Information and Control, Vol. 8, No. 5, October 1965,pp. 455-467.

(13) J. F. Kaiser, "Some Practical Considerations in the Realization ofLinear Digital Filters", Proceedings Third Allerton Conference onCircuit and System Theory, Monticello, Illinois, October 1965, pp.621-633.

(14) G. E. Heyliger, The Scanning Function Approach to theDesign of Numerical Filters, Report R-63-2, Martin Co.,Denver, Colorado, April 1963.

(15) R. J. Graham, Determination and Analysis of NumericalSmoothing Weights, NASA Technical Report No. TR-R-179,December 1963.

(16) E. B. Anders et al., Digital Filters, NASA Contractor ReportCR-136, December 1964.

(17) D. G. Watts, Optimal Windows for Power Spectra Estimation,Mathematics Research Center, University of Wisconsin, MRC-TSR-506, Sept ember 1964.

(18) E. Parzen, Notes on Fourier Analysis and Spectral Windows,Appiied Mathematics and Statistical Laboratories, TechnicalReport No. 48, May 15, 1963, Stanford University, California.

(19) G. A. Campbell and R. M. Foster, Fourier Integrals forPractical Applications, D. Van Nostrand, 1948, p. 113 pair 872.1.

(20) J. F. Kaiser, "A family of window functions having nearlyideal properties", November 1964, unpublished memorandum.

(21) D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions,Fourier analysis and uncertainty - I and II", B. S. T. J. Vol. 40,No. 1, January 1961, pp. 43-84.

(22) P. E. Fleischer, "Digital realization of complex transferfunctions", Simulation, Vol. 6, No. 3, March 1966, pp. 171-180.

(23) M. A. Martin, Digital Filters for Data Processing, GeneralElectric Co., Missile and Space Division, Tech. Info. SeriesReport No. 62-SD484, 1962.

(24) S. A. Schelkunoff, "A mathematical theory of linear arrays",B.S. T. J. Vol. 22, January 1943, pp. 80-107. Mark Tsu-HanMa, A New Mathematical Approach for Linear Array Analysisand Synthesis, Ph.D. thesis, Syracuse University, 1961,University Microfilms No. 62-3050.

A-2

(25) G. M. Jenkins, "A survey of spectral analysis", AppliedStatistics, Vol. XIV, No. 1, 1965, pp. 2-32.

(26) H. H. Robertson, "Approximate design of digital filters,"Technometrics, Vol. 7, No. 3, August 1965, pp. 387-403.

(27) W. K. Linvill, "Sampled-data control systems studied throughcomparison of sampling with amplitude modulation, "Trans.AIEE, Vol. 70, Part II, 1951, pp. 1779-1788.

(28) A. Susskind, Notes on Analog-Digital Conversion Techniques,John Wiley, New York, 1957. See especially Chapter II,Sampling and Quantization by D. Ross.

(29) D. T. Ross, Improved Computational Techniques for FourierTransformation, Servomechanisms Laboratory Report, No.7138-R-5, Massachusetts Institute of Technology, Cambridge,Massachusetts, June 25, 1954.

(30) C. Jordan, Calculus of Finite Differences, Chelsea, 1960,(Reprint of 1939 Edition).

(31 H. M. James, N. B. Nichols, R. S. Phillips, Theory of Ser-vomechanisms, McGraw-Hill, New York, 1947, pp. 231-261.

(32) J. R. Ragazzini and G. F. Franklin, Sampled-Data ControlSystems, McGraw Hill, 1958.

(33) E. I. Jury, Sampled-Data Control Systems, John Wiley andSons, Inc. 1958.

(34) J. T. Tou, Digital and Sampled-Data Control Systems, McGraw-Hill, 1959.

(35) E. Mishkin and L. Braun, Jr., Adaptive Control Systems,McGraw Hill, New York, 1961, pp. 119-183.

(36) E. I. Jury, Theory and Application of the z-Transform Method,John Wiley, New York, 1964.

(37) H. Freeman, Discrete-Time Systems, John Wiley, 1965.

(38) P. M. DeRusso, R. J. Roy, C. M. Close, State Variablesfor Engineers, John Wiley, 1965, pp. 158-186.

(39) R. B. Blackman, Linear Data-Smoothing and Prediction inTheory and Practice, Addison-Wesley, Reading, Massachusetts,

1965.

(40) C. Lanczos, Applied Analysis, Prentice Hall, Inc., EnglewoodCliffs, New Jersey, 1956.

A-3

(41) R. B. Blackman, J. W. Tukey, The Measurement of PowerSpectra from the Point of View of Communication Engineering,Dover, 1959.

(42) M. A. Martin, "Frequency Domain Applications to date Process-ing," IRE Transactions on Space Electronics and Telemetry, VolSET-5, No. 1, March 1959, pp. 33-41.

(43) J. F. A. Ormsby, "Design of Numerical Filters with Appli-cations to Missile Data Processing, "Jour. ACM, Vol. 8,No. 3, July 1961, pp. 440-466.

(44) A. J. Monroe, Digital Processes for Sampled Data Systems,John Wiley and Sons, Inc., New York, 1962.

(45) R. M. Golden, "Digital Computer Simulation of CommunicationSystems Using the Block Diagram Compiler; BLODIB, "ThirdAnnual Allerton Conference on Circuit and System Theory,Monticello, Illinois, October 1965, pp. 690-707.

(46) A. Tustin, "A Method of Analyzing the Behavior of LinearSystems In Terms of Time Series, "Jour. IEE, Vol. 94,Part II A, May 1947, pp. 130-142.

(47) J. M. Salzer, "Frequency Analysis of Digital ComputersOperating In Real Time, "Proc, IRE, Vol. 42, February 1954,pp. 457-466.

(48) R. Boxer, S. Thaler, "A Simplified Method of Solving Linearand Non-Linear Systems, "Proc. IRE, Vol. 44, January 1956,pp. 89-101.

(49) R. Boxer, "A Note on Numerical Transform Calculus, "Proc.IRE, Vol. 45, No. 10, October 1957, pp. 1401-1406.

(50) D. C. Baxter, The Digital Simulation of Transfer Functions,National Research Laboratories, Ottawa, Canada, DME ReportNo. MK-13, April 1964.

(51) C. J. Drane, Directivity and Beamwidth Approximations forLarge Scanning Dolph-Chebyshev Arrays, AFCRL PhysicalScience Research Papers No. 117, AFCRL-65-472, June 1965.

(52) H. L. Garabedian (Ed.), Approximation of Functions, ElsevierPublishing Co., 1965, see especially Walsh pp. 1-16 and Cheney

pp. 101-110.

(53) E. W. Cheney and H. L. Loeb, "Generalized rational approxi-mation, "J. SIAM, Numerical Analysis, B, Vol. 1, 1964, pp.11-25.

A-4

(54) Josef Stoer, "A direct method for Chebyshev approximation byrational functions, "JACM, January 1964, Vol. 11, No. 1, pp. 59-69.

(55) R. M. Golden and J. F. Kaiser, "A computer program for thedesign of continuous and sampled-data filters", to be published.

(56) C. M. Rader and B. Gold, Digital Filter Design Techniques,Lincoln Laboratory Report, M. I. T., Preprint JA2612, September 1965.

(57) H. Holtz and C. T. Leondes, "The synthesis of recursivefilters, "Jour. ACM, Vol. 13, No. 2, April 1966, pp. 262-280.

(58) L. Weinberg, Network Analysis and Synthesis, McGraw Hill,1962.

(59) D. A. Calahan, Modern Network Synthesis, Hayden, New York,1964.

(60) J. E. Storer, Passive Network Synthesis, McGraw Hill, New York,1957, pp. 287-302.

(61) P. Broome, "A frequency transformation for numerical filters,"Proc. IEEE, Vol. 52, No. 2, February 1966, pp. 326-7.

(62) P. E. Mantey, Convergent Automatic-Synthesis Procedures forSampled-Data Networks with Feedback, Stanford ElectronicsLaboratories, Technical Report No. 6773-1, SU-SEL-112,Stanford University, October 1964.

(63) J. R. B. Whittlesey, "A rapid method for digital filtering,Comm. "ACM, Vol. 7, No. 9, September 1964, pp. 552-556.

(64) T. Y. Young, Representation and Analysis of Signals, Part X.Signal Theory and Electrocardiography, Department ofElectrical Engineering, Johns Hopkins University, May 1962.

(65) P. W. Broome, "Discrete orthonormal sequences, "Jour. ACM,Vol. 12, No. 2, April 1965, pp. 151-168. Archambeau et al.,

"Data processing techniques for the detection and interpretationof teleseismic signals, "Proc. IEEE, Vol 53, No. 12, December1965, pp. 1860-1994, see especially p. 1878.

(66) H. W. Bode, Network Analysis and Feedback Amplifier Design,Van Nostrand, 1945, pp. 47-49.

(67) M. Mansour, "Instability criteria of linear discrete systems,"Automatica, Vol. 2, No. 3, January 1965. pp. 167-178.

(68) C. E. Maley, "The effect of parameters on the roots of anequation system, "Computer Journal, Vol. 4, 1961-2. pp. 62-63.

A-5

(69) J. G. Truxal, Automatic Feedback Control System Synthesis,McGraw Hill Book Co., Inc., New York, 1955, pp. 223- 250.

(70) F. F. Kuo, Network Analysis and Synthesis, John Wiley,New York, First Edition, 1962, pp. 136-137, (Second Edition,pp. 148-155).

(71) C. Pottle, "On the partial-fraction expansion of a rationalfunction with multiple poles by a digital computer, "IEEE Trans.Circuit Theory, Vol. CT-11, March 1964, pp. 161-162.

(72) W. R. Bennett, "Spectra of quantized signals", B. S. T. J.Vol. 27, July 1948, pp. 446-472.

(73) B. Widrow, "A study of rough amplitude quantization by meansof Nyquist sampling theory, "Trans, IRE on Circuit Theory,Vol. CT-3, No. 4, December 1956, pp. 266-276.

(74) B. Widrow, "Statistical analysis of amplitude quantizedsampled-data systems, "Trans. AIEE Applications and Industry,No. 52, January 1961, pp. 555-568.

(75) F. B. Hills, A Study of Incremental Computation by DifferenceEquations, Servomechanisms Laboratory Report No. 7849-R-1,Massachusetts Institute of Technology, Cambridge, Massachusetts,May 1958.

(76') J. B. Knowles and R. Edwards, "Effect of a finite-word-lengthcomputer in a sampled-data feedback system, "Proc. IEE Vol.112, No. 6, June 1965, pp. 1197-1207.

(77) J. B. Knowles and R. Edwards, "Simplified analysis of computa-tional errors in a feedback system incorporating a digital

computer, "S. I. T. Symposium on Direct Digital Control, April 22,1965, London.

(78) J. B. Knowles and R. Edwards, "Complex cascade programmingand associated computational errors, "Electronics Letters, Vol. 1,No. 6, August 1965, pp. 160-161.

(79) J. B. Knowles and R. Edwards, "Finite word-lergth effects inmultirate direct digital control systems, "Proc. IEE, Vol. 112,No. 12, December 1965, pp. 2376-2384.

(80) B. Gold and C. Rader, "Effects of quantization noise in digitalfilters, "Proceedings Spring Joint Computer Conference, 1966.Vol. 28, pp. 213-219.

(81) J. H. Wilkinson, Rounding Errors in Algebraic Processes,Prentice H-Iall, Englewood Cliffs, New Jersey, 1963.

A-6

(82) J. W. Cooley and J. W. Tukey, "An algorithm for the machinecalculation of complex Fourier series, "Mathematics of Compu-tation, Vol. 19, No. 90, April 1965, pp. 297-301.

(83) R. A. Gaskill, "A versatile problem-oriented language forengineers, "IEEE Transactions on Electronic Computers,Vol. EC-13, No. 4 (August, 1964), pp. 415-421.

(84) R. D. Brennan and R. N. Linebarger, "A survey of digitalsimulation: digital analog simulator programs, "SimulationVol. 3, No. 6 (December, 1964), pp. 22-36.

(85) J. J. Clancy and M. S. Dineberg, "Digital simulationlanguages: a critique and a guide, "AFIPS ConferenceProceedings, Vol. 27, Part I (1965), Spartan Books,

Washingron, D.C., pp. 23-36.

(86) J. C. Strauss and W. L. Gilbert, SCADS: a programmingsystem for the simulation of combined analog digitalsystems, Carnegie Institute of Technology, March, 1964.

(87) W. M. Syn and D.-G. Wyman, DSL/90 Digital SimulationLanguage User's Guide, IBM Corporation, San Jose,California, July, 1965.

(88) R. W. Burt and A. P. Sage, "Optimum design and erroranalysis of digital integrators for discrete system simula-tion, "AFIPS Conference Proceedings, Vol. 27, Pa rt I(1965), Spartan Books, Washington, C. D., pp. 903-914.

(89) M. E. Fowler, "A new numerical method for simulation,"Simulation, Vol. 4, No. 5 (May, 1965), pp. 324-330.

(90) C. C. Cutler, "Transmission Systems Employing Quantiza-tion, "U. S. Patent No. 2, 927, 962, March 8, 1960 (filedApril 26, 1954).

(91) T. G. Stockham, Jr., "High speed convolution and correlation,"Proceedings Spring Joint Computer Conference, 1966, Vol. 28,pp. 229-233.

(92) H. D. Helms, "Fast Fourier transforms methods of computingdifference equations arising from z-transforms and autoregressions,(to appear).

(93) J. L. Kelly, Jr., C. Lochbaum, and V. A. Vyssotsky, "Ablock diagram compiler", B. S. T. J., Vol. 40, No. 3 (May,,1961)pp. 669-676.

A-7

(94) M. R. Schroeder et al., New methods for speech analysis-synthesis and bandwidth compression, Congress Report ofthe Fourth International Congress on Acoustics, Copenhagen, 1962.

(95) L. S. Frishkopf and L. D. Harmon, "Machine recognition ofcursive script, "Symposium on Information Theory, London(1960), C. Cherry, Editor, Butterworth and Co. Ltd, London(1961), pp. 300-316.

(96) B. J. Karafin, "The new block diagram compiler for simulationof sampled-data systems, "AFIPS Conference Proceedings,Vol. 27, Part I (1965) , Spartan Books, Washington, D. C. pp. 53-62.

(97) A study of Math Model Input/Output Parameters for theComputer Aided Analysis Program HASD 6420-821429,Lockheed Electronics Company.

(98) G. Franklin, "Linear Filtering of Sampled Data", IREConv. Rec., Vol. 3, Pt IV, pp 119-128, 1955.

(99) R. P. Brennan and R. N. Linebarger, "An Evaluation ofDigital Analog Simulator Languages", I. F. I. P. 1965Proceedings, Vol. 2.

(100) J. R. Hurley and J. J. Skiles, "DYSAC", 1963 SJCC,Vol. 23, Spartan Books, Washington, D. C.

(101) V. C. Rideout and L. Tavernini, "MAD BLOC", Simulation,Vol. 4, No. 1, January 1965.

(102) M. L. Stein, J. Rose and D. B. Parker, "A Compiler withAn Analog Oriented Input Language (ASTRAC)", Proc. 1959WJCC.

(103) F. J. Sansom and H. E. Peterson, "MIMIC - Digital SimulatorProgram", SESCA Internal Memo 65-12, WPAFB, May 1965.

(104) R. T. Harnett and F. T. Sansom, "MIDAS ProgrammingGuide", Report No. 5EG-TDR-64-1, WPAFB, Ohio,January 1964.

(105) M. Palevsky and J. V. Howell, "DES-' 1", Fall JCC,Vol. 24, Spartan Books, Inc., Washington, D. C., 1963.

(106) R. D. Brennan and IH. Sano, "PACROLUS", Fall JCC,Vol. 26, Spartan Books, Inc., Washington, D. C., 1964.

(107) R. N. Linebarger, "DSL/90", Paper at Joint MeetingMidwestern and Central States Simulation Councils,May 1965.

A-8

(108) R. A. Gaskill, J. W. Harris, and A. L. McKnight,"DAS-A Digital Analog Simulator", Proc. 1963Spring JCC, AFIPS Conference Proc., Vol. 23, p. 83.

(109) G. E. Blechman, "An Enlarged Version of MIDAS",S&I Div. NAR, June 1964; Simulation, Vol. 3, No. 4,October 1964.

(110) M. E. Fowler, "A New Numerical Method for Simulation",Simulation, pp. 324-330, May 1965.

(111) M. E. Fowler, "An Example Showing Use of Root LocusTechniques to Study Nonlinear Systems", TR, August 12,1964, IBM R&D Ctr., Palo Alto, California.

(112) SAI Proposal No. 69-045, dated October 1969, "TimeDomain Simulation of Apollo Telecommunications Lines".

(113) W. E. Thompson, "Network with Maximally Flat Delay,"Wireless Engineer, Vol. 29, pg 255, October 1952.

(114) "On the Design of Filters by Synthesis, " R. Saul and E. Ulbrich,IRE Transactions on Circuit Theory, December 1958.

(115) "The Design of Filters Using the Catalog of Normalized Low-PassFilters, " R. Saal, Telefunken, 1963.

(116) "Passive Network Synthesis, " James E. Storer, McGraw-Hill, 1957.

A-9

APPENDIX B

ASYSTD LIBRARY DESCRIPTIONS

The ASYSTD library consists of a collection of models developed

by both Systems Associates, Inc. and NASA MSC, Space Electronics

Division. The following material describes the use of the models. The

descriptions are grouped under various identifiers, an index of which

follows. Several blank Library forms have been included for future use.

Signal Generators

* Gaussian Noise

* Pulse Generator

a Square Wave Generator

* Table Generators

o Periodic Table Generator

o Transcendental Function Generators

Modulators

* Amplitude Modulators

o Frequency Modulators (Sine Wave)

* Frequency Modulator (Square Wave)

o Phase Modulators (Sine Wave)

* Phase Modulator (Square Wave)

o Delta Modulator

Demodulator

o Amplitude Demodulators

o Phase Demodulators

o Frequency Demodulators

o Frequency Demodulator with Feedback

B-1

Filters

· General Filter Model

o Butterworth

o Chebychev

* Bessel

o Butterworth-Thompson

o Elliptic

o Quadratic

o Lead Lag Function

o Lead Function

* Matched Filter

Limiter s

* Soft Limiters

o Hard Limiters

e RF Soft Limiter

o RF Hard Limiter

Transforms

o Fourier Transform (FFT) (and Inverse)

o Haar Transform (and Inverse)

* Hadamard Transform (and Inverse)

o Ordered Hadamard Transform (and Inverse)

Coders

o Analog-to-Digital

o Digital-to-Analog

* Sample Hold Digital-to-Analog

o Multi- Level PCM

Math

o Complex Adder

e Complex Multiply

o Differentiator

o Integral with Initial Conditions

o Integral

B-2

Miscellaneous

* Interleaver

e De-Interleaver

o Time Delay

o Phase Shifter

o Signal Split

o Time Latch

* Zero Crossing Detector

B-3

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

GAUSSIAN NOISE GENERATOR Sig. Gen. 1 April, 1972

LIBRARY MODEL NAMES

GNOISE

DESCRIPTION

This function provides noise modeling capability, providingthe SNR and ENB of the generator are defined.

USAGE

N1 < GNjDISE (SNR, ENB, ISTART) > N2

where: SNR is the signal-to-noise ratio desired in ENB(equivalent noise bandwidth) assuming a 1 wattsignal level.

ISTART is a positive integer (>0) for' initializingthe random number generator.

DETAILED DESCRIPTION

WHITE GAUSSION:

WATTS/ HzS.D.

SAI 72-001-1

SYSTE MSASSOCIATES

-;4'~~~~-

SYSTEMSASSOCIAI ES

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

GAUSSIAN NOISE GENERATOR Sig. Gen. Z April, 1972

where

1 1s = DT sampling rate

2 1lifscai =2

T9iZDT

or

i qir1. = Za~2cDTI

(Watts /Hz)

2o = i : t ENB = 2r- DT-'- ENB0o i

(watts)

where ENB = equivalent noise bandwidth under consideration.

For a given SNR in bandwidth,BW:

SN -

O

1 0 SNR/10

S = signal power in BW (watts)

or

or

N = S . 1 0 - SNR/10o

= 2 Z DT * ENBi

-i. =s IX' 1 0S NR/1 0 2DT ENB

A PPLICA TION

This model is a function and may be used in expressions.

SAI 72-001-2

where

YST'MS ~" "~ SE MASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

GAUSSIAN NOISE TWO Sig. Gen. I1 April, 1972

LIBRARY MODEL NAMES

GNOIS2

DESCRIPTION

This model provides noise modeling capability, providingthe spectral density desired.

USAGE

N1 <GNOZIS2 (ETA, ISTAR-T) > N2

where: ETA is the desired spectral density (watts/Hz)

ISTART is a positive integer (>0) for initializingthe random number generator

DETAILED DESCRIPTION

See "Gaussian Noise Generator"

I1

SNR/l0ETA 10 /1ENB

APPLICATION

This model is a function and may be used in expressions.

SAI 72-001-1

'S "YST "'EM'S ' ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE-

PULSE GENERATOR Sig. Gen. 1 April, 1972

LIBRARY MODEL NAMES

PULSE

DES CR IPTION

This model produces a periodic output of pulses of the shapedescribed below.

USAGE

N1 < PULSE(RATE, TD, TR, TL, TF) > NZ

where: RATE = frequency of output

TD = delay time

TR = rise time

TL = level time

TF = fall time

OUTPUT

The maximum value is plus one and the minimum value is zero.

TRI. TL ITF

1/RATE

APPLICATION

This model is a function and may be used in expressions.

SAI 72-001-1

"S YSTEM "'ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

SQUARE WAVE GENERATOR Sig. Gen. 1 April, 1972

LIBRARY MODEL NAMES

SQSQUARE WAVE

USAGE

N1 < SQ(RATE) > N2

where: RATE = frequency of the square wave outputat node N2

OUTPUT

A square wave of period 1/RATE whose maximumvalue is plus one and whose minimum value isminus one.

SAI 72-001-1A II I I I ~ I I _

ffSYSTEMSASSOCIATES

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

TABLE Sig. Gen. 1 April, 1972

LIBRARY MODEL NAMES

TABLE

DESCRIPTION

This function provides a piece-wise linear function formodeling both driving functions and non-linearities.

USAGE

N1 < TABLE (XIN, X1,Y1,X2, YZ, X3, Y3, X4, Y4, X5, Y5 > N2

where: XIN = independent variable

Five. point pairs describing(Note: Out-of-range valuesend point values)

the functionassume the

(Example)

OUTPUT

(X5, Y5)

(X2, Y2)

(X4, Y4)

(X1, Y1) (X3, Y3)

SAI 72-001-1

X1,. Y1 l

X5, Y5

OUTPUT

XIN

ASYSTD LIBRARYSYSTEhlSi

ASSOCIATES

MODEL GROUP ID PAG E DATE

TABLE Sig. Gen. 2 April, 1972

APPLICATION

This model is a function and may be used inexpressions.

SAI 72-001-2

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

PERIODIC TABLE FUNCTION Sig. Gen. 1 April, 197

LIBRARY MODEL NAMES

PERIODIC TABLE FUNCTIONPTABLE

DESCRIPTION

This model provides the periodic function capability.output is periodic with period T5.

USAGE

N1 < PTABLE (T1, Y1, T2, YZ, T3, Y3, T4, Y4, T5, Y5) >

where: T1, Y1

T5, Y5

and

OUTPUT

i Five point-pairs describing the function

T5 = Period of the function

(Example

OUTPUT (T4,...

/(T3, Y3)

(T2, Y2)

(T1, Y1)

~--- -- 1IIIIII/I

(T5, Y5)

/."

TIME

In this example T1=0; if T/IO, the output is set to Y1 for0 sTIME sT1

APPLICATION

This model is a function and may be used in expressions.

SAI 72-001-1

f ASYSTEMSASSOCIATES

The

NZ

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

TABL2 Sig. Gen. 1 April, 1972

LIBRARY MODEL NAMES

TABL2

DESCRIPTION

This function provides a piece-wise linear function for modelingboth driving functions and non-linearities, and provides zerooutput levels for out of range conditions.

USAGE

N1 < TABL2 (XIN, X1,YI,XZ, Y2, X3, Y3,X4, Y4, X5,Y5)> N2

where: XIN = independent variable

X1, Yl

X5, Y5 -five point pairs describing the function

OUTPUT

This model is the same as model "TABLE" except out-of-rangevalues (XIN<X1 or XIN > X5) yield an output of zero.

APPLICATION

This model is a function and may be used in expressions.

SAI 72-001-1

! SYSTEM M SASSOCIAITES

i Jli

SYSTEM sASSOCIATES

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

TRANSCENDENTAL FUNCTIONS Sig. Gen. 1 April, 1972LIBRARY MODEL NAMES

SIN SINECOS COSINETAN TANGNT

DESCRIPTION

These elements are FORTRAN transcendental functions orutilize FORTRAN functions.

USAGE (Example)

N1 < SIN ($) > N2

N2 is set to the trigonometric sine of N1

SIN (x) ) SINE (y)

COS (x) x in radians COSINE (y)

TAN (x) TANGNT (y)

y in cycles

APP LICA TION

These elements are functions and may be used in expressions.

SAI 72-001-1

ASYSTD LIBRARYVSYSTEMSASSOCIATES

MODEL GROUP ID PAGE DATE

AMPLITUDE MODULATOR Modulator 1 April, 1972

LIBRARY MODEL NAMES

AM MODULATORAMMOD

I

DESCRIPTION

The Linear Amplitude Modulator provides classical modulationcapability to the ASYSTD user. This element is the basebandmodel.

USAGE

N1 <AMMOD(BETA, FC) > N2

where: BETA = Modulation Index (ratio)

FC = Carrier frequency

OUTPUT

Let INPUT(t) be the real input to the model (value at node N1)and Vo(t) be the real output of the model, then

Vo(t) = (1.0 + BETA-INPUT (t)) .cos (2TrFC Time)

R ES TR IC TIONS

BETA*'INPUT(t) <1. 0 for no over-modulation.

APPLICATION

An example of using the model in a system is as follows:

N2

INPUT < SINE (T) > N1

N1 .<AMMOD (1. 0, 100 E3)> NZ~~~~~~~~. .. . . .,!

SAI 72-001-1

SYSTEMSASSOCIATES

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

RF AMPLITUDE MODULATOR Modulator I 1 April, 1972

LIBRARY MODEL NAMES

RF AMPLITUDE MODULATORRAMMOD

DESCRIPTION

The Linear Amplitude Modulator provides classical modulationcapability to the ASYSTD user. The output of this model is acomplex baseband signal which represents the modulated carrierin the baseband.

USAGE

Nl

where:

< RAMMOD (BETA, PHI, MODE) > NZ

BETA = Modulation Index (ratio)

PHI = Instantaneous Phase Jitter

MODE = 1.0 for Double Sideband (DSB)

MODE = 0. 0 for Double Sideband-Suppressed Carrier

OUTPUT

Let i(t) be the real input to the model (node Nl),

then: Vo(t) = IMODE + BETA*i(t)jej(Oct + PHI)

translating Vo(t) to baseband:

Vo(t) = Vo(t)e-jc t

or Vo(t) = IMODE + BETAi(t)l

e j P H I = Vr(t) +jVi(t)

where: Vo(t) is the complex baseband output signal at N2

with Vr(t) = IMODE + BETA-i(t)I COS(PHI)

Vj(t) = IMODE + BETA :i(t)| SIN(PHI)

SAI 72-001-1L --- - j

ASYSTD LIBRARY;- ; JS S

SYSTEMSASSOCIATES

MODEL GROUP iD PAGE DATE

RF AMPLITUDE MODULATOR Modulator 2 April, 1972

RESTRICTIONS

IBETA>*i(t)I _l. 0

APP LICATION

for no over-modulation

I

This model is used in place of the amplitude modulator whencarrier translation is required.

SAI 72-001-2

SY-sTEM~s\ ASYSTD LIBRARYASSOCIA1 ES

MODEL GROUP ID PAGE DATE

LINEAR FREQUENCY MODULATOR Modulator 1 April, 1972

LIBRARY MODEL NAMES

FM MODULATORFMMOD

DESCRIPTION

The Linear Frequency Modulator Model provides a classicalmodel for this type of angle modulation. The carrier outputmagnitude is defined as unity.

USAGE

N1 < FMMOD(DF, FC) > N2

where: DF = frequency deviation (I-Iz) of the carrier per unit input

FC = carrier frequency

OUTPUT

Let the signal at N1 at time T be i(t).Let the signal at N2 at time T be Vo(t).

then: Vo(t) = SINE(FC;:-t + DFY: i(T) d TS TART

NOTE: The arguments of the SINE function is in Hz.

APPLICATION

FMMOD is for use when no carrier translation is required inthe simulation.

SAl 72-001-1

FSYSTE~ s MASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

RF LINEAR FREQUENCY MODULATOR Modulator 1 April, 1972

LIBRARY MODEL NAMES

RF FM MODULATORRFMMOD

DESCRIPTION

The Linear Frequency Modulator model provides a classical modelfor this type of angle modulation. The carrier output magnitudeis defined as unity.

USAGE

N1 < RFMMOD(DF) > N2

where: DF = frequency deviation (Hz) of the carrier per unit input.

OUTPUT

Let i(t) be the real input to the model (node N1), then for theideal FM modulator

Vo(t) = ej(oct + /o i(t)dt)

where: 3 = Z TrDF

translating Vo(t) to baseband:

Vo(t) = Vo(t)e-J c t

or t

Vo(t)= ejo i(t)dt = Vr(t) + jVj(t)

where: Vo(t) is the complex baseband output signal at N2

with: Vr(t) = COS (f3Jti(t)dt)

tVj(t) = SIN (3fo i(t)dt)

APPLICATION

This model is used in place of the FREQUENCY MODULATORmodel when carrier translation is required in the sin-uation.

SAI 72-001-1

ASYSTD LIBRARYASYSTECASASSOCIAIES

MODEL GROUP ID PAGE DATE

SQUARE WAVE FREQUENCY MODULATOR Modulators 1LIBRARY MODEL NAMES

SQUARES WAVE FREQUENCY MODULATORSQFMOD

DESCRIPTION

The Square Wave Frequency Modulator provides a model forthis type of angle modulation with ideal limiting.

USAGE

N1 < SQFMOD(DF, FC) > N2

where: DF = frequency deviation (cycles) of the carrierper unit input

FC = carrier frequency

OUTPUT

Let the signal at N1 at time T be INP(T).Let the signal at N2 at time T be OUT(T).

TThen: F(T) = SINE(FC*T + DF*J/ INP(t)dt)

TSTARTlinear frequency

modulation ]

NOTE: The arguments of the SINE function is in cycles

OUT(T) = +1OUT(T) = -1

when F(T)when F(T)

SAI 72-001-1

<0

SYSTEMS '-- EMASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

LINEAR PHASE MODULATOR Modulator 1 April, 1972

LIBRARY MODEL NAMES

PHASE MODULATORPMMODDPMMOD

DES CR IPTION

The Linear Phase Modulator provides a classical model for thistype of angle modulation. The carrier output level is definedas unity.

USAGE

N1 < PMMOD(BETA, TC) > N2

where: BETA = Phase (Radians) deviation per unit input

FC = Carrier frequency (Hz)

NOTE: Modulation Index = BETA: Input

OUTPUT

Let the signal at N1 at time T be i(t)Let the signal at N2 at time T be Vo(t)

then: Vo(t) = sin (2 Tr-,FC'-t+BETA*'i(t))

APPLICATION

This model is for use when no carrier translation isrequired in the simulation.

SAI 72-001-1I------ - -- - - ----- - I

SYSTEMS] ASYSTD LIBRARYj ASSOCIATES

MODEL GROUP ID PAGE DATE

RF LINEAR PHASE MODULATOR Modulator 1 April, 1972

LIBRARY MODEL NAMES

RF PHASE MODULATORRPMMOD

DESCRIPTION

The Liner Phase Modulator provides a classical model for thistype of angle modulation. The output is the complex basebandsignal.

USAGE

N1 < RPMMOD(BETA) > N2

where: BETA = Phase (Radians) deviation per unit input

OUTPUT

Let i(t) be the real input to the model, then:

Vo(t) = e j t)ct + 3-i(t)}

translating Vo(t) to baseband:

Vo(t) = Vo(t)e- c t

orVo(t)= ej' i (t)= Vr(t) + jVj(t)

where: Vo(t) is the complex baseband output signal at N2

with Vr(t) = COS(.-i(t))

Vj(t) = SIN( 3.i(t))

APPLICATION

This model is used in place of the FM MC)DULATOR model whencarrier translation is required in the simulation.

ISAI 72-001-1

Il l , I i ................. . ...........

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

SQUARE WAVE PHASE MODULATOR Modulator I 1 April, 1972

LIBRARY MODEL NAMES

SQUARE WAVE PHASE MODULATORSQPMOD

DES CRIPT ION

The Square Wave Phase Modulator provides a model for this typeof angle modulation with ideal limiting,.

USAGE

N1 < SQPMOD(BETA, FC) > N2

where: BETA = Phase (Radians) deviation per unit input

FC = Carrier frequency

NOTE: Modulation Index = BETA-'Inputmax

OUTPUT

Let the signal at N1 at time T be INP(T).Let the signal at N2 at time T be OUT(.T).

F(T)

OUT (T)

OUT(T) =

= sin (2 I *'FC:C'T + BETA*',INP(T))

+1

-1

linear phase]modulation I

when F(T) > 0

when F(T) < 0

SAI 72-001-1

ASYSTEMS'ASSOCIATES

- -- - --- -- -

=

SY'S T" 5is ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

DELTA MODULATION Modulator 1 April, 1972

LIBRARY MODEL NAMES

DELTA MODULATORDELMOD

DESCRIPTION

Delta modulation is a coded modulation system nearly as efficient asPCM, requires more bandwidth than PCM, but has much simplercircuitry. These advantages make delta modulation quite attractiveas a standard model. The output waveform magnitude is definedas + l.

USAGE

N1 < DELMOD(PW, PPS)> N2

where: PW = Pulse width (unit time)

PPS = Pulse repetition rate (pulses/unit time)

OUTPUT

In a delta modulation system, only the changes in'signal amplitudefrom sample to sample are output. The process consists of utilizinga pulse generator (clock), one shot multi-vibrator, an integrator,and a difference circuit.

let e (ti ) = input(t) -Out(t) dt

where output(t) = Sign (e(t) ) M: b (t)

where b (t) is a finite pulse of width PW

The above process is clocked at a repetition rate of PPS

SAI 72-001-I

Irr

. '-1

S ST E hi SASSCCIAT S

ASYSTD LIBRARY

MIODEL GROUP iD PAGE DATE

I¶ DELTA MODULATION [Modulator 2 April, 1972

EXAMPLE:

INPUT SIGNAL

RECONSTRUCTED SIGNAL

TIME

DELTA MODULATOR OUTPUT

The width of the pulses in the Delta Modulator output is PW. Thereis one positive or negative pulse every 1/PPS. The input signal andthe signal which can be reconstructed from the Delta Modulator outputhave the same scale. lach step is 1/PPS wide and PW high.

SAI 72--001-2

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

DELTA MODULATION Modulator 3 April, 1972

RESTRICTIONS

In general, the delta nmodulator cannot follow the input signalwhenever:

|d input(t)| > PW ::PS

To prevent overload, PW and PPS should be adjusted so that:

d input(t)dt max

< PW-PPS

which is usually satisfied if:

Aoo sPW'PPS

where: A = Peak value of input

6) = Maximum frequency of input

If PW and PPS cannot be adjusted to meet this condition(note PAVWSl/PPS), then the input to the delta modulatormust be properly scaled.

In the case where:

d input(t)| < < PW:PPS "d-t' r Imax

PW may be decreased or the input signal scaled to providemore information in the delta modulator output.

APPLICATION

The delta modulator is normally used in pulse coding anaudio signal for subsequent transmission via a modulatedcarrier. As such, this model will be mainly used ingenerating a baseband signal.

REFERENCE

For a description of delta modulation and a bibliography, see:H. R. SCHINDLERi, "Delta Modulation",IEEE SPEC T]RUM, October 1970, pp. 69-78

SAI 72-001-2

SYSTEM SASSOCIATES

----- _- -lL

V S YSTEMS ASYSTD LIBRARYJASSOCIATES

MODEL GROUP ID PAGE DATE

AMPLITUDE DEMODULATOR Demod. 1 April, 1972

LIBRARY MODEL NAMES

AMPLITUDE DEMODULATORAMDEM

DES CRIPTION

This linear Amplitude Demodulator provides a rudimentary modelfor use in the ASYSTD library. The basic model is a full waverectifier followed by a user selected filter function chosen for theparticular application.

USAGE

N1 < AMDEM > N2

NOTE: N2 must be the input to a filter.

OUTPUT

The output signal at NZ is simply the absolute value of thesignal at Nl

NZ(T) = INi(T)I

APPLICATION

This model is for use in the baseband region. Its outputmust be fed through an averaging filter to eliminate thecarrier.

SAI 72-001-1

yS Y S T E M SM ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

RF AMPLITUDE DEMODULATOR Demod. 1 April, 1972

LIBRARY MODEL NAMES

RF AM DEMODULATORRAMDEM

DESCRIPTION

This model is a rudimentary Amplitude Demodulator for usein modeling in the RF region.

USAGE

N1 < RAMDEM(GAIN) > N2

where: GAIN = Amplification of the model(typically 1/BETA, seeRF AMPLITUDE MODULATOR)

OUTPUT

Let X be the complex signal at N1

X = Xr + jXi

XI = (Xr2 + xi 2 ) 1/2

Let Y be the output at N2

Y = GAIN'' (IXI-1.)

APPLICATION

This model should be followed with a user selectedfilter for accurate simulation.

SAI 72-001-1

{s Y S T E M14 ~ ASYSTD LIBRARYASSOCIATES

MODEL GROUP i D PAGE DATE

PHASE DEMODU LATOR Demod. 1 April, 1972

LIBRARY MODEL NAMES

PHASE DEMODU LATORPMDEMM

DESCRIPTION

This Phase Demodulator simply takes the integral of an FMdemodulator output.

USAGE

N1 < PMDEMM(DV, FC) > N2

where: FC = Center Frequency

DV = Output Magnitude per Unit Phase Deviation(Volts /Radians)

OUTPUT

The Phase Demodulator output is given by DV :fFMDEMOD(t) dtwhere FMDEMOD(t) is the output of an FMDEMOD with asensitivity of Iv/radian.

APPLICATION

This model is to be used with external filtering.

SAI 72-001-1I-lll I~M I - -I

¸

-'_

S Y SE M S ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

RF PHASE DEMODULATOR Demod. 1 April, 1972

LIBRARY MODEL NAMES

RF PHASE DEMODULATORRFPDEM

DES CRIP TION

This model represents an ideal wide band phase demodulator.

USAGE

N1 < RFPDEM(DV) > N2

where: DV = Output Magnitude per Unit Phase Deviation(Volts/Radians)

OUTPUT

Let the complex input at N1 be X = Xr + jX i

Then the output of this model is DV:TAN -1 (-X)

APPLICATION

This model is to be used with external filtering.

SAi 72-001-1

SYS T EM S ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

FREQUENCY DEMODULATOR WITH FEEDBACK Demod. 1 April, 1972

LIBRARY MODEL NAMES

FMFB

DESCRIPTION

The Frequency Demodulator with Feedback Model (FMFB) provides

an alternate demodulation process capability. The basic modelconsists of a multiplier, IF filter, FM discriminator (FMDEMOD)

and a Voltage Controlled Oscillator (FMMOD). The RF filter and

post'detection low pass filter are external to the model.

USAGE

N1 < (FMFB (NIF,NTYPE, AR, EM, BIF, FIF, GAIN, FC, DV, DF) > N2

where: NIF -IF Filter Order (<_10)

NTYPE-Type of Filter Function:

= 1 for Butterworth

= 2 for Chebyshev

= 3 for Bessel

= 4 for Butterworth-Thomson

= 5 for Elliptic

AR -Amplitude Ripple (d3B)

EM -M-Factor for Butterworth-Thomson

Stop Band Ratio for Elliptic (if positive)

Modular Angle (Degrees) for Elliptic(if negative)

BIF -IF Filter Bandwidth

GAIN -Detector Gain + VCO Amp Gain

FIF -IF Frequency

ISAI 72-001-1

ASYSTD LIBRARYlSYSTEMStASSOCIATES

MODEL GROUP ID PAGE DATE

FREQUENCY DEMODULATOR WITH FEEDBACK Demod. 2 April, 1972

FC -Carrier Frequency

DV -FM Discriminator Constant (Volts/Hz)

DF -VCO Deviation (e.g., Hz/Volts)

NOTE: N1 is the output of an RF filterlow pass filter.

and N2 is the input to a

DETAILED DESCRIPTION

RFFILTERING

Le

I L - I

~~~~~~~~~~~~I ~~~~~~~~II I

II

POST-DETECTIONFILTERING

el(t) = A(t) cos (oat 4 i(t) )

and

e 2 (t) = -B sin (WVCO t + O(t) )

where

qi(t) = PfS(t)

0(t) = p'fe4(t)

and

e3(t) =A(t)B sint / IEte -3 (t) 2 sin[ IF t + 4i(t) - 0(t)]

-sin [ (WIF + w¢)t + ¢c(t) +

SAI 72-001-2

o(t) ]

--

et

ASYSTD LIBRARYSYSTE MSASSOCIATES

MODEL GROUP ID PAGE DATE

FREQUENCY DEMODULATOR WITH FEEDBACK Demod. 3' April, 1972

assuming the IF filter passes only the first term

e3(t) =A()B sin (woFt + ; i(t) - 0(t)

the output of the FM discriminator is ideally

e 4 (t) =d [i(t) - O(t)] DV D\ [f3S(t) - 3'e4 (t) ]

e 4 (t) = DV S(t)

APPLICATION

The FMFB demodulator utilizes a tracking principle to achievegood SNR performance.

SAI 72-001-2

'SYSTEMS ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

FILTER Filter 1 April, 1972

LIBRARY MODEL NAMES

FILTER

DESCRIPTION

The modeling of filters, or continuous functions relies on severalcomputer routines previously developed by SAI which perform thevarious functions described in Appendices A and C. For ease intheir use, an interface routine is written called FILTER, withseveral entry points as is explained below.

When utilizing any Filter model in a simulation of an RF link,translation of the filter to the baseband region is necessary forefficient simulation. The translation parameters are reflectedin the reference to the Filter model.

DETAILED DES CR IPTION

The detailed description for generating the various filter functionsin the s domain is described in Appendix A. Once the function ofs is known, the bilinear z transform is derived. In order toreduce round-off errors, the function is represented by seconddegree sections, or quadratic factors. The bilinear z-transformconverts a factor of s to a factor of the same degree in z, that is:

O(s) _ a s + als + a Fzz + Flz + F0(s) 2 1I o 2 1 o 0(z)ITs) 2 2- 1 I(z)

b(s) bs2 + b Dzz + Dlz- + D I

NOTE: D is normalized to entry

z1 is a unit delay

The difference equation for one of the quadratic factors willthen be:

O(t) = F 2 1(t - 2DT) + F 1 I(t - DT) + F I(t)

- D 2 (t -2 DT) - D 1 0(t - DT)

1,/. SAI 72-001-1

ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

FILTER Filter 2 April, 1972

where: DT is the sampling time.

If the filter is not being translated, the quadratic factors are

cascaded. However, when translating the filter (described in

Appendix A), both real and imaginary coefficients of s result

and the function is represented by parallel quadratic factors.The representation of the function as a sum of terms ratherthan a product eliminates the necessity of computing the roots

of a polynominal in determining Kr(s) and Ki(s), (see Appendix

A).

When using a translated filter, the run time can be reduced

significantly in trade for exact representation of the filter.Reduction of approximately one-fourth is realized by using

an equivalent low pass function; or one-half by assumingsymmetry of the filter (i.e., Ki(s) = 0). This is accomplished

when referencing one of the functions as described below.

USAGE

N1 < FILTER(NP, IF, IG, FX, BW, FC, AMP, AR, EM)> N2

All variables must be included whether they are applicableor not.

where: NP = filter order

IG = filter geometry

1 for Low Pass

2 for High Pass

3 for Band Pass

4 for Band Stop

AR = amplitude ripple (dJF3)

EM = M-factor for Butterworth-Thomson or stop-bandratio (>0) or modulator angle (<0) for Elliptic functions

FX = arithmetic center frequency

BW = bandwidth

FC = translation frequency (i. e., translate suchthat FC becomes zero)

AMP = voltage gain at FX

SAI 72-001-2---- � I - -I-----------------�--- I-

ASYSTD LIBRARYASSOCIATEs

MODEL GROUP ID PAGE DATE

FILTER Filter 3 April, 1972

IF = filter function

= 1 for Butterworth

= 2 for Chebyshev

= 3 for Bessel

= 4 for Butterworth-Thomson

= 5 for Elliptic

Alternate references to filters are as follows:

BUTTERWORTH (NP, IG, FX, BW, FC, AMP)

CHEBYSHEV (NP, IG, FX, BW, FC, AMP, AR)

BESSEL (NP, IG, FX, BW, FC, AMP)

BUTTERWORTH THOMSON (NP, IG, FX, BW, FC, -AMP, EM)

ELLIPTIC (NP, IG, FX, BW, FC, AMP, AR, EM)

Special Cases:

a) A model is available to characterize a filterfrom frequency response data (see: GENERALFILTER).

b) QFACTOR (AMP, Al,A2,A3,A4, A5,A6)

used to describe:

Als + A2s + A3AMP ~',-'A4s Z + A5s + A6

c) LEADLAG (AMP, F1, F2, F3, F4)

- - used to describe:

(A El +1 )( E2 AMP *

2 F3 (z4l)

SAI 72-001-2-~~~~~~~~~

_-- , . .

ASYSTD LIBRARYS Y S T Eh SASSOCIATES

MODEL GROUP ID PAGE DATE

FILTER Filter 4 April, 1972

if:

F2 = 0 then one zero is eliminated

Fl = 0 then both zeros are eliminated

F4 = 0 then one pole is eliminated

F3 = 0 then both poles are eliminated

d) LEAD FUNCTION (AMP, Fl, F2, F3)

used to describe:

AMP * (2 F1 1) ( F + 1)Fs ± 1)

and is otherwise the same as the LEADLAG function.

APPLICATIONS AND RESTRICTIONS

When utilizing the above function, any time FC->0, an RF filteris referenced (i. e., complex inputs and outputs) rather than abaseband filter (i. e., real inputs and outputs). The followingtable describes the conditions set up by FC and FX.

SAI 72-001-2

FC FX IG Result

0 - - Baseband filter simulation

>0 >0 3 RF translated filter

>0 . O 3 Symmetric translated filter (Q = co)

>0 0 ? I Equivalent low pass function

*' SYS ' T E M S tASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

BUTTERWORTH FILTER Filter 1 April, 1972

LIBRARY MODEL NAMES

BUTTERWORTHBUTWTHBUFUNCTION

DESCRIPTION

For a description of Butterworth filters, see Appendix C,Section C. 2. 2.

USAGE

N1 < BU TTERWORTI-I(NP, IG, FX, BW, FC, AMP) > N2

NP = filter order

IG = filter geometry

= 1 for Low Pass

= 2 for High Pass

= 3 for Band Pass

4 for Band Stop

FX = arithmetic center frequency

BW = bandwidth

FC = translation frequency (i. e., translate suchthat FC becomes zero)

AMP = voltage gain at FX

APPL] CATION

For applications and restrictions in using this model,see the discussion on the model FILTER.

SAI 72-001-1... .

'S Y S"T E M ~ ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

CHEBYSHEV FILTER Filter 1 April, 1972

LIBRARY MODEL NAMES

CHEB YSI-IEVCHEBYTCHEBYCHEFF

DESCRIPTION

For a description of Chebyshev filters, see Appendix C,Section C. 2. 3.

USAGE

N1 < CHEBYSHEV(NP, IG, FX, BW, FC, AMP, AR) > N2

where: NP = filter order

IG = filter geometry

= 1 for Low Pass

= 2 for High Pass

= 3 for Band Pass

= 4 for Band Stop

AR = amplitude ripple (dB)

FX = arithmetic center frequency

BW = bandwidth

FC = translation frequency (i. e., translate suchthat FC becomes zero)

AMP = voltage gain at FX

APPLICATION

For applications and restrictions in using this model, seethe discussion on the model FILTER.

SAI 72-001-1-Il ... ..

SYSTE M S ASYSTD LIBRARYASSOCIATES

MODEL I GROUP ID PAGE DATE

BESSEL FILTER Filter 1 April, 1972

LIBRARY MODEL NAMES

BESSELBE FUNCTION

DES CR IPT ION

For a description of Bessel filters, see Appendix C,Section C. 2.4.

USAGE

N1 < BESSEL(NP, IG, FX, BW, FC, AMP)> N2

NP = filter order

IG = filter geometry

= 1 for Low Pass

= 2 for High Pass

= 3 for Band Pass

= 4 for Band Stop

FX = arithmetic center frequency

BW = bandwidth

FC = translation frequency (i. e., translate suchthat FC becomes zero)

AMP = voltage gain at FX

APPLICATION

For applications and restrictions in using this model,see the discussion on the model FILTER.

SAI 72-001-1

7 SYSTEM S \ ASYSTD LIBRARYASSOCIATES

MODEL .GROUP ID PAGE DATE

BUTTERWORTH THOMSON FILTER Filter 1 April, 1972

LIBRARY MODEL NAMES

BU TTERWORTH THOMSONBT FUNCTIONBU TOM

DESCRIPTION

For a description of Butterworth Thomson filters, seeAppendix C, Section C. 2. 5.

USAGE

N1 <BUTTERWORTH THOMSON(NP, IG, FX, BW, FC, AMP, EM)>N2

NP = filter order

IG = filter geometry

= 1 for Low Pass

= 2 for High Pass

= 3 for Band Pass

= 4 for Band Stop

FX = arithmetic center frequency

BW = bandwidth

FC = translation frequency (i. e., translate suchthat FC becomes zero)

AMP = voltage gain at FX

EM = M-factor

APPLICATION

For applications and restrictions in using this model,see the discussion on the model FILTER.

SAI 72-001-1

~'~"""~SYSTEMS X ~ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

ELLIPTIC FUNCTION FILTER Filter 1 April, 1972

LIBRARY MODEL NAMES

ELLIPTICELIPTCEL FUNCTION

DESCRIPTION

For a description of Elliptic Function Filters, seeAppendix C, Section C. 2. 6.

USAGE

N1 < ELLIPTIC(NP, IG, FX, BW, FC, AMP, AR, EM)> N2

where: NP = filter order

IG = filter geometry

= 1 for Low Pass

= 2 for High Pass

= 3 for Band Pass

= 4 for Band Stop

FX = arithmetic center frequency

BW = bandwidth

FC = translation frequency (i. e., translate suchthat FC becomes zero)

AM.P = voltage gain at FX

AR = amplitude ripple (dB)

EM = stop-band ratio if positive modular angle ifnegative

APPLICATION

For applications and restrictions in using this model, seethe discussion on the model FILTER.

SAI 72-001-1

SYSTEM ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAG E DATE

GENERAL FILTER Filter 1 April, 1972

LIBRARY MODEL NAMES

GENERAL FILTERGENRAL

DES CRIPTION

The General Filter model determines an arbitrary elementtransfer function by the complex curve fitting method. Theprocedure is entirely analogous to familiar curve fittingtechniques except that the quantities involved are complexnumbers. It requires an assumption on the part of the user as tothe number of poles and zeros which characterize the transferfunction of the element in question. From an appropriatenumber of representative amplitude and phase response samplesover the frequency range of interest, the values of these complexpoles and zeros which characterize the element transferfunction may then be determined,

DE TAILED DESCRIPTION

(See also Appendix C)

A generalized element transfer function H(s) is customarilywritten in the form:

NZ

A (s- Z.)H(s) i=l (1)

H(s)(s-P.)

s Pi=lwhere: s = jo, complex frequency

Pi = complex pole (s + joi

)

Z i = complex zero (s +joi )

NP = number of poles (also filter order)

NZ = number of zeros

A = multiplicative real constant

The poles and zeros are always either complex conjugatepairs or single real values.

SAI 72-001-1

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

GENERAL FILTER Filter 2 April, 1972

For each response sample at frequencyck the poles and zerosare related to the empirically determined amplitude and phasethrough

NZ

A 1 (jwk - Zi)i=1

NP

(jiWk - Pi )i=l

= a k + p k (2)

where

2 +72Magnitude response = + +

Phase response = tan 1 p/a

Hence, for each response sample point, the right side ofEquation (2) is determined and the left side is a complexexpression in the Pi's and Zi's. If the form of H(s) isassumed by specifying the number of poles and zeros, thePi's, Zi's, and A are determined by the set of NP+NZ+1such complex equations which result from the substitutionof corresponding phase and amplitude response samples ata like number of frequencies. The actual solution of this sys-tem of complex linear equations is effected by standardlibrary subroutines.

USAGE

Ni <GENRAL(NP, NZ,IDB, FC, IG, BW, AMP)> N2

where: NP = assumed number of poles

NZ = assumed number of zeros

IDB = 1 if response amplitude data is to be in dB

= 0 if response amplitude data is normalized to 1. 0

FC = translation frequency (i. e., translate such thatFC becomes zero)

SAI 72-001-2

SYSTEMSASSOCIATES

- -� --

ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

GENERAL FILTER Filter 3 April, 1972

IG = filter geometry

= 1 for Low Pass

= 2 for High Pass

3 for Band Pass

4 for Band Stop

BW = bandwidth

AMP = voltage gain (ratio) mid-way between the upperand lower cutoff frequencies

INPUT

The number of frequency response data points should equalNP+NZ + 1.

Input frequency response data is read in through the subroutinePOLZER, one card per response data point, in the order:Frequency (Hz), Amplitude (dB or relative magnitude), Phase(degrees). The input data format is (IPE15.4, OP2F15.4).An input data set for a general 3rd order filter with two zeros(NP+NZ+l = 6) is as follows:

FR EO LUE NC Y A1lMPL ITUDE

1. 43 20 -0 54, 7750-051. 09 PO -0 41, 67 10 -0 42. 69 70 -0 43. 37 40 -0 4

-3.-15.-19.

00 (U003044 206820710061 60

- 10 .3 210- 34 .924 0- 87 .339 0

-1 41 .91301 57 .0 05 01 46 .5 06 0

SAI 72-001-2

P HA SE

-.- " .- .

'SYSTEMS'' ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

QUADRATIC FACTOR Filter 1 April, 1972

LIBRARY MODEL NAMES

QFACTQFACTORQUADRADIC FACTOR

DESCRIPTION

This model is used to describe the transfer function:

H(s) = AMP Als + A2s + A3H(s} = AMP :

A4s + A5s + A6

(see Appendix C, Section C. 1)

USAGE

N1 <QFACTOR(AMP,A1,A2,A3,A4,A5,A6)> N2

where: AMP = amplification constant

A1-A6 = constants specifying the transfer function

SAI 72-001-1

ASYSTD LIBRARY3~~~~~~~~~~~~

SYSTEMSASSOCIATES

MODEL GROUP ID PAGE DATE

LEAD LAG Filter 1 April, 1972

LIBRARY MODEL NAMES

LEAD LAGLOOP FILTER

DESCRIPTION

This model is used to describe the transfer function:

P F1 · l~ 2 F)H(s) = AMP * FZ

)(see Appendix C, Section C.' 1)

(see Appendix G, Section C. 1)

USAGE

N1 <LEADLAG(AMP, F1, , F2, F3, F4) > .N2

where: AMP =

F1-F4 =

amplification constant

constants specifying the transfer function, and if:

F2 = 0

Fl = 0

F4 = 0

F3 = 0

then one zero is eliminated

then both zeros are eliminated

then one pole is eliminated

then both poles are eliminated

SAI 72-001-1

ASYSTD LIBRARYSYSTEMS

ASSOCIATES

MODEL GROUP ID PAGE DATE

LEAD FUNCTION Filter 1 April, 1972

LIBRARY MODEL NAMES

LEAD FUNCTION

DESCRIPTION

This model is used to describe the transfer function

s sF 2F2 + ))H(s) = AMP* ~ + 1 Z

(see Appendix C, Section C. 1)

USAGE

N1 <LEAD FUNCTION(AMP, Fl, F2, F3)> N2

where: AMP = amplification constant

Fl-F3 = constants specifying the transfer function,and if:

F2 = 0 then one zero is eliminated

F1 = 0 then both zeros are eliminated

F3 = 0 the pole is eliminated

SAI 72-001-1

r i \~~~-·SYSTE MSASSOCIATES

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

MATCHED FILTER Filter 1 April, 1972

LIBRARY MODEL NAMES

MATCHED FILTERMFLTER

DESCRIPTION

The Matched Filter model is a simple integrate and dumproutine clocked to the Bit Time.

USAGE

N1 < MFLTER(BT) > NZ

where: BT = bit time

OUTPUT

The output at N2 is the trapezoidal approximation of theintegral of the signal at N1. Every BT, this integralis reset to zero.

BLOCK DIAGRAM

N1 N2

0.0 B

T

RESTR I C TIONS

The integrate-Dump process is asynchronous and startsat time equal to zero, requiring the user's discretionin its use.

SAI 72-001-1

'V'~ ':~" ~'' SYSTE'- "MS'~ 'ASYSTD LIBRARYASSOCIATES

MODEL IGROUP ID PAGE DATE

SOFT LIMITER Limiter 1 April, 1972

LIBRARY MODEL NAMES

SOFT LIMITERSOFTY

USAGE

N1 < SOFTY(A,SLOPE)> N2

where: A :maximum amplitude of output

SLOPE = slope of transition limit

OUTPUT

OUT PUT

A

SLOPE = OUTPUT / INPUT

INPUT

APPLICATION

This element is for use in baseband modeling.

SAI 72-001-1

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

HARD LIMITER Limiter 1 April, 1972

LIBRARY MODEL NAMES

HARD LIMITERHARD

USAGE

N1 <HARD> N2

OUTPUT

The absolute value of the output at N2 is 1.of the output is the same as the input at N1.

The sign

APP LICATION

This element is for use in baseband modeling.

SAI 72-001-1

SYSTEMSASSOCIATES

ASYSOITEMSASSOCIATES

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

RF SOFT LIMITER Limiter 1 April, 1972

LIBRARY MODEL NAMES

RF SOFT LIMITERRFSOFT

USAGE

N1 <RFSOFT(A, SLOPE)> N2

where: A = maximum amplitude of output

SLOPE = slope of transition limit

OUTPUT

Let X = Xr + jXi be the complex signal at N1and Let Y = Yr + jXi be the complex signal at N2

IXL

,03(X)

= (Xr2 + Xi2 ) = magnitude of X

= tan-1 (Xi/Xr) = phase of X

Then the output at N2 is such that:

1) ,0(Y) = A(X)

= F(IXI ) as described by the graph below:

1Yl

APPLICATION

This element is for modeling in the RF region.

SAI 72-001-1

?

2) IYI

IYI/ Ixl = SLOPEIXI

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

RF HARD LIMITER Limiter 1 April, 1972

LIBRARY MODEL NAMES

RF LIMITERRFLIM'r

USAGE

N1 < RF LIMITER > ,N2

OUTPUT

Assume the input at N1 is described by:

X = Xr + jXi = [Xr2 + Xi2I1/2 j tan (Xi/Xr)

e

then the output at N2 is:

Y = Yr~ + jYi = Ceij tan 1Y = Yr + jYi = C e (Yi/Yr)

where:CXr = 1/2

Yr = [XrZ + Xi2I

Yicxi 1/2

[Xr2 + xiz2

In this model C = 1.

In other words, the phase of the signal is maintained butthe magnitude is set to 1.

APPLICATION

The element is for use in modeling in the RF region.

SAI 72-001-1

ISYSTEMS\

ASSOCIATES

I

'> ''" SYSTEMS' M'~ 'ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

FOURIER TRANSFORM Transform 1 April, 1972

LIBRARY MODEL NAMES

FOURT IFOURTFOURIER INVERSE FOURIER

DES CR IPTION

This model samples an input signal and calculates the DiscreteFourier Transform of these samples. Its output is the coefficientsof this transform. IFOURT performs the inverse transform,reconstructing the input signal to FOURT.

USAGE

N1 < FOURT(N, TW) > NZor

N1 <IFOURT(N, TW)> NZ

where: N = number of samples per transform

TW = time window per transform

NOTE: Although N can be any positive integer, the transformis much faster if all the prime factors of N are 2, 3 or 5.

NOTE: The actual time window used is the multiple of N*-DTnearest TW.

OUTPUT

Each TW, this model takes N samples of the input at N1, andcalculates the Discrete Fourier Transform (or the inverse ofthe transform). The output of the model during this TW is theN transformed values produced during the previous TW.

NOTE: The input and the output of this model are complex.

SAI 72-001-1

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MODEL GROUP ID PAGE DATE

FOURIER TRANSFORM Transforms 2 April, 1972

REFERENCE

For a discussion of this transform, see COMSAT Laboratories,"Orthogonal Transform Feasibility Study, Final Report",Contract NAS9-11240, November 1971, Section 3.2.

APP LICATION

The models INTLEV and DELEAV have been provided to dealwith the complex inputs and outputs of this model. During thefirst TW, FOURT outputs a sync pulse of all ones to lock inDELEAV and IFOURT, compensating for any delays in the system.

SAI 72-001-2

"SY~ISTEM1S \ ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

HAAR TRANSFORM Transforms 1 April, 1972

LIBRARY MODEL NAMES

HAAR IHAARINVERSE HAAR

DESCRIPTION

This model samples a signal and outputs the HAAR Transformof these samples. (IHAAR-Inverse HAAR Transform -reconstructs the signal given the transformed values.

USAGE

N1 < HAAR(N, LOG2N, TS)> N2

or N1 <IHAAR(N, LOG2N, TS)-> N2 for the inverse

where: N = number of samples per transform(N must be a power of 2)

LOG2N = log base 2 of N, N = 2LOG2N

TS = time window -per transform

NOTE: The actual time window used is the integermultiple of N:DT nearest TS.

OUTPUT

Each TS, this model takes N samples of its input, and takesthe transform of these samples (or the inverse transform),producing N transformed values. The output of this modelduring this time window is the N transformed values calculatedduring the previous TS.

REFERENCE

For a discussion of HAAR functions and the HAAR Transform,see COMSAT Laboratories, "Orthogonal Transform Feasi-bility Study, Final Report", Contract NAS9-11240,November 1971, Section 3.4.

SAI 72-001-1

ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAG E DATE

HAAR TRANSFORM Transforms 2 April, 1972

APPLICATION

The output of the HAAR Transform during the first TS is +1.IHAAR uses this string of ones as a sync pulse to lock onto the transformed coefficients.

SAI 72-001-2

S Y S T E N ASYSTD LIBRARYASSOCIAl ES

MODEL GROUP ID PAGE DATE

HADAMARD TRANSFORM Transform 1 April, 1972

LIBRARY MODEL NAMES

HDMRD IHDMRDHADAMARD INVERSE HADAMARD

DESCRIPTION

This model samples a signal and outputs the HADAMARDTransform of these samples. (IHDMRD-Inverse HADAMARDTransform-reconstructs the signal given the transformedvalues.

USAGE

N1 < HDMRD(N, LOGZN, TS)> NZ

or N1 < IHDMRD(N, LOG2N, TS)> N2 for the inverse

where: N = number of samples per transform(N must be a po ver of 2)

LOG2N = log base 2 of N, N = 2LOG2N

TS = time window per transform

NOTE: The actual time window used is the integer multipleof N*'.DT nearest TS.

OUTPUT

Each TS, this model takes N samples of its input, and calculatesthe transform (or the inverse transform) of these samples,producing N.transformed values. The output during this tinmewindow is the N transformed values determined during theprevious TS.

REFERENCE

For a discussion of this transform, see COMSAT Laboratories,"Orthogonal Transform Feasibility Study, Final Report",November 1971, Contract NAS9-11240, Section 3.3.

SAI 72-001-1

ASYSTD LIBRARYiSYSTEMSASSOCIATS MASSOCAT ES

MODEL GROUP ID PAGE DATE

HADAMARD TRANSFORM Transform 2 April, 1972

APPLICATION

The output of the HDMRD Transform during the first TSis +1. IHDMRD uses this string of ones as a sync pulseto lock on to the transformed values.

SAI 72-001-2iii I-- -

[': Y S TES E'M:ASYSTD LIBRARYASSOCIAl ES

MODEL GROUP ID PAGE DATE

ORDERED HADAMARD TRANSFORM Transforms 1 April, 1972

LIBRARY MODEL NAMES

OHM\R D IOHMR DORDERED HADAMARD INVERSE ORDERED HADAMARD

DES CRIPT ION

This model samples the input signal and outputs the OrderedHadamard Transform of these samples. (IOHMRD - InverseOrdered Hadamard Transform - reconstructs the signal giventhe transformed values.

USAGE

N1 < OHMRD(N, LOG2N, TS) > N2or

N1 <IOHMRD(N, LOG2N, TS)> N2 for the inverse

where: N = number of samples per transform(N must be a power of 2)

LOG2N = log base 2 of N, N = 2LOGZN

TS = time window per transform

NOTE: The actual time window used is the integer multipleof N-:-DT nearest TS.

OUTPUT

Each TS, this model takes N samples of its input and calculatesthe transform (or the inverse transform) of these samples,producing N transformed values. The output during this timewindow is the N transformed values determined during the previousTS.

APPLICATION

The output of the OHMRD Transform during the,first TS is +1.IOHMRD uses this string of ones as a sync pulse to lock on tothe transformed values.

SAI 72-001-1- ~ ~ ~ ~ ... .. nlll I" i....

SYV -S ST E M S \ ASYSTD LIBRARY

7ASSOCIATES

MODEL GROUP ID PAGE DATE

ANALOG-TO-DIGITAL CONVERTER Coders 1 April, 1972

LIBRARY MODEL NAMES

ATOD

DES CR IPTION

The A/D Converter model determines a bit sequence based uponthe analog input level at sampling time. The output is a binarybit-stream (0 or +1). Flexibility is provided by inputting thenumber of bits per word, peak input level, minimum inputlevel, and bit time.

USAGE

N1 <ATOD(NBIT, FLOOR, CEILING, BT)> N2

where: NBIT = number of digital bits per analog word

FLOOR = a lower bound of the analog input

CEILING = an upper bound of the analog input

BT = bit time (the actual bit time is themultiple of DT closest to BT)

DETAILED DESCRIPTION

ATOD represents an analog value with a string of NBIT binarybits (0 or +1). This string of bits may be considered a binary NBITnumber, B, whose value is within the range 0 (all 0 bits) to 2 -1(all one bits). FLOOR is presented by the value 0, and CEILINGis represented by the value 2NBIT. Each word time (NBIT* BT),ATOD constructs this number B such that the expression

FLOOR + B1* ((CEILING-FLOOR)/2NBIT)

is as close to the analog input as the range and resolution allow.

SAI 72-001-1

AT VSYSTEMSASSOCIATES

ASYSTD LIBRARY

MODEL GROUP ID PAGE DAT E

ANALOG-TO-DIGITAL CONVERTER Coders 2 [April, 1972

OUTPUT

Each BT, ATOD selects the next most significant bit of thedigital word, to track the value of the analog input.

APPLICATION

ATOD may be used with either DTOA or SHDTOA as thedecoder.

SAI 72-001-2

SY S' YT E M S 'ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

DIGITAL- TO-ANALOG CONVERTER Coders I1 April, 1972

LIBRARY MODEL NAMES

DTOA

DES CRIP TION

The D/A Converter determines an analog value from a binarybit stream (0 or +-1) and the model parameters. This modelassumes the output is continuous and attempts to produce outputwith as few abrupt changes as possible.

N1 < DTOA(NBIT, FLOOR, CEILING, BT)> N2

where: NBIT = number of digital bits per analog word

FLOOR = a lower bound of the analog output

CEILING = an upper bound of the analog output

BT = bit time (the actual bit time is the multipleof DT closest to BT)

NOTE: These parameters are related to the A/D Converterwhich coded the signal.

OUTPUT

Each bit time, DTOA examines the new bit of the digital word.If, by-some combination of remaining bits, the current analogoutput value can be represented, then the output remains the same.Otherwise, the output is adjusted up or down until it is withinrange. For a description of the relationship between the inputbit stream and the analog value, see Analog to Digital Converter.

APPLICATION

Since this model tries to maintain the analog output at a constantlevel, only changing it when it has to, this model is best for usewhere the analog signalis continuous.

SAI 72-001-1

ASYSTD LIBRARYASSOCIAI EDs

MODEL GROUP ID PAGE DATE

SAMPLE-HOLD DIGITAL-TO-ANALOG CONVERTER Coders 1 April, 1972

LIBRARY MODEL NAMES

SHDTOA

DESCRIPTION

The Sample-hold DIA Converter determines an analog value froma binary bit stream and the model parameters. This modeldetermines a value during one word time and outputs that valueduring the entire next word time.

USAGE

N1 < SHDTOA(NBIT, FLOOR, CEILING, BT) > NZ

where: NBIT = number of digital bits per analog word

FLOOR = a lower bound of the analog output

CEILING = an upper bound of the analog output

BT = bit time (the actual bit time is the multipleof DT closest to BT)

NOTE: These parameters are related to the A/D converterwhich coded the signal.

OUTPUT

Each digital word time (NBIT*BT), SHDTOA forms an analog valuefrom the input and its parameters (for a description of the relation-ship between the input bit stream and the analog value, see Analogto Digital Converter). During this word time, its output is the analogvalue calculated during the previous word time.

APPLICATION

This model is for use when discrete values are being decoded,such as output from the orthogonal transform models.

SAI 72-001-1

-SYSTEMS ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

MULTI LEVEL PCM Coders 1 April, 1972

LIBRARY MODEL NAMES

MULTI LEVEL PCMMLTPCM

DES CRIPTION

This code modulator produces an m-level signal based upona serial input bit stream (polar or binary).

USAGE_

N1 <MLTPC.M(BT, M)> N2

where: BT = bit time

M = number of levels (symbols)

N = LOG 2M

The signal at the input mode (e. g., N1) is assumedto be a polar or binary bit stream.

OUTPUT

A serial-to-parallel conversion is made and a gray code levelselection is used in generating an output bit stream at a rate ofN-:BT. Output levels are normalized to a pealk value of unity(+1), represented by equal levels separated by 1/(M-l). Theminimum level (0) corresponds to the null symbol.

BLOCK DIAGRAM

Functionally, the model is represented as follows:

SAI 72-001-1

SYSTEMSASSOCIATES

ASYSTD LIBRARY

MODEL GROUP ID PAG E DATE

MULTI LEVEL PCM Coders 2 April, 1972

SERIALDATA - N- BIT REGISTER

N = LOG2 M. -~l....

OUTPUT

DETAILED DESCRIPTION (Example)

The serial bit stream is loaded into an N-bit register. Attime intervals of N*'BT, the register is sampled and the out-put waveform value (0 to +1) is determined from the reflected (gray)code in the register. The output is held at this level for N-:BT, atwhich time the register is sampled for the next word. The followingdiagram depicts the time sequence for an arbitrary input bit stream.The parameters for this example are:

M = 16 (4 Bits)

BT = 1Time

INPUT WAVEFORM

1XI i Xl ]2 4 6 8

TIME

I0 1 1, '1 0

BIT STREAM

10 12

012

456789

I, 101 0 :1 . 11

12131415161718

.1920

Register History

Contents1234

1---10--100-10011---10--101-10111---10--101-10101---10--100-1001

00--001-0011

SAI 72-001-2

GRAY DECODERSAMPLE AND HOLD

is_ ZWORDCLOCKJ

N* BT

Output

0000

14/1514/1514/1514/1513/1513/1513/1513/1512/1512/1512/1514/1514/1514'/1514/1514/152/15

4 lF4 __J

ASYSTD LIBRARY- SYSTEMS

ASSOCIAT ES

MODEL GROUP ID PAGE DATE

MULTI LEVEL PCM Coders 3 April, 1972

APPLICATION

The multi-level coder may be used to drive the FM and PMmodulators to produce m-ary PM carrier signals. Attentionshould be made to appropriate scaling of the MLTPCM out-put to produce the correct modulating signal magnitudes.

SAI 72-001-2

YS TEMS ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

COMPLEX ADDER MATH I1 April, 1972

LIBRARY MODEL NAMES

COMPLEX ADDERCADD

DESCRIPTION

The complex input to this model is added to a specified complexnumber passed through the argument list.

USAGE

N1 < CADD(XREAL, XIMAGE) > N2

where: XREAL = the real part of the addendXIMAGE = the imaginary part of the addend

OUTPUT

The complex output at N2 is the complex sum of (XREAL + i-*:XIMAGE)and the input at N1.

SAI 72-001-1

ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

COMPLEX MULTIPLIER MATH 1 April, 1972

LIBRARY MODEL NAMES

COMPLEX MULTIPLIERCMU LT

DESCRIPTION

The complex input to this model is multiplied by a specifiedcomplex number passed through the argument list.

USAGE

N1 < CMULT(XREAL, XIMAGE) > N2

where: XREAL = the real part of the multiplierXIMAGE = the imaginary part of the multiplier

OUTPUT

The complex output at N2 is the complex product of(XREAL + i ::XIMAGE) times the input at N1.

SAI 72-001-)

SY ST "TEM' S ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

DIFFER ENTIATOR MATH 1 April, 1972

LIBRARY MODEL NAMES

DIFFERENTIATORDIFFERDIF

DESCRIPTION

This model differentiates the input signal utilizing thebilinear z-transform of s.

USAGE

N1 < DIFFER > NZ

OUTPUT

Let the signal at N1 at time T be INP(T).Let the signal at N2 at time T be OUT(T).

Then:

OUT(T)= 2'(INP(T)-INP(T-DT)/DT] - OUT(T-DT)

where OUT (TSTART-DT) = 0

With this scheme, the output may alternate wildly above andbelow the actual differential. The fluctuation is proportionalto the derivative error at time = 0, since it is initialized tozero. If the output of the differentiator is fed into a filter,this fluctuation does not matter. This scheme has the advantagethat if the output of the differentiator is fed into one of the systemintegrators, the input samples at N1 can be reconstructedexactly.

SAI 72-001-1

SYTMd 'S' J" ""' T" E~ MASYSTD LIBRARY

MODEL GROUP ID PAG E IDATEINTEGRAL WITH INITIAL CONDITIONS MATH 1 April, 1972

LIBRARY MODEL NAMES

INTEGRAL WITH INITIAL CONDITIONSINTGIC

DESCRIPTION

This model provides for integration with initial conditions.

USAGE

N1 < INTGIC(FV) > N2

where: FV = initial value of the integral at TIME=TSTART

OUTPUT

This model integrates the input at N1 using the trapezoidalrule approximation. The output at N2 is this integral plusFV, the first value (initial value) of the integral.

SAI 72-001-1_ _--- - . .--- - - - -- I _ .I

S YSTEMSE ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID !PAGE DATE

INTEGRATOR MATH 1 April, 1972

LIBRARY MODEL NAMES

INTEGRAT ORINT GR T

DESCRIPTION

This model integrates the input signal using the trapezoidalrule, which is the bilinear z-transform of 1/s.

USAGE

N1 < INTGRT > NZ

OUTPUT

The output at NZ is the trapezoidal approximation ofthe input signal at N1.

SAl 72-001-1.-- ..- ... . .A

SYSTE M S ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

INTERLEAVER MISC. 1 April, 1972

LIBRARY MODEL NAMES

INTLEVINTERLEAVE

DESCRIPTION

The Interleaver allows complex values to be carried over asingle line. During the first half of one sample time, theoutput of this model is the real part of the input. During theremainder of the sample time, the output is the imaginarypart of the input.

USAGE

N1 < INTLEV(N, TW) > NZ

where: N = number of samples per TW

TW = Time Window

NOTE: This model is usually used in conjunction with amodel such as the Fourier Transform, where Nand TW would be identical to the parameters ofthe Fourier Transform.

OUTPUT

Each sample time (TW/N), INTLEV samples the complexinput and stores the real and imaginary parts. It themoutputs the real part of the input for (TW/N)/2 and theimaginary part for the remainder of the sample time.

APPLICATION

This model was designed to appear after the Fourier Transform,

or other models with complex outputs. It converts a complexvalued signal to a real signal for use by other models whichcan only deal with real signals. See also DE-INTERLEAVER.

SAI 72-001-1.. . . I .......... II I _ . .l

VS YS T[E k s- ASYSTD LIBRARYASSOCIAI ES

MODEL GROUP ID PAGE DATE

DE-INTERLEAVER MISC. 1 April, 1972

LIBRARY MODEL NAMES

DELEAVDEIN TER LEA VE

DESCRIPTION

The De-interleaver decoder real signals output by the Interleaverback into their complex form. It causes a phase delay of onesample time.

USAGE

N1 < DELEAV(N, TW) > N2

where: N = number of sanples per TW

TW = time window

NO.TE: These parameters should be the same as those in theInterleaver

OUTPUT

Each sample time (TW/N) this model samples the input for thereal value. One half sample time later it gets the imaginaryvalue from the input. The output of the model during this sampletime is the complex value found in this way during the previoussample time.

APPLICATION

This model is used in conjunction with the Interleaver.Particularly to reconstruct complex values for input tothe Inverse Fourier Transform. It is started by the sync pulsefrom the Fourier Transform.

SAI 72-001-1

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

DELAY MISC. 1 April, 1972

LIBRARY MODEL NAMES

DELAY

DESCRIPTION

This model introduces a specified time delay into a real signal.

USAGE

N1 < DELAY(LAG) > N2

where LAG = an integer number of Dj to delay the signal

OUTPUT

The output at N2 at timeT -LAG*I:DT.

T equals the input at N1 at time

SAI 72-001-1

SYSTEMSCAATES

sS E s E ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

PHASE SHIFTER MISC. 1 April, 1972

LIBRARY MODEL NAMES

PHASE SHIFTERPHSHFT

DES CR IPTION

This model causes a phase shift (delay) of a specifiednumber of degrees.

USAGE

N1 < PHSHFT(DGREES, FC) > NZ

where DGREES = number of degrees to delay signal

FC = frequency of input signal

SAI 72-001-1-.- . .. . .....

ASYSTD LIBRARY

LIBRARY MODEL NAMES

SPLIT

DESCRIPTION

The input signal is split into its real and imaginary parts.

USAGE

N1 < SPLIT > NZ

OUTPUT

The real part of NZ is set to COS (N1).part of N2 is set to SIN (N1).

The imaginary

SAI 72-001-1

ASSOCIATES~ASSOCIATES~

- II f N ~~~~~~~I

S1YSTEMSASSOCIATES

ASYSTD LIBRARY

MODEL GROUP ID PAGE DATE

TIME LATCH MISC. 1 April, 1972LIBRARY MODEL NAMES

CALINB

DESCRIPTION

This model provides a time dependent latching function whichsets the output equal to the input for time LAG*-DT.

USAGE

N1

where

< CALINB (LAG) > N2

LAG = an integer number of DT's before thesignal can pass through this model.

OUTPUT

N2 = 0 for T

NZ = Nlfor T

LAG*DT

LAG*DT

SAI 72-001-1

SY 'S TEMS ASYSTD LIBRARYASSOCIATES

MODEL GROUP ID PAGE DATE

ZERO CROSSING DETECTOR MISC. 1 April, 1972

LIBRARY MODEL NAMES

ZERO CROSSING DETECTORZRODET

DESCRIPTION

This model detects when the input signal becomes zeroor crosses the zero reference.

USAGE.

N1 < ZRODET > NZ

OUTPUT

N2 is generally set to zero. If, during one simulationstep (DT) the signal at N1 goes to zero or crosses zero,N2 is set to 1 for that DT only.

SAI 72-001-1

ISYSTEMS

ASSOCIAI [S

ASYSTD LIBRARY

LIBRARY MODEL NAMES

SAI 72-001-1

SYSTESI;ASSOCIATES b

LIBRARY MODEL NAMES

SAI 72-001-i

ASYSTD LIBRARY

I 71

g.:,SYSTE SNASSOCAlIES

ASYSTD LIBRARY

LIBRARY MODEL NAMES

SAI 72-001-1

ASS l 1 .

SYS TUNIASSr:OCIA IIS

ASYSTD LIBRARY

LIBRARY MODEL NAMES

SAI 72-001-1

SjYS T I his ASYSTD LIBRARYASSOCIAT ES

MODEL GROUP ID PAGE DATE

LIBRARY MODEL NAMES

I -~~~~~~~~~~~~~~~~~~~~~~~~~~~,

SAI 72-001-1

APPENDIX C

DISTRIBUTION LIST

NASA /MSCFacility and Laboratory Support BranchHouston, Texas 77058

Attention: Mr. Jerry CarlsonMail Code BB321 (77)

NASA/MSCTechnical Library BranchHouston, Texas 77058

Attention: Ms. Retha ShirkeyMail Code JM6

NASA /MSCManagement Services DivisionHouston, Texas 77058

Attention: Mr. John T. WheelerMail Code JM7

NASA /MSCSpace Electronics System DivisionHouston, Texas 77058

Attention: Mr. C. T. DawsonTechnical Monitor, EE8

C-1

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