LINEARITY
THE MODELS USED ARE ALL LINEAR.
MATHEMATICALLY THIS IMPLIES THAT THEY
SATISFY THE PRINCIPLE OF SUPERPOSITION
AN ALTERNATIVE, AND EQUIVALENT,
DEFINITION OF LINEARITY SPLITS THE
SUPERPOSITION PRINCIPLE IN TWO.
NOTICE THAT, TECHNICALLY, LINEARITY CAN
NEVER BE VERIFIED EMPIRICALLY ON A SYSTEM.
BUT IT COULD BE DISPROVED BY A SINGLE
COUNTER EXAMPLE.
IT CAN BE VERIFIED MATHEMATICALLY FOR THE
MODELS USED.
USING NODE ANALYSIS FOR RESISTIVE
CIRCUITS ONE OBTAINS MODELS OF THE
FORM
v
IS A VECTOR CONTAINING ALL THE NODE
VOLTAGES AND
f
IS A VECTOR DEPENDING
ONLY
ON THE INDEPENDENT SOURCES.
IN FACT THE MODEL CAN BE MADE MORE
DETAILED AS FOLLOWS
HERE,
A,B,
ARE MATRICES AND
s
IS A VECTOR
OF ALL INDEPENDENT SOURCES
FOR CIRCUIT ANALYSIS WE CAN USE THE
LINEARITY ASSUMPTION TO DEVELOP
SPECIAL ANALYSIS TECHNIQUES
FIRST WE REVIEW THE TECHNIQUES
CURRENTLY AVAILABLE
