node analysis general node analysis topology passive sign convention
0First, regular Node analysis with a reference point( No topology )
Then, General Node analysis , No reference point( with topology )
one goal is to try and write\use pos+ ohms law as much as possible,
without any extra labels on the diagram.
Of coarse the circuit diagram and equation writing becomes more
implicit\elided\obfuscated , especially during a review or trouble-shooting
of how the Eqs. were written ,...months later.
Besure this implicitness is not lost. Make note it some how.
That's what I tried to do here. To document every problem like this
would be too combersome and too much extra effort.
all the details of the Eq. writing are fully shown.
All Eqs. and the parts( terms ) of each Eq. are
fully explained as they are written. Leaving no
guess work as to "how did I do that" ?
Eventually, there are so many implicit labels\assumptions
( no labels at all )
we can become lost in the maze of implicit-ness .
I tried to make it as explict as possible.
Without all the explaining, the Eqs. actually
write pretty simple and straight forward, yeah,
after we "tune-in" to all the implicit-ness .
later, using the
LaPlace transform on RLC circuits, the exact
same techniques of DC analysis get used.
reminder:
voltage and current are vector quantities. we need a magnitude and a sense of orientation( direction ) to fully define a vector.
For voltage that is: magnitude with a + - polarity .
For current that is: magnitude with an arrow direction.