Once a
while it is useful to be able to derive the circuit equation, this will ease
the design process. Below are some
points to consider when performing circuit equation derivation:

1.
If
you already know the purpose of circuit, use that info to do the derivation.

2.
Most
circuit can be modeled as y = mx +c, so you must define what is desired x
(input) and y (output) prior to the actual derivation itself.

3.
Keep
all variable names short – to ease your derivation.

4.
Always
try to inspect the circuit and equation for opportunity to simplify the equation.

a.
For
example, if a group of terms keep repeating itself, use a new term to represent
them.

b.
Sometimes
it is easier and more intuitive to use current as your parameter.

5.
Acknowledge
characteristic of circuit component – such as

a.
Opamp input pins will generally be at the same
potential (hence the term “virtual ground” for inverting Opamp
with non-inverting pin tied to “Ground”.

b.
Base
emitter of BJT will always be a diode drop.