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.