Operational Amplifiers#
Definition: Operational Amplifier
A operational amplifier is a finite-gain differential voltage amplifier such that the currents \(i_{-}\) and \(i_{+}\) flowing into the \(+\) and \(-\) inputs, respectively, are always zero:
Notation
The symbol for an operational amplifier is the same as the one for finite-saturation differential voltage amplifier. The fact that \(i_{-}\) and \(i_{+}\) are always zero needs to inferred from context:
Definition: Ideal Operational Amplifier
An ideal operational amplifier (ideal op-amp) is an infinite-gain differential voltage amplifier such that the currents \(i_{-}\) and \(i_{+}\) flowing into the \(+\) and \(-\) inputs, respectively, are always zero:
Notation
The symbol for an ideal operational amplifier is the same as the one for infinite-gain differential voltage amplifiers. The fact that \(i_{-}\) and \(i_{+}\) are always zero needs to inferred from context:
Of course, no physical component can get \(i_{-}\) and \(i_{+}\) to be exactly zero. However, we can get them to be really close to zero, on the order of a few tens of nanoamperes.
Theorem: Ideal Op-Amp Equivalent Models
An ideal op-amp is equivalent to:
- an open circuit and an independent voltage source with voltage \(-V_{sat}\) when \(v_d \lt 0\);
- a nullor when \(v_d = 0\);
- a open circuit and an independent voltage source with voltage \(+V_{sat}\) when \(v_d \lt 0\).
Proof
TODO