# Operational Amplifier (Op-Amp)

The operational amplifier is an electronic circuit that is widely used in many practical electronic systems such as TVβs, stereos, phones, control systems, medical equipment, etc.

Main Operations of Op-Amp:

- Amplification
- Addition
- Subtraction
- Differentiation
- Integration
- Filtering
- Many more, including non-linear operations

Inverting amplifier?? β this is when the output voltage is inverted (opposite sign).

### Symbol Conventions Explained

- $v_{p}$ is positive voltage
- $v_{n}$ is negative voltage
- $v_{o}$ is like output voltage
- Positive DC Power Supply ($V_{CC}$)
- Negative DC Power Supply ($βV_{EE}$)

Other

- $v_{i}$ is like input voltage, also written as $v_{d}$, equal to $v_{i}=v_{p}βv_{n}$

### Non-Ideal Op-Amp Model

### Ideal Op-Amp Model

If we assume it is an ideal op-amp, it makes the analysis of op-amp circuits very easy and quick.

**Assumptions**

- We assume Input resistance $R_{i}$ is very large, so $i_{p}=i_{n}=0$
- Voltage gain $A$ is very large, so $v_{p}=v_{n}$

### Finding Output voltage $v_{o}$

Sometimes, in the question, they might ask to give the output voltage.

This is as simple as $v_{0}=Av_{in}$, where $A$ is the voltage gain.

However, you need to make sure that $βV_{EE}β€v_{0}β€+V_{cc}$ If it is not met, you use whichever one saturates.

Ex: if you calculate $v_{0}=β15V$ but $V_{E}E=10V$, then the output saturates at $v_{0}=β10V$

### Voltage Transfer Characteristics

The non-ideal/ideal op-amps described above are created based on the properties described below.

I still donβt understand a lot, but I am writing these notes hoping to extend on them in the future.

The Op-Amp only operates at certain voltages. It must satisfy: $β£v_{i}β£β€0.1ΒmV$

This implies that $v_{p}βv_{n}$ (condition for linear region)

The gain $A$ is how much the voltage is gained $A=v_{i}v_{0}β$

$A$ represents this slope. Ideally, this slope is infinite so we instantly go from negative saturation to positive saturation.

The reality is represented by the graph below.

### Related

Think about the difference between this and Buck Converter / Buck Converter / Boost Converters. Thereβs several differences as explained in this reddit post.