Calculating Relationship between Input and Output Voltages for op-amp Configurations

Operational Amplifiers (Op-amps)

An operational amplifier, or op-amp, is a high-gain electronic voltage amplifier with a differential input and typically a single-ended output.
In an ideal op-amp, the gain is infinite, input impedance is infinite, while output impedance is zero.
Open loop gain refers to the gain of an op-amp without positive or negative feedback and it is extremely high, approximately infinity.
The inverting terminal (-) and non-inverting terminal (+) are the two inputs to an op-amp.
The output voltage Vout of the op amp is given by the open-loop gain multiplied by the differential voltage.

Inverting Op-amp Configuration

An inverting amplifier is a special case of the differential amplifier where the feedback is connected to the inverting input.
The gain in an inverting amplifier is calculated with the formula Ao = - Rf/Rin, where Rin is the input resistance and Rf is feedback resistance. The negative sign shows that the output is inverted.
If input voltage Vin is applied to the inverting terminal and non-inverting terminal grounded, the output voltage Vout is inverted and amplified.

Non-Inverting Op-amp Configuration

The non-inverting amplifier is a specific type of differential amplifier that amplifies the input voltage while maintaining the same polarity.
The gain in a non-inverting amplifier is calculated with the formula Av = 1 + (Rf/Rin), where Av indicates the non-inverting voltage gain.
If input voltage Vin is applied to the non-inverting terminal and the inverting input is grounded, the output voltage Vout is non-inverted and amplified.

Op-amp as a Comparator

An op-amp comparator is a circuit that compares two input voltages. The output switches states between when one input is greater than the other.
The reference voltage Vin is applied at one of the inputs and the second input voltage Vinput, which is to be compared, is applied at the other input.
If Vin > Vinput, the output voltage Vout is negative, and if Vin < Vinput Vout is positive.
A comparator is an example of an op-amp circuit with positive feedback.

Remember, understanding how op-amps work and the relationship between input and output voltages is essential for understanding analogue electronic control systems.