General conditions for operational amplifiers
    Operational amplifiers (or commonly referred to as Op-amp) can be ideal amplifiers with unlimited gain and bandwidth when used in open-loop mode, with typical DC gain far exceeding 100,000 or 100dB.
    The basic operational amplifier structure is a 3-terminal device with 2 inputs and 1 output (excluding power connection).
    An operational amplifier can be powered by dual positive power supplies (+V) and the corresponding negative power supply (-V), or by a single DC power supply voltage.
    The two main laws related to operational amplifiers are that they have an infinite input impedance (Z = ∞), resulting in "no current flowing into either of its two input terminals" and a zero input offset voltage V1 = V2.
    The operational amplifier also has zero output impedance (Z = 0).
    The operational amplifier senses the difference between the voltage signals applied to its two input terminals and then multiples it by A predetermined gain (A).
    This gain (A) is usually referred to as the "open-loop gain" of the amplifier.
    By connecting a resistor or reactance element between the output terminal and an input terminal of an operational amplifier to close an open loop, the open-loop gain can be significantly reduced and controlled.
    Operational amplifiers can be connected in two basic configurations, namely inverting and non-inverting.

Basic operational amplifier circuit
    For negative feedback, if the feedback voltage is "inverted" from the input, the total gain of the amplifier will decrease.
    For positive feedback, if the feedback voltage is "in phase" with the input, the total gain of the amplifier will increase.
    By directly connecting the output back to the negative input terminal, 100% feedback can be achieved, thereby generating a voltage follower (buffer) circuit with a constant gain of 1 (unit).
    Change the fixed feedback resistor (R) to a potentiometer, and the circuit will have adjustable gain.

Operational amplifier gain

The gain-bandwidth product of the operational amplifier
    Open-loop gain, also known as the Gain-bandwidth product (GBP), can be very high and is a standard for measuring the performance of amplifiers.
    A very high GBP can make the operational amplifier circuit unstable because a microvolt input signal can cause the output voltage to enter a saturated state.
    The total gain of the amplifier can be controlled by using an appropriate feedback resistor (R).

Differential amplifiers and summation amplifiers

Differential and summation amplifiers
    Voltage adders or adders can be fabricated by adding more input resistors at the inverting or non-inverting input terminals.
    A voltage follower operational amplifier can be added to the input terminal of a differential amplifier to generate a high-impedance instrumentation amplifier.
    The output generated by a differential amplifier is proportional to the difference between the two input voltages.
    Differentiator and integrator circuits
    Differential amplifiers and integral amplifiers
    The output generated by an integrating amplifier is a mathematical operation of integration.
    The output produced by a differential amplifier is a mathematical operation of differentiation.
    Both integrators and differential amplifiers have resistors and capacitors connected to the operational amplifier and are affected by their RC time constants.
    In its basic form, differential amplifiers have instability and noise issues, but additional components can be added to reduce the overall closed-loop gain.