An integrator op-amp circuit is a type of electronic circuit that uses an operational amplifier (op-amp) to perform mathematical integration on an input signal. Integration is a mathematical operation that calculates the accumulated sum of a function over a given interval. In the context of electronics, an integrator circuit produces an output voltage that is proportional to the integral of its input voltage over time.
The basic integrator op-amp circuit consists of an op-amp connected with a feedback capacitor and a resistor. Here's how it works:
Op-Amp Configuration: The op-amp is usually connected in an inverting configuration, where the input is applied to the inverting (-) terminal, and the non-inverting (+) terminal is grounded. This configuration ensures that the op-amp's inverting terminal is at virtual ground, which simplifies the analysis.
Feedback Capacitor (C): The feedback element of the circuit is a capacitor connected between the output of the op-amp and the inverting input terminal. This capacitor accumulates charge over time.
Input Signal (Vin): The input signal, which is the signal you want to integrate, is applied to the inverting (-) input terminal of the op-amp.
Feedback Resistor (R): A resistor is connected in parallel with the capacitor. This resistor helps control the rate at which the capacitor accumulates charge and discharges.
Output Voltage (Vout): The output voltage is taken from the junction between the capacitor and the resistor. It's important to note that since the op-amp is in an inverting configuration, the output voltage will be inverted with respect to the input voltage.
When the input voltage changes, the op-amp's inverting terminal attempts to maintain the virtual ground condition. As the input voltage changes, the op-amp's output voltage changes as well, causing a voltage difference between the inverting and non-inverting terminals. This voltage difference causes a current to flow through the feedback resistor and into the capacitor. The capacitor charges and discharges, effectively integrating the input signal over time.
Mathematically, the relationship between the input voltage (Vin), the feedback resistor (R), the feedback capacitor (C), and the output voltage (Vout) can be described using the equation:
Vout = - (1 / RC) ∫ Vin dt
Where:
Vout is the output voltage.
Vin is the input voltage.
R is the feedback resistor.
C is the feedback capacitor.
∫ denotes the integral operation with respect to time (t).
The negative sign in the equation arises due to the inverting configuration of the op-amp. This circuit is commonly used in applications such as waveform generation, signal processing, and control systems, where integration is required.