A switched-capacitor integrator is an electronic circuit that performs analog integration without using continuous resistors or inductors. Instead, it relies on the charging and discharging of capacitors in a switched manner to achieve the integration function. This type of circuit is commonly used in analog signal processing and analog-to-digital converters. Here's how it works:
Basic Principle: The fundamental principle behind a switched-capacitor integrator is the transfer of charge between capacitors through switches. When switches are turned on, they connect capacitors in a certain configuration, allowing charge to be transferred. When the switches are turned off, the charge is held on the capacitors.
Switched-Capacitor Network: The switched-capacitor integrator typically consists of two capacitors (C1 and C2) and a set of switches. These switches are controlled by clock signals. The switches are usually implemented using MOSFET transistors, which can be controlled to create specific charge transfer paths.
Integration Process: To perform the integration operation, the input signal (Vin) is applied to one side of the capacitor network, and the output (Vout) is taken from the other side.
During the sampling phase: The switches are configured to connect the input signal (Vin) to capacitor C1 and disconnect it from capacitor C2. As a result, C1 charges up to the input voltage.
During the integration phase: The switches are then flipped, connecting C1 to C2 and disconnecting them from the input signal. The charge on C1 is transferred to C2. This transfer of charge is proportional to the integral of the input voltage over time.
Output Voltage: The output voltage (Vout) is taken from capacitor C2. It represents the integrated value of the input signal over time. The relationship between the input voltage (Vin), output voltage (Vout), and capacitor values is described by the equation: Vout = - (C1/C2) * Vin.
Clock Frequency: The clock frequency used in the switches determines the integration time and the overall accuracy of the integration process. Higher clock frequencies allow for shorter integration times but may introduce noise and other non-ideal effects.
Switched-capacitor integrators have several advantages, including high accuracy, low component variations (since they mainly rely on capacitors), and ease of integration in integrated circuits. They are widely used in applications where analog integration is required, such as signal filtering, analog-to-digital conversion, and various control systems.