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The surprising secret behind switched capacitor circuits: How do they mimic resistors?
In the field of electronic engineering, Switched Capacitor Circuit (SC circuit for short) is gradually becoming a technology that cannot be ignored, especially in the design of integrated circuits. This type of circuit uses switches to control the charging and discharging process of the capacitor to achieve the effect of simulating a resistor. With the fusion of digital and analog circuits, SC circuits are becoming increasingly important in various applications.
The principle of switched capacitor circuits is based on the movement of charge in the capacitor during the opening and closing of the switch. This technique uses non-overlapping clock signals to control the switches to ensure that no two switches are off at the same time at any time. This makes the design of switched capacitor filters much simpler and more efficient because it relies on the ratio of capacitance to switching frequency without requiring precise resistor values.
Typically, SC circuits are implemented using metal-oxide-semiconductor (MOS) technology, including MOS capacitors and MOS field-effect transistor (MOSFET) switches.
Basic principles of switched capacitors to simulate resistors
The simplest switched capacitor circuit usually consists of a capacitor and two switches that alternately connect the input and output of the capacitor to move charge from one end to the other at a specified switching frequency. Such a circuit can be regarded as an analog resistor, and its equivalent resistance can be expressed as:
R_equivalent = 1 / (C_S * f)
Among them, C_S is the capacitance of the capacitor, and f is the switching frequency. More specifically, this process follows a current-voltage relationship similar to Ohm's law.
Advantages of switched capacitor circuits
Switched capacitor circuits have many significant advantages over traditional resistors. For example, because the switch transfers charge in discrete pulses, this approach can approximate a continuous resistive operation when the switching frequency is significantly higher than the bandwidth of the input signal.
Switched capacitor circuits are theoretically considered a lossless resistor because their working principle avoids the heat loss of traditional resistors.
Application fields
Switched capacitor analog resistors are widely used in integrated circuits because such circuits are easier to reliably produce a wide range of resistance values and require relatively small silicon area. This same circuit can be used as a sample-and-hold circuit for discrete-time systems such as ADCs. In the appropriate clock phase, the capacitor samples the analog voltage through the switch, and in the second phase, this held sample value is output to the control circuit through another switch for processing.
Electronic filters replace traditional resistors with switched capacitor resistors, which allows filters to be made using only capacitors and switches, without relying on actual resistors.
Improvements and Challenges
Although switched capacitor circuits offer many advantages, there are also some challenges, especially when it comes to parasitic effects. Where parasitic capacitance is significant, circuit performance can be affected, prompting engineers to develop parasitic-insensitive circuit designs.
These spurious-insensitive circuits are commonly used in discrete-time electronic circuits such as quadratic filters, antialiasing structures, and delta-sigma data converters. The development of these technologies will further enhance the practicality of switched capacitor circuits.
Conclusion: What will happen in the future?
As technology advances and new electronic components become available, switched capacitor circuits will play a role in an increasing number of applications. They not only make an important contribution to improving circuit efficiency, but also bring greater design flexibility. In the future, we can expect this type of technology to become more common in integrated circuit designs and find new application areas to further expand its potential. Do you think switched capacitor circuits can replace traditional resistors and become the mainstream of electronic circuit design?
