Switched Capacitor Circuits

What Are Switched Capacitor Circuits?

Switched capacitor circuits are analog discrete-time circuits that implement signal processing functions by transferring charge into and out of capacitors under the control of periodically operated switches. Because the amount of charge transferred per clock cycle depends on capacitor ratios rather than on absolute resistance values, switched capacitor circuits achieve precision performance that passive RC networks cannot match in standard integrated circuit fabrication. The technique bridges the boundary between continuous-time analog circuits and digital sampled-data systems, allowing filters, integrators, and data converters to be realized on the same silicon substrate as digital logic.

The approach traces to the early 1970s and gained wide adoption after researchers demonstrated that CMOS transmission gates could serve as low-charge-injection switches and that the ratio matching of on-chip capacitors could be held to within 0.1% without calibration. This accuracy made switched capacitor filters competitive with active RC designs for audio and telecom applications requiring tight frequency tolerances.

Discrete-Time Operation and the Equivalent Resistance Principle

A switched capacitor circuit operates on discrete samples of the input signal, taken at each clock transition. The most fundamental building block is the switched capacitor resistor: a capacitor C switched between two nodes at clock frequency f behaves as a resistor of value 1/(fC). This equivalence, described in the foundational IEEE paper on switched-capacitor circuit design, allows designers to replace large on-chip resistors with small capacitors, a critical advantage because resistors consume far more die area than capacitors in CMOS processes.

The clock frequency also sets the Nyquist limit for the sampled signal, so anti-aliasing filters at the input are required whenever the input bandwidth approaches half the clock rate. Non-overlapping two-phase clock schemes are standard, ensuring that charge transfer is complete before the next sampling phase begins.

Filters and Integrators

The switched capacitor integrator is the core functional block from which higher-order filters are assembled. By cascading integrators in biquad or ladder topologies, designers realize low-pass, band-pass, high-pass, and notch responses whose corner frequencies track the clock frequency. Because corner frequency is proportional to the capacitor ratio and the clock, rather than to an RC time constant, the filter characteristic shifts predictably when the clock changes, a property that CMOS analog circuit design textbooks from UCLA identify as the key advantage over continuous-time alternatives.

Switched capacitor filters found early commercial deployment in telephone subscriber line interface circuits, where a single-chip solution needed to implement the hybrid function, anti-aliasing, and reconstruction filtering simultaneously within tight passband ripple specifications.

Analog-to-Digital Conversion and Synthesizers

The charge-redistribution successive approximation ADC, widely used in microcontrollers and mixed-signal SoCs, is a direct application of switched capacitor principles. A binary-weighted capacitor array samples the input, and the comparator resolves each bit by comparing redistributed charge against a reference. Clock accuracy translates directly to conversion accuracy.

In frequency synthesizers, switched capacitor techniques implement discrete-time loop filters and sample-and-hold stages within phase-locked loops, as detailed in IEEE Xplore coverage of switched-capacitor circuits in mixed-signal design. The ability to tune filter coefficients by adjusting the clock frequency simplifies programmable synthesizer architectures.

Applications

Switched capacitor circuits have applications in a range of fields, including: