Switched capacitor

A switched capacitor (SC) is an electronic circuit that implements a function by moving charges into and out of capacitors when electronic switches are opened and closed. Usually, non overlapping clock signals are used to control the switches, so that not all switches are closed simultaneously. Filters implemented with these elements are termed switched capacitor filters, which depend only on the ratios between capacitances and the switching frequency, and not on precise resistors. This makes them much more suitable for use within integrated circuits, where accurately specified resistors and capacitors are not economical to construct, but accurate clocks and accurate relative ratios of capacitances are economical. SC circuits are typically implemented using metal–oxide–semiconductor (MOS) technology, with MOS capacitors and MOS field effect transistor (MOSFET) switches, and they are commonly fabricated using the complementary MOS (CMOS) process. Common applications of MOS SC circuits include mixed signal integrated circuits, digital to analog converter (DAC) chips, analog to digital converter (ADC) chips, pulse code modulation (PCM) codec filters, and PCM digital telephony.

Charge is transferred from in to out as discrete pulses, not continuously. This transfer approximates the equivalent continuous transfer of charge of a resistor when the switching frequency is sufficiently higher (≥100x) than the bandlimit of the input signal. The SC circuit modeled here using ideal switches with zero resistance does not suffer from the ohmic heating energy loss of a regular resistor, and so ideally could be called a loss free resistor. However real switches have some small resistance in their channel or p–n junctions, so power is still dissipated. Because the resistance inside electric switches is typically much smaller than the resistances in circuits relying on regular resistors, SC circuits can have substantially lower Johnson–Nyquist noise. However harmonics of the switching frequency may be manifested as high frequency noise that may need to be attenuated with a low pass filter. SC simulated resistors also have the benefit that their equivalent resistance can be adjusted by changing the switching frequency (i. e., it is a programmable resistance) with a resolution limited by the resolution of the switching period. Thus online or runtime adjustment can be done by controlling the oscillation of the switches (e. g. using an configurable clock output signal from a microcontroller).

SC simulated resistors are used as a replacement for real resistors in integrated circuits because it is easier to fabricate reliably with a wide range of values and can take up much less silicon area. This same circuit can be used in discrete time systems (such as ADCs) as a sample and hold circuit. During the appropriate clock phase, the capacitor samples the analog voltage through switch S1 and in the second phase presents this held sampled value through switch S2 to an electronic circuit for processing.

Electronic filters consisting of resistors and capacitors can have their resistors replaced with equivalent switched capacitor simulated resistors, allowing the filter to be manufactured using only switches and capacitors without relying on real resistors.

Switched capacitor simulated resistors can replace the input resistor in an op amp integrator to provide accurate voltage gain and integration. One of the earliest of these circuits is the parasitic sensitive integrator developed by the Czech engineer Bedrich Hosticka.

The delaying parasitic insensitive integrator has a wide use in discrete time electronic circuits such as biquad filters, anti alias structures, and delta sigma data converters. This circuit implements the following z domain function:

One useful characteristic of switched capacitor circuits is that they can be used to perform many circuit tasks at the same time, which is difficult with non discrete time components (i. e. analog electronics). The multiplying digital to analog converter (MDAC) is an example as it can take an analog input, add a digital value to it, and multiply this by some factor based on the capacitor ratios. The output of the MDAC is given by the following:

The MDAC is a common component in modern pipeline analog to digital converters as well as other precision analog electronics and was first created in the form above by Stephen Lewis and others at Bell Laboratories.

Switched capacitor circuits are analysed by writing down charge conservation equations, as in this article, and solving them with a computer algebra tool. For hand analysis and for getting more insight into the circuits, it is also possible to do a Signal flow graph analysis, with a method that is very similar for switched capacitor and continuous time circuits.