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.
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.
[2] The simplest switched-capacitor (SC) circuit is made of one capacitor
Recall that Ohm's law can express the relationship between voltage, current, and resistance as: The following equivalent resistance calculation will show how during each switching cycle, this switched-capacitor circuit transfers an amount of charge from in to out such that it behaves according to a similar linear current–voltage relationship with
between its plates is: Therefore, when S1 is closed while S2 is open, the charge stored in the capacitor
Exactly how much charge gets transferred can't be determined without knowing what load is attached to the output.
So the average electric current (rate of transfer of charge per unit time) from in to out is: The voltage difference from in to out can be written as: Finally, the current–voltage relationship from in to out can be expressed with the same form as Ohm's law, to show that this switched-capacitor circuit simulates a resistor with an equivalent resistance of: This circuit is called a parallel resistor simulation because in and out are connected in parallel and not directly coupled.
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.
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.
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.
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.
- it increases (or decreases) its voltage each cycle according to the charge that is being "pumped" from
and rewrite the last equation divided by dt: Therefore, the op-amp output voltage takes the form: This is the same formula as the op amp inverting integrator where the resistance is replaced by a SC simulated resistor with an equivalent resistance of: This switched-capacitor circuit is called "parasitic-sensitive" because its behavior is significantly affected by parasitic capacitances, which will cause errors when parasitic capacitances can't be controlled.
The delaying parasitic insensitive integrator[clarification needed] has a wide use in discrete time electronic circuits such as biquad filters, anti-alias structures, and delta-sigma data converters.
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.
[4] Switched-capacitor circuits are analysed by writing down charge conservation equations, as in this article, and solving them with a computer algebra tool.
