# Good Switched-Capacitor Circuitsswitched-Capacitor Circuits Introduction Report Example

Type of paper: Report

Pages: 8

Words: 2200

Published: 2021/03/23

## Introduction

As opposed to continuous time capacitor circuits in analog signal processing, Switched Capacitor (SC) circuits find wide range of applications in discrete time signal processing. These circuits function by charging and discharging capacitors with the help of switches to provide flow of charge in desired direction. SC filters are embedded in integrated circuits due to their inherent temperature and voltage characteristics.

## A typical SC circuit is equivalent to a discrete time resistance. Consider a simple example of a SC circuit:

Clock pulses are applied on switches to perform transition between two voltage sources shown in the figure. It is made sure that the clock pulses don’t overlap so that the voltage sources are not short circuited. It is assumed that VA>VB so that the net charge moves from A to B. When C1 is not present, the capacitor is charged to VB. As soon as C1 is applied, capacitor attains charge equivalent to VA. The net charge developed by capacitor is ΔQ=C(VA-VB). During clock cycle C2, this differential charge is transferred to output connected at terminal point represented by VB. The discrete charge transferred is evaluated by:
I=CVA-VBT
T is time period for one clock pulse. As it is obvious, the SC circuit exhibits the behavior of a discrete resistor with value T/C. This property enables SC circuits to find a huge range of applications in digital signal processing.

## Advantages and Properties of SC Circuits

Accurate frequency response and dynamic ranges are available.
Easy to analyze with z-transform.
Since filter capacitance is found from ratio of capacitors, relative matching is easily obtained.
The frequency response can be tuned as a function of clock provided by crystal oscillators.
High order DC gains can be provided.
Applications of Switched Capacitor Circuits
Switched Capacitor circuits are used in a variety of applications such as digital audio, instrumentations, power management, wireless communication, high speed and high accuracy data conversion and digital filters etc. Some of the most common applications of SC circuits are described below:
The delay generated by insensitive integrator configuration of SC circuits is used in anti-alias structures, biquad filters, and delta sigma data converters.
One of the most interesting applications of SC circuits is their ability to perform multiple circuit tasks in parallel. This ability is difficult to achieve with continuous-time circuits. Take an example of multiplying Digital to Analog converter that takes an analog input, add digital value to it, and multiply it with capacitor ratios.

## SC circuits find applications in signal processing blocks such as voltage controlled oscillators, gain stages, and modulators.

SC circuits play a significant role in discrete time filtering of signals. In simple sense, the analog signal is first passed through anti-aliasing filters for removing undesired signals that lie beyond the half the clock frequency. Then, Sample and Hold circuit is employed for sampling the analog data prior to SC filtering. SC filters will perform the desired purpose and then output is passed through Sample and Hold circuit again. At the last step, we have reconstruction filter to form the continuous signal at the output.
SC filters may perform functions such as low-pass, high-pass, band-pass signal filtering. Filtering may be performed in more than one stages depending upon the requirements.
Switched Capacitor circuits are used for designing efficient data converters that are important for interfacing digital and analog world. SC circuits can take the form of a plethora of data converter architecture and configurations. Integrated CMOS data converters can also be derived from SC circuits.
SC circuits are involved in Nyquist rate and oversampled data converters. Some examples of ADCs in this regard are two-step, flash, pipelined, successive approximation, and cyclic.
The application of Switched capacitor circuits in DC-DC converters takes the motivation from the rapidly growing requirements of having small size and light weight, low-cost power management, and high conversion efficiency. DC-DC converters are always preferable where time-varying voltage sources are involved in the circuitry. SC circuits replace the big-size magnetic circuits for DC-DC conversion. It is possible to design the whole converter on just a single chip. A specialized switching array is designed that supplies the desired voltage to the circuitry. Apart from small size and ease of integration, SC DC-DC converters also provide the advantages of high switching frequency, low fabrication cost, good conversion efficiency, and reduced voltage-mode electromagnetic interference.
There are some issues involved in DC-DC conversion efficiency such as reduction in voltage due to parasitic voltage and on-resistance. However, these problems can be overcome with advanced technologies for fabricating integrated circuits.
With the advancement in mobile technology, the subscribers for 2G and 3G services are growing rapidly. In order to make the mobile technology successful, wireless transceivers must perform efficiently. Multistandard and multiband capabilities are core concern in this regard. These capabilities are provided by SC Delta-sigma modulators.
When multiple standards are incorporated in the RF transceiver, the circuits tend to become complex and carry low integration capability. The transition from single to multiband circuits is not straightforward. It involves designing transmitters and receivers from the scratch. Designing multistandard ICs for RF is quite a difficult task. SC circuits make these designing tasks somewhat simple.
While designing wireless receivers, SC data converters provide the best performance that meets the design criteria of wireless receivers. The factors of merit for RF receivers such as linearity, selectivity, sensitivity, and dynamic range are improved by SC circuits.
SC circuits are also applied in the shape of differential amplifiers for reducing the common mode gain and amplifying the differential signals applied at the input. This circuit is built in an economical manner with high performance.
Switched capacitors can also be configured as Lock-in Amplifiers for passing the signals that closely matched with the input carrier. The circuit will form highly narrow Passband that will pass signals closely matched with the carrier. The components not related to carrier are severely rejected. Such kind of amplifiers can even extract signals 120DB below the noise signal.
The huge challenge for SC circuits is to perform optimally in the presence of low input voltage and mismatches in circuits. When you talk about low-voltage supply and tiny integration level, many analog circuit components are automatically ruled out of the question. SC circuits satisfy the challenge of designing high voltage gain amplifiers with sufficient output swing even in the presence of low input voltages. However, the only problem is the reduction in the input swing range. This feature leads to compromise in Signal to Noise ratio. In order to have sufficient SNR, large sampling capacitors may be used. But, when you use large values of capacitance, the speed and dynamic response of the circuit will be severely affected.
Switched capacitors are also used for clock boosting. For this purpose, cross-coupled configuration with two NMOS transistors is used. The capacitors are charged alternately with supply voltages. The limitation of circuit lies with reference to gate-oxide breakdown of CMOS. The crucial terminal voltages of switch must be kept below the supply voltage to ensure long term operation.
The floating switch problem is removed in switch Op-Amps with the help of Switched Capacitors. The switch itself is eliminated. The circuit can be made with simple SC integrators in series. However, turning Op-Amps On/off is not fast as compared to the case with the switches. So, the response will be slightly sluggish. Due to low-power and low-voltage constraints, the gain bandwidth product and slew rate are compromised. The accuracy, dynamic range, and linearity of the overall circuit are damaged.
SC circuits find application for auto-zeroing by storing low frequency random noise and offset DC voltage by using capacitors. For this purpose, two clock phases are used: a cancellation and a sampling phase. During the phase of sampling, the flicker noise and DC offset are sampled and then stored on the capacitors. These stored errors are subtracted from the signal during the cancellation phase. This technique is quite effective in reducing the effect of the DC offset and also the flicker noise.
The correlated double sampling technique is used as a generalization of auto-zeroing that uses SC circuits. This method overcomes the limitation of the previous method that assumed that the magnitude error is a DC signal. This assumption is invalid where we need to consider the effect of finite op-amp gain.
Switched capacitors are important parts of variable gain amplifiers. These circuits carry high stability with wide range of digitally variable gains. Instead of complex configurations of FETs and relays for achieving the same characteristics, simple SC chips are used in variable gain amplifiers.
SC circuits are also important for signal conditioning. Sensors used for measuring various physical phenomena such as temperature and humidity require some kind of conditioners for representing the data in a useful manner. SC circuits provide this facility in simple and economical manner.

## Voltage controlled current sources can be designed from Switched Capacitor circuits.

SC circuits are used for sensing current through shunt in either of its supply rails. This circuit is vital for solar and battery-powered systems.

## A simple SC circuit can act as analog multiplier of two signals.

Switching regulators with high current are easily possible with SC circuits. The most amazing feature of such circuits is that they don’t require inductors at all.

## Reducing Mismatches in Switched Capacitor Circuits

The capacitor matching accuracy is related to designing SC circuits with practical values of capacitances. The best mismatch accuracy achieved so far is 0.02% in existing CMOS technologies. To alleviate these problems, the design should make the required parameters independent of capacitor mismatch as far as possible.
Extensive research has been carried out to minimize capacitor mismatches in switched capacitor circuits. Following are some of the methods used in the literature:
References’ refreshing cyclic A/D and D/A converters, using switched capacitors, is a renowned method to reduce capacitor mismatch. In this method, reference voltage is changed periodically for compensating for the non-ideal loop gain. The linearity of A/D and D/A becomes almost completely independent of component ratios. These converters comprise only two MOS operational amplifiers with moderate gain and some capacitors.
Ratio-independent technique is used to reduce the dependency of circuits performance attributes such as linearity and gain independent of mismatches in components. This method also requires high performance op-amps with high value of gain-bandwidth products.
In order to relax the accuracy requirements of op-amps in reducing capacitor-mismatch, the ratio-independent technique can be used in coherence with gain and offset insensitive design. The previous method can also be complemented with correlated double sampling scheme.
The capacitor error averaging approach is also effective in reducing the capacitor mismatch in switched capacitor circuits. This method has some drawbacks also. The conversion rate will be compromised by a factor of three and the power budget will be doubled.
In addition to the aforementioned techniques, the designers can tune capacitors in SC circuits using shunt variable capacitors. The shunt capacitors will be tuned until the capacitance matches with other capacitors in the circuit. The shunt capacitors are realized in reality by using an array of capacitors driven by digital logic that increases the cost and area.
Background calibration has gained interest in recent times to reduce capacitor mismatches in SC circuits. This idea is extremely popular because background calibration can be easily done without affecting the normal performance of the switcher capacitor circuits. Such kind of calibration is done either in digital or analog domain. The digital calibration contains digital circuitry for cancellation capacitor mismatches. Some popular digital calibration methods use oversampled delta-sigma modulators to take the mismatches to a high frequency range and then filtering them out. This method may also be referred to as mismatch shaping. The only limitation is due to speed for oversampling. For analog calibration, the practical circuits are few and far between because analog calibration circuits need to be linear and more accurate as compared to the original circuit that needs to be calibrated. On the other hand, digital calibration circuits are more viable since they carry low fabrication cost and scalability.

## Conclusions

The bottomline is that Switched Capacitor circuits play a significant role in modern electronic circuits for a variety of purposes related to discrete time signal processing. They are easy to fabricate, scalable, require low power, and carry some other great advantages that rule out the possibilities of using analog circuits. Their limitations arise due to mismatches in capacitance values such as reduction in accuracy and linearity. Capacitor-mismatch can be reduced by using plenty of methods that calibrate the mismatched capacitance or eliminate the dependence of performance parameters on circuits’ capacitance.

## References

Liu, Mingliang Michael. "Demystifying switched capacitor circuits". Newnes, 2006.
Williams, Jim. "Applications for a Switched-Capacitor Instrumentation Building Block." Linear Technology Corporation, Application Note (1985).

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