Switched-capacitor Networks Research Articles

Analysis and sensitivity of periodically switched linear networks

A completely general computer-oriented method for exact frequency-domain analysis of multiphase periodically switched linear networks is presented. Input signals can be either continuous or sample-and-held. The theory is valid even for cases where the network variables are discontinuous during switching. An algorithm to compute sensitivity of the response to element changes is also given. The method unifies analysis of general switched linear networks and ideal switched capacitor networks to a single algorithm. Equation formulation is based on the two-graph modified nodal analysis. The theoretical results presented are compared to previously published results. The theories have been implemented in a computer program. Numerical results of the analysis of three networks are given. They show the usefulness of the program in the analysis and design of switched networks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A switched-capacitor macromodel approach to the computer-aided analysis of switched-capacitor networks

A switched-capacitor macromodel (SCM) suitable for the analysis of arbitrary-phase SC networks (SCN) is presented, which reduces the number of nodes and the size of simulation equations of SCN drastically. The effect of the disconnected state of capacitors in multiphase cases on the compressed equations is discussed. Subsequently, a general z-domain equation formulation for arbitrary-phase SCNs is derived, and an algorithm implementing the SCM approach is developed. The z-domain equation formulations of the single-pole model of operational amplifiers for two cases are given as well, which can be used in the SCM approach. The SCM approach is illustrated by a four-phase SCN which has been stimulated by using a program, SCMAP, implementing the algorithm. >

Direct by-inspection derivation of signal-flow graphs for multiphase stray-insensitive switched-capacitor filters

A direct by-inspection method for the derivation of signal-flow graphs (SFGs) for multiphase stray-insensitive switched-capacitor (SC) networks is presented. Compared to this method, others are relatively complicated and not direct in the sense that they require intermediate steps. The multiphase analysis presented in the paper is a generalisation of the method shown previously (see A. Dabrowski, 1987), where a by-inspection signal-flow graph analysis of biphase SC networks is described. Whereas only a brief summary of the derivation rules and an example are given here, the underlying theory will be published elsewhere.< >

A note on statistical sensitivity computation in switched-capacitor networks

The sensitivity of switched-capacitor (SC) networks to the ratios of capacitances is considered. A special form of the modified Tellegen's theory is proposed and used to formulate simple closed-form matrix equation for the multiparameter sensitivity calculation. The results of a computer verification of the proposed sensitivity computation method on both a low-pass fifth order and a bandpass sixth-order elliptic filter agree well with results obtained using the Monte Carlo method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

General analysis of large linear switched capacitor networks

A new time and frequency domain analysis method is presented for nonideal switched capacitor networks that is orders of magnitude faster than existing techniques. This efficiency is achieved by developing a formulation such that a continuous AC analysis is not required; this allows the system to be solved as an entirely discrete one. A special compression technique reduces the solution of this discrete system to that of solving the network in one phase only. This final solution step, which ordinarily requires O( nu /sup 3/) operations ( nu is the matrix order), is rendered more efficient by reducing the system to upper Hessenberg form in a preprocessing step, when the solution cost is reduced to O( nu /sup 2/) operations. Sparse matrix techniques, optimal ordering and interpretive code generation are all used to advantage. Performance is compared with existing programs.< >

Filter realisation by passive network simulation

General simulation methods of passive networks are investigated. A new simulation approach based on LU matrix decomposition is presented. This approach can be used to design active-RC, switched-capacitor and digital networks. The resulting system demonstrates very low sensitivities with respect to component values. New digital realisations, in particular, reveal structures of low complexity, high speed of operation and low cost of implementation.

Explicit formulas for analyzing general switched-capacitor networks

Explicit formulas are derived for analyzing switched-capacitor (SC) networks of the most general type. Using these formulae a simple analysis method is obtained to compute the frequency-domain responses of multiphase SC networks containing real resistors. The formulas presented in this paper make it possible to specify arbitrary switch timing waveforms and to insert arbitrary built-in input and/or output sampling functions. Most of the practical linear SC analysis problems can be solved efficiently by these formulas without special knowledge of the lengthy derivations.

Design techniques for switched-capacitor broad-band phase-splitting networks

A phase-splitting network is another type of circuit that is suitable to be integrated using the switched-capacitor (SC) technique. However, using existing all-pass SC configurations to realize such networks results in excessive capacitance spread because phase-splitting networks have very low real poles under a wide signal frequency band. Simple analytical expressions derived in this paper show that combining first-order sections of such networks into low- Q biquads does not reduce the capacitance spread unless the dynamic range of the filter can be sacrificed. A new biquad configuration is proposed for capacitor area efficient realization of low pole all-pass filters. The biquad combines a T -cell with a conventional integrator. The T -cell integrator realizes the low pole with a product of two capacitance ratios instead of a single capacitance ratio to reduce the capacitance spread. A simple and systematic design procedure is presented for the determination of capacitance values as a function of the poles to be realized. The design procedure achieves minimum total capacitance and equal dynamic range for all amplifiers simultaneously. Commonly performed rescaling of capacitance values after computer simulation is not necessary. The new biquad attenuates offset and flicker noise. However, finite amplifier dc gain and white noise have greater influence on the filter performance. Analytical expressions for transfer function deviations are derived which indicate the amplifier dc gain necessary for a given \omega_0 tolerance. Computer simulations show that the total integrated noise of the T -cell biquad only slightly increases compared to that of the conventional biquad realizing the same function. A design example is given which illustrates the design procedure. Compared to the realization of the same transfer function with conventional biquads, T -cell realization reduces the total capacitor area by almost a factor of 20.

A method for frequency-domain analysis of switched-capacitor filters

In this paper, a new method is proposed for the frequencyresponse evaluations of switched-capacitor networks of any topology. It relies on reducing the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> -transform impulse response of the SCN into a rational function form. Closed-form expressions for the coefficients of the rational expansion, as well as its degree, are given. Illustrative examples showing the merits of this new approach over the existing one .are also included.

Simplified analysis off arbitrary switched-capacitor networks

A general method is presented which allows a closed-form analysis of switchedcapacitor (SC) networks with several phases, arbitrary duty cycles and with nonideal operational amplifiers. The method is based on a new equivalent representation of SC networks in the zdomain and on flow-graph techniques. The equivalent z-domain representations of SC networks proposed in this paper are compatible with classical circuit-theory considerations, and they are simpler and require a smaller number of elements than the equivalent circuits previously proposed. The usefulness and efficiency of the method proposed is illustrated with some examples. Moreover, it is shown how to transform the z-domain SC networks into equivalent time-continuous (analogue) circuits to analyse them in the frequency and/or time domain by use of conventional general-purpose circuit simulation programs. A user-ready implementation on SPICE is also proposed.

Method for analysis of switched-capacitor networks containing operational amplifiers with finite DC gain and bandwidth

An analysis technique is proposed which takes into account the effect of finite DC gain and the gain-bandwidth product of operational amplifiers (OAs) on the response of switched-capacitor (SC) networks operated by a biphase or a multiphase clock. The general matrix equation of the network in the z-domain is split into two subsets: external charge conservation equations (CCEs), which are set up for the passive part of the network, and internal CCEs, based on equivalent OA representations. The technique is simple, versatile, applicable to SC networks of any topology and suitable for creating a computeraided analysis system. Examples are given for both to confirm the advantages of equivalent OA representations and to illustrate the technique's efficiency.

Systematic approach to the time multiplexing of stray-insensitive SC networks

General conditions of the time multiplexing of N independent switched capacitor (SC) circuits are reviewed. Subsequently, the conditions for SC and operational amplifier (OA) multiplexing in dependent stray-insensitive SC circuits are derived. It is shown that equal-valued SCs can always be time multiplexed, whereas only uncoupled OAs can be time multiplexed. Systematic procedures for deriving stray-insensitive time multiplexed SC circuits from a given biphase stray-insensitive SC circuit are formulated. In OA multiplexed circuits, more OAs are, in general, required for a smaller number of clock phases and vice versa. A number of time-multiplexed circuits are derived from some well known biphase SC circuits. Practical results taken on simulated timemultiplexed circuits derived by the proposed procedures are in close agreement with those taken on their unmultiplexed counterparts.

Optimisation of parasitic insensitive switched capacitor biquads

A powerful technique is described for the optimisation of parasitic insensitive switched capacitor (SC) biquads. The proposed method minimises the total capacitance and the component spread necessary for realising a 2nd-order transfer function by a parasitic insensitive SC network. The increase in the network insensitivities due to the minimisation of the total capacitance is controlled by multiple criteria optimisation techniques. The method allows the optimisation to be performed with a variable network topology without, however, requiring large computational times. The number of components in the final network is limited and the dynamic range of the filter is also controlled. An example is given which demonstrates the possibility of considerable design improvement by using the proposed technique.

Hand analysts of switched-capacitor networks

A method is given for hand analysis of switched-capacitor networks. Very few rules need be remembered, and the result is in the form of a matrix equation, which can be solved by any suitable method.

ANSWICAP—a computer-aided method for symbolic transfer function determination on switched capacitor networks

An efficient computer-aided method (ANSWICAP) is presented for determining the transfer function in ideal switched capacitor networks with n-phases. The rational function representing the transfer function may be obtained symbolically as a function of z and of as many capacitors and gains of the circuit as are desired. Application of the method takes the input signal to be a sampled data signal, and that the network to be periodically switched.

Switched Capacitor Networks for Voice Communication

Switched Capacitor Networks for Voice Communication

Switched-capacitor filters using unity-gain amplifiers

Switched-capacitor networks having second-order filter characteristics are presented. Realization is by means of unity-gain amplifiers as buffers. The circuits have small sensitivities, good dynamic range and a reasonable spread of capacitor values. The filters can be used for high-Q realization and a relatively high frequency range.

Simple technique for analysis of SC networks using general-purpose circuit simulation programs

A new technique is proposed which enables the transformation of a large class of switched-capacitor (SC) networks into equivalent time-continuous (analogue) circuits to analyse them by use of standard, general-purpose circuit simulation programs such as SPICE It is based on a block partitioning, i.e. a total SC network is divided into small building blocks. It is shown how basic SC building blocks like integrators and summers can be modelled by equivalent two-ports containing only resistors, lossless transmission lines and current-controlled voltage sources. Furthermore, some new offset-free SC integrator schemes based on multi-step integration algorithms are also described.

A computing method for obtaining derivatives of denominator and numerator of network functions with respect to elements and sensitivity analysis

AbstractVarious sensitivities necessary for prediction and evaluation of changes in characteristics of networks due to the changes in the value of elements and for optimization of networks, can be computed by using the derivatives of denominators and numerators of network functions with respect to elements. However, existing computing methods of derivatives are not suitable when the number of elements m is m &gt; n (where the size of the matrix representing the network is n × n), that is, the sensitivity analysis which must be computed with respect to many elements. This paper presents a method to compute higher‐order derivatives of denominators and numerators of digital, analog and switched capacitor networks, using Vlach's redundancy improved method. Also, the proposed method and existing methods are compared with respect to the memory size and the number of multiplications required. It is shown that this method is more effective for analyzing the sensitivity for many elements. Finally, the method is implemented here and applied to several examples for element sensitivity analysis.

Direct analysis of stray-insensitive switched-capacitor networks using signal flow graphs

A method for the direct closed-form analysis of switched-capacitor networks using signal-flow graph (SFG) techniques is presented. Although the networks must conform to certain constraints, these include the constraints required for insensitivity to stray capacitance. The method of analysis is noteworthy for its simplicity of use, because it permits the signal-flow graph of a switched capacitor network to be drawn directly by inspection. Arbitrary network functions can then be obtained using signal-flow graph theory. An additional advantage of the method is due to the insight afforded into the functioning of a network by its signal-flow graph. The reverse procedure of synthesizing an SC network by deriving the signal-flow graph corresponding to a given transfer function, and then transforming the SFG into a physical network, is thereby also simplified.