A This paper will explicate the basic constructs underlying the operation of the switched capacitance, every bit good as the usage of switched-capacitors to recognize compact and various circuits already familiar to the undergraduate pupil of electronics. One set of illustration circuits include easy tunable active filters ; specific illustrations of filter designs that incorporate switched-capacitors will be developed, and the usage of a commercially available switched-capacitor integrated circuit, the MF10, to implement the designs will be shown. Another illustration circuit is an instrumentality amplifier that is more compact and has a higher CMRRA than the conventional realisation. Linear Technology ‘s LTC1043 serves as the vehicle for this circuit. By showing the public-service corporation of the modern switched-capacitor IC in these two of import electronic maps, it is hoped that teachers and pupils in technology engineering will include the survey of the switched-capacitor in advanced electronics classs.

## I. Introduction

This paper aims to demo how the switched-capacitor construct can be used to recognize a broad assortment of active filters that have the advantages of concentration and tunability.A A In peculiar, the accounts and design illustrations presented here will utilize mathematical tools familiar to the electronics engineering and technology undergraduate pupil. We will non utilize the Z-transform, which is the strictly right tool for analysing sampled-data waveforms.A A

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The paper will show the undermentioned subjects. First, the basic thoughts behind the usage of the switched-capacitor to replace resistances in active filter circuits will be explained.A Second, the usage of the switched-capacitor to implement lossless, lossy, and differential planimeters, which are the anchor of many switched-capacitor filter circuits, particularly those based on National Semiconductor ‘s MF10 IC [ 1 ] .A A Third, illustration designs of active filters utilizing the MF10 will be presented.A

Before detailing the operation of switched-capacitor circuits, it will be utile to understand the motive behind, and applications of, these circuits. Basically, switched-capacitor techniques have been developed in order to let for the integrating on a individual Si bit of both digital and linear maps. Because really big graduated table integrated ( VLSI ) circuits rely on MOS transistors and pico-farad scope MOS capacitances, any realisation of parallel circuits on a bit will hold to utilize these elements. By comparing, conventional parallel circuits use theA ratioA of oppositions to put the transportation maps of amplifiers, and theA magnitudesA of oppositions to find the operation of current-to-voltage and voltage-to-current convertors. Finally, theA valuesA of RC merchandises are used in active filters and signal generators to find the frequence responses of those circuits. When one moves to the Si bit and strives to accomplish the same functionality in a much reduced country and utilizing the tools of MOS engineering, this is what one discovers. First, switches, small-value capacitances, and nice op-amps are easy plenty to recognize in MOS engineering. Second, utilizing that same engineering, it is really hard and uneconomical of Si die country to do resistances and capacitances with the values and truth encountered in audio and instrumentality applications [ 2,3 ] . As we will see in the subsequent subdivisions, interior decorators have overcome these troubles by recognizing that ( 1 ) resistances can be replaced by MOS switches that are quickly turned on and off, and MOS capacitances, and that ( 2 ) the clip invariables originating from these simulated oppositions and the MOS capacitances are given in the signifier of electrical capacity ratios. The fact that capacitance ratios command the clip invariables means that these invariables now can take advantage of the superior matching of electrical capacities fabricated on Si, every bit good as their ability to track each other with temperature.A

If these are undoubted advantages for the VLSI interior decorator, what can the board-level circuit design expect to accomplish with the usage of switched-capacitors? For one thing, as we will see shortly, non merely are the clip invariables of the switched-capacitor circuit superior in their control, but these clip invariables are tunable through the simple expedient of altering the frequence of the clock pulses that drive the circuit. Furthermore, the integrated circuit bundles that are now available support a figure of filtrating maps in one bundle, therefore cut downing footmarks needed on circuit boards to recognize a given set of parallel functions.A

Although switched-capacitors were developed in order to run into the demand to integrate parallel, active filters on Si along with digital maps, they have since found many other utilizations [ 2 ] . These include, besides filters, instrumentality amplifiers, voltage-to-frequency convertors, informations convertors, programmable capacitance arrays, balanced modulators, peak sensors, and oscillators.

## II. BASIC SWITCHED-CAPACITOR OPERATIONA

The kernel of the switched-capacitor is the usage of capacitances and parallel switches to execute the same map as a resistor.A A This replacing resistance, along with op-amp based planimeters, so forms an active filter.A A Before diging excessively far into existent filter designs, nevertheless, it makes sense to inquire why one would desire to replace the resistance with such an seemingly complex assembly of parts as switches and capacitors.A A It would look from the generation of parts that the switched-capacitor would be country intensive.A A As a affair of fact, for the resistance values that one seeks in certain filter designs, this is non the case.A A Furthermore, the usage of the switched-capacitor will be seen to give frequence tunability to active filters.A A Figure 1 [ 2, 3 ] shows the basic apparatus for a switched-capacitor, including twoA N-channel Metal-OxideA SemiconductorA Field-EffectA Transistors ( NMOS ) and a capacitor.A A There are two clock stages, A A , which are non-overlapping. The MOSFET ‘s, either M1 or M2, will be turned ON when the gate electromotive force is high, and the tantamount opposition of the channel in that instance will be low, A . Conversely, when the gate electromotive force goes LOW, the channel opposition will look likeA A .A A With such a high ratio of OFF to ON oppositions, each MOSFET can be taken for a switch. Furthermore, when the two MOSFET ‘s are driven by non-overlapping clock signals, so M1 and M2 will carry on during alternate half-cycles.A A A

This makes the two-MOSFET agreement equivalent to a single-pole, double-throw switch ( SPDT ) .A A One can now utilize a symbolic switch image, as in Figure 2a below, to stand for the circuit.A A The operation of this circuit is as follows. When the switch is thrown to the left, the capacitance will bear down up toA A . When the switch is thrown to the right, the capacitance will dispatch down to/charge up toA A . As a consequence of these back-to-back shift events, there will be a net charge transportation ofA .A A Now, if one flips the switch back and Forth at a rate ofA A A cycles/sec, so the charge transferred in one 2nd isA , which of class has the units of current.A A One can claim that an mean current, A A . IfA A A A is much higher than the frequence of the electromotive force wave forms, so the exchanging procedure can be taken to be basically uninterrupted, and the switched-capacitor can so be modeled as an tantamount opposition, as shown below in Figure 2b.A A The value of the tantamount opposition is given by: A

Therefore, this tantamount opposition, in concurrence with other capacitances, and Op-amp planimeters, can be used to synthesise active filters.A A It is now clear from Equation ( 1 ) how the usage of the switched-capacitor leads to tunability in the active filters, by changing the clock frequency.A

This tantamount opposition has characteristics which make it advantageous when realized in integrated-circuit signifier: A

( a ) A A A A High-value resistances can be implemented in really small silicon country. For illustration, a 1-Mi?-A resistance can be realized with a 10-pF capacitance switched at a clock rate of 100 kilohertzs.

( B ) A A A Very accurate clip invariables can be realized, because the clip changeless is relative to theA ratioA of electrical capacities, and reciprocally relative to the clock frequence:

A . Capacitor ratios, particularly in massive signifier, are really robust against alterations in temperature, and clock frequences can besides be purely controlled, so that accurate clip invariables are now available in the switched-capacitor technology.A

The chief restraint in utilizing the switched-capacitor is that inherent in all sampled-data systems: the clock frequence must be much higher than the critical frequence set by the RC merchandises in the circuit. Furthermore, on either side of the parallel switches, i.e. , the MOSFET ‘s, there must be basically zero-impedance nodes ( electromotive force beginnings ) .A A There are a figure of other restraints which the unsuspecting designer/user might overlook [ 3, p. 725 ] : A

( a ) A A A A The tantamount opposition formed by the action of the switched-capacitor can non be used to shut the negative-feedback way in an op-amp all by itself.A One must remember that to guarantee stableness, the op-amp ‘s feedback way must be closed continuously, while the switched-capacitor is a sampled-data building of a resistance, and therefore non uninterrupted.

( B ) A A A Circuit nodes can non be left floating.A A That is, there must ever be a resistive way to land so that charge does non construct up on the capacitance plates.

( degree Celsius ) A A A A The bottom home bases of the MOS capacitances must be connected to land or to a electromotive force beginning. There is an intrinsic, parasitic electrical capacity associated with the MOS capacitance ‘s underside home base [ 4 ] . This parasitic electrical capacity can be between 5 % and 20 % of the coveted value ; moreover, it behaves nonlinearly with electromotive force [ 4 ] .A A Therefore, it must be connected to AC land or a electromotive force beginning so that this nonlinear part of the electrical capacity will non impact the overall response of the switched-capacitor filter. In practical footings, this means that capacitive electromotive force splitters with three or more capacitances, and circuits that switch both terminals of a capacitance in sequence to the inputs of an op-amp, are used.

( vitamin D ) A A A The noninverting pin of the op-amp should be kept at a changeless electromotive force. If this pin is connected to the signal in some manner, so the practical short circuit between op-amp inputs means that the inverting input is no longer a practical land, and so an unwanted change of filter response due to the MOS capacitance ‘s parasitic electrical capacity will happen ( see point ( degree Celsius ) above ) .A

## A

## III. SWITCHED CAPACITOR INTEGRATORSA

The op-amp planimeter is the most often chosen edifice block for switched-capacitor filters.A A The standard RC planimeter is shown in Figure 3a, and its analysis and description can be found in any electronics text [ 5, 6 ] .A

A A Again, one notes the fact that this new planimeter has no resistances, which take up inordinate Si die country. Besides, the -3 dubnium frequence, A A , depends on a ratio of electrical capacities, non on an RC product.A A The tolerances for ratios are much easier to command than the tolerances for merchandises. Finally, this characteristic frequence of the planimeter is inherently settable with a simple alteration in the clock frequency.A

The typical values of electrical capacities used in switched-capacitor engineering scope from 0.1 pF to 100 pF. These are low plenty values that the isolated electrical capacities of the MOS switches, of the interconnects, and of the “ home bases ” of the switched-capacitors themselves can all hold a important consequence on the coveted frequence response of the filters designed with switched-capacitors. The effects of isolated electrical capacity have been reduced greatly by dual-switch constellations [ 2, 7 ] . Figure 4 shows explicitly the clock phasing of the MOS switches which acts to extinguish the transeunt charge transportation through the isolated electrical capacities, Cs1 and Cs2, besides indicated in the figure.A A In kernel, charge transportation merely takes topographic point through the capacitorA A . Figures 5a and 5b show both the inverting and noninverting stray-insensitive planimeter. The noninverting stray-insensitive planimeter is obtained merely by exchanging the clock phasing on transistors M2 and M4.

Figure 5b.A A Switch scene for stray-insensitive non-inverting planimeter.

A Because of the importance of the planimeter to switched-capacitor filters, it is necessary to be familiar with the discrepancies of the integrator.A A These include the summing planimeter, the differential planimeter, the integrator/summer, and the lossy planimeter. All of these play a function in the synthesis of switched-capacitor filters. The summing planimeter, shown below in Figure 6, has a response given by: A

Figure 7 shows the differential integrator.A A The easiest manner to understand this circuit is to look at what happens to the charge accretion on the capacitorA A A when the switches are thrown to the left.A A In this instance, the capacitance charges up to a value ofA A . When the switches are thrown to the right, the charge on the capacitance is poured into the op-amp ‘s summing node. The mean current, presuming the exchanging rate ( = clock frequence ) is high plenty, is given by

A The lossy planimeter provides a simple, first-order lowpass response with addition. This circuit is realized by puting a switched-capacitor ( i.e. , a fake resistance ) in analogue with a feedback capacitance, Figure 8. In general, the easiest manner to analyse the response of more complex switched-capacitor circuits such as this one is to replace all switched-capacitors with their resistance equivalents. Once the transportation map is found for a circuit with resistances ( and discrete capacitances ) , so the switched-capacitor equivalents of the resistances ( Eq. 1 ) can be placed back in the transportation map to obtain the concluding consequence. For the lossy planimeter, the analysis returns as follows: A

## IV. SWITCHED CAPACITOR BIQUADRATIC FILTERS

A The biquad constellation [ 8 ] usually features a lossy inverting planimeter, a lossless inverting planimeter, and a unity-gain-inverting amplifier.A A In the standard active RC constellation, this requires three op-amps.A A However, the switched-capacitor realisation of the biquad needs merely two op-amps to execute the same map. One op-amp performs the lossy inverting integrating map, while the 2nd op-amp performs lossless, noninverting integrating. Although one can plan an equal switched-capacitor version of the biquad by doing a resistor-by-resistor replacing in the standard RC biquad filter, such an execution has been found to hold intolerably broad electrical capacity spreads, particularly when higher filter Q ‘s are sought [ 2 ] . Alternatively, Figure 9 shows the biquad filter with improved electrical capacity ratios. This circuit provides the highpass and bandpass responses. Merely as with the analysis of the lossy planimeter, a reasonably complete analysis of this circuit will be made here.A

The usage of a stray-insensitive switched-capacitor ( A A ) with jumping clock stages makes possible the noninverting signifier above. In order to finish the analysis, one has to cipher the highpass filter response.A A The end product node of the first op-amp, which gives the highpass filter response, can be seen to be the superposition of two signals at the summing node of the op-amp: A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A

A Although Eq. 13 does in fact display the standard signifier for theA frequencyA response of a bandpass filter, there is nil in the look that gives the addition of the filter circuit.A A In fact, from the signifier of the transportation map, and from simulation, it can be seen that the circuit in Figure 9 has no resonating addition. The same applies to the highpass filter look in Eq. 14.A A It is clear that a utile active filter circuit formed from switched-capacitors must possess some electromotive force addition in the passband. Of class, it is possible to merely “ tack on ” an amplifier to the end product of the circuit. However, an elegant solution is to turn the 2nd op-amp in Figure 9 into a summing planimeter, in which the input signal is injected into the 2nd op-amp via an tantamount opposition derived from another switched-capacitor. Figure 10 shows the execution of this thought. In Figure 10, the SPDT switches, labeled S1, are shown closed in the first half of the clock cycleA A .A A

The analysis of this circuit in order to deduce the bandpass filter transportation map follows a way similar to the 1 followed in Eq. 13, although more boring. We will merely show the chief consequences here and continue to the simulation of the circuit.A A Superposition of input signals to each of the op-amp ‘s input pins givesA

A In order to imitate the public presentation of switched-capacitor webs, it is necessary to recognize that these circuits are a loanblend of both uninterrupted and sampled-data signals.A A In fact, switched-capacitor circuits are uninterrupted in amplitude and discrete in clip. Because of this combination, simulation with conventional circuit simulators such as PSPICEi?”A presents a job. The presence of switched electromotive forces means that a transeunt analysis must be performed. At the same clip, the desire to find the frequence response across a broad scope of frequences means that a transeunt analysis must be performed for each coveted frequence. This is a really time-consuming procedure because one has to wait until the steady province is reached. One manner to get the better of this job within a SPICE-type simulator is to implement all the design equations in z-transforms. These z-domain theoretical accounts will let one to execute frequency-domain simulation of complex switched-capacitor circuits. Although the z-transform is the strictly right mathematical tool for the analysis of sampled-data systems, it is non truly available to the bulk of technology engineering pupils. The theoretical account component used as the simulation meat in SPICE for z-domain analysis is called theA storistorA [ 10 ] . It consists of conductances, a lossless transmittal line for hold effects, and controlled beginnings. In order to imitate the frequence response of something every bit simple as an planimeter, one is required to pattern every bit many as seven storistors, four capacitances, and an op-amp subcircuit. Give the long experience of many pupils and teachers with the SPICE plan, this might be an acceptable option. However, the size of the input files for even simple switched-capacitor circuits ( beyond the planimeter ) , together with the mathematics required to understand the z-transform, will likely discourage many from this approach.A

This paper will utilize a possibly less well-known simulation bundle called APLACi?”A [ 11-12 ] ( originallyA AnalysisA Program forA LinearA ActiveA Circuits ) . The APLAC plan has been under uninterrupted development since 1972. Since 1988, the Nokia Corporation, developers of radio communicating merchandises, has sponsored continued betterment in the system design and electromagnetic capablenesss of the APLAC plan. The peculiar strengths of the APLAC plan are its usage of object oriented programming techniques, which permit easy version of theoretical accounts to the circuit environment in which a constituent finds itself. Besides, the plan has a really extended library of system degree blocks, and the ability to pattern electromagnetic behaviour of components.A

For our present intents, one of the attractive forces of the APLAC plan is its usage of the whirl built-in to pattern circuits with both frequency-dependent and transeunt behaviours. This characteristic is of import for switched-capacitor circuits. The frequency-dependent parts of the circuit can be analyzed squarely. However, the frequence response of the time-dependent parts of the circuit ( such as switches and beginnings ) is calculated by making a frequency-domain equivalent circuit by agencies of the whirl integral.A

In the circuit of Figure 10, the following values of constituents and parametric quantities are used: A

These values give a resonant ( halfway frequence ) electromotive force addition of A0A = 10, a Q = 50, and a halfway frequence ofA A f0A = 20 kilohertz. The consequences of the simulation are shown below, in Figure 11.

Figure 11.A APLAC simulation of bandpass filter with addition, from Figure 10. From Probe tool of simulator, peak addition is 3.32 dubnium, and centre frequence is at f0 = 17.8 kilohertz.

The consequences show a fake addition of merely 3.3 dubnium, and the centre frequence is off by ~2 kilohertz. This inaccuracy is due to the usage of ideal MOS switches in the manus computations taking up to Eq.A A 16. The APLAC theoretical account for the switches assumes an RonA = 100A i?- , and an RoffA A = 100 ki?-.A A APLAC has the capableness to optimise the circuit ‘s constituent values to accomplish desired circuit behaviours.

## V. APPLICATION OFA MF-10A

The MF-10 is a cosmopolitan switched-capacitor filter supplied by National Semiconductor [ 1 ] . The MF-10 uses the two-integrator cringle construction to recognize lowpass, highpass, bandpass, notch, and allpass maps through externally chosen, distinct, resistances. The existent switched-capacitor planimeters are internal to the bit, while the external resistances give the user flexibleness in configuring his/her ain response. However, to take advantage of constituent tracking with temperature, etc. , all responses are designed to be maps of resistance ratios only.A A Figure 12 shows the summing amplifier and two-integrator cascade internal to each subdivision of an MF-10. The tunability of a peculiar filter ‘s critical frequence, A A , is determined by a logic degree applied to a 50/100/CL frequence ratio programming pin. In other words, the critical frequence will beA

A ; if the scheduling pin is tied to land, the factor is 100, otherwise, if tied to a HIGH ( positive power supply ) , the factor will be 50. Figure 12 shows how the notch, bandpass, and lowpass filter maps are realized by the MF-10. Because the summing amplifier is outside the two-integrator cringle, this constellation will be faster and let a greater scope of operating frequencies.A

The analysis of the transportation maps for the three transportation maps mentioned above follows the form in Eq. 13-14. By review, one sees thatA

## VI.A A A SWITCHED-CAPACITOR IMPLEMENTATION APPLIFIERA i‚?A LTC1043A

Although the initial drift for the development of the switched-capacitor was the chance and demand to synthesise active filters that would be compatible with MOSFET engineering, the early 1980 ‘s found many other utilizations for the switched-capacitor. Linear Technology has developed the LTC1043 [ 9 ] , which contains double switched capacitance webs, along with an on-chip non-overlapping clock generator, oscillator, and charge equilibrating circuitry. The clock generator controls both of the switch webs, while the charge equilibrating circuitry is designed to call off any effects due to isolated electrical capacity. The on-chip oscillator has a fixed frequence of 185 kilohertz. An external capacitance can be connected across pins 16 and 17 ( for the instrumentality amplifier ) to give any coveted clock rate. The coveted clock rate can be found fromA

A ; the 24-picofarad electrical capacity is the internal electrical capacity responsible for the oscillator ‘s fixed frequence. A

Among the circuits developed from the LTC1043 are instrumentality amplifiers, lock-in amplifiers for observing highly little parametric quantity displacements in detector applications, and signal conditioners for Pt opposition temperature sensors ( RTD ) , comparative humidness detectors, and LVDT ‘s. The instrumentality amplifier is a standard op-amp circuit presented in many electronics texts [ 5-6 ] , and is designed to magnify little difference signals such as might be found in measuring or transducer applications. At the same clip, common-mode or noise signals picked up by the lines feeding the amplifier must be suppressed, particularly as these signal degrees are frequently larger in amplitude than the sought-for difference signals. Figure 13 shows the LTC1043 combined with a standard non-inverting op-amp to give an instrumentality amplifier with a common-mode rejection ratio ( CMRR ) ofA A & gt ; 120 dubnium. Figure 14 shows the same circuit with the A? LTC1043 as a black box.

Figure 13.A Instrumentation amplifier utilizing A? of LTC 1043 switched-capacitor, along with LF356/353 op-amp in non-inverting constellation.

A The operation of this circuit is as follows. First, the double switch, when flipped to the left, charges the capacitance C1A up to the difference V1A – V2. Second, on the following clock pulsation, the switches will so dump the charge represented by that electromotive force difference onto C2. Third, the uninterrupted clocking from the oscillator will coerce C2A to finally develop a electromotive force equal to the difference electromotive force. Finally, the difference electromotive force, with the common-mode signal stripped off by the LTC1043 is amplified by the op-amp. It is interesting to detect several characteristics of this circuit and compare them to the standard instrumentality amplifier. By utilizing the capacitance C1A ( the alleged “ winging capacitance ” ) , the common-mode electromotive force nowadays at the inputs is looking into a capacitive electromotive force splitter, between the C1A and the LTC1043 ‘s parasitic electrical capacity. This parasitic electrical capacity is typically less than 1 picofarad, so the AC value of the CMRR is & gt ; 120 dubnium. By comparing, Analog Device ‘s AD624 instrumentality amplifier can travel every bit high as 130 dubnium for high additions, up to 60 Hz. Because of the capacitive electromotive force splitter from the LTC1043, this instrumentality amplifier shows higher CMRR, over a wider scope of electromotive force additions, and to a higher frequency.A A

## VII.A A CONCLUSIONSA

This paper has presented the necessities of operationA A of switched-capacitor webs, with a particular accent on its usage in planing active filters. Unlike active filters based on the conventional op-amp, switched-capacitor filters have critical frequences that are easy pin-settable. Furthermore, they require less power than the conventional op-amp based web because of their trust on CMOS engineering. Finally, for the functionality provided on a individual bit, they take up less room on circuit boards. Alternate usage of the switched-capacitor web in an instrumentality amplifier has besides been presented. The operation of this device is a small easier to digest for some pupils than treatment of active filters ; it is hoped that teachers and pupils can utilize the information herein to widen their familiarity with modern integrated circuits.A

The presentation of consequences here is in a signifier which teachers and high-level pupils in electronics engineering can accommodate to the course of study in engineering programs.A