current mode versus voltage mode

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 45, NO. 2, FEBRUARY 1998 173

Current-Mode Versus Voltage-Mode -Biquad Filters: What the Theory Says

Jirayuth Mahattanakul and Chris Toumazou,Member, IEEE

Abstract—As there is a growing interest in the design ofso called “current-mode filters,” this paper is concerned withan investigation into the general performance criteria and thespeed/dynamic range limits of current-modeGGGmmm-CCC based filters,compared to conventional voltage-modeGGGmmm-CCC filters. It is shownhere that, as far as speed, dynamic range, and power consumptionare concerned and provided that both kinds of filter topologyemploy the same type of transconductors and capacitors, theresult comes out in the favor of the use of the voltage-mode filterprocessing as a solution for realizing high performanceGGGmmm-CCCfilters.

Index Terms—Analog design, current-mode circuits, filters.

I. INTRODUCTION

RECENTLY, there have been attempts at applying current-mode techniques to various kinds of electronic circuit

design. Rather than representing the processing signal byvoltage quantities, the current-mode technique involves usingcurrent signals. Current-mode signal processing may be de-fined as the processing of current signals in an environmentwhere voltage signals are irrelevant in determining circuitperformance [1]. This may be the case for circuits that arespecifically designed to operate with low impedance nodessuch that voltage swings are small and time constants are short.However, the term “current-mode” has also be used to describea system which has a current transfer function [2]–[11]. This isparticularly true of the current-mode integrator and filter basedupon classical - realizations. In these current-mode filtersthe active element used in the circuit is the transconductor.However, to convert from a voltage-mode transfer functionto a current-mode transfer function the transconductors aresimply repositioned in the filters.

In this paper, we investigate and comprehensively comparethe general performance criteria and inherent fundamentallimits of the conventional voltage-mode - filter withrecent so-called “current-mode” filter approaches. We willpresent a detailed theoretical analysis of both types and discussadvantages and disadvantages.

Manuscript received December 18, 1995; revised July 23, 1996. This paperwas recommended by Editor J. Choma, Jr.

J. Mahattanakul is with the Mahanakorn University of Technology, Bangkok10530, Thailand.

C. Toumazou is with the Department of Electrical and Electronic Engineer-ing, Imperial College of Science, Technology, and Medicine, University ofLondon, London SW7 2BT, U.K.

Publisher Item Identifier S 1057-7130(98)01640-1.

Fig. 1. A second-order filter topology.

II. A REVIEW OF - FILTERS

Excluding direct realization, there are generally three meth-ods for realizing low-sensitivity designs of high-order filters,namely, the cascade approach, the multiple-loop feedback orcoupled-biquad approach, and the ladder simulation approach[12].

In the first two methods, the high-order function is factor-ized into subnetworks of second-order sections. The resultingsecond-order biquad network can be considered as an inter-mediate building block for high-order filters. As shown in theblock diagram of Fig. 1, the second-order filter itself is, in turn,composed of two integrators embedded in negative feedbackloops. As a result, most CT filters contain integrators as basicbuilding blocks.

Generally, four types of operational amplifier, namelyvoltage-controlled voltage source (voltage amplifier), voltage-controlled current source (transconductance amplifier),current-controlled current source (current amplifier),and current-controlled voltage source (transresistanceamplifier) exist. However, most work on high-frequencyfilters concentrate upon the transconductance amplifier. Todate, - filters are the most popular technique used inimplementing integrated high frequency continuous-timefilters [13]. Their popularity stems from the fact that thetransconductors are very easy to implement in monolithicform, transconductors generally have higher bandwidth thanoperational amplifiers, can be tuned electronically, and canlead to simple circuitry [14].

Fig. 2(a) shows a conventional - integrator whichcomprises a transconductor, used for converting an inputvoltage to a proportional amount of current, and an integratingcapacitor, used for integrating and converting the current backto voltage form.

A - second-order filter can be obtained by connectingintegrators of Fig. 2(a) in feedback as shown in Fig. 1. Atypical example is shown in the circuit of Fig. 2(b) whichsimultaneously provides both low-pass and bandpass output

1057–7130/98$10.00 1998 IEEE

174 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 45, NO. 2, FEBRUARY 1998

(a)

(b)

Fig. 2. (a) A voltage-modeGm-C integrator. (b) A voltage-modeGm-Cbiquad filter.

voltage. The integrator and the filter circuit shown in Fig. 2 area voltage-mode - integrator and a voltage-mode -biquad filter, respectively, for the reason that both of theirinput and output signals are represented by voltage quantities.

Alternatively, a typical - current-mode integrator andbiquad filter are shown in Fig. 3(a) and (b), respectively,in which now the input and output signals are currents. Itcan be seen that the circuit components of both the voltage-and current-mode circuits are essentially the same; the onlydifference being their ordering arrangement. As such, thecurrent-mode circuits of Fig. 3 could be classified as-integrators/filters as opposed to the - integrators/filtersof Fig. 2. Note that if transconductor and are excludedfrom the filters of Fig. 2(b) and (c), the resulting circuits areidentical, i.e., they become the core positive-feedback loopof the - oscillators which can provide either oscillatingvoltage (by tapping the voltage across or ) or oscillatingcurrent (by copying output current of transconductor or

).The voltage transfer function of the circuit of Fig. 2(b) and

the current transfer function of the circuit of Fig. 3(b) are thesame and given by

(1)

and

(2)

where is the transconductance function of the transcon-ductor , respectively.

Since the voltage-mode and the current-mode biquad filtersare essential the adjoint [7] of each other, the sensitivity and

(a)

(b)

Fig. 3. (a) A current-modeGm-C integrator. (b) A current-modeGm-Cbiquad filter.

the small signal operation at every frequency of both circuitsis the same.

The identical transfer functions also implies that the non-linearity of both circuits caused by the nonlinear characteristicof the transconductors and the capacitors should be the same.Therefore, we can expect that both circuits possess the samedegree of linearity.

Although both small and large signal operation of both filtertypes may be the same, some of the other important featuressuch as power supply voltage and current, power consumption,dynamic range, etc., will differ and it is these performancedifferences which are the subject of this paper.

A. Transconductor Considerations

The performance of a - integrator/filter relies heavilyupon the various characteristics of the transconductor em-ployed. The main focus in this section is on linearity andnoise of the transconductor since both of them have a majorinfluence on a dynamic range which is a very importantperformance criterior for the integrator/filter particularly forradio frequency (RF) applications.

The literature available on high frequency transconductordesign is exhaustive. We describe simple generic exampleshere purely for comparative purposes and not to presentstate of the art design. The circuits of Fig. 4(a) and (b)are transconductors which exploit the– characteristic ofthe bipolar transistor operating in forward active region andMOSFET operating in saturation region, respectively. Thetransconductance of these circuits is the transconductance ofthe driver transistors and can be varied by changing biascurrents.

The differential form of the transconductor of Fig. 4(a) and(b) are shown in Fig. 4(c) and (d), respectively. The advantageof using a differential structure is that the linearity of the outputsignal is improved by the absence of even-order distortion.

MAHATTANAKUL AND TOUMAZOU: - BIQUAD FILTERS 175

(a) (b)

(c) (d)

Fig. 4. Simple transconductor: (a), (b) single-ended circuit and (c), (d) differential circuit.

(a)

(b)

Fig. 5. (a) Transconductor design of [2] and (b) transconductor design of [3].

Various attempts can be made to increase the linearity ofthe transconductors of Fig. 4. However, since tradeoff betweenlinearity and speed/noise is common in transconductor design,

the more linear transconductor is more likely to be a low speedand noisy one. For example, the linearity of the transconductorof Fig. 4 can be improved by emitter/source degeneration but


(a)

(b)

Fig. 6. CCII-based transconductor.

at the expense of lower transconductance gain, lower speed,and higher noise.

Because of the simple structures, the - filters thatemploy the transconductors of Fig. 4 can operate at very highfrequency but obviously the distortion of their output signalwill be considerably high as well. This is the case for the high-frequency current-mode filter designs of [2] and [3] where thecurrent-mode integrator design of [2] and [3] are shown inFig. 5(a) and (b), respectively.

It can be clearly seen that the transconductor part of thecircuit of Fig. 5(a) is similar to the transconductor of Fig. 4(b),i.e., it consists of the metal–oxide–semiconductor (MOS)transistor(s) acting as a nonlinear– converters connectedto the current source(s).

In the circuit of Fig. 5(b), if – are assumed to beideal and almost perfectly matched (since there is a positivefeedback loop in the circuit and so if they are ideal andperfectly matched, the circuit will be dc unstable), it can beshown that the current flowing into the grounded capacitor is

and the actual circuit can be reduced to an equivalenttransconductor shown on the right of Fig. 5(b). Therefore thesimilarity of the transconductor part of the circuit of Fig. 5(b)and the transconductor of Fig. 4(a) can now be seen.

The design of current-conveyor (CCII)-based filters havebeen proposed in many research publications. Some of them[5], however, are nothing more than - filters in disguise.Essentially a CCII with a resistor on its terminal is atransconductor. Fig. 6(a) and (b) shows two ways of connect-ing a resistor with a CCII to form transconductance blocks.The basic schematic of the CCII itself is shown in Fig. 7.

1) Transconductor Linearity:Theoretically, the transcon-ductance gain of the transconductor should remain constantregardless of the level of the input voltage. However, inpractice this is only the case for a certain level of input voltage.Beyond that level the transconductance gain tends to deviate,i.e., the output current is not linearly dependent on the inputvoltage anymore. This will result both in an output signal

distortion and an amplitude-dependent transconductance [13].Thus to avoid these problems, the level of the input voltagemust be kept small enough so that the transconductor exhibitslinear – conversion.

For example, when the transconductor of Fig. 4(d) is drivenby a pair of balanced signals, its transconductance gain can befound to be

(3)

where is the amplitude of the input voltage and , thesmall-signal transconductance gain, equals .

It can be seen from (3) that only when is muchsmaller than , the transconductance gain of thecircuit is largely independent of . Under such conditions,the dominant harmonic distortion of , HD3, can be foundto be

HD3 (4)

where where is the amplitude of theoutput current. Similarly when the transconductor of Fig. 4(c)is driven by a sinusoidal input voltages which is small enoughto make the transconductance gain, ,the dominant harmonic distortion of the output current can beexpressed as

HD3 (5)

Also when the CCII of Fig. 7(b) is directly used as a transcon-ductance amplifier ( and ) and issinusoidal and restricted to a small value so that

, the dominant harmonic distortion of its outputcurrent is

HD3 (6)

The implication of (4)–(6) is that the ratio between the peakamplitude of the output current and the bias current, plays animportant role in dictating the level of distortion of the outputcurrent. However, apart from the limited bias current, the levelof power supply voltage also has an impact on the linearityof the circuit. This usually occurs when the voltage headroomof any circuit node approaches zero and the signal becomesclipped and distorted, e.g., in the case of the- integratorof Fig. 2(a) when it is driven by a low-frequency voltage.However in the circuits of interest, i.e., the biquad filtersof Figs. 2(b) and 3(b), when single-stage transconductors areemployed the ratio of the output current to bias current isthe main factor of distortion. In these circuits the level ofpower supply voltage plays much less of a role in dictating thelinearity of the circuit since the signals will be highly distortedby the limited bias current long before the voltage at any nodereaches the level of supply voltage. The above discussion canbe confirmed by firstly considering the graphs of Fig. 8 whichare the plots of HD3 versus derived from (4) to (6). Sinceevery nodes in the biquad filters of Figs. 2(b) and 3(b) arealso the input terminal of the transconductor elements, it can


(a) (b)

(c)

Fig. 7. (a) Basic schematic of CCII, (b) using single transistor, and (c) using mixed translinear loop (class AB complementary).

Fig. 8. Plot of jVinj versus HD3 of the transconductors of Fig. 4(d) [using (4) withIBIAS = 100 �A, k0= 100 �A/V2, andW = L], Fig. 4(c)

[using (5)] and Fig. 7(b) [using (6)].

be seen from Fig. 8 that the voltage level of these nodes haveto be restricted to a relatively much smaller value, comparedto the usual supply voltage level, to keep the level of distortionof signal in a reasonable range.

The conclusion is therefore that the level of supply voltageis not a main limited factor of the linearity of these circuitssince the output current of the transconductor usually drivesthe device out of the linear region well before voltage limits

start to dominate. Although the above conclusion is the resultof the analysis of the transconductor circuits of Fig. 4(c) and(d) (class A) as well as the transconductor circuits of Fig. 7(b)and (c) (class AB), we believe that it is generally true for anysingle-stage transconductor.

2) Review of Instantaneous Companding and Lineariza-tion Technique:Recently, there has been interest in a newfamily of current-mode filter topologies based upon so-called


log-domain processing originally proposed by Adams [15].The technique is particularly attractive since first it is thelarge-signal transfer function of the filter that is linearizedand not the individual transconductance elements as would bethe case in more classical - based filters. Second, suchlinearization is based upon direct exploitation of the nonlinearcharacteristic of the device, in this case the p-n junctionof a silicon diode. Furthermore Frey [10], [16] ingeniouslyshowed that the large-signal characteristic of the bipolar-junction transistor (BJT) can be directly utilized to synthesizethese log-domain filters by mapping from state-space lineardifferential equations. BJT technology is employed becauseof its unique – exponential relationship, which is used asthe state variable, together with the use of the well-knowntranslinear circuit principle for global current transfer functionlinearization. Seevinck has also shown a BJT realization ofthis class of integrator, but referred to it as a compandingintegrator [11] based upon earlier work reported by Tsividiset al. [17]. In these integrators, companding describes thelinearization mechanism in which signals are first compressedto a intermediate integration node and then subsequentlyexpanded (companding). Tsividis [18] has classified this groupof integrators as belonging to the “instantaneous compandingintegrators” type. The definition instantaneous was used todistinguish between syllabic companding in the classical com-munication systems. Since a linear transconductance elementcannot be elegantly realized by using– exponential charac-teristics straightforwardly, then the instantaneous compandingtype filter is thus suitable for BJT, as well as weak inversionMOS, and this ties in well with the literature where mostrecent work has actually concentrated on this class [19]–[25].Essentially “log-domain” integrators/filters exploit the factthat BJT technology can elegantly be employed to realizelinear current transfer functions based upon translinear loops.However, we believe that if a linear transconductor can bedirectly realized, the more classical - filter synthesismethods should be employed and our analysis in the followingsections would, therefore, be relevant. This seems to beparticularly true for MOS realizations where in fact varioustechniques exist for transconductor linearization based on thesquare-law characteristic of FET [26]–[31].

3) Transconductor Noise:Noise is another limitation onthe dynamic range of the transconductor. Any transconductorcan be represented as a noiseless device accompanied byequivalent noise sources (Fig. 9). Generally, the noise sourcescan be expressed as voltage and current noise

(7)

(8)

where is Boltzman’s constant and is absolute temperatureand by neglecting noise generated by the biasing circuitry,the value of , the voltage noise factor and the currentnoise factor of the previous transconductors can be foundin Table I.

It can be seen from the above table that, in any case,is always much larger than . There are other kinds of

Fig. 9. Transconductor with equivalent noise sources.

Fig. 10. Voltage-modeGm-C biquad filter.

TABLE IVOLTAGE NOISE FACTOR AND CURRENT NOISE

FACTOR OF VARIOUS TRANSCONDUCTORS

transconductor which are and are not based on the abovecircuits. Most transconductors are developed to overcome theproblem of nonlinearity and poor tunability. Although manyof them are likely to conform to (7) and (8), some may not.However, for ease of analysis in the following sections, wewill restrict our interest only in the transconductors that haveequivalent noise sources that can be approximated by (7) and(8).

B. Analysis of Voltage-Mode - Filter

Fig. 10 shows a voltage-mode - biquad filter, equiva-lent to the circuit of Fig. 2(b). For convenience if the transcon-ductance function of every transconductor is assumed fre-quency independent, i.e., , it can be shownthat

(9)

(10)


where

and

1) Signal Handling Capability versus Power ConsumptionAnalysis: In this section, we will consider the relationshipbetween the signal handling capability and power consumptionof the voltage-mode - biquad filter. Since all nodalvoltages and branch currents shown in the circuit of Fig. 10can be expressed as a function of complex frequencytheamplitude of these signals are thus varied with the frequency ofthe input signal and will reach a maximum value at a particularfrequency. The maximum amplitude of these signals can beexpressed as

ifif

ifif

(11)

where is the amplitude of the input voltage,

and

Note that (11) is derived from the assumption that all thetransconductors exhibit infinite bandwidth. However, (11) isstill a good approximation in the more practical case wherethe bandwidth of each transconductor is much higher than.

As discussed in Section II-A-1, to avoid excessive outputsignal distortion and amplitude-dependent effective transcon-ductance, the ratio between the peak amplitude of outputcurrent and the bias current,, of each transconductor shouldbe kept small. If of every transconductor in the circuitof Fig. 10 is assumed to be equal, the quiescent powerconsumption of the circuit, , can be expressed as

(12)

where is the level of supply voltage of the circuit.By using (9)–(12), we obtain

(13)

where

if

if

As an alternative to (13), can also be expressed as

(14)

where

if

if

As discussed earlier, one can improve linearity of thetransconductors by decreasing, however according to (13)and (14), the power consumption of the circuit will be in-creased. Thus the tradeoff between power consumption andlinearity is evident.

Also it can be seen from (13) and (14) that one can lowerby reducing supply voltage, . However, is requiredto be high enough to guarantee that all the active devices in thetransconductors are operating in the appropriate region. Lateron, (13) and (14) will be used in determining the relationshipbetween the quiescent power consumption and the dynamicrange of the filter.

2) Noise Calculation:Fig. 11 shows the voltage-modebiquad filter of Fig. 5 with the inclusion of equivalent

input noise-voltage and noise-current generators for eachtransconductor. From the circuit of Fig. 11, with the inputnode grounded, by using (7) and (8) it can be shown thatthe total equivalent voltage output noise at nodes 1 and 2is given by

(15)

where

and

(16)

where

It can be seen from (15) and (16) that the noise of the filteris inversely dependent on the value of the effective capacitor,

, of the filter.


Fig. 11. Voltage-modeGm-C biquad filter with noise sources.

3) Dynamic Range Consideration:Dynamic range of a cir-cuit is defined as the ratio of the maximum and minimumsignal level which the circuit can handle at the same time.The minimum signal level is determined by the noise of thecircuit, the maximum level by distortion [32]. Mathematically,the dynamic range can be expressed as

DRsignal

noise(17)

where signal is the magnitude of the output signalwhen its THD reaches %.

Regarding the low-pass output voltage, the dynamic rangeof the circuit of Fig. 10, DR , can be expressed as

DR (18)

Combining (14), (16), and (18) yields

DR(19)

For the bandpass output voltage, the dynamic range of thecircuit of Fig. 10, DR , can be expressed as

DR (20)

Combining (13), (15), and (20) we get

(21)

And clearly we see the interactive relationship between power,speed, and dynamic range.

C. Analysis of Current-Mode - Filter

Fig. 12 shows a current-mode - biquad filter equiva-lent to the circuit of Fig. 3(b) where in [2], transconductorsare of the type in Fig. 4(a). Again if the transconductors areassumed frequency independent, i.e., , it can beshown that

(22)

(23)

where

and

1) Highest Signal Handling Capability versus Power Con-sumption Analysis:By following the procedure outlined inSection II-B-1, we find that

(24)

where

if

if

or alternatively,

(25)

where

if

if

2) Noise Calculation:Fig. 13 shows the current-modebiquad filter of Fig. 12 with the inclusion of an

equivalent input noise-voltage and noise current generatorsof each transconductor.

So far, in the voltage-mode case, the transconductors areassumed to be frequency independent and the output noiseis calculated by integrating the noise spectrum from zero


Fig. 12. Current-modeGm-C biquad filter.

Fig. 13. Current-modeGm-C biquad filter with noise sources.

to infinity (excluding flicker noise). However if the same isapplied to the transconductor of the current-mode -filter of Fig. 13, the total output noise currents contributed bythe noise source would be infinity.

To avoid this, we need to limit the integrating frequency toa finite value. Also, in order to produce a more precise answer,parasitic effects of the transconductor should be includedinto the calculation. Yet this would make the noise calculationmuch more complicated. Hence in order to obtain a reasonableanswer without introducing unnecessary complexity, the noisespectral density of the noise sources insideof Fig. 13 willbe integrated up to a frequency well aboveyet lower thanthe frequency where stray parasitics take effect.

Hence by using (5) and (6), letting whereis the upper bound integrating frequency for the noise sourcesinside and assuming that in the frequency range below,each noise source in is constant as a function of frequency,it can be shown that the total noise currents of the circuit ofFig. 13 is given by

(26)

where

and

(27)

where


It can be seen from (26) and (27) that the output noise currentsdepend heavily on , the upper bound integrating frequency.Note that (26) and (27) are not valid for too high a value of

, which is the case when not all noise sources insidearea constant function of frequency.

3) Dynamic Range Consideration:For the low-pass outputcurrent of the circuit of Fig. 12, the dynamic range DRcanbe expressed as

DR (28)

if

if

if

if

and according to (24)–(27),

if

if

if

if


TABLE IIFIGURE OF MERIT,F OF VOLTAGE-MODE AND CURRENT-MODE Gm-C FILTERS

Combining (24), (26), and (28), we get

DR(29)

For the bandpass output current, the dynamic range of thecircuit of Fig. 8, DR , can be expressed as

DR (30)

Combining (25), (27), and (30) yields

DR(31)

D. Comparison Between Voltage-Mode andCurrent-Mode Biquad Filter

In order to compare the current-mode to voltage-modebiquad filter, each filter will be represented by an appropriatefigure of merit, defined as

DR(32)

The figure of merit is simply a measurement of the effi-ciency of the filter since it encapsulates the dynamic rangewhich represents the range of signal levels for which the filterwill perform properly, which represents the speed, andwhich is the power required by the filter to achieve such DRand .

Thus by using (32) along with (19), (21), (29), and (31),Table II is constructed, where according to (13)–(16), theequations and are shown at the bottom ofthe previous page. Fig. 14 shows an example of the contourplot of the ratio between the figure of merit of the current-mode over the voltage-mode biquad filter when, the ratiobetween the upper bound integrating frequency over, equals10, and are unity and assuming that

.It can be seen in Fig. 14(a) and (b) that, in both low-

pass and band-pass cases, in the specified range of gain and, - is always larger than - which

concludes that the voltage-mode - biquad is the higherperformance design.

E. Simulation Results

In order to verify our analysis, the voltage-mode low-passfilter of Fig. 10 and the current-mode low-pass filter of Fig. 12were simulated (using BNR 0.8 m BiCMOS technologyparameters) and the results compared. In both circuits,

pF were used and all the transconductor blocks arerealized from the transconductor circuit of Fig. 4(d) (with oneinput node grounded) where the dimension of each MOS andthe bias current of each transconductor block are chosen in a

TABLE IIIDIMENSION OF MOSFET AND BIAS CURRENTS USED IN THE SIMULATION

way that of every transconductance block is equal. Table IIIshows the dimensions of each MOSFET and the bias currentof each transconductor block.

Both circuits are designed to have a second-order low-passcharacteristic with dc gain of 1, of 10 and of 3 MHz.The simulation results of both circuits are shown in Fig. 15and Table IV.

The plots of Fig. 15 illustrate that the linearity of both typesof simulated filters are effected by the ratioin the same way,i.e., when the ratio of both circuits are equal, they possessa comparable degree of linearity. It can also be shown thatwhen the ratio of both types of filters are the same, thevoltage across capacitors, and , between both circuitsare also equal and hence the distortion of the output signals ofboth circuits are comparably dependent on the level of suchvoltages. This is an important observation since it suggeststhat, for the same level of output distortion, voltage swingsacross capacitors are the same for both current and voltagemode filters based upon - topologies.

According to Table IV, the output noise of the voltage-modefilter is relatively the same whether the upper bound integrationfrequency is 30, 100, or 500 MHz. This stems from the factthat the magnitude response of all noise sources in such acircuit are shaped down at high frequency by the feedbackmechanism. However, as seen from Table IV, this is not thecase for the current-mode filter since the output transconductor

of the circuit is not in the feedback loop and hence themagnitude response of its noise sources are not shaped downat high frequency by feedback.

Table V shows the comparison between the calculated andsimulated values of - - where thecalculated values obtained from using Tables I and II and thesimulated results from Table IV.

As expected, as the upper integration frequency increases,

- is relatively more larger than - . Alsoan error between the calculation and simulation results growsas the upper integration frequency increases. This stems fromthe fact that when the upper integration frequency is too high,our analysis of the noise of the current-mode filter will give aless precise answer (see Section II-C-2).

F. Conclusion and Discussion

We have performed an analysis on various aspects ofthe biquad - filter, namely, signal handling capacity,power consumption, noise, and dynamic range. Based on theseproperties, the figure of merit function has been developed andit is found to be heavily dependent on the value of gain and

of the filter.As implied by the plots of Fig. 15, the voltage-mode filters

of Fig. 10 and the current-mode filters of Fig. 12 possess a


(a)

(b)

Fig. 14. The contour plots ofFcurrent-mode=Fvoltage-mode of theGm-C biquad filter: (a) low-pass:Fcurrent-mode=Fvoltage-mode = V �2V

= I �2I

and (b) bandpass:Fcurrent-mode=Fvoltage-mode = V �2V

= I �2I

.

comparable degree of linearity when the ratioof both circuitsare equal. This should also be true even in the extreme casewhen the signal clipping caused by the limited power supplyvoltage level occurs. Since, as mentioned in Section II-E, thedistortion of the output signals of both circuits are comparablydependent on the level of the voltages across the integratingcapacitors, then the clipping of these voltages would effectthe distortion of the output signals of both types of circuitsin a similar manner. Therefore, in general, the linearity ofboth circuits should still be relatively the same even when theclipping occurs. Consequently, although the argument withinthis paper is based upon the assumption that nonlinearity inthe transconductance amplifier is dominated by the magnitude

of the output current and its relationship to the bias currentlevel and not by the voltage clipping induced by the limitedpower supply voltage, our argument should still be valid inthe clipping case.

It can be seen from Fig. 14 that, over a wide range ofgain and , the voltage-mode filter outperforms its current-mode counterpart, at least in terms of our figure of merit.This stems largely from the fact that none of the equivalentnoise sources of the transconductor employed in the voltage-mode filter topology directly contributes to the output signal,i.e., the bandwidth of the output noise signal is shaped downby the filter topology. This is, however, not the case forthe current-mode filter where the equivalent noise source of


Fig. 15. The plots of� versus the simulated THD level of the output signals of the voltage-mode filter of Fig. 10 and the current-mode filter of Fig. 12(the ratio � is varied by changing the level of the input signals).

TABLE IVSIMULATION RESULTS OF THEVOLTAGE-MODE FILTER OF

FIG. 10 AND THE CURRENT-MODE FILTER OF FIG. 12

TABLE VCALCULATED AND SIMULATED VALUES OFFcurrent-mode=Fvoltage-mode

its output transconductor directly contributes to the outputsignal. This should also be true in the case of the-oscillators mentioned in Section II since, in a current-mode

- oscillator, the oscillating output current is obtained byconnecting a transconductor to the capacitor node and the noisesource of this output transconductor also directly contributesto the output signal.

In general the assumption has been that the linearity ofthe voltage-mode filter is the same as the current-mode. Inthe literature current-mode implementations actually use singlenonlinear devices for the transconductor [2] and so the strengthof this comparison is based upon classical voltage-mode

- topology also using similar nonlinear transconductors.As such it is clear from this work that for the same linearity,voltage-mode filter processing would be the overall higherperformance filter topology. Although this paper has beenrestricted to the more general - based filter topology, intheory the conclusion should apply to all realizations of-based biquad filters, for instance the ones that employ multipleoutput OTA [2], [6] since such OTA’s would simplify the

filter design similarly for both voltage-mode and current-modefilters.

ACKNOWLEDGMENT

The authors would like to acknowledge the referees ofthis paper who helped us improve the paper enormously.The authors would also like to thank Prof. Paul R. Gray ofUniversity of California, Berkeley, for his encouragement andvaluable discussion.

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Jirayuth Mahattanakul received the B.E. (elec-tronics) degree from King Mongkut’s Institute ofTechnology, Ladkrabang, Bangkok, Thailand, in1990 and the M.Sc. degree in electrical engineeringfrom Florida Institute of Technology, in 1992.

From 1992 to 1994, he was a planning engineerfor Telecom Asia Corp., Thailand. Since 1994,he has been with Mahanakorn University ofTechnology, Bangkok, Thailand and is currentlyworking toward the Ph.D. degree at ImperialCollege of Science, Technology, and Medicine,London, U.K.

Chris Toumazou (M’87) is the Mahanakorn Profes-sor of Analog Circuit Design in the Department ofElectrical Engineering, Imperial College, London,England. He received the B.Sc. degree in engineer-ing and the Ph.D. degree in electrical engineeringfrom Oxford Brookes University, Oxford, England,in 1983 and 1986, respectively. Chris is a mem-ber of the IEE Professional Group E10 Committeeon Circuits and Systems (U.K.) and was recentlyelected to the steering committee for the EuropeanNEAR program (Network for European Analogue

Research). He is also a member of the Analog Signal Processing Committeeof the IEEE Circuits and Systems Society for which he was Chairman(1992–1994) and is also Member of the Circuits and Systems Chapter ofthe U.K. and Republic of Ireland Section of the IEEE. Dr. Toumazou is alife member of the Electronics Society of Thailand. His research interestsinclude current-mode analogue signal processing, high frequency, low poweranalogue integrated circuit design in bipolar CMOS and GaAs technology andArtificial Intelligence applied to analogue circuit design. He is a co-winner ofthe IEE 1991 Rayleigh Best Book award for his part in editing “Analog ICDesign: The Current-Mode Approach” and is also the recipient of the 1992IEEE CAS Outstanding Young Author Award for his work with Dr. DavidHaigh on High Speed GaAs opamp design, as well as a co-winner of the1995 IEE Electronics LettersBest Paper Premium Award. He has also editedand contributed several chapters to various books in the field of analogue ICdesign, has authored or co-authored more than 180 technical publications inthe area and holds four international patents. Dr. Toumazou is an AssociateEditor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, PART II. Hewas also recently elected as Vice-President for Technical Activities for IEEECircuits and Systems Society.

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