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Evaluation of Single op-amp Topologies For Extremely Narrow Band-Pass Filter Design
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Evaluation of Single op-amp Topologies For Extremely Narrow Band-Pass Filter Design

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Narrow Band pass filtering techniques have been a challenging task since the inception of audio and telecommunication applications. The challenge involves keeping Quality factor, gain and......

Narrow Band pass filtering techniques have been a challenging task since the inception of audio and telecommunication applications. The challenge involves keeping Quality factor, gain and mid-frequency of the filter independent of each other. Other most important aspect is keeping the filter stable, keeping mid-frequency immune to circuit component tolerances and to achieve the mid-frequency at the accurate value. The requirements turns more stringent when working with low frequency Narrow band-pass filters where even the shift in few Hz would cause great frequency errors. The selection of right topology for best performance is the key to successful design. This paper objectively compares the relative performance of popular single op-amp narrow band-pass topologies.

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  • 1. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 1Evaluation of Single op-amp TopologiesFor Extremely Narrow Band-Pass Filter DesignRAMAN K. ATTRICertified Engineering Manager / International Project ManagerRkattri@rediffmail.comAbstract: Narrow Band pass filtering techniques havebeen a challenging task since the inception of audio andtelecommunication applications. The challenge involveskeeping Quality factor, gain and mid-frequency of thefilter independent of each other. Other most importantaspect is keeping the filter stable, keeping mid-frequency immune to circuit component tolerances andto achieve the mid-frequency at the accurate value. Therequirements turns more stringent when working withlow frequency Narrow band-pass filters where even theshift in few Hz would cause great frequency errors. Theselection of right topology for best performance is thekey to successful design. This paper objectivelycompares the relative performance of popular single op-amp narrow band-pass topologies.Indexing Items: Filters, Band-pass filter, Narrow band-passfilter, Quality factor, Filter topologies, Multiple Feedbackfilter, Sallen-key Filter, Deliyaanis Filter, Active Twin-T filterI INTRODUCTION:Band-pass filter design has nevertheless been achallenge in view of many interrelated dependenciesin the circuit parameters. In Band-pass filter, qualityFactor (Q) and mid frequency Gain (Am) of the filter aregenerally inter related and thus do not give theindependent control. Always there have to be somedesign tradeoffs. Broadband pass filters are quite easyto integrate and designer is at ease to pick up any ofthe topology mostly one-amp topology, perform fewcalculations and design the filter. The designrequirements in broad band pass filter design aregenerally not stringent, so it is easy to design suchfilters without worrying that designing a filter couldbecome another serious project too. But in case ofnarrow band-pass filter the circuit stability poses somedifficult requirements. At raw level, designing a narrowband pass filter can simply be thought of as process ofincreasing the Q value of the normal broad Band-passfilter by changing the key component value whichcontrols the Q. But question is which element? Quitesurely designer will be able to spot the key elementcontrolling the Q value, but is it sure that changing Qvalue is not going to affect other parameter badly?This paper explores the possibility of designing suchsingle op-amp based extremely narrow band-passfilter.The higher Q value creates circuit instability,oscillations and makes the circuit very sensitive to thecircuit component tolerances. If we are trying todesign an extremely stable narrow band-pass filterworking at low frequency where even a 1% errormeans a big deviation. For designing such filter havingvery high Q value and still having nominal gain, thedesign restrictions would mount up. The goal of suchan accurate narrow band-pass filter of course wouldbe to peak at exact desired mid frequency with anaccuracy of +5Hz thus detecting only the desiredfrequency within a narrow bandwidth and rejectundesired frequencies outside this window. It is worthmentioning that in narrow band-pass filter, thebandwidth parameter just indicates the total span of3db down points on both sides of the mid frequencycurve and does not indicate if the mid-frequencyoccurs at the desired value or not. Since the Q value isratio of mid-frequency with the band-width, aparticular value of the Q will impose restrictions onachieving calculated bandwidth. Thus desired Q valuecan be achieved by limiting the bandwidth parameter,but do the circuit peak exactly at the said mid-frequency? This is the key performance parameter ofsuch circuits. Another challenge in such designs wouldbe that can we keep the mid-frequency stable andinsensitive to component tolerance values?This seemingly easy task itself becomes so criticalbecause circuit’s ability to accurately peak at desiredfrequency with an accuracy of + 5 Hz with a narrowband-width of 10-20Hz around this peak mid-frequency and to reject the rest of the frequencydetermines the success of the design. The circuitwould be required to peak exactly at the definedfrequency in such cases. The critical applications ofsuch requirements are numerous ranging fromtelephony, communication and many more.While searching for narrow-band filter designdocuments, one would find that only a limitedliterature is available for comparison of various filterperformances so as to enable a designer to selectquickly the topology best suited for his applications. Inthe absence of such literature one has to resort to
  • 2. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 2simulating all the topologies and end up wasting lot oftime. The selected topology also sometime does notperform very well practically in view of manyconsiderations which are generally not documentedand comes with experience only.Practical Challenges in making a Narrow band passfilter circuit are numerous. The required Q value,mid0frequency Gain and the accuracy needed inpeaking at centre frequency determine the practicalchallenges that we may encounter. Thus a seeminglyeasy challenge turns a real design challenge in theabsence of right kind of bench marked comparisons.This tempted me to write this paper.In this paper an objective comparison of performanceand design considerations of various single op-amptopologies suitable for making the extremely narrowband-pass filter and the guidelines for selection ofbest filter topology are being highlighted. An effort toconsolidate the observations from various sourcesrelated to each topology has been done. Thedescription has been concentrated on relativecomparison of various single op-map topologies,guidelines for selecting right topology and tips forcomponent selection for narrow band pass filterdesign. It is assumed that the reader is having basicunderstanding of filters. The following discussion isexclusively applicable to narrow band-pas filters wherethe mid-frequency is few hundreds of hertz. However,the same can be applied to the design of higherfrequency filters as well since those generally tolerateloose accuracy specifications unless strictly needed byany specific application.II DESIGN REQUIREMENTS FOR LOW FREQUENCYEXTREMELY NARROW BAND-PASS FILTERS:The narrow band-pass circuit would be required todetect a particular frequency. As an example, let usassume that we are required to design a narrow-bandfilter which detects a tone of 627 Hz frequency (a lowfrequency, where a 1% error in centre frequencymeans a shift of 6 Hz on either side, thus defeating thedesign purpose). The discrete frequencies in rangefrom 500Hz to 1000Hz are normally used in telephonywire tracing equipments and can be sent on workingor non-working pairs. Normally odd frequency whichare not multiple of 50 or 60Hz harmonics are chosen.The choice of such frequency is generally as per thesuitability of the manufacturer. The frequencies aregenerally kept low, so that deviation is also low. Thesuccess of such instrumentation is dependent uponaccurately detecting the injected tone. Such a detectorcircuit would filter out all the rest of the frequencies bysubstantial attenuation. The general designrequirements for such single tone detector circuitswould include all or some of the followingdependending upon the application:a) High overall Q value (Q = 25 to 50)b) Gain should not be very high (G=5)c) Bandwidth less than 20Hzd) Centre frequency: 627Hze) Accuracy & stability of mid-frequency: + 1 % (+ 6Hz max)f) Single supply (+5V) operationg) Roll-off of minimum 12 db per decade on eachside of the centre frequencyh) Power supply Harmonics Rejection(600Hz, 650Hz,660Hz multiples of 50/60Hz around centre freq))i) Use not more than 2 discrete IC chips (fewer thebetter)j) Low cost circuitk) Independent adjustment of Q without affectingcentre frequencyl) Independent adjustment of gain without affectingQThe last two requirements are very stringent. Theseseem so easy, but in actual practice most of the filtersexhibit strong Q and Gain relationship that changingone will either change other parameter or will shift thecentre frequency of the filter.The circuit is required to detect a tone of 627 Hzaccurately, to provide a high gain at centre frequency.The bandwidth of 10-20Hz is selected to ensure thepower supply harmonics to filter out along with otherundesired frequencies. The nearest harmonics of 60Hzpower harmonics is 600Hz and 660Hz and that of 50Hz is 600Hz and 650Hz. Suchconsideration/requirements ensure that we do notneed to worry about AC harmonic noise. Maximum 10Hz bandwidth can be allowed on either side of themid-frequency to ensure more than 20 db attenuationto nearest harmonics 600Hz and 650Hz frequencies.Above requirement of filtering the harmonics alsoneeds a steeper roll-off from 3db points. The roll-offrequirement needs a minimum 2ndorder filter. Theresponse type (viz. Butterworth, Chevyshev, Elliptic,Bessel) does not matter for the band-pass filter, sinceit has extremely narrow band. However the filtershaving low pass and high pass stages cascaded to getthe band-pass function may be Chevyshev or elliptic
  • 3. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 3(mind the ripples in pass band & attenuation band) forsteeper roll-off .The first requirement of having high Q poses anotherproblem of choosing a right op-amp. With High Q, theop-amp gain bandwidth product GBW can be easilyreached, even with the gain 20dB. At least 40dB ofheadroom should be allowed above the centrefrequency peak [1]. Op-amp slew rate should also besufficient to allow the waveform at centre frequency toswing to the amplitude required.Single supply requirements should be obvious as,most the electronics circuits and particularly hand-heldunits work on batteries and requires operation fromsingle supply.What makes the Single op-amp configurationattractive to designer? They may cost less, may requirefewer passive components, occupy less space onboard and could be tested easily. As a designer, ourfirst preference would have been choosing a singleop-amp topology. But single op-amp topology isassociated with so many other design considerationswhich are not obvious right in the beginning. Thepaper is intended to address the non-obvious designproblems and performance considerations of suchsingle op-amp topologies.When working with high Qs one must be very carefulwith layout and component selection. This is becausehigh Q circuits have a tendency to exhibit instabilitywith slight component mismatch. They also are morelikely to oscillate due to this instability [2].III OPTIONS AVAILABLE FOR FILTER TOPOLOGIESA simple survey on internet would reveal that there areso many topologies for designing the filters [3] [4].However the textbooks have very limited literature onall of these topologies. Many more complextopologies are being evolved regularly, but some ofthe topologies have their established base in popularapplications. At the beginning of the design, adesigner would have many options of topologieswhich may potentially be used to design the narrowBand-pass circuits. The few of the options are beingenumerated here. Only those options have beenreviewed and analyzed which could be driven by singlesupply and employ single op-amp. To sum up, thereare single op-amp, two op-amp as well as three orfour op-amp topologies available to the electronicsdesigners.SINGLE OP-AMP TOPOLOGIESa) Sallen-keyb) Multiple Feedback (MFB)c) Deliyannisd) Active Twin-TTWO OP-AMPS TOPOLOGIESe) FliegeTHREE & FOUR OP-AMPS TOPOLOGIESf) State variableg) Biquadh) Tow-Thomas Biquadi) Akerberg-Mossberg Biquadj) KHN Topologyk) Berka-Herpy toplogyl) Michael-BhattacharyaThe discussion has been limited to basic one op-ampfilter topologies only. The filter topology derivativesand 2 as well as 3 op-amp topologies are notdiscussed in this paper, which in itself require quitedetailed considerations, worth addressing in aseparate design paper. The suitable single supplydriven single op-amp topologies options a designermay have are: Sallen Key, Multiple Feedback, ActiveTwin-T and Deliyannis. The considerations related toeach topology would be addresses one by one.A. Sallen-key TopologyAt first glance this topology appears very attractivesince it use only one op-amp and a few passivecomponents. This is obviously the simplest and themost popular topology for which a large amount ofliterature is available in the text books and is easy tointegrate quickly [1] [5]. The Sallen-Key topology isone of the most widely-known and popular second-order topologies. It is low cost, requiring only a singleop amp and four passive components to accomplishthe tuning. It employs two RC filters in successionconsisting of 3 resistors and 2 capacitors with one op-amp as shown in the figure [1].The performance is generally very predictable. Atransfer function equation can be derived and givesthe values of parameters in terms of componentsvalues as under [1]:
  • 4. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 4Fig [1]: Sallen-key Band-pass Circuit with dual supplyWhere fm is the mid frequency, Am is the gain at midfrequency, G is the Inner feedback gain of the op-amp,Q is the filter qualityIt is obvious from the above equations that midfrequency gain is very much dependent on feedbackgain and feedback gain is dependent on value of thefeedback resistor. To find the feedback resistor value,either set a fix value of Am or fix the value of Q.To set frequency of the band-pass, fm is specified tocalculate R as under with equal value of Capacitors C.Because of dependency between Q and Am, there aretwo options to solve for R2: either to set the gain atmid-frequency:Or to design for a specified Q:So the Sallen-key circuit has the advantage that thequality factor (Q) can be varied via inner gain Gwithout modifying the mid frequency.A drawback is, however, that Q and Am can not beadjusted independently because both are dependentupon the inner gain G. For example fixing G=2 willgive Am=2, Q= 0.5 and if we want to have high Q letsus say equal to 10, then G=2.9 and Am will be 29.Fig [2]: Frequency response of SK BPF filter G=2.95,Am=14, Q=3, BW=200Hz, Fm=627HzOne can obtain a limited maximum Q value, as shownin Fig [2], in this circuit and thus is not recommendedfor applications that need a high Q. For a single op-amp Sallen-Key filter, the Q is typically around 5 or so[6]. Further this generally works best when gain is nearor little greater than 1 and Q is less than 3. Changingthe gain of a Sallen-Key circuit also changes the filtertuning and the style. It is easiest to implement aSallen-Key filter as a unity gain Butterworth. Generallyit gives high gain accuracy with unity gain [7].Another drawback is that the gain of this circuit isrelatively low (-3Q) compared to the minimumrequired open loop gain of the amplifier (90Q2). Thismeans that the GBW product of the amplifier must besignificantly higher than the maximum cutofffrequency of the filter resulting in requiring a higherperformance amplifier than expected to ensure it doesnot adversely affect the filter response [6].One more restriction on its use is that it works only inNon-inverting configuration. It exhibit greater chancesof oscillation when G approaches 3, because then Ambecomes infinite and causes circuit to oscillate. Singlesupply operation for Sallen-key BPF would require onemore buffer op-amp [1]. It is obvious that it is notsuitable to our intended application, as we need highQ value.
  • 5. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 5There are instances where the Sallen-Key topology is abetter choice. As a rule of thumb, the Sallen-Keytopology is better if:1) Gain accuracy is important, and2) A unity-gain filter is used, and3) Pole-pair Q is low (e.g., Q < 3)At unity-gain, the Sallen-Key topology inherently hasexcellent gain accuracy. This is because the op amp isused as a unity-gain buffer. The unity-gain Sallen-Keytopology also requires fewer components—tworesistors vs three for MFB (discussed in next section).In our application there are no suitable tradeoffbetween Am and Q. Texas Instruments Single SupplyExpert [4], an online design guide for different kinds offilter, also does not recommend making high or low Qband-pass filters using Sallen-Key topology.B. Multiple Feedback (MFB) TopologyTo obtain a slightly higher Q, another simple option isto move to the multiple feedback infinite gainarchitecture shown in Figure [3].Fig[3]: MFB Filter circuit with Dual Supply[]This topology again requires a single amplifier andprovides for Qs in the range of 25. Using thistopology, the gain is (-2Q2) is still relatively lowcompared to the amplifiers GBW product (20Q2atresonance), but not nearly as low as the Sallen-Keyapproach [6]. Further it does not require inputcapacitance compensation. MFB topology is veryversatile, low cost, and easy to implement.Unfortunately, calculations are somewhat complex. Itgives an easy way of single supply operation ininverting configuration [4,7]. The single supply circuitconfiguration is shown in Fig [4].Fig[4] : MFB filter with Single supplyThe equations for the MFB derived from its transferfunction are [1]:Where B is the bandwidth of the BPFThe MFB band-pass allows to adjust Q, Am, and fmindependently. Bandwidth and gain factor do notdepend on resistor R3. Therefore, R3 can be used tomodify the mid-frequency without affectingbandwidth, B, or gain, Am [1]. However we run thesimulation and observed that change in R3 will causechange in gain also.For low values of Q, the filter can work without R3;however, Q then depends on Am via:This topology without R3 is called Deliyannis [3], and isuseful for low Q values only. However Deliyannis hasan extra gain resistor set too.The components values can be fixed as under if we fixfm, Gain and Q values:
  • 6. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 6The gain and Q value are very much related to eachother as is the case with Sallen-key [1]. It is used whenHigh gain and High Q values are needed. Since weneeded a high Q (and if possible high gain too), MFBappeared to be a good choice for extremely narrowband-pass filter design. Only trouble is that lesssimplifications are available to ease design unlikeSallen-key. The fig [5] shows the frequency response ofthe MFB filter which exhibits the sharp peak andsteeper roll-off, one among the other parameters weshall be looking for.Fig [5]: Frequency response of MFB filter with G=2,Q=30, BW=21, Fm=627Both the Sallen Key and the multiple feedbackarchitectures are fairly sensitive to external componentvariations [4]. MFB particularly is very sensitive tovariation in R3 resistor, but not to other componentvariations. Higher the Q value the smaller will be thevalue for the resistor. At very high Q values, the valueof this resistor can be in few hundred ohms. Veryprecise resistors and capacitors are needed to makenarrow band pass filter with MFB topology. Further theoverall response of the MFB filter over the tolerancesof the capacitors and resistors is also very important.The Monte Carlo simulation results for the MFB filter isshown in Fig [6].This simulation is showing a variation of mid frequencyfrom 623Hz to 633Hz with 1% resistors and 2%capacitors. Stability factor is very important aspecthere when working on high Q values. Obviously MFBscores better than Sallen-key topology on manyfactors and parameters.Fig[6]: Monte Carlo Simulation of MFB Filter over 1%resistor and 2% capacitor tolerancesAt this point, it is worth mentioning that TI AnalogFilter expert site [4] does not recommend thistopology for low as well as high Q Band-pass filters. Ifwe integrate the above circuit experimentally, it willsurely work as simulated, but the observations indicatethat MFB was very sensitive to the tolerances of theresistor R3.The configurations of Sallen-key and MFB appearsimilar. Both the topologies are compared briefly inTable [1].Table [1]: Comparison of Sallen Key and MFBtopologies (reference [8])Sallen-Key Multiple FeedbackNon-inverting InvertingVery precise DC-gain of 1Any gain is dependent on theresistor precisionLess components for gain= 1Less components for gain > 1or < 1Op-amp input capacitymust possibly be takeninto accountOp-amp input capacity hasalmost no effectResistive load forsources even in high-passfiltersCapacitive loads can becomevery high for sources in high-pass filtersNot sensitive tocomponent variation atunity gainLess sensitive to componentvariations and superior highfrequency response
  • 7. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 7C. Active Twin-T Topology:Most of the single tone detector circuit employs twin-Ttopology, so this would be a topology worth making astudy in little more detail in order to check if this couldbe a suitable topology for extremely narrow band passfilters. This topology is very attractive, but is knownmostly for notch filter configuration. However thistopology also works very well in narrow band-passmode. The beauty of this topology is that it canspecifically be used to achieve narrow peaks. Thistopology is based on two passive (RC) twin-T circuitsas shown in Figure [7], each of which uses threeresistors and three capacitors [7].Fig [7]: Two R-C T circuits to make Twin-T circuitThe most important thing is that the matching thesesix passive components is critical. Components fromthe same batch are likely to have very similarcharacteristics. The entire network can be constructedfrom a single value of resistance and a single value ofcapacitance, running them in parallel to create R/2 and2C in the twin-T schematics [7]. The sharpest responsewill come when the components are matched (byusing components from the same batch and bycreating R/2 and 2C by paralleling 2 of the values usedfor R and C, respectively).In total, it requires 6 passive components andminimum one op-amp. The twin-T topology can bemade with one as well as two op-amps [3]. One op-amp configuration is shown in Fig [8] and two op-amps configuration is shown in Fig [9].The twin-T circuit has the advantage that the qualityfactor (Q) can be varied via the inner gain (G) withoutmodifying the mid frequency fm. However, Q and Amcannot be adjusted independently [1].Fig [8]: Twin-T band-pass filter with dual supplyFig [9]: Two op-amp implementation of Twin-T BPFwith dual supplyTo set the mid frequency of the band-pass, specify fmand C, and then solve for R:Because of the dependency between Q and Am, thereare two options to solve for R2: either to set the gainat mid frequency in circuit of Fig [8]:Or design for a specific Q:As mentioned earlier non-inverting and inverting bothversions are available. Further there is also two op-amp implementation found in the literature [3, 7].For single supply operation, circuit configuration ischanged a little (refer to figure [10]) at input side [4, 7].Here where gain is controlled by R4 and R5. R7 is thetuning resistance for adjusting Q value. However Q cannot be changed freely without affecting otherparameters. It has been observed that Q is hard to
  • 8. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 8control in this circuit [4, 7]. Absolute levels ofamplitude will be hard to obtain [4, 7].Fig [10]: Twin-T BPF with single supplyIt was mentioned just in the beginning of this sectionthat matching is required for perfect functioning ofTwin-t filter. However in practice, this High Q circuitsBand-pass circuit made with Twin-t would oscillateand become unstable if the components are matchedtoo closely [7]. In order to have better control on Q,the components need to be mismatched slightly andbest to de-tune it slightly. By selecting the resistor tovirtual ground to be one E-96 1% resistor value off, forinstance. It may be noted that mismatching wouldaffect the gain also [4].As per Texas Single Supply Analog Filter online guide,theoretically this circuit is considered to be mostsuitable for use as a high sensitivity single tonedetector [4]. Incidentally the application intended byus is same. Practically, we observe that this circuitneeds lot of care in component selection whiledesigning. High precision components add to the costof the circuit.Before finalizing the circuit, we would like to evaluatethe other topologies as well. In the absence of anyother stable topology Twin-T could have been thestrong contender for the application along with MFB.The frequency response (Fig [11-A]) of Twin-T is surelygood enough but the roll off is not as steeper as MFB.A Monte Carlo analysis as shown in Fig [11-B] alsoshows that there are bigger variations in Centrefrequency with respect to the tolerance. The centrefrequency with same tolerance as used for MFB,however centre frequency can be seen varying from622Hz to 638Hz, which indicate that Twin-T is moresensitive to component tolerances.In that regard MFB scores better than Twin-T in mostof the aspects. In that case a trade-off could have beenmade between MFB and Twin-T w.r.t to their relativeperformance. But still many more topologies areavailable which need to be evaluated, thanks to thedesigners.Fig [11-A]: Frequency response of Twin-T BPF withG=5, Q=30, BW=20, Fm=627Fig[11-B]: Monte Carlo Simulation of Twin-T Filter over1% resistor and 2% capacitor tolerancesD. Modified Deliyannis topologyIf the reader observe the circuit diagram of MFB(Fig[3]) and Deliyannis Filter ( Fig [12]), they will find
  • 9. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 9that Deliyannis filter is just the MFB modified filter withattenuator resistor R3 missing [3]. Ideally thatcombination of MFB is used when low Q value isneeded, as it was pointed out in the discussion of MFB.However with some modification in basic Deliyannis, ahigh Q value is possible to achieve [9]. The feedbackresistor in MFB is split into 2 and attenuator resistor isconnected as it is as shown in Fig [13].Fig [12]: Basic Daliyannis Band-pass filter with dualsuppliesFig [13]: Modified Dalianis Band-pass filter with dualsupplies and feedback resistor split into two resistorsThe circuit works on single supply and itsconfiguration with single supply would be as shown infig [14].Fig [14 a]: Daliyaanis Band-pass filter with singlesupplyFig [14 b]: Daliyaanis Band-pass filter with inputattenuationFor the simplified circuit, we choose C1=C2 andR1=R4= R in such a way thatThe gain and Q of the circuit are interlocked [9] andcontrolled by R1 and R4 through the equation below:Because Gain and Q are linked together, gain resistorsR5 and R6 can be used as a voltage divider to reducethe input level and compensate for this effect asshown in Figure [14b]. When Gain and Q approachone, R5 can be shorted and R6 can be opened [12].The resistor R3 depends upon the Gain value and canbe selected using equation:AndIf R3 is doubled, R2 must be halved and vice versa. Ifone is tripled, the other must be one third, etc. R2 andR3 must always be related in this way. Otherwise, thecenter frequency and other circuit characteristics arechanged. If R1 = R2 = R3 = R4, then Q and Gain areboth equal to one.This filter acts as BPF as shown in its frequencyresponse diagram fig [15-A], with very sharp peak, thelower roll-off is not as steep as MFB, but the gain ismuch higher than MFB. A Monte Carlo analysis in Fig[15-B] indicate a centre frequency variations from624Hz to 638 Hz which is comparable to MFb andbetter than Twin-T.Only obstacle would have been the gain and Q beingsame [9]. In order to keep the Q high, gain has to bekept high. The Daliyaanis is supposed to be better interms of the variation due to component tolerances.However, the circuit performance is not as good as
  • 10. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 10MFB and not very much suitable to our application.MFB still score better than Deliyannis topology.Fig [15-A]: Frequency response of Deliyannis BPF withG=Q=10, BW=60, Fm=627Fig[15-B]: Monte Carlo Simulation of Deliyanis filterover 1% resistor and 2% capacitor tolerancesIV TRADE-OFFS IN PERFORMANCE ENHANCEMENTTECHNIQUES FOR SINGLE OP-AMP TOPOLOGYProperties of single op-amp topologies namely SallenKey, MFB, Deliyaanis and Active Twin-T are comparedin Table [2]. The properties of interest to a designerwhile designing a band-pass filter could beindependent control of Q, Fm and Am, sharpness ofpeak, stability and accuracy of the mid-frequency,sensitivity to component variations, types ofcomponents and op-amps required, single supplyoperation and oscillations.Still above table can only be considered as a guidelineand is nevertheless comprehensive in view of thetrade-offs involved between various interlinkedparameters. Further the relative importance of variousparameters to be traded-off depends on the natureand type of the application, stringent requirementsthereon and criticality of the results sought from thefilter.While selecting the right topology out of thesetopologies, it was our intention that theimplementation of filter should be such that we wouldhave complete control over:· The filter corner / center frequency· The gain of the filter circuit· The Q of band-pass filtersUnfortunately, such is not the case— complete controlover the filter is seldom possible with a single op amp.If control is possible, it frequently involves complexinteractions between passive components, and thismeans complex mathematical calculations that manydesigners may avoid. If the designer needs toimplement a filter with as few components as possible,there will be no choice but to resort to traditionalfilter-design techniques and perform the necessarycalculations. More control usually means more opamps, which may be acceptable in designs that will notbe produced in large volumes, or that may be subjectto several changes before the design is finalized [7].As we have seen from our observations from Sallen-key, MFB, Twin-T topologies and Deliyannis, there aresurely trade-offs involved in extremely narrow band-pass filter design. The most desirable situation for us isof course to implement a filter with a single op ampthus reducing the cost, but at the same time we wouldlike to have filter which can work with ordinarycomponents without severely degrading theperformance. An additional quad op-amp just cost$0.30 whereas a single high quality 2% capacitor itselfmay costs around $0.20 each and a 1% metal filmresistor costs around $0.02 each. So MFB or Twin-Tfilter capacitors each requiring high quality 2 to 3numbers of capacitors and similar number of resistorwould cost more than a multiple op-ampconfiguration which is stable enough to work withnormal components.
  • 11. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 11Table [2]: Comparison on popular single op-amp topologiesProperty Sallen key MFB Deliyaanis Active twin-TAvailability of Band-passconfigurationyes yes yes YesQ value obtainable Lowest (Q =3 to5)Medium (Q>25) Low to High(Q>0.5 to Q=100)Highest (Q>100)Dependence of Q and Am (mid-frequency gain)StrongAm=3QStrongAm=2Q2Yes (interlockedand equal) Am=QYesFlexibility to change Q via innergainYesQ= 1/ (3-G)No YesQ=GYesChances of oscillations at high Q Low Medium Low HighestGain value obtainable High (1 to X) High (1 to 10) Higher (1 to Q) Highest (>10)Gain accuracy High at unity gain Low (dependsupon resistorprecision)Low LowProvision of increasing inner gainin the circuitYes Yes Yes YesPossible narrow Bandwidth >100Hz <30 <30 <20Independent control of mid-frequency fm without affecting BWor Q---- Yes (via attenuatorresistor)---- ----sharpness of Mid-frequency curvepeakno yes Yes YesErrors in mid-frequency due to2% component tolerances--- 1.3 % --- ----Steepness of Lower and upperroll-off curveNo Highest on bothsidesHigh on one sideand low on otherLowSuitability for single supplyoperationNo yes Yes YesNumber of op-amps needed insingle stage without extra gaincontrol1 1 1 1 or 2Configuration (Non-inverting orinverting)Non-inverting Inverting Inverting InvertingRequired Gain-Bandwidthproduct of op-ampHigh (90Q2) Low (20Q2) ? ?Input Capacitance CompensationrequiredYes No No NoNumber of passive componentsrequired (including componentsin input coupling and gainfeedback path)7+1 5 +3 6+1 6+3Possibility of further circuitsimplification5 components atG=1No No NoSensitivity to external componentvariationLow (least atG=1)High (mainly toone resistor)Medium HighestNeed for precision components No (Low) Yes (High) Yes (Medium) Yes (Highest)Mathematical equations Easy Complex Complex MediumSuitability for Tone detection Low High High Highest
  • 12. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 12Instead of resorting to multiple op-amp configuration,if a designer would like to stick to single op-amptopologies (reason being the simplicity of architectand easy calculations), then he could cascade twostages of similar topology together with little relaxeddesign restrictions. The possible solutions withcascading of one op-amp topologies would dependupon the fact whether gain is independent of Q or not.In case Gain and Q are independent and trouble is justto counter instability due to high Q of single stage,then we could go for a solution which involves: Use two stages cascaded together; this will requiretwo op-amps Use low value of Q for each stage, cascading willgives a steeper roll-off and hence better Q Provide limited gain to each stage and if neededadd additional gain amplifier stageSuch a solution is depicted in the figure [16].Fig [16]: Cascading of Filter stagesAnother scenario could be that Q and G areinterrelated so that only high gain can give high Qvalues. Then we can think of keeping the Q and Gainboth at normal values and attenuating the gain aftercascading. Whatever the case may be, fromperformance point of view, the cascading gives muchbetter results in terms of higher Gain (20Db), high Qvalue, narrower Bandwidth B and sharper roll-off. Sincethe Q curve become sharper due to extra roll-off andgain control remains independent, our intentions atdesign goals would be fulfilled. The above solutionsare definitely going to make the number ofcomponents little more than whatever is required for a2 or 3 op-amp topology, but it may be worth doing it.Going one step further, two different kinds oftopologies each working at relaxed Q and Gainrestrictions could be cascaded to take the advantageof the multiple topology in one design. There arecircuits which cascade SK and MFB circuit together toform the filter. Such tradeoff could pay off in terms ofstable circuit parameters, nominal number of passivecomponents, ease of design modifications in laterphases and sticking to the basics of the filter designscience.As a designer, if one has made up the mind forcascading, it would be worth analyzing two op-ampand three op-amp topologies too. Even the two op-amp implementation like fliege topology gives verygood results comparable to MFB or Active Twin-T interms of peaking, sharpness and number of passivecomponents being used [1,4]. On the other hand mostof the biquad based multiple op-amps topologies too,like state variable, akerberg-mossberg and biquad etc,too score much better on stability, immunity tocomponent tolerances and high Q values independentof gain [6, 7]. However the relative comparison ofthese topologies would be the subject matter of otherdesign paper and will not be discussed here.V PRACTICAL TIPS FOR COMPONENT SELECTION FORNARROW BAND-PASS FILTERSFor single op-amp topologies components selection isvery important aspect. This is because of the fact thatthe deviations from nominal values of the passivecomponents of course have influence on the frequencyresponse of the filter [8]. These deviations may becaused by component tolerances or due to the fact,that under normal circumstances the ideal values arenot available. As a rough estimation it is possible tosay: The lower the stage order is, the lower theinfluence of deviations on the frequency response is.Higher stage orders have a higher quality factor Q anddeviations of R and C impinge on the resultingfrequency response roughly proportional to the Q-factor. We recommend carrying out Monte Carlosimulation of desired parameter over all the toleranceranges of the components involved.The tolerance of the selected capacitors and resistorsaffects the filter sensitivity and on the filterperformance. Sensitivity is the measure of thevulnerability of a filter’s performance to changes incomponent values. The important filter parameters toconsider are the corner frequency, fm, and Q.For example, when Q changes by 2% due to a 5%change in the capacitance value, then the sensitivity ofQ to capacity changes is expressed as [1]:The following sensitivity approximations apply tosecond-order Sallen-Key and MFB filters:Filter Stage-1(Normalgain, littlehigh Q)GainAmplifierStage(High gain)Filter Stage-2(Normalgain, littlehigh Q)
  • 13. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 13Although 0.5 %/% is a small difference from the idealparameter, in the case of higher-order filters, thecombination of small Q and fm differences in eachpartial filter can significantly modify the overall filterresponse from its intended characteristic.Figures [17] show how an intended eighth-orderButterworth low-pass can turn into a low-pass withTschebyscheff characteristic mainly due to capacitancechanges from the partial filters [1]. The differencebetween ideal and real response peaks with 0.35 dB atapproximately 30 kHz, which is equivalent to anenormous 4.1% gain error, can be seen.Fig [17]: Deviation from ideal response due to changein CapacitorIf this filter is intended for a data acquisitionapplication, it could be used at best in a 4-bit system.In comparison, if the maximum full-scale error of a 12-bit system is given with half LSB, then maximum pass-band deviation would be – 0.001 dB, or 0.012%.Resistors come in various packaging with differentprecision. It is always recommended to go for 1%resistor tolerances. These resistors are easily availablenow. Metal film resistors are preference for filternetworks. Carbon film resistors may also be usedbecause their negative temperature coefficient can beused to advantage to minimize the passive sensitivityof a circuit (if the capacitors have a positivetemperature coefficient). Carbon composition resistorsare not suitable for filter networks because of theirhigh temperature coefficient and high noise level.Carbon composition variable resistors are also notrecommended. A general overview of types of suitableresistors available for good filter design is given inTable [3].Table [3]: Suitability of Various resistorsTypeTemp. Coeff.ppm/degCStandardTolerances %CommentsMetal film -25 to 100 1low cost; mostwidely usedCermet film 200 0.5,1larger, costlier thanmetal filmCarbon film -200 to -500 2,5,10,20low cost; negativetemp.coeff.To sum up, some points regarding the selection ofresistors are [5, 10]:– Values in the range of a few hundred ohms to a fewthousand ohms are best.– Use metal film with low temperature coefficients.– Use 1% tolerance (or better) from E96 series [7].– Surface mount is preferred.Capacitors are the real accuracy controlling andvariation controlling components, thus it requiregreater attention in their selection particularly fornarrow band-pass filter circuits. These days’ capacitorscome in various types, the few ones shown in theTable [4]. To minimize the variations of fm and Q, NPO(COG) ceramic capacitors are recommended for high-performance filters [1]. These capacitors hold theirnominal value over a wide temperature and voltagerange. COG-type ceramic capacitors are the mostprecise. Their nominal values range from 0.5 pF toapproximately 47 nF with initial tolerances from + 0.25pF for smaller values and up to +1% for higher values.Their capacitance drift over temperature is typically30ppm/oC. Other precision capacitors are silver mica,metallized polycarbonate, and for high temperatures,polypropylene or polystyrene. Predictable negativetemperature coefficient of polystyrene capacitors canbe used to advantage with metal film or cermet filmresistors to minimize passive sensitivity [1].
  • 14. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 14Table [4]: Various types of capacitors suitable for filterdesignTypeTemp. Coeff.ppm/degCCommentsNPO ceramic +30most popular for activefiltersFilm: MPC + 50metallizedpolycarbonateFilm:Polystyrene-120larger than MPC; meltsat low temp.Mica -200 to + 200larger, costlier thanNPOSince capacitor values are not as finely subdivided asresistor values, the capacitor values should be definedprior to selecting resistors. Capacitor values can rangefrom 1 nF to several uF. The lower limit avoids comingtoo close to parasitic capacitances [1]. If precisioncapacitors are not available to provide an accuratefilter response, then it is necessary to measure theindividual capacitor values, and to calculate theresistors accordingly. The capacitor range is chosendepending upon the mid-frequency range. A simpleguideline is enumerated in the table [5].Table [5]: Mid frequency vs recommended capacitorvaluesFm = Frequency Cut Capacity in pFfrom to from to10 100 100000 470000100 500 22000 100000500 1000 6800 390001000 5000 2700 100005000 10000 1000 330010000 50000 560 1500100000 500000 330 1000Some points regarding capacitor selection includes [5,10]:– Avoid values less than 100 pF.– Use NPO if at all possible. X7R is OK in apinch. Avoid Z5U and other low qualitydielectrics. In critical applications, even higherquality dielectrics like polyester,polycarbonate, mylar, etc., may be required.– Use 1% tolerance components. 1%, 50V, NPO,SMD, ceramic caps in standard E12 seriesvalues are available from various sources [5, 7].– Capacitors with only 5% tolerances should beavoided in critical tuned circuits [7]– Surface mount is preferred.The most important op amp parameter for properfilter functionality is the unity-gain bandwidth. Ingeneral, the open-loop gain (AOL) should be 100times (40 dB above) the peak gain (Q) of a filtersection to allow a maximum gain error of 1%. Theconcept is self explanatory from Fig [18].Fig [18]: Q value relationship with amplifier’s GBWThe following equations are good rules of thumb todetermine the necessary unity-gain bandwidth of anop amp for an individual filter section [1].1) First-order filter:2) Second-order filter (Q < 1):3) Second-order filter (Q > 1):Besides good dc performance, low noise, and lowsignal distortion, another important parameter thatdetermines the speed of an op amp is the slew rate(SR) [1]. For adequate full power response, the slewrate must be greater than the following expression:
  • 15. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 15A manufacturer’s data book will usually include theunity-gain bandwidth in the op amp’s electricalcharacteristics. Often, a minimum, typical andmaximum value will be given, from which the GBWtolerance can be estimated:The range of op amp tolerances is wide; from around15% to about 50%, with the mean approximately 30%.The GBW temperature coefficient must be estimatedfrom a graph of (normalized) unity gain bandwidthversus free air temperature. This graph is not alwaysprovided. Typical coefficient values might be 1000 to7000 ppm/degC. Some of the LMV series op-ampsfrom National or TI and TLV series op-amps from TIare good candidates for single supply extremelynarrow band pass filter applications.To avoid auto-oscillations connect two 100000 pFcapacitors between ground and power pins (+V, -V) ofop amp IC as shown in Fig [19].Fig [19]: Power supply DecouplingVI CONCLUSIONA relative comparison in practical difficulties faced inextremely narrow band-pass filter design using singleop-amp topology has been given in paper. Out thestudies made for single op-amp topologies, we findthat MFB could be a good topology to use with rightkinds of components. The Sallen-Key and MFBarchitectures also have trade-offs associated withthem. The simplifications that can be used whendesigning the Sallen-Key provide for easier selectionof circuit components, and at unity gain, it has no gainsensitivity to component variations. The MFB showsless overall sensitivity to component variations and hassuperior high-frequency performance. The best filterdesign may be a combination of MFB and Sallen-Keysections. This flexibility can be quickly leverages bysome of the popular filter design software such asFilterPro to define the component values of the samedesign using both circuit types and then use some ofthe sections from one topology design with somefrom the other topology design to build your filterdesign [11]. Thus cascading of same or differenttopologies can give better results. When cascading isthe necessity in order to produce stability in the mid-frequency performance, immunity to componenttolerances and elimination of circuit oscillations, themultiple op-amp topologies such as State Variable,Akerberg-Mossberg, biquad, Tow-Thomas designs areworth considering. These designs outweigh single op-amp topologies on achieved performance vs spentcost scale.Acknowledgementsa) Texas Instuments, USA, www.ti.comb) National Semiconductor, USA, www.national.comReferences[1] Thomas Kugelstadt, Active Filter Design techniques: Op-amps for every one, Texas Instruments www.ti.com, DesignReference SLOD006B, Aug 2002.[2] Kerry Lacanette, A basic Introduction to filters-Active,Passive and Switched-capacitor, National Semiconductorwww.national.com , Application Note 779, April 1991[3] Electronics Circuit Collection – Second order Band-passFilter Design Topologies,http://www.technick.net/public/code/circuits.php[4] Single Supply Analog Expert: On-line Filter design Guide,Texas Instruments, http://www-k.ext.ti.com/SRVS/Data/ti/KnowledgeBases/analog/document/faqs/ssexpert.htm ,[5] James Karki, Analysis of the Sallen-key Architecture, TexasInstruments www.ti.com, Application Report SLOA024A,July 1999[6] A beginners Guide to filter topologies, Maxim, ApplicatioNote 1762, Sept 2002[7] Bruce Carter, A single Supply op-amp circuit collection,Texas Instruments www.ti.com, Application ReportSLOA058, Nov 2000[8] Ube Bies, Design and Dimensioning of Active Filters,http://www.beis.de/Elektronik/Filter/ActiveLPFilter.html ,April 2005
  • 16. R. Attri Instrumentation Design Series (Electronics), Paper No.3, September, 2005Copyrights © 2005 Raman K. Attri P. 16[9] Bruce Carter, Filter design in thirty second, TexasInstruments www.ti.com, Application Report SLOA093, Dec2001[10] Jim Karki, Active Low Pass filter design, Texas Instrumentswww.ti.com, Application Report SLOA049A, Cot 2000[11] John Bishop, Bruce Trump, R. Mark Stitt, FilterPro MFB andSallen-Key Low-Pass Filter Design Program, TexasInstruments www.ti.com, Application Report SLOA001A,Nov 2001[12] Bruce Carter, More Filter design on Budget TexasInstruments www.ti.com, Application Report SLOA096, Dec2001Further Readings1. Steven Green, Design Notes for 2-pole filter design withdifferential inputs, Cirrus Logic www.cirrus.com, ApplicationNote AN48, Mar 20032. Rod Elliott, Multiple Feedback Bandpass filter, Elliott SoundProducts, http://sound.westhost.com, Jul 20003. Analog Filter Design Demystified, Maxim, Application Note AN1795, April 20024. A Filter Design Primer, Maxim, Application Note 733, Feb, 20015. Alireza Aghashani, State Variable Topology (Second-OrderActive Filters Based on the Two-Integrator-Loop Topology), SanJose State University, http://www.engr.sjsu.edu/filter/ FilterDesign Web Assisted Course EE175, 20006. Active Filter Solutions, Filter Solutions, www.filter-solutions.com7. Paul Tobin, Electric Circuit Theory Notes-Chapter 8: StateVariable Topology, Dublin Inst of Technologywww.electronics.dit.ie/staff/ptobin/3cover1.pdf , 1998Filter Design Software Tools1. SWIFT ((Switcher with Integrated FETTechnology) Designer, Texas Instruments2. FilterPro for windows, Texas instruments3. MicroCAP 8.0, Spectrum SoftwareAut hor Det a ils:Author is Global Learning and Training Consultantspecializing in the area of performance technology.His research and technical experience spans over 16years of project management, product developmentand scientific research at leading MNC corporations.He holds MBA in Operations Management, ExecutiveMBA, Master degree in Technology and Bachelordegree in Technology with specialization inElectronics and Communication Engineering. He hasearned numerous international certification awards -Certified Management Consultant (MSI USA/ MRAUSA), Certified Six Sigma Black Belt (ER USA),Certified Quality Director (ACI USA), CertifiedEngineering Manager (SME USA), Certified Project Director (IAPPM USA), toname a few. In addition to this, he has 60+ educational qualifications,credentials and certifications in his name. His interests are in scientific productdevelopment, technical training, management consulting and performancetechnology.Contact: +44 20 7979 1979E-mail: rkattri@rediffmail.comWebsite: http://sites.google.com/site/ramankumarattriLinkedIn: http://www.linkedin.com/in/rkattri/Copyright InformationWorking paper Copyrights © 2005 Raman K. Attri. Paper can becited with appropriate references and credits to author. Copyingand reproduction without permission is not allowed.