Designing High Speed Active Filters Mark Sauerwald September
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Designing High Speed Active Filters
Mark Sauerwald
September 1997
Filters built from resistors (R), inductors capacitors known passive filters dominant type filter high frequency applications. performance these filters typically limited inductors which large, expensive from ideal electrical sense. using amplifiers feedback, same filter characteristics achieved without inductors, these filters known "active filters". active filter will perform well only extent that amplifiers behave ideal sense, traditionally active filters have been limited applications frequencies below 1MHZ. With advent cost, very high speed operational amplifiers, feasible realize active filters with frequency ranges tens MHZ. With some newer high speed amplifiers such CLC449 1.2GHz bandwidth amplifier, filters with corner frequencies above 100MHz have been built. This application note will provide recipe realize active filters using cost, high speed operational amplifiers. filter topology that used Sallen-Key Filter which uses operational amplifier fixed gain block. This filter topology used with current feedback voltage feedback amplifiers, will shown design pass, high pass band pass filters using this filter topology. This application note discusses printed circuit board which will allow prototype active filters pole complexity. This complete treatment subject active filters, there several good books published that topic, some which listed bibliography. This simple method getting circuit that will work most applications. topics covered are: Filter Types Introduction second order, pass Sallen-Key Filter. RC:CR Transformations realize second order, high pass Sallen-Key Filters. Cascading filter sections achieve higher order filters Band Pass Filters. Sensitivities component values select Op-amp active filter Compensation finite Bandwidth Amplifiers National active filter evaluation boards Filter Types There large number different types filter responses. this application note, will concern
1997 National Semiconductor Corporation
Printed U.S.A.
ourselves with three which have found most useful. Butterworth Response Butterworth response maximizes flatness pass band filter. response very flat near then begins slowly roll that -3dB cutoff frequency, approaches ultimate rolloff rate -20ndB/decade where order filter. Butterworth filters used very important maintain gain flatness, especially frequencies. Bessel Response addition altering magnitude input signal depending upon frequency, filters introduce delay into signal which dependent upon frequency. This introduces frequency dependent phase shift which distorts non-sinusoidal signals. Just Butterworth response maximizes amplitude flatness through pass band, Bessel Response minimizes phase non-linearity pass band. Chebyshev Response some applications, most important factor fast filter cuts unwanted signal. Faster rolloff than what seen Butterworth filter achieved willing accept some ripple passband. Appendix contains tables with parameters required design filters order with Butterworth, Bessel, Chebyshev responses. There tables Chebyshev response: 0.1dB maximum ripple passband, ripple passband. Introduction Second Order, Pass Sallen-Key Filter circuit shown figure pole, Sallen-Key Pass Filter. This filter (and pole filter) characterized three parameters: gain filter. measure corner frequency filter, while measure closely spaced poles plane. values given
unitless units radians/sec. Divide
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Figure Sallen-Key Pass Filter with Equal methodology design particular filter select desired values then above equations determine component values required. obtained from filter table appendix your cutoff frequency will given from design specification. most filters, actual value that design must adjusted factor found filter table proper -3dB frequency. another parameter that will provided part filter specification. Since these three parameters completely independent, possible meet three points simultaneously. this case, should select another value then amplifier before after filter make overall gain meet system requirements. example Butterworth filter desired 0.707) with gain then find that there positive value which will provide required filter. Since negative value implies negative value resistor, need find another solution. however select 1.5, then using 0.707 obtain required obtain proper overall gain, place amplifier with gain 2.66 front filter. Even doing these things, possible that there will solution desired filter, especially high sections. this case, methodology filter with equal shown appendix This much more versatile circuit, somewhat more difficult design. methodology selecting component values outlined below: Select obtain desired amplifier that using current feedback amplifier, follow guidelines data sheet select appropriate values Determine value required using following equation value found design table:
step select select select this still does work, then appendix Arbitrarily select value Determine value multiplying your desired cutoff frequency value found filter design table. your frequency specification remember multiply into radians/sec. Determine value required using equation below:
turns large small practical purposes, select another value big, select larger value small select smaller value then back step Example: Design Butterworth filter, with cutoff frequency 10MHz, gain 1.5. CLC430 will used this example. Select 700, 1.4K CLC430 data sheet. Find from table: 0.707, this determine 0.707 required Arbitrarily select 0.1µF 62.8E6 10MHz filter Calculate turns 0.23 small, therefore smaller return step Select 100pF. 225, much better. Figure illustrates final filter topology.
112.5
100pF
100pF
CLC430
1.4k
Figure Example Pass Filter With slight modifications, CLC430's evaluation board, CLC730013, used test this circuit. some cases, difficult realize desired filter with constraint equal valued capacitors. this case, appendix obtain expressions where capacitors take different values. This most often necessary when trying realize filter with high
cannot positive real solution then select another value back
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Transform Pass Filter into High Pass Filter changing capacitors into resistors, resistors into capacitors, pass filter changed into high pass filter. make high pass filter from lowpass filter, replace each capacitor value with resistor value each resistor with capacitor value example 100pF capacitors example circuit from previous section should replaced with resistors, resistor should replaced with 71pF capacitor, resistor should replaced with 142pF cap. Alternately calculate component values using method similar that shown previous section. Figure second order Sallen-Key High pass filter. given
When cascading filters, question that arises what order sections should placed. answer this same answer filter questions depends". factors that need considered when cascading filter sections liable have intermediate signals that might clip distort?" "How important noise me?" filters with sections where there large maximum amplitude signal between stages larger than input output amplitude. This lead undue distortion signal. This will most likely issue there filter sections with large input signals large. Strategies that used combat this effect stages with lowest gains first, cascade higher gain sections later. Another that dynamic range could increased would op-amp with larger dynamic range. CLC432 dual, current feedback op-amp that well suited active filter applications output voltage swing 28Vpp when driving light load. order minimize broadband noise that present active filter, stages should cascaded with highest highest gain sections first, then followed lower gain sections. Other strategies that should considered when trying noise using lowest possible value resistors reduce thermal noise select noise amps such CLC428, dual, voltage feedback amp. from previous paragraphs, order which place filter stages dependent upon requirements your application. There best cascade your filter stages. Component Value Sensitivities component values used realizing filter exactly what calculations arrive they won't then filter characteristics will different from what desired. Even time spent trimming components exact desired value, variations caused temperature shifts, aging other external internal sources will cause filter characteristics vary. good design will result minimal variation filter characteristics result component value variations that might expected. estimate effect filter characteristics component values vary, sensitivity figures used. sensitivity figure tells much variation there will characteristic when parameter changed. Hence refers incremental change incremental change then there will variation variation parameters with which most concerned filter designs therefore would useful look what component variations have effect these parameters, determine what these sensitivities are.
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Figure Sallen-Key High Pass Filter Cascading Filter Sections Higher order filters realized cascading lower order filters. filter order realized cascading second order sections. Note that obtain fourth order Butterworth filter cascade second order Butterworth filter sections. pole locations fourth order filter different different values will need used each section. Cascading active filters Sallen-Key topology easy. Since output impedances filters very small, cascading them consists just connecting section next (each filter section designed assuming source impedance.) filter order desired, last pole added with simple passive filter output active filter shown Figure
Figure Order Sallen-Key Filter
defined d(InA) d(Inx)
gain that intending measure bandwidth. Recommended Gain Range Your filter design will dictating gains which will setting your amps. chosen voltage feedback amp, gains outside recommended gain range liable lead lower than expected bandwidth best oscillation worst. current feedback amp, operation gains outside recommended range liable force resistor values which small large practical realization. Noise input voltage current noises will contribute noise output filter. applications where noise major concern, will need calculate these contributions well contributions thermal noise resistors circuit) determine added noise encountered with active filter acceptable. Noise reduced selecting noise, high speed amps such CLC425 CLC428. Dynamic Range filters which have high sections, possible that there will intermediate signals that larger than either input signal output signal. filter operate properly, these signals must passed without clipping excessive distortion. Secondary Specifications addition four primary specifications above, there several secondary parameters that want take into consideration. These would include phase linearity (this generally better current feedback amps), packaging (duals, quads available?), power dissipation, price availability technical support.
lowpass filter Figure equation that describes variables, hence only sensitive ratio resistor values which determined this filter sensitivity that have worry most about sensitivity which very large high sections. Selecting Active Filter Although there many factors that into selecting application, most filter applications satisfied looking just four parameters:
Bandwidth Recommended Gain range Noise Dynamic Range
Bandwidth general rule, when selecting filter, make certain that bandwidth least intended filter frequency, preferably 20x. example design 10MHz pass filter, with least 100MHz bandwidth. designing high pass filter, make certain that bandwidth amps will sufficient pass your signal. Another point watch that your must have this bandwidth under conditions that intend example, same gain, signal level power supply voltage. that specified 100MHz because 100MHz bandwidth with ±15V supplies, 50mV output level gain likely useful 10MHz filter application. doubt, configure amplifier that considering
Summary High Speed Dual Amps
Bandwidth Recommended (with 500mV Gain Range output, (MHz) filter applications CLC412 CLC416 CLC428 LM6172 LM6182 CLC5602 CLC5622 CLC432 1-20 Noise Voltage (nV/Hz) Noise Current (pA/Hz) inverting/non-inverting 12/2 16/3 8.5/6.9 10/7.5 13/2 Output Dynamic Range (100 load) +3.1/-2.9 +3.5/-3.5 +3.5/-3.5 +9/-8.5 ±3.8 ±3.8 +6/-6
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Compensation Finite Bandwidth Amplifiers analysis that have done, have assumed that amps ideal amps with infinite bandwidth. Unfortunately, price delivery these amps makes them poor choice actual realizable filters. effect using real place ideal slightly lower corner frequency filter, somewhat clever, compensate this pre-distorting component values components that final filter much closer what wanted. mathematical background this explained application note OA-21. Since goal this application note make design active filters easy, going skip development work, directly final result. make this method there parameter that will need know that intend use, this time delay through amplifier, called value obtained different ways: look frequency response plots that considering using. Find frequency which phase delay 180°, multiply this frequency take reciprocal obtain time delay through amplifier. case CLC412, 180° frequency about 300MHz, multiplying taking reciprocal yields time delay, 1.7ns. Another that value with National spice model, provide amplifier, configured want with pulse, measure delay between input edge output edge.
Figure Pass Sallen-Key Filter filter shown Figure calculate values following way: Calculate solving: where
Once have with
Figure Schematic Active Filter Board
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Active Filter Boards make prototyping active filters easier, Comlinear designed different active filter evaluation boards. schematic first board shown Figure consists CLC109 CLC111) input buffer, followed four cascaded Sallen filter sections, realized with dual amps. board designed using surface mount components, resistors capacitors interchangeable. This board available from National Semiconductor CLC730061 board shipped bare PCB. bottom views evaluation board shown Figure other board also allows four cascaded biquad sections restricts user designs using since rather than amps, this board uses quad, unity gain buffer.
board ordered part number CLC730023 fully documented CLC114 evaluation board datasheet, available National Semiconductor Literature #660114-001 1997 Comlinear Databook. Conclusion Using principles outlined this application note, active filter design need daunting task. feel free impress your friends cocktail party whipping pencil paper doing design 5MHz pass filter. don't have tell them easy really just them bask their awed looks.
Figure Bottom Views Active Filter Evaluation Board
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Appendix Filter Design Tables
Butterworth Pass Filter 0.707 1.000 0.541 0.618 0.518 0.555 0.510 Attenuation (dB)
1.306 1.620 0.707 0.802 0.601
1.932 2.247 0.900
2.563
Bessel Pass Filter 1.274 1.453 1.419 1.561 1.606 1.719 1.784 0.577 0.691 0.522 0.564 0.510 0.533 0.506
1.327 1.591 1.760 1.691 1.824 1.838
0.806 0.917 0.611 0.661 0.560
1.507 1.907 2.051 1.958
1.023 1.127 0.711
1.685 2.196
1.226
ripple Chebyshev Filter 1.82 1.300 1.153 1.093 1.063 1.045 1.034 0.767 1.341 2.183 3.282 4.633 6.233 8.082 Attenuation (dB) 3.31 12.24 23.43 34.85 46.29 57.72 69.16
0.969 0.789 0.797 0.834 0.868 0.894
0.619 0.915 1.332 1.847 2.453
0.539 0.513 0.575 0.645
0.599 0.846 1.183
0.377 0.382
0.593
1.00 ripple Chebyshev Filter 1.050 0.997 0.993 0.994 0.995 0.996 0.997 0.957 2.018 3.559 5.556 8.004 10.899 14.240 Attenuation (dB) 11.36 22.46 33.87 45.31 56.74 68.18 79.62
0.494 0.529 0.655 0.747 0.808 0.851
0.785 1.399 2.198 3.156 4.266
0.289 0.353 0.480 0.584
0.761 1.297 1.956
0.205 0.265
0.753
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Appendix Non-Equal Sallen-Key Filter Methodology circuit shown Figure pole, Sallen-Key pass filter similar seen body this application note. difference that this figure have removed constraint that capacitors remain equal adding additional degree freedom. Like filter from Figure this filter characterized three parameters: gain filter. measure corner frequency filter, while measure closely spaced poles plane. values given
Arbitrarily select value This value should small filters should larger higher filters. Remember that standard values capacitors limited, should chosen with this mind. Determine value required using following equation value found design table:
(mn)2 mnRC unitless units radians/sec. Divide
cannot positive real solution then select another value back step Arbitrarily select value Determine value multiplying your desired cutoff frequency value found filter design table. your frequency specification remember multiply into radians/sec. Determine value required using equation below: 0mnC
turns large small practical purposes, select another value big, select larger value small select smaller value then back step Appendix Transfer Functions Some Filters
Figure Pole Sallen-Key Pass Filter with Unequal Capacitors methodology design particular filter select desired values then above equations determine component values required. obtained from filter table appendix your cutoff frequency will given from design specification. most filters, actual value that design must adjusted factor found filter table proper -3dB frequency. another parameter that will provided part filter specification. methodology selecting component values outlined below: Select obtain desired amplifier that using current feedback amplifier, follow guidelines data sheet select appropriate values
Transfer function filter Figure
2C1C2
R1C1 2C1C2
Transfer function filter Figure
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Appendix Bibliography Franco: Design with Operational Amplifiers Analog Integrated Circuits, McGraw Hill, 1988 Lacanette, ed.: Switched Capacitor Filter Handbook, National Semiconductor, April 1985 Temes Mitra: Modern Filter Theory Design, Wiley, 1973 Steffes: Simplified Component Value Pre-Distortion High Speed Active Filters OA-21, Comlinear, March 1993 A.B. Williams, F.J. Taylor: Electronic Filter Design Handbook, McGraw Hill 1988
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