AN38 - FilterCAD User
Contents
1. STAGE fo Q fn Sorted for Reduced Harmonic Distortion 1 0 9989 15 0154 1 2227 2 0 8454 3 0947 1 4953 3 0 4618 0 7977 3 5990 Sorted for Low Noise 1 0 8454 3 0947 1 4953 2 0 9989 15 0154 1 2227 3 0 4618 0 7977 3 5990 In the first instance the section with the highest fo and the highest Q is paired with the lowest fn and placed first in the cascade order The second highest Q is paired with the second lowest f and so on This pairing minimizes the difference between the highest peak and the lowest gain in each second order section Referring to Table 4 4 which gives the resistor values and lowpass gains for the stages we see that the first stage has a very low gain of 0 067 and that most of the gain is provided by stage three which has the lowest Q Thus the input swings of the individual Stages are minimized input induced distortion is reduced and an overall gain of 1 for the circuit is obtained In the case of mode 3A sections lowpass gain for the first section is determined by R4 R1 and lowpass gain for subsequent Stages is determined by R4 divided by RL of the previous Stage The final gain stage is provided by the external op amp and is determined by RG RL Highpass gain is not taken into account here an38f AN38 22 AI MYR Application Note 38 0 1 THD N 0 01 100 1k FREQUENC2. Each mode 1 section requires three resistors and the final mode 3 section requires four To calculate the resis tor values press ESC to exit the Device screen then press R On pressing P to select 1 tolerance resistors FilterCAD displays the values in Table 3 1 This completes the implementation of our Butterworth lowpass example Table 3 1 Resistors for Butterworth Lowpass Example STAGE R1 R2 R3 R4 1 16 50k 16 50k 10 00k 2 16 20k 10 00k 25 50k 3 10 00k 12 10k 10 70k 4 15 00k 20 50k 10 00k 20 50k an38f AN38 14 LI MYR Application Note 38 A CHEBYSHEV BANDPASS EXAMPLE For our next example we ll design a bandpass filter with a Chebyshev response We ll assume you know your way around the program reasonably well at this point so we ll dispense with telling you specific keys to press unless we introduce a new feature For our Chebyshev design we ll select a maximum passband ripple of 0 05dB an attenu ation of 50dB and a center frequency of 5000Hz We ll specify a pass bandwidth of 600Hz and a stop bandwidth of 3000Hz This results in another 8th order filter consist ing of four 2nd order bandpass sections with their corner frequencies staggered around 5000Hz and moderate Qs illustrated in Table 3 2 4 Table 3 2 fp Q and fp Values for 8th Order Chebyshev Bandpass STAGE fo Q fn 1 4657 8615 27 3474 0 0000 2 5367 2699 27 3474 INFINITE 3 4855 119
3. 3 1 0000 2 5629 INFINITE 4 1 0000 0 5098 INFINITE Table 4 2 Resistor Values for 8th Order Butterworth Lowpass STAGE R1 R2 R3 R4 DC GAIN Optimized for Reduced Harmonic Distortion 1 61 90k 60 90k 35 00k 60 90k 0 98 2 57 60k 35 00k 77 35k 35 00k 0 61 3 43 20k 42 35k 35 00k 42 35k 0 96 4 39 20k 71 75k 35 00k 71 75k 1 83 Total 1 05 Optimized for Low Noise 1 60 20k 60 90k 35 00k 60 90k 1 01 2 41 60k 42 35k 35 00k 42 35k 1 00 3 56 20k 35 00k 77 35k 35 00k 0 60 4 43 20k 71 75k 35 00k 71 75k 1 66 Total 1 05 visible in Figure 4 5 In both examples the distortion takes asignificant dip as we approach the corner frequency This is Somewhat deceptive however since in this region the third and higher harmonics begin to be attenuated by the filter While giving better harmonic distortion performance Figure 4 5 has a wideband noise spec of 90uVays whereas Figure 4 6 yielded a wideband noise spec of 80uVpms Our second example is a 6th order elliptic lowpass filter again normalized to 1Hz and realized in two versions one optimized for noise and the other optimized for harmonic distortion This example has a maximum passband ripple of 1dB astopband attenuation of 50dB acorner frequency of 1Hz and a stopband frequency of 1 20Hz The clock to an38f LI M AN38 21 Application Note 38 0 1 THD N AVMs
4. TECHNOLOGY Application Note 38 November 1990 FilterCAD User s Manual Version 1 10 WHAT IS FilterCAD FilterCAD is designed to help users without special expertise in filter design to design good filters with a minimum of effort Itcan also help experienced filter designers achieve better results by providing the ability to play what if with the values and configuration of various components With FilterCAD you can design any of the four major filter types lowpass highpass bandpass and notch with Butterworth Chebyshev Elliptic or custom designed response characteristics Bessel filters can be realized by manually entering pole and Q values but FilterCAD cannot synthesize a Bessel response in this version FilterCAD is limited to designs which can be achieved by cascading state variable 2nd order sections FilterCAD plots amplitude phase and group delay graphs selects appropriate devices and modes and calculates resistor values Device selection cascade order and modes can be edited by the user LICENSE AGREEMENT DISCLAIMER This copy of FilterCAD is provided as a courtesy to the customers of Linear Technology Corporation Itis licensed for use in conjunction with Linear Technology Corporation products only The program is not copy protected and you may make copies of the programas required provided that you do not modify the program and that said copies are used only with Linear Technology Corporation produc
5. aad a 2 5VRMS 0 01 100 1k 10k FREQUENCY AN38 F4 5 Figure 4 5 THD Performance 8th Order Butterworth Sorted for Reduced THD 8 70 i 2 ws 80 10 2 S 90 2 amp 100 30 110 40 1 2 5 10 20 FREQUENCY kHz GAIN AND NOISE OF SECOND ORDER ELLIPTIC SECTION BANDLIMITING NOISE FROM PREVIOUS SECTION Q 0 79 fo 4 6kHz fy 36kHz 0 1 2 5VaMs I THD N S l 1Vams 0 01 100 1k 10k FREQUENCY Figure 4 6 THD Performance 8th Order Butterworth Sorted for Reduced Noise g 70 0 2 wi 80 10 2 S 20 2 amp 100 30 110 40 1 2 5 10 20 FREQUENCY kHz GAIN AND NOISE OF SECOND ORDER ELLIPTIC SECTION Q 15 fo 10KHZ fn 12 2kHz Figure 4 7 Using Cascade Order to Band Limit Noise filter cutoff frequency ratio is 100 1 The cascade orders for the two sections are given in Table 4 3 The case of an elliptic filter is more complex than the Butterworth in that the 2nd order responses have fp values notches or 0s as well as fos and Qs The ratio of f to fo in a particular section affects the height of the resonance peaks resulting from high Qs The closer fp is to fo the lower the peak Table 4 3 fo Q and fp Values for 6th Order Elliptic Lowpass
6. of 1 at DC the frequencies in the vicinity of fo will receive an additional boost from the resonance peak resulting in a gain greater than 1 for AN38 F4 3 FREQUENCY Figure 4 3 DC Gain of 1 Results in Amplitude Greater Than OdB at fp DC Gain is Reduced Attenuating Frequencies in the Passband those frequencies see Figure 4 3 and the LTC1060 data sheet Depending on the strength of the input signal the output from the high Q stage may saturate the following input stage driving itinto its non linear region and thereby creating distortion Setting the gain of the high Q stage so that the peak at fg does not exceed OdB results in a DC gain of less than 1 for the stage This has the effect of significantly attenuating most of the frequencies in the passband thereby minimizing the excursions of the input amplifier Although this strategy reduces harmonic distortion it can create noise problems because the noise generated by a 2nd order stage increases with Q As a rule of thumb noise can be regarded as increasing at approximately the square root of Q When the output from the high Q stage is amplified by subsequent stages in order to bring the overall passband gain up to 1 its noise component is amplified proportionally Figure 4 4 Thus as we Stated previously THD optimization is inimical to noise optimization so the best cascade is acompromise between the two ji fo FREQUENCY HIG
7. on the numeric keypad The arrow can move in either fine or coarse increments To select course move ment press the key To select fine movement press the key Move the arrow to one corner of the area that you wish to magnify and press Enter Next move the arrow to the opposite corner of the area of interest As you move the arrow you will see a box expand to enclose the area to be magnified If you want to relocate the box you must press ESC and restart the selection process When the box encloses the desired area press Enter an38f AN38 8 LI MYR Application Note 38 and the screen will be redrawn and a new graph will be plotted within the selected range Note that the program actually calculates new points as appropriate for the higher precision of the magnified section It is possible to zoom in repeatedly to magnify progres sively smaller areas of the graph There is a limit to this process but the available magnification is more than adequate for any practical purpose If you want to output the magnified graph to the plotter or a disk file you can do so Just press ESC once to return to the GRAPH MENU screen change the Output device to plotter or disk press Enter and then proceed with the plotting process as described later To zoom out to the previous graph press L for Large You can zoom outas many times in succession as you have zoomed in Note however that for eac
8. pants method If you lack such erudi tion however it is beyond the scope of the program or this manual to supply it Nevertheless novice designers can make productive use of FilterCAD s custom response feature by entering design parameters from published tables An example of this technique will be found in the following section STEP TWO GRAPHING FILTER RESPONSE After you have designed your filter the next step is item two on the MAIN MENU GRAPH Filter Response You can graph the amplitude phase and or group delay characteristics of your filter and you can plot your graph on either a linear or logarithmic scale The graph also highlights the 3dB down point s for Butterworth filters Only and the point s where the calculated attenuation is achieved An additional option on the Graph Menu is called Reduced View This option displays a reduced view of your graph in a window in the upper right hand corner of the full sized graph This feature is useful in conjunction with the Zoom option Use the Up Arrow and Down Arrow keys to move through the list of graph parameters and press the Spacebar to step through the selections for each parameter that you wish to modify When all of the graph parameters have been set correctly press Enter to begin plotting the graph Plotting to the Screen If you chose the screen as your output device FilterCAD will immediately begin plotting the graph Generating
9. peak The most noise in cascaded filters is contributed by the stages with the highest Qs the noise being greatest in the vicinity of the resonance peaks By placing the stage with the lowest Q and the lowest fo last in the cascade order we place much of the noise contributed by previous stages outside the passband of this final stage resulting in a reduction of the overall noise Also because the final stage is the lowest in Q it contributes relatively little noise of its own This technique allows the realization of selective elliptic lowpass filters with acceptable noise levels Optimizing for Harmonic Distortion Distortion in switched capacitor filters can be caused by three factors First distortion can be produced by load ing The CMOS amplifiers that are used in LTC switched capacitor filter devices are not suited to driving heavy loads For best results no node should see an impedance of less than 10kQ and you will observe that FilterCAD never calculates a resistor value below this limit Further it may be desirable when trying to obtain optimal distor tion performance to scale up resistor values calculated by FilterCAD by a factor of two or three to minimize loading The second factor that affects distortion performance is the clock frequency Each LTC switched capacitor filter device has an optimum clock frequency range Using a clock frequency significantly above the optimal range will result in increased distortion F
10. to get from a Specification to a working design with the least time and effort accept the device and modes that FilterCAD selects To complete the implementation process press ESC to exit the device screen then press R to calculate the resistor values You can calculate absolute values by pressing A Or the nearest 1 tolerance values by pressing P There is one more option on the implementation menu that we have not yet examined Edit CASCADE ORDER This option allows you to exchange poles and zeros among and edit the cascade order of the 2nd order sections that make up your filter This represents one of the most arcane and esoteric aspects of filter design even the experts are sometimes at a loss to explain the benefits to be gained by tweaking these parameters So once again we must recommend that the novice leave this feature alone SAVING YOUR FILTER DESIGN Item 4 on the MAIN MENU SAVE Current Filter Design allows you to save your design to disk Press 4 to save your design By default a new file will be saved with the name NONAME while a file that was previously saved and loaded will be saved under its previous name If you want to save the file under a different name just type it in at the cursor position Type the file name only eight characters or fewer do not type an extension All files are saved with the extension FDF Filter Design File By default the file will be stored in t
11. 0 again and repeat the process previously described Implementation When you are satisfied with the optimization press to proceed with the implementation This won t do anything obvious except to clear the window where the optimization information is displayed so press D to view the selected device cascade order and modes When the Device screen is first displayed it will show detailed specifications of the selected part To see the Note 2 FilterCAD will not optimize custom filter designs nor will it select the modes for such designs This is just another indication that custom designs are the province of experienced designers an38f AN38 10 LI MYR Application Note 38 mode diagrams of the 2nd and 1st order sections that implement the design press the Down Arrow key to move the cursor through the cascade order list on the left hand side of the screen You will have probably observed that on the implementa tion menu this screen is entitled Edit DEVICE MODEs and youcan infact manually edit both the device selection and the modes of the 2nd and 1st order sections This capability however is one that the novice user would be best advised to ignore If you manually edit the device selection or the modes you are essentially ignoring the expertise that is built into the program in favor of your own judgment Experienced designers may choose to do this under some circumstances but if you want
12. 0 11 3041 0 0000 4 5149 2043 11 3041 INFINITE The Qs of the sections have been kept within reasonable limits by specifying the very low minimum passband ripple of0 05dB Thatthis should be the case may not be obvious until you consider thatthe passband ripple consists of the product of the resonant peaks of the 2nd order sections By keeping the passband ripple to a minimum the Qs of the individual sections are reduced proportionally You can verify this fact by changing the passband ripple to a higher value and observing the effect on the Qs of the 2nd order sections Next we ll graph the response of our design The result appears in Figure 3 3 We have reset the frequency range of the graph to focus on the area of interest Observe that the slope of the amplitude response rolls off quite steeply in the transition region and that the slopes become more gradual well into the stopband In other words the slope is not constant This is a characteristic of Chebyshev fil ters The characteristic passband ripple is not observable at the current scale but we can see it by zooming in on the passband Note 4 It is possible to design a bandpass filter from a mixture of highpass and lowpass or highpass lowpass and bandpass sections but FilterCAD will not do this When you specify a particular filter type all of the sections used to realize the design will be of that same type To zoom first press to select coarse motion then
13. 10dB Of course this capacitor resistor combination constitutes a passive 1st order lowpass stage with a corner frequency at 1 27RC In the case of the values indicated above the corner frequency will appear so far out in the passband that it is unlikely to be significant However if the notch is needed at a frequency below 20kHz the capacitor value will need to be increased and the corner frequency of the 1st order stage will be lowered proportionally For a capacitor of 100pF and an R2 of 10k the corner frequency will be 159kHZz a value that is still unlikely to cause problems in most applications For a capacitor of 500pF a value that might prove necessary for a deep notch at a low center frequency and an R2 of 20k the corner frequency drops down to 15 9kHz If maximum stopband attenuation is more important than a wide passband such a solution may prove acceptable Adding resistors in parallel with R2 produces one additional problem it increases the Q that we just controlled with the capacitors across R4 Resistor values must be adjusted to bring the Q down again Table 4 6 contains the parameters for a real notch filter which actually meets our 60dB attenuation spec using the techniques previously outlined This is essentially the clock tunable 8th order notch filter described in the LTC1064 data sheet Note the mixture of modes used This is a solution that FilterCAD is incapable of proposing It should be apparent that the meth
14. 3 only five seconds shy of the record The main function of this screen however is to print a design report This report will include all of the information about your filter available on the design optimization and implementation screens except for the mode diagrams You can also print the gain phase and group delay of your filter design by pressing P Note that if you have not completed the design process by implementing the design and calculating resistor values the REPORT AVAILABLE line will say PARTIAL A partial report lacking modes and resistor values can be printed but for a complete report you must implement and calculate resistor values QUITTING FilterCAD The ninth and final item of FilterCAD s MAIN MENU END FilterCAD is self explanatory If you haven t saved your current design before attempting to exit the program FilterCAD will ask you if you wish to do so Press Y to exit the program or press N to remain in FilterCAD an38f AN38 12 LI MYR Application Note 38 Now that we have examined the principal features of Fil terCAD let s walk through a few typical filter designs to get a better idea of how the program works A BUTTERWORTH LOWPASS EXAMPLE First we ll design a Butterworth lowpass filter one of the most basic filter types Load FilterCAD if you haven t already done so and press 1 to go to the design screen Select lowpass as the design type and Butt
15. 3 4 fo Q and fp Values for Lowpass Elliptic Examples STAGE fo Q fn and the gain of stage one has been set to 1 for improved Highest f Not Removed dynamics When we view the Device screen we ll see the i 478 1819 0 6059 BAAD 3055 specs of the LTC1164 and two diagrams of the mode 3 7 TAT S747 1 3988 3032 7089 network followed by two diagrams of the mode 2 network l a 3 939 2728 3 5399 1472 2588 with different f Q and f values see Figures 3 5A and g 4 1022 0167 13 3902 1315 9606 3 5B Calculating the 1 resistor values produces the results in Table 3 3 eee ae 1 466 0818 0 5905 INFINITE Table 3 3 Resistors for Chebyshev Bandpass Example 2 723 8783 1 3544 2153 9833 STAGE R1 R2 R3 R4 3 933 1712 3 5608 1503 2381 1 115 0k 10 00k 68 10k 10 70k 4 1022 0052 13 6310 1333 1141 2 215 0k 10 00k 113 0k 11 50k a When we graph our two elliptic examples Figures 3 6A 3 17 80k 10 00k 205 0k 64 90k and 3 6B we see that the response of the filter without the 4 90 90k 10 00k 105 0k 165 0k highest fn removed shows four notches in the stopband and a gradual slope after the last notch whereas the filter TWO ELLIPTIC EXAMPLES g p For our next example we will design a lowpass filter with an elliptic response We ll specify a maximum passband with the highest f removed exhibits only three notches followed by a steeper slope Both examples have the steep initial r
16. AX gt GAIN gt fs fc FREQUENCY Figure 2 2 Highpass Design Parameters Amay Maximum Passband Ripple fc Corner Frequency fs Stopband Frequency Ayn Stopband Attenuation 0dB AMAX GAIN l fc FREQUENCY Figure 2 4 Notch Design Parameters Ajay Maximum Passband Ripple fc Center Frequency PBW Pass Bandwidth SBW Stop Bandwidth Ayn Stopband Attenuation an38f AN38 6 AI MYR Application Note 38 case of Butterworth response must be 3dB the stopband attenuation in dB the corner frequency also known as the cutoff frequency in Hz and the stopband frequency If you chose a bandpass or notch filter you must enter the maximum passband ripple and the stopband attenuation followed by the center frequency in Hz the pass bandwidth in Hz and the stop bandwidth in Hz The meanings of these various parameters in the different design contexts are illustrated in Figures 2 1 to 2 4 Ifyou chose acustom response you re in an entirely different ball game which will be described later Type in the parameters for your chosen filter pressing Enter after each parameter If you want to go back and alter one of the parameters you have previously entered use the Up Arrow and Down Arrow keys to move to the appropriate location and retype the parameter When you have entered all of the correct pa rameters move the cursor to the last param
17. GN screen then press 1 to re enter the DESIGN screen Move the cursor to FILTER RESPONSE and use the Spacebar to select CUSTOM You can now edit the fo Q and fh values for the 2nd order and 1st order sections in the window at the bottom of the screen When you custom ize an existing design the normalization frequency is automatically set to the previously specified corner center frequency It can however be edited by the user To design a custom filter from scratch simply select CUSTOM as your response type upon first entering the DESIGN screen then type in the appropriate fo Q and fn values for the desired response By default the normaliza tion value for custom filters is 1Hz Once you have entered your values you can change the normalization frequency to any desired value and FilterCAD will scale the fo and f frequencies accordingly To change the normalization frequency press N type in the new value and press Enter By alternately graphing the resulting response and modify ing the fo Q and fp values almost any kind of response Shape can be achieved by successive approximations It should be understood that true custom filter design is the province of a small number of experts If you have an38f LI M AN38 7 Application Note 38 a feel for the type of pole and Q values that produce a particular response then FilterCAD will allow you to design by this seat of the
18. H Q LOW GAIN SECTION GAIN AN38 F4 4 fo FREQUENCY SUBSEQUENT SECTION WITH LOWER Q HIGHER GAIN NOISE FROM PREVIOUS SECTION IS BOOSTED Figure 4 4 Noise Generated by a High Q Low Gain Stage Is Amplified by a Subsequent Low Q High Gain Stage an38f AN38 20 LI MYR Application Note 38 MORE PRACTICAL EXAMPLES To illustrate how the sorting of cascade order can affect performance we will examine two concrete examples The first is an 8th order Butterworth lowpass filter nor malized to 1Hz The maximum passband ripple is 3dB the stopband attenuation is 48dB the corner frequency is 1Hz and the stopband frequency is 2Hz Two different versions of this design were implemented one with the cascade order sorted for decreased harmonic distortion THD and the other sorted for lowest noise Table 4 1 shows the fo Q and f values for both versions of our example Of the four stages three have Qs of less than 1 and one has a Q greater than 2 5 The two cascade orders differ only in the position of this high Q section Observe that in the first case the highest Q stage was placed in the second position rather than the first as the previous discussion indicated This is a compromise to minimize harmonic distortion while maintaining acceptable noise performance In the second case the highest Q section is placed in the third position followed immediately by the section with the lowest Q Since this is a Butte
19. NS8 5 Application Note 38 STEP ONE THE BASIC DESIGN The first item on FilterCAD s MAIN MENU is DESIGN Filter To access the DESIGN Filter screen press 1 On the DESIGN Filter screen you make several basic deci sions about the type of filter you re going to design First you must select your basic filter type lowpass highpass bandpass or notch Press the Spacebar to step through the options When the filter type that you want is displayed press Enter lt OdB AMAX GAIN fc fs FREQUENCY Figure 2 1 Lowpass Design Parameters Amax Maximum Passband Ripple fc Corner Frequency fs Stopband Frequency Am n Stopband Attenuation fc FREQUENCY Figure 2 3 Bandpass Design Parameters Amay Maximum Passband Ripple fc Center Frequency PBW Pass Bandwidth SBW Stop Bandwidth Ayn Stopband Attenuation Next you must select the type of response characteristic you want Butterworth Chebyshev Elliptic or Custom Again use the Spacebar to step through the options and press Enter when the response type you want is displayed Next you will enter the most important parameters for your filter Exactly what these parameters will be depends on the type of filter you have chosen If you have selected lowpass or highpass you must enter the maximum pass band ripple in dB must be greater than zero or in the lt OdB AM
20. Y AN38 F4 8 Figure 4 8 THD Performance 6th Order Elliptic Sorted for Reduced THD 200 0 100 1k 5k FREQUENCY AN38 F4 10 Figure 4 10 Noise Performance 6th Order Elliptic Sorted for Reduced THD Inthe second example 2nd order stages have been sorted for reduced noise In this case the stage with the highest Qand f is placed in the middle of the cascade order and is followed immediately by the stage with the lowest Q and fo Most of the gain is provided by stage three which would tend to boost the noise generated by the previous stage but the greater than 2 1 ratio between the fgs of the two sections causes much of the noise generated by stage two to fall outside of stage three s passband see Figure 4 7 This produces the band limiting effect described previously and improves the overall noise performance of the circuit significantly Figures 4 8 through 4 11 detail noise and THD performance of the two 6th order elliptic examples 0 1 THD N 0 01 100 1k FREQUENCY AN38 F4 9 Figure 4 9 THD Performance 6th Order Elliptic Sorted for Reduced Noise 200 100 1k 5k FREQUENCY AN38 F4 10 Figure 4 11 Noise Performance 6th Order Elliptic Sorted for Reduced Noise NOTCHES THE FINAL FRONTIER Notch filters especia
21. cludes the following files If after installing the program you have difficulty in running FilterCAD check to be sure all of the necessary files are present README DOC Optional if present includes updated information on FilterCAD not included in this manual INSTALL BAT Automatic installation program installs FilterCAD on hard drive FCAD EXE Main program file for FilterCAD FCAD OVR Overlay file for FilterCAD used by FCAD EXE FCAD ENC Encrypted copyright protection file DO NOT TOUCH FDPFEXE Device parameter file editor used to update FCAD DPF see Appendix 1 4J LT LTC LTM Linear Technology the Linear logo LTspice and FilterCAD are registered trademarks and QuikEval is a trademark of Linear Technology Corporation All other trademarks are the property of their respective owners an38f LI M AN38 1 Application Note 38 FCAD DPF Device parameter file holds data for all device types supported by FilterCAD ATT DRV AT amp T graphics adapter driver CGA DRV IBM CGA or compatible graphics driver EGAVGA DRV EGA and VGA graphics drivers HERC DRV Hercules monochrome graphics driver ID DRV Identification file for all driver specifica tions Note Once you have configured FilterCAD and selected your display type you can delete unnecessary drivers if you need to conserve disk space Be sure not to delete any drivers Before You Begin Please check the FilterCAD program to see if it conta
22. e Response Having graphed our filters response we will next go to the implementation screen to transform it into a practical design Press ESC twice to exit the graph display then press 3 to go to the implementation screen The first step is to optimize Lacking any other pressing need we ll optimize for noise the default optimization strategy We ll use a clock frequency ratio of 50 1 and we ll leave auto device selection ON Press 0 to execute optimization FilterCAD selects the LTC1164 and indicates that the Qs have been intermixed for the lowest noise Next press for implement and then D to display the device screen This screen shows detailed specs of the LTC 1164 and in the window on the left hand side of the screen indicates that all four of the 2nd order sections in the design will use mode 1 Press the Down Arrow key and you ll see a diagram of a mode 1 network like the One in Figure 3 2 in place of the LTC 1164 specs Press the Down Arrow three more times and you ll see three more examples of the same network differing only in the Q values This con figuration would be fine except for one thing the LTC 1164 has four 2nd order sections but the fourth lacks an acces sible summing node and therefore cannot be configured in mode 1 You must manually change the mode of the last stage to mode 3 This illustrates the limitations of the present version of FilterCAD Figure 3 2 Mode 1 Network
23. e and phase characteristics of our Butterworth lowpass filter Press ESC to return to the MAIN MENU then press 2 to go to the graph menu We re going to output this graph to the screen so press Enter to begin graphing immediately In a few seconds or a few minutes depending on the type of computer system you re using you should see a graph very much like the one in Figure 3 1A Amplitude in dB s is indicated on the left side of the graph and phase in degrees is indicated on the right side If you have your graph parameters set differently than FilterCAD s defaults your graph may show less of the frequency and amplitude range than the figure If you don t see a graph substantially like the One in Figure 3 1A you may need to adjust the graph s ranges Exit the graph screen go to the MAIN MENU and select 6 CONFIGURE FilterCAD Next select item 6 Configure DISPLAY Parameters followed by item 2 Change GRAPH Window GAIN E GROUP DELAY n gt FILTER RESPONS B PHASE DEO FILTER TYPE gctum ATTEN 49 1442 db FREQUENCY 312 99 Hz O3 1000 Hz GAIN 39 75 db e r a so LT OA o f ST a Rh E KI U TTT i CT TTEN ATT WEE Ch sof TM E C T TT TAA AT T T e eee ee eee N e A S T T T NA T Con E EE ENN i ESC exit ar P plot requency Figure 3 1A Butterworth Lowpass Filter Response Observe the characteristic amplitude and phase response curves of the But
24. e will select mode 3 for all sections because the three sections each have different corner frequencies and mode 3 provides for independent tuning of the individual sections by means of the ratio R2 R4 We ve seen what the mode 3 network looks like before so we won t duplicate it here Having selected the mode we can calculate resistor values The results are shown in Table 3 7 PHASE DEO FILTER TYPE 3db POINT NA GAIN nie ne i F e C BIESEN S CO es T PER re E E ET N CUM se oz i conn ae so HH maii Mi R N AT eee MI sso 00 EA Ei Ban aa HH W T T a20 Ese exit ALT P plot Figure 3 8 6th Order Lowpass Bessel Response Table 3 7 Resistors for 6th Order Bessel Lowpass Example STAGE fo Q fn STAGE R1 R2 R3 R4 1 1 606 0 510 INFINITY 1 13 00k 33 20k 10 00k 13 00k 2 1 691 0 611 INFINITY 2 10 50k 29 40k 10 00k 10 50k 3 1 907 1 023 INFINITY 3 10 00k 36 50k 17 40k 10 00k an38f AN38 18 AJ White Application Note 38 EDITING CASCADE ORDER As stated earlier in this manual optimizing performance by editing cascade order and or swapping pole and Q values is among the most arcane esoteric aspects of active filter design Although certain aspects of this process are understood by experienced designers current knowledge is not sufficiently systematic to guarantee the success of algorithmic optimization Hence the need for manual edit ing In the discussion that fol
25. ency accuracies when compared to active RC filters Chebyshev and elliptic designs can achieve greater stopband attenuation for a given number of 2nd order sections than can Butterworths o A T see ERA Ea a e E D a d ot A E E A OO A SC FTE O ieee oo Figure 1 8 6th Order Elliptic Lowpass Response an38f AN38 4 LI M Application Note 38 Application Note 38 Filters are typically built up from basic building blocks known as 1st order and 2nd order sections Each LTC filter contains circuitry which together with an external clock and a few resistors closely approximates 2nd order filter functions These are tabulated in the frequency domain 1 Bandpass function available at the bandpass output pin refer to Figure 1 9 SW Q G s Hogep 8 Howe s sw Q 0 Hopp Gain at Wo fo 27 fo is the center frequency of the com plex pole pair At this frequency the phase shift between input and output is 180 Q Quality factor of the complex pole pair It is the ration of fg to the 3dB bandwidth of the 2nd order bandpass function The Q is always mea sured at the filter BP output 2 Lowpass function available at the LP output pin refer to Figure 1 10 2 G s Hop 7 7 0 S S Q 5 Hop DC gain of the LP output BANDPASS OUTPUT NVN GA GAIN V V ft fo fH f LOG SCALE a _ 4 fi fvi f x c 0 Figure 1 9 2
26. erworth as the response type Now we have four additional parameters to enter The passband ripple mustbe specified as 3dB this places the cutoff frequency 3dB down with respect to the filters DC gain Should you desire a Butterworth response with other than 3dB pass band ripple you can do so by going to the custom menu Let s select an attenuation of 45dB a corner frequency of 1000Hz and a stopband frequency of 2000Hz Press Enter after each parameter When the last parameter is entered FilterCAD will synthesize the response We soon see that the result is an 8th order filter with an actual attenuation of 48 1442dB at 2000Hz It is composed of four 2nd order lowpass sections all with corner frequencies of 1000Hz and modest Qs Having the same corner frequency for all of the cascaded sections is a characteristic of Butterworth filters This is a good time to experiment with some of the filters parameters to see how they affect the result ing design Try increasing the attenuation or lowering the stopband frequency You ll discover that any modification that results in a significantly steeper roll off will increase the order of the filter proportionally For instance reducing the stopband frequency to 1500Hz changes results in a filter of order 13 If a very steep roll off is required and some ripple in the passband is acceptable a response type other than Butterworth would probably be preferable Next we ll graph the amplitud
27. es in the passband may also be modified either in amplitude ripple or in phase Real world filters all represent compromises steepness of slope ripple and phase shift plus of course cost and size FilterCAD permits the design of filters with one of three response characteristics plus custom responses These three response types which are known as But terworth Chebyshev and Elliptic represent three different compromises among the previously described characteristics Butterworth filters Figure 1 6 have the optimum flatness in the passband but have a slope that GAIN FREQUENCY Figure 1 5 Ideal Lowpass Response Figure 1 7 6th Order Chebyshev Lowpass Response rolls off more gradually after the cutoff frequency than the other two types Chebyshev filters Figure 1 7 can have a steeper initial roll off than Butterworths but at the expense of more than 0 4dB of ripple in the passband Elliptic filters Figure 1 8 have the steepest initial roll off of all But exhibit ripple in both the passband and the stopband Elliptic filters have higher Qs which may if not carefully implemented translate to a noisier filter These high Qs have made elliptic filters difficult to implement with active RC filters because of the increased stability and center frequency accuracy requirements Elliptic filters can be implemented with SCFs due to their inherently better Stabilities and center frequ
28. eter in the list and press Enter FilterCAD will now calculate and display additional param eters of the filter you have designed including its order actual stopband attenuation and gain and will display a list of the 2nd order and 1st order sections needed to realize the design along with their fo Q and fh values as appropriate These numbers will be used later to implement your filter design and calculate resistor values FilterCad will in many cases prevent you from entering inappropriate values For instance in the case of a lowpass filter the program will not permit you to enter a stopband frequency that is lower than the corner frequency Similarly in the case of a highpass filter the stopband frequency must be lower than the corner frequency In addition you cannot enter a maximum passband ripple value that is greater than the stopband attenuation nor can you enter a set of values that will lead to a filter of an order greater than 28 Custom Filters The custom response option on the DESIGN screen can be used in two ways It can be used to modify filter de signs created by the method previously described or it can be used to create filters with custom responses from scratch by specifying a normalization value and manually entering the desired f Q and fp values for the necessary 2nd order and 1st order sections To edit the response of a filter that has already been designed press ESC to exit the DESI
29. ew devices except the fields will contain data Use the keys to page through the devices to find the one you wish to edit move the cursor to the fields that you want to modify and type in the new data You must press Enter to accept the new value in each field Press ESC when you have finished editing The remainder of the options on the Device Parameter File Editors main menu are self explanatory APPENDIX 2 Bibliography For more information on the theory of filter design consult one of the works listed below 1 Daryanani Gobind Principles of Active Network Syn thesis and Design New York John Wiley and Sons 1976 2 Ghausi M S and K R Laker Modern Filter Design Active RC and Switched Capacitor Englewood Cliffs New Jersey Prentice Hall Inc 1981 3 Lancaster Don The Active Filter Cookbook India napolis Indiana Howard W Sams amp Co Inc 1975 4 Williams Arthur B Electronic Filter Design Handbook New York McGraw Hill Inc 1981 PgDn Note Applications and algorithms by Nello Sevastopoulos Philip Karantzalis and Richard Markell and PgUp an38f Linear Technology Corporation TWD I NEAD AN38 26 1630 McCarthy Blvd Milpitas CA 95035 7417 OI ONK 408 432 1900 FAX 408 434 0507 www linear com LINEAR TECHNOLOGY CORPORATION 1990
30. frequencies present at their input In addition it is possible to create filters with more complex responses which are not easily categorized a CS ae ae Sa ee a AA Fe mv AN M HN eS eas Ga aa R a Pt 0 E ee a A E A E 100 oe Press ESC to Return Frequency Hz Figure 1 4 Notch Response The range of frequencies that a filter passes is known logi cally enough as its passband The range of frequencies that a filter attenuates is known as its stopband Between the passband and stopband is the transition region An ideal filter might be expected to pass all of the frequen cies in its passband without modification while infinitely attenuating frequencies in its stopband Such a response Note 1 While allpass filters don t affect the relative amplitudes of signals with different frequencies they do selectively affect the phase of different frequencies This characteristic can be used to correct for phase shifts introduced by other devices including other types of filters FilterCAD cannot synthesize allpass filters an38f LI M AN38 3 Application Note 38 is shown in Figure 1 5 Regrettably real world filters do not meet these imaginary specifications Different types of filters have different characteristics less than infinite rates of attenuation versus frequency in the transition region In other words the amplitude response of a given filter has a characteristic slope Frequenci
31. ges where fo gt fo K 50 The overall gain of 27 29dB has been evenly distributed among stages two through four ripple of 0 1dB an attenuation of 60dB a corner frequency of 1000Hz and a stopband frequency of 1300HZz In the case of an elliptic response we have one additional ques tion to answer before the response is synthesized When we have entered the other parameters FilterCAD asks Remove highestf Y N This question requires a bit of explanation An elliptic filter creates notches by summing the highpass and lowpass outputs of 2nd order stages To create a notch from the last in a series of cascaded 2nd order stages an external op amp will be required to sum the highpass and lowpass outputs Removing the last notch from the series eliminates the need for the external op amp but does change the response slightly as we will see Note The last notch can be removed only from an even order elliptic filter If you are synthesizing an elliptic response for the first time and you are uncertain what order of response will result answer NO when asked if you want to remove the last notch If an even order response results you can go back and remove the last notch if you wish For comparison we will synthesize both responses The f Q and f values for both designs both are 8th order are shown in Table 3 4 Observe that the removal of the high est fn produces slight variations in all of the other values Table
32. h suc cessive zoom out the graph is recalculated and replotted If you have done several successive zooms and you want to get back to the full sized graph without the intermediate Steps it will be quicker to press ESC twice to return to the MAIN MENU then re enter the GRAPH screen Printing the Screen You can dump your screen graph to your printer at any time by pressing Alt P This same feature can be used from the Device Screen see the implementation section to print FilterCAD s mode diagrams The screen print routine will check to see whether your printer is connected and turned on and will warn you if itis not If your printer is connected and turned on but off line FilterCAD will put it on line and begin printing Once printing begins however FilterCAD does no error checking so turning off your printer or taking it off line to stop printing may cause the program to hang up Plotting to a Plotter HPGL File or Text File If you choose to send your graph to a plotter or to an HPGL disk file you will first be shown the PLOTTER STATUS MENU First you will be asked GENERATE CHART Y N You are not being asked here whether you want to plot a graph but whether when you plot to disk or plotter you want to draw the grid or only plot the data This may seem like an absurd choice but it is here for a reason If you are plotting to a plotter you could overlay the response graphs of several different filte
33. he current directory the directory that was active when FilterCAD was started This directory will be displayed at the top of the screen If you want to save the file to a different directory press Home then type in a new path When the file name and path are correct press Enter to save the file If there is already a file on the disk with the name that you have selected FilterCAD will ask whether you want to overwrite the file Press Y to overwrite the file or press N to save the file under a different name Note 3 Of course there is no harm in the novice experimenting with the advanced features of FilterCAD provided he or she realizes that the results of such experiments will not necessarily be useful filter designs an38f LI M AN38 11 Application Note 38 LOADING A FILTER DESIGN FILE To load a Filter Design File that you have previously saved select 5 on the main menu The LOAD FILE MENU screen will display a directory of all of the FDF files in the current directory Use the cursor keys to move the pointer to the name of the file you want to load and press Enter lf there are more FDF files than can be displayed on the screen at one time press the PgDn key to see additional files If you want to load a file from a different directory press p then type in the new path You can also enter a mask to restrict the file names which will appear on the screen This mask can cons
34. ing pole and Q values When you set the response on the Design screen to Custom and press Enter the usual parameter entry stage is bypassed and you go directly to the fg Q and fp section where you can enter any values you want We ll use values from Table 3 6 fora filter normalized to 3db 1Hz The published table from which these values were taken didn t mention f values at all so when the author typed them in initially he left the fn values as he found them as zeros The result was not the desired lowpass filter but its highpass mirror image This shows the kind of trap that awaits the unwary Once the values have been entered they can be re normalized for any desired corner frequency Just press Enter In this case we will re normalize to 1000Hz which simply multiplies the f values in the table by 1000 Looking atthe graph of the resulting response Figure 3 8 we see the characteristic Bessel response with its droopy passband and very gradual initial roll off When we go to Table 3 6 fo Q and fn Values for 6th Order Lowpass Bessel Normalized for 1Hz the implementation stage the process is a little different than we are accustomed to FilterCAD won t optimize a custom design nor will it specify the mode s It will however select the device the envelope please the LTC1164 Now we need to go to the device screen and manually select the mode for each of the three 2nd order sections W
35. ins the README DOC file This file if present will contain important information about FilterCAD not included in this manual Please read this file before attempting to install and use FilterCAD To display the README file on your screen type TYPE README DOC Enter Press Ctrl S to pause scrolling Press any key to resume scrolling To print a hard copy of the README file on your printer type TYPE README DOC gt PRN Enter Procedure for FilterCAD Installation in Win7 PC The FilterCAD installation in Win7 downloads reliably to a target folder 1 If an LTC program like LTspice or QuikEval has been installed then the following directory folder exists a C Program Files LTC in a 32 bit system or b C Program Files 86 LTC in a 64 bit system If not then create a directory folder as in a or b The FilterCAD download is at http www linear com designtools software Filter 2 Start the FilterCAD download and open the FilterCAD zip to extract the FilterCADv300 exe Right Click on FilterCAD exe and select Run as an administrator then select the following Directory C Program Files LTC in a 32 bit system or C Program Files 86 LTC in a 64 bit system 3 Go to C Program Files LTC in a 32 bit system or C Program Files 86 LTC in a 64 bit system Open OPEN THIS FOLDER TO INSTALL FilterCAD and Run SETUPexe then FilterCAD is installed in C Program File
36. ist of any of the characters that DOS allows for file names including the DOS wildcards and By default the mask is allowing all file names to be displayed To change the mask press M then type in a new mask of up to eight characters For example if you named your FDF files in such a way that the first two letters of the file name represented the filter type LP for lowpass HP for highpass etc you could change the mask to LP to display only the lowpass filter design files Note If you attempt to load an FDF file created with an earlier version of FilterCAD the program willissue a warning and ask you whether you want to abort loading or proceed at your own risk Differences between FDF files from dif ferent versions of FilterCAD are minor and you should be able to load and use earlier FDF files without difficulty Caution When you load a filter design file FilterCAD DOES NOT prompt you to save any design currently in memory so when a new file is loaded any unsaved work in memory will be lost PRINTING A REPORT Item 7 on the MAIN MENU SYSTEM Status Reports displays a varied collection of information on your system such as the date and time the presence or absence of a math coprocessor and the status of your printer and com munications ports It also shows the state of progress of the current design including the total design time Gosh a 6th order Butterworth lowpass in 00 05 2
37. lliptic Examples ACT 3db POINT GAIN Ese exit ALT P plot Figure 3 6B Lowpass Elliptic Highest fn Removed Calculating 1 resistor values for clock to fo ratio 50 1 clock frequency equals 50 000Hz for our two elliptic variations yields the results in Table 3 5 Ry and R are the resistors which sum the highpass and lowpass outputs of the successive stages and Rg is the resistor that sets the gain of the external op amp Therefore there is one fewer Ry R pair in the version with the last fa removed and Rg is found only in the last stage of the first example Also R1 the resistor connected to the inverting input of the input amplifier is used only for the first stage The Ry R pair takes the place of R1 in subsequent stages R4 AN38 F3 7 Figure 3 7 Mode 3A Network STAGE R1 R2 R3 R4 Rg Ru RL Highest f Not Removed 1 24 90k 10 00k 17 40k 17 80k 237 0k 57 60k 2 10 50k 73 20k 10 00k 21 50k 12 70k 3 10 00k 30 90k 11 30k 21 50k 10 00k 4 19 60k 24 30k 86 60k 10 20k 294 0k 10 00k Highest f Removed 1 26 10k 10 00k 17 40k 19 10k 261 0k 56 20k 2 10 50k 75 00k 10 00k 23 20k 13 00k 3 10 00k 31 60k 11 50k 22 60k 10 00k 4 18 70k 23 20k 86 60k an38f LI MW AN38 17 Application Note 38 A CUSTOM EXAMPLE For a simple example of how the custom design option works we ll design a 6th order lowpass Bessel filter by manually enter
38. lly those with high Qs and or high attenuations are the most difficult to implement with universal switched capacitor filter devices You may de sign a notch filter with FilterCAD with specifications that purport to yield a stopband attenuation of greater than 60dB and find that in practice an attenuation of 40dB or less is the result This is primarily due to the sampled data nature of the universal filter blocks signals of equal amplitude and opposite phase do not ideally cancel when summed together as they would do in a purely analog system Notches of up to 60dB can be obtained but to do so requires techniques not covered by this version of FilterCAD Some of these techniques will be examined here an38f LI M AN38 23 Application Note 38 Table 4 4 Resistor Values for 6th Order Lowpass Elliptic 100 1 fei to fe STAGE R1 R2 R3 R4 Rg Ru RL LOWPASS GAIN Sorted for Low THD 1 150 0k 10 00k 150 0k 10 00k 15 00k 10 00k 0 067 2 11 80k 43 20k 16 50k 22 60k 10 00k 1 650 3 16 90k 28 70k 78 70k 11 50k 130 0k 10 00k 7 870 External Op Amp 1 150 Total 1 000 Sorted for Low Noise 1 43 20k 10 00k 36 50k 14 00k 110 0k 48 70k 0 324 2 10 00k 150 0k 10 00k 15 00k 10 00k 0 205 3 28 00k 48 70k 130 0k 11 50k 130 0k 10 00k 13 00 External Op Amp 1 150 Total 0 993 Table 4 5 fo Q and fn Values for 40kHz 60dB Notch Table 4 6 fo Q and fn Values for 40kH
39. lows we will consider briefly the underlying principals of optimization for minimizing noise or harmonic distortion This will be followed by some concrete examples illustrating the effect of these principles on real world filter designs It should be emphasized that the fine tuning process described here may or may not be necessary for a particular application If you need as sistance in maximizing performance of a filter using LTC parts do not hesitate to contact our applications depart ment for advice and counsel Optimizing for Noise The key to noise optimization is the concept of band limit ing Band limiting of noise is achieved by placing the 2nd order section with the lowest Q and lowest f in the case ofa lowpass filter astin the cascade order To understand why this works we must consider the response shapes of 2nd order sections A 2nd order section with a low Q begins rolling off before fo Figure 4 1 The lower the Q the farther into the passband the roll off begins 2nd order sections with high Qs on the other hand have resonance peaks centered at fo Figure 4 2 The higher the Q the 0 01 0 1 1 10 100 1k 10k FREQUENCY Hz AN38 F4 1 Figure 4 1 Low Q 2nd Order Lowpass Response higher the resulting
40. nd Order Bandpass Section LOWPASS OUTPUT 3 Highpass function available only in mode 3 at the HP output pin refer to Figure 1 11 g o Q a4 G s H OnE eee Hopp gain of the HP output for gt GLK 4 Notch function available at the N output for several modes of operation s s w Q 2 s 04 G s Hon2 Hong gain of the notch output for f BLK Honi gain of the notch output for f0 f n 27 fp is the frequency of the notch occurrence These sections are cascaded the output of one section fed to the input of the next to produce higher order filters which have steeper slopes Filters are described as being of acertain order which corresponds to the number and type of cascaded sections they comprise For example an 8th order filter would require four cascaded 2nd order sections whereas a 5th order filter would require two 2nd order sections and one 1st order section The order of a filter also corresponds its number of poles but an explanation of poles is outside the scope of this manual A HIGHPASS OUTPUT Hop HoHP 0 707 Hopp GAIN V V fc fp f LOG SCALE fp fe f LOG SCALE f i bates Hop Hoip x Figure 1 10 2nd Order Lowpass Section eral 202 I Je 20 ol 20 A 20 Neat Fal oil Ja 1 al hf m i Hop Honp X ih Qy 40 Figure 1 11 2nd Order Highpass Section an38f Q o 1 402 LI M A
41. ods for notch filters described here are primarily empirical at this point and that the account given here is far from comprehensive We have not even touched on optimizing these filters for noise or distortion for instance No simple rules can be given for this process Such optimization is possible but must be addressed on a case by case basis If you need to implement a high performance notch filter and the tips above prove inadequate please call the LTC applications department for additional assistance APPENDIX 1 The FilterCAD Device Parameter Editor The FilterCAD Device Parameter Editor FDPFEXE al lows you to modify the FilterCAD Device Parameter File FCAD DPF This file contains the data about LTC switched capacitor filter devices which FilterCAD uses in making device selections in its implementation phase The Device Parameter Editor is a menu driven program that has a similar command structure to FilterCAD Its main menu includes the following entries 1 ADD New Device 2 DELETE Device 3 EDIT Existing Device 4 SAVE Device Parameter File 5 LOAD Device Parameter File 6 CHANGE Path to Device Parameter File 9 END Device Parameter Editor The principle reason for editing the Device Parameter File is to add data for new LTC devices that were released after this revision of FilterCAD To enter data for a new device press 1 You will see a blank form with fields for the necessary parameters Use the arrow key
42. oll off and extremely non linear phase response an38f AN38 16 LI MYR Application Note 38 GAIN db Sor DELAY nS FILTER RESPONSE org tH FILTER TYPE GAIN Et db COMIC oo TTT T TTN msi n C g CO T TTT TTSS TE TT T T A E TSN li Be exit ALT P piot Figure 3 6A Lowpass Elliptic Highest fn Not Removed in the vicinity of the corner frequency that are essential characteristics of the elliptic response If your only goal is stopband attenuation greater than 60dB either imple mentation would be satisfactory and the version with the highest f removed would probably be selected due to its lower parts count When we optimize our two elliptic filters for noise Filter CAD selects the LTC1164 and specifies mode 3A for all four stages Mode 3A is the standard mode for elliptic and notch filters as it sums the highpass and lowpass outputs of the 2nd order sections as described previously When we go to the Device screen we see four mode 3A diagrams each showing the external op amp as in Figure 3 7 In practice this external summing amp is not needed in every case When cascading sections the highpass and lowpass outputs of the previous section can be summed into the inverting input of the next section an external summing amp being required only for the last section If the highest f is removed external op amps can be dispensed with entirely Table 3 5 Resistor Values for Lowpass E
43. or information on accept able clock frequency ranges consult LTC data sheets and application notes If you do not observe these two design 0 01 0 1 1 10 100 1k 10k FREQUENCY Hz AN38 F4 1 Figure 4 2 High Q 2nd Order Lowpass Response an38f LI M AN38 19 Application Note 38 factors any attempt to optimize THD performance by editing cascading order will likely be wasted The third factor is distortion introduced by the non linear effects of the internal op amps when they swing close to their rails Both the gain and the position of the highest Q section are significant factors in this process As previously discussed high Q 2nd order sections Q gt 0 707 have a resonance peak in the vicinity of fg In order to maintain an overall gain of 1 for the circuit and to minimize distortion it is necessary to give high Q stages a DC gain of less than 1 and proportionally increase the gain of subsequent stages Note that FilterCAD automatically performs dynamic Optimization for designs based exclusively on mode 3A independent of the cascading order of the 2nd order sec tions If each stage were given a gain of 1 the overall gain for the circuit would of course be 1 However when a high Q section has a gain
44. ortion Note however that optimizing for harmonic distortion will result in the worst noise performance The Optimization screen also allows you to select the ratio of the internal clock frequency to fo 50 1 or 100 1 and the clock frequency in Hz and to turn automatic device selection on and off It should be understood that the clock frequency ratio represents the state of a particular pin on the device and does not necessarily correspond to the actual ratio of the clock frequency to fo Thus if you change the clock frequency to a value other than that automatically selected by FilterCAD the frequency ratio will not change accordingly Novice filter designers are advised to use the clock frequency selected by FilterCAD unless there is acompelling reason to do otherwise and to leave automatic device selection ON Clock frequencies and frequency ratios are not arbitrary but have a relationship to the corner or center frequency that depends upon the selected mode For more information on clock frequen cies frequency ratios and modes consult LTC product data sheets When you have selected the characteristic for optimization and adjusted the other options to your satisfaction move the cursor back to OPTIMIZE FOR and press 0 FilterCAD will respond by displaying the selected device and mode s and its rationale for selecting a particular cascade order If you want to re optimize for some other characteristic press
45. our example performance will gradually deteriorate One of the problems that we will encounter is Q enhancement Thatis the Qs ofthe stages will appear slightly greater than those set by resistors Note that Q enhancement is mostly a problem in modes 3 and 3A and is not limited to notches but occurs in LP BP and HP filters as well This results in peaking above and below the notch Q enhancement can be compensated for by placing small capacitors 3pF to 30pF in parallel with R4 mode 2 or 3 With this modification Q enhancement can be compensated for in notch filters with center fre quencies as high as 90kHz The values suggested here are compromise values for a wide range clock tunable notch If you want to produce a fixed frequency notch you can use larger caps at higher frequencies At least in the case ofthe LTC1064 Q enhancementis unlikely to bea problem below 20kHz Adding capacitors at lower frequencies will have the effect of widening the notch As mentioned previously the other problem in imple menting notch filters is inadequate attenuation For low frequency notches stopband attenuation may be increased by boosting the clock to notch frequency up to 250 1 Attenuation may also be improved by adding an38f AN38 24 AI MYR Application Note 38 external capacitors this time in parallel with R2 modes 1 2 and 3A Capacitors of 10pF to 30pF in this position can increase stopband attenuation by 5dB to
46. r designs on one sheet of paper for comparison If you drew the grid every time you would end up with a mess This option allows you to draw the grid on the first pass then plot only the data on successive passes This same process can be used albeit with slightly more effort when plotting to a disk file The procedure here is to plot two or more separate files the first with the grid turned on and the remainder with the grid turned off Then exit FilterCAD and use the DOS COPY command to concatenate the files For example if you wanted to concatenate three HPGL files named SOURCE SOURCE2 and SOURCES into a single file called TARGET you would use the following syntax COPY B SOURCE1 SOURCE2 SOURCES TARGET Enter After you have answered the question GENERATE CHART Y N the remainder of the PLOTTER STATUS MENU will be displayed Here you can select the dimensions of your graph the pen colors to be used and whether to print the design parameters below the graph When you have determined that the plotter options are set correctly press P to begin plotting If you wish to exit the PLOTTER STATUS MENU without plotting press ESC You can also plot your graph as a set of data points for gain phase and group delay plotted to disk in ASCII text format Select DISK TEXT an38f LI M AN38 9 Application Note 38 as the output device Then select which parameters to plot and press Enter You will
47. rworth filter all of the sections have the same fp Nevertheless because the low Q section has a droopy passband see Figure 4 2 it still has the effect of band limiting the noise from the preceding section Mode 3 was selected for all stages because it produces lower harmonic distortion than mode 1 The clock frequency ratio is 50 1 with an actual clock frequency of 400kHz giving an actual fo value of 8kHz These two designs were breadboarded using the resistor values given in Table 4 2 All of the resistor values calculated by FilterCAD were multiplied by 3 5 to minimize loading except for the R1 values which were selected to set the gains for the various sections so that no node will go above 0dB lowpass gain for mode 3 R4 R1 The harmonic distortion performance was measured yielding the results in Figures 4 5 and 4 6 The graphs indicate total harmonic distortion as a percentage of the input voltage Each graph shows THD performance for inputs of 1V and 2 5Vpms The difference between the two designs with a 1Vpgms input is negligible but with a 2 5V input a clear improvement in harmonic distortion is Table 4 1 fo Q and fp Values for 8th Order Butterworth Lowpass STAGE fo Q fn Sorted for Reduced Harmonic Distortion 1 1 0000 0 6013 INFINITE 2 1 0000 2 5629 INFINITE 3 1 0000 0 9000 INFINITE 4 1 0000 0 5098 INFINITE Sorted for Low Noise 1 1 0000 0 6013 INFINITE 2 1 0000 0 9000 INFINITE
48. s LTC FILTERCAD in a 32 bit system or C Program Files 86 LTC FILTERCAD in a 64 bit system END HARDWARE REQUIREMENTS A list of the graphics adapters and modes supported by FilterCAD will be found in the Configuration section FilterCAD is a calculation intensive program and should therefore be run on the most powerful system available WHAT IS A FILTER A filter is a circuit that selectively passes a certain range of the frequencies present at its input to its output while blocking attenuating other frequencies Filters are nor mally described in terms of the frequencies that they pass Mostfilters conform to one of four common types Lowpass filters pass all frequencies below a specified frequency called the cutoff frequency and progressively attenuate an38f AN38 2 LI MYR Application Note 38 Figure 1 3 Bandpass Response frequencies above the cutoff frequency Highpass filters do exactly the opposite they pass frequencies above the cutoff frequency while progressively attenuating frequen cies below the cutoff frequency Bandpass filters pass a band of frequencies around a specified center frequency attenuating frequencies above and below Notch or band Stop filters attenuate the frequencies around the center frequency passing frequencies above and below The four basic filter types are illustrated in Figures 1 1 to 1 4 There are also allpass filters which not surprisingly pass all of the
49. s to move through the fields and type in the appropriate values from the LTC data sheet Press Enter to accept the data in each field then press ESC an38f LI M Information furnished by Linear Technology Corporation is believed to be accurate and reliable However no responsibility is assumed for its use Linear Technology Corporation makes no representa tion that the interconnection of its circuits as described herein will not infringe on existing patent rights ANS8 25 Application Note 38 when you have finished entering the data Don t forget to SAVE the new DPF file The program will inform you that the FCAD DPF already exists and ask you whether you want to overwrite it Press Y to save your file Another possible reason for using the Device Parameter Editor isto delete some devices from the Device Parameter File so that FilterCAD could only select devices that you have on hand To delete a device press 2 When it shows you a device name on the screen press Y to delete the device from the file or press N to cycle through the list of devices until it displays the one that you wish to delete You can also use the Device Parameter Editor to edit the data for a device supported by this version of FilterCAD in the eventthatthe specifications for that device are revised To edit a device already in the Device Parameter File press 3 You will see a form like the one described previously for adding n
50. terworth response The amplitude curve is the one that begins at OdB and begins to fall off sharply around 1000Hz of course if you have a color display you can make the amplitude and phase curves easily distinguishable by assigning them different colors The amplitude in the passband is extremely flat you could magnify a small segment of the passband many times and still find no observable ripple and the slope of the roll off begins just before the corner frequency reaching the 3dB down point which in a Butterworth response is synonymous with the corner frequency at 1000HZz and continues to roll off at the same constant rate to the stopband and beyond In theory the slope will continue to an38f LIJ LINEAR AN38 13 Application Note 38 roll off atthis same rate all the way to an infinite attenuation at an infinite frequency The phase response begins at 0 slopes exponentially to near 360 as it approaches the corner frequency then continues down until it asymptotes to 720 inthe filters stopband Butterworth filters offerthe most linear phase response of any type except the Bessel Figure 3 1B shows the phase response of the Butterworth lowpass filter using a linear phase scale 0 10 AMPLITUDE 20 30 40 za 50 60 3 70 80 PHASE 90 100 110 120 0 1000 FREQUENCY Hz AN38 F3 1b Figure 3 1B Butterworth Lowpass Phas
51. the graph is a calculation intensive process It is here that the speed and power of your CPU and the presence or absence ofa math coprocessor will become evident The graph will be generated in a matter of seconds Note however that the speed of calculation and plotting can be increased by reducing the number of data points to be plotted To modify this parameter use the Change GRAPH Window option found under item 6 Configure DISPLAY Parameters on the Configuration Menu The number of points can range from 50 to 500 Of course choosing a smaller number of points will result in a courser graph but this may be an acceptable trade off for quicker plotting The Zoom Feature When you display the graph on the screen you have the additional option of magnifying or zooming in on areas of the graph that are of particular interest Before using the zoom feature it is a good idea to enable the Reduced View option on the graph menu When you zoom in the area of the zoom will be indicated by a box on the reduce view of the full sized graph Note the arrow in the lower right hand corner of the graph This arrow can be used to select the region of the graph to zoom in on It can also be used to pinpoint the frequency and gain values of any given point on the graph These values are displayed at the upper right hand corner of the screen The location of the arrow is controlled by the arrow keys the cursor control keys
52. then be prompted for a file name into which the data will be placed These points may then be imported to a spreadsheet program for example for data manipulation lf your graph consists mostly of straight horizontal lines or slopes this indicates that the frequency and amplitude ranges of the graph are probably not set appropriately for the particular filter you are graphing e g a graph frequency range of 100Hzto 10 000Hz for a highpass filter with a corner frequency of 20Hz To adjust the frequency and gain ranges of your graph use the Change GRAPH Window option found under item 6 Configure DISPLAY Parameters on the Configuration Menu IMPLEMENTING THE FILTER The third item on the MAIN MENU IMPLEMENT Filter is where we transform the numbers generated in step one into practical circuitry There are several steps to this process Optimization The first step is to optimize your filter for one of two char acteristics You can optimize for lowest noise or lowest harmonic distortion When you optimize for noise the cascaded sections are ordered in such a way as to produce the lowest output noise when the filter input is grounded In the absence of any other conflicting design criteria this is the most obvious characteristic for optimization When you optimize for harmonic distortion the sections are cascaded so as to minimize the internal swings of the respective amplifiers resulting in reduced harmonic dist
53. ts While we have made every effort to ensure that FilterCAD Operates in the manner described in this manual we do not guarantee operation to be error free Upgrades modifications or repairs to this program will be strictly at the discretion of Linear Technology Corporation If you encounter problems in installing or operating FilterCAD you may obtain technical assistance by calling our applications departmentat 408 432 1900 between 8 00 a m and 5 00 p m Pacific time Monday through Friday Because of the great variety of operating system versions and peripherals currently in use we do not guarantee that you will be able to use FilterCAD successfully on all such systems If you are unableto use FilterCAD Linear Technology Corporation does guarantee to provide design support for LTC filter products by whatever means necessary Linear Technology Corporation makes no warranty either expressed or implied with respect to the use of FilterCAD or its documentation Under no circumstances will Linear be liable for damages either direct or conse quential arising from the use of this product or from the inability to use this product even if we have been informed in advance of the possibility of such damages FilterCAD Download The FilterCAD tool although not supported can be downloaded at www linearcom Locate the downloaded file on your computer and manually start installation in that directory Your FilterCAD distribution in
54. use the arrow keys on the cursor keypad to move the arrow to one corner of the rectangle you want to zoom in on just outside the pass band then press Enter Now move the arrow again and you ll see a box expand to enclose the area to be magnified When the box encloses the passband press Enter again and the new graph will be calculated and plotted It may require two or three consecutive zooms but eventu ally you ll get a close up of the passband that shows the 0 05dB ripple quite clearly as in Figure 3 4 Note that in this figure the graph style has been reset to linear To return to the full scale graph press FILTER RESPONSE FILTER TYPE iexit ALT P plot Figure 3 3 Chebyshev Bandpass Response E GAIN db GROUP DELAY n3 PHASE DEO FILTER TYPE sss pecans 54 2635 4 FREQUENCY 4748 66 O 3a PO GAIN 0 2 FILTER RESPONSE CHEBYCHEU ESC exit ALT P plot Figure 3 4 Close Up of Passband an38f LI M AN38 15 Application Note 38 R4 AN38 F3 5a Figure 3 5B Mode 2 Network Now we ll implement our design optimizing as before for lowest noise We will select clock to fg ratio equal to 50 1 and clock frequency equal to 250 000Hz Once again the LTC1164 is selected and the Qs of the sections are in termixed for the lowest noise This time mode 3 has been chosen for the first two stages where fo lt fo 50 and mode 2 has been selected for the remaining two sta
55. z 60dB Notch STAGE fo Q fn STAGE fo kHz Q fn kHz MODE 1 35735 6793 3 3144 39616 8585 1 40 000 10 00 40 000 1 2 44773 1799 3 3144 40386 8469 2 43 920 11 00 40 000 2 3 35242 9616 17 2015 39085 8415 3 40 000 10 00 40 000 1 4 45399 1358 17 2105 40935 5393 4 35 920 8 41 40 000 3 We will start by using FilterCAD to enter the parameters for an elliptic notch response We ll specify a maximum passband ripple of 0 1dB an attenuation of 60dB a center frequency of 40kHz a stop bandwidth of 2kHz and a pass bandwidth of 12kHz Given these parameters FilterCAD synthesizes the response shown in Table 4 5 This 8th order filter claims an actual stopband attenuation of greater than 80dB a level of performance that would be exceedingly difficult to achieve in the real world A working filter with an attenuation of 60dB can be achieved but only be devi ating significantly from the advice provided by FilterCAD Switched capacitor filter devices give the best performance when certain operating parameters are kept within par ticular ranges Those conditions which produce the best results for a particular parameter are called its figure of merit For example in the case of the LTC1064 the best specs for clock to center frequency ratio fo K fo accuracy are published for a clock frequency of 1MHzand aQ of 10 As we depart from this figure of merit as we must do to produce the 40kHz notch in
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