Designing Filters with the AD66 Greensboro, NC Abstract: This paper introduces the basics o designing digital ilters or the AD66. This article assumes a basic knowledge o ilters and their construction and implementation. The reader is encouraged to visit other reerences to gain more detailed knowledge o what digital ilters are and how they work. The reerences in the bibliography are a good place to start. The AD66 is a decimating digital receiver chip used in the implementation o a digital receiver ollowing an analog to digital converter such as the AD664 or the AD66. The AD66 consists o a complex NCO, quadrature mixers, second order cascaded integrated comb (CIC) ilter, ith order CIC and a ram coeicient inite impulse response ilter (RCF). Together, these orm a versatile receiver AIC with many dierent user conigurations. Real, Dual Real, or Complex Inputs cos Complex NCO -sin I Q CIC Filters External ync Circuitry I Q FIR Filter JTAG Port I Q Output Format µp or erial Control About the AD66 As shown, there are our main signal processing stages: a Frequency Translator, two Cascaded Integrator Comb FIR Filters (CIC, CIC) and a RAM Coeicient FIR Filter (RCF). Following requency translation is a ixed coeicient, high speed decimating ilter that reduces the sample rate by a programmable ratio between and 6 (Note: Decimation o in CIC requires X or greater clock into AD66). This is a second order, cascaded integrator comb FIR ilter. The data rate into this stage equals the input data rate, samp. The data rate out o CIC, samp, is determined by the decimation actor, M CIC. Following CIC is a second ixed-coeicient, decimating ilter. This ilter, CIC, urther reduces the sample rate by a programmable ratio rom to 3. The data rate out o CIC, samp, is determined by the decimation actor, M CIC. Each CIC stage is a FIR ilter whose response is deined by the decimation rate. The purpose o these ilters is to reduce the data rate o the incoming signal so that the inal ilter stage, a FIR RAM coeicient sum-o-products ilter (RCF), can calculate more taps per output. As shown in block diagram o the chip, on-chip multiplexers allow both CIC ilters to be bypassed i desired. erial or Parallel Outputs The ourth stage is a sum-o-products FIR ilter with programmable -bit coeicients, and decimation rates programmable rom to 3. The RAM Coeicient FIR Filter can handle a maximum o 6 taps. The overall ilter response or the AD66 is the composite o all three cascaded decimating ilters: CIC, CIC, and RCF. Each successive ilter stage is capable o narrower transition bandwidths but requires a greater number o CLK cycles to calculate the output. More decimation in the irst ilter stage will minimize overall power consumption. Designing with the AD66 When designing ilters or the AD66, the cascaded perormance o each o the ilter stages must be considered. Thereore, each stage should be understood beore looking at cascaded perormance. nd order CACADED INTEGRATOR COMB FILTER The CIC ilter is a ixed-coeicient, decimating ilter. It is constructed as a second order CIC ilter whose characteristics are deined only by the decimation rate chosen. This ilter can process signals at the ull rate o the input port (6MHz) in all input modes. The output rate o this stage is given by the equation below. AMP AMP = M CIC The decimation ratio, M CIC, is an unsigned integer that may be between and 6. This stage may be bypassed under certain conditions by setting, M CIC equal to. Bypass o the CIC can only take place when CLK is two or more times the input data rate, AMP. This is because the I and Q data is processed in parallel within the CIC ilter, and the I and Q output data is then multiplexed through the same data pipe beore it enters the CIC ilter. The gain and pass-band droop o the CIC can be calculated with the ollowing equations. From this, the gain and passband droop can be calculated. Later, it will be shown how to correct or pass band droop o the CIC ilters. ( log( M CIC input _ ) ( M CIC ) CIC = ceil level OL CIC = input CIC _ + level The scale actor, CIC is a programmable unsigned integer between and 6. This serves as an attenuator that can reduce the gain o the CIC in 6dB increments. For the best dynamic range, CIC should be set to the smallest value possible (i.e. lowest attenuation) without creating an overlow condition. This can be saely accomplished using the equation below, where input_level is the largest raction o ull-scale possible at the input to this AD66 (normally ).
The requency response o the CIC ilter is given by the ollowing equations. z H( z) = CIC + z MCIC MCIC sin π H( ) = CIC + sin π AMP AMP CIC Rejection The table below illustrates the amount o bandwidth in khz that can be protected with various decimation rates and alias rejection speciications. The data in this table assumes an input sample rate o 6MHz, but it may be scaled to any other allowable sample rate. The passband requirements with respect to other sample rates may also be scaled up to the 6MHz rate in order to select the amount o decimation allowed or a given rejection speciication. The table can be used as a tool to decide on how to distribute the decimation in between CIC, CIC and the RCF. M CIC -db - - - - -db 6dB 7dB 8dB 9dB khz 63. 64.3 367.9 6.9 6.3 6.4 3 98. 7.8 3.8 78.3. 6.6 4 79.3 4. 6.9 4.3 8.9 46. 64. 37 3..6 68. 38.4 6 4.7 38.4 8..6 7.9 3.6 7 48. 76 7. 89. 8.3 8 43.3 43.3 38. 78. 44.3 9 378 7.3 3.8 7. 39.6.3 34.3 96.3.8 63.3 3.8. 3 78.9.9 7.7 3.6 8.4 8.6 64.3 93.6 3 3 6.9 3 64.9 86.6 49 7.7.6 4 4.4 4. 8. 4.6.7 4. 9.3 3 7. 4.6 4. 3.6 6. 3.8 7. 4.6.7 CIC Alias Rejection Table ( AMP = 6MHz) Example Calculations Goal: Implement a ilter with an Input ample Rate o MHz requiring db o Alias Rejection or a 7kHz passband. olution: First scale the passband to a 6MHz rate using the equation below. 6MHz AMP = * PA _ BAND AMP Find the -db column on the right o the table and look down this column or a value greater than or equal to your passband reerenced to 6MHz. Then look across to the extreme let column and ind the corresponding decimation rate. Reerring to the table, notice that or a decimation o 4, the requency having -db o alias rejection is 46.kHz. This is greater than the 4.kHz calculated. Thereore, the maximum bound on CIC decimation or this condition is 4. Additional decimation means less alias rejection than the db required. Although an M CIC less then 4 would still yield the required rejection, overall power consumption is reduced when using the largest decimating possible. Decimation in CIC lowers the data rate, and thus reduces power consumed in subsequent stages. The plot below shows the CIC transer unction with respect to the CIC output rate when a decimation o 4 is used. The irst plot is reerenced to the input sample rate, the complex spectrum rom - AMP / to AMP /. The second plot is reerenced to the CIC output rate, the complex spectrum rom - AMP / to AMP /. The aliases o the CIC can be seen to be olding back in towards the edge o the desired ilter passband. It is the level o these aliases as they move into the desired passband that are important. 3 4 6 7 8 9 3 4 6 7 8 9.4.3.....3.4 / samp.4.3.....3.4 / samp CIC Alias Rejection, M CIC = 4 The set o plots below show a decimation o 6 in the CIC ilter. The lobes o the ilter drop as the decimation rate increases, but the amplitudes o the aliased requencies increase because the output rate has been reduced. (6MHz / MHz) * 7kHz = 4.kHz.
3 4 6 7 8 9 3 4 6 7 8 9.4.3.....3.4 / samp.4.3.....3.4 / samp CIC Alias Rejection, M CIC = 6 th order CACADED INTEGRATOR COMB FILTER The third signal processing stage, CIC, implements a sharper ixed-coeicient, decimating ilter than CIC. The input rate to this ilter is AMP. The maximum input rate is given by the equation below. N CH equals two or Dual Channel Real input mode; otherwise N CH equals one. In order to satisy this equation, M CIC can be increased, N CH can be reduced, or CLK can be increased. AMP N CLK CH The scale actor, CIC is a programmable unsigned integer between and. It serves to control the attenuation o the data into the CIC stage in 6dB increments. For the best dynamic range, CIC should be set to the smallest value possible (lowest attenuation) without creating an overlow condition. This can be saely accomplished using the equation below, where OL CIC is the largest raction o ull scale possible at the input to this ilter stage. This value is output rom the CIC stage then pipe-lined into the CIC. CIC is ignored when this ilter is bypassed by setting M CIC =. CIC OL ( ( M OL ) = ceil log CIC CIC CIC ( MCIC ) = OL + CIC CIC The requency response o the ilter is given by the ollowing equations. The gain and passband droop o CIC should be calculated by these equations. Both parameters may be compensated or in the RCF stage. z H( z) = CIC + z MCIC M sin π H( ) = CIC + sin π CIC AMP AMP The output rate o this stage is given by the equation below. AMP = M AMP CIC CIC Rejection The table below illustrates the amount o bandwidth in khz that can be protected with various decimation rates and alias rejection speciications. The data in this table assumes that the input sample rate is 6MHz but may be scaled to any sample rate. The passband requirements with respect to other sample rates may also be scaled up to the 6MHz rate in order to select the amount o decimation allowed or a given rejection speciication. The maximum input rate into the CIC is 3.MHz. The table is reerenced to 6MHz to allow or direct comparison with the CIC ilter. 3
M CIC -db -6dB -7dB -8dB -9dB -db khz 6647.7. 4. 39.8 6 69. 3.8 438.7 33.8 669.9 4.8 77.4 4 438.7 364. 637. 6 73.6 378.4 394.3 669.6 6.9 746.3 4.3 36.4 6 773.6.9 8. 47.7 93. 96.3 7 39.9 94.8 76. 7. 3.9 83.7 8. 77. 386.3. 98. 733. 9 87.7.4 36. 8. 64.4 688.6 373.. 93.3 73. 9.7 37.3.3.9 8.7 666.4 38. 4.7 47. 93. 7.3 6.8 494. 3 33. 6.3 86.7 698 6.4 46.8 4 98.3 8.8 648.7. 44.6 3.8 9. 747.9 6.9 49.9 396.6 6 6.6 863. 7.6 68.4 46. 37. 7 998.6 8.6 66.6 3. 433.7 3.4 8 943.4 767.7 64..7 49.7 33. 9 894 77. 9. 479. 388.3 33.8 849.4 69.3 6 4.4 369 98. 89. 68.6 3.4 433.8 3. 84. 77. 68.7. 44. 33.6 7. 3 739 6. 489 396.3 3. 9. 4 78.3 76. 468.7 379.8 37.8 48.7 68 3. 4 364.7 9. 38.8 6 63.9 3.3 43.8 3.7 84. 9.7 7 69.8.6 46.8 337.7 73.7. 8 67.3 494.4 4 3.7 64 3.3 9 86.4 477.4 388. 34. 4.9 6 3 66.9 46. 37. 34. 46.4 99. 3 48.7 446.6 363. 94.3 38. 9.7 3 3. 43.7 3.8 8. 3. 86.7 CIC Alias Rejection Table ( AMP = 6MHz) The plots below represent the CIC transer unction with respect to the CIC output rate or a decimation o 4. The irst plot is reerenced to the Input ample Rate and shows the complex spectrum rom - AMP / to AMP /. The second plot is reerenced to the CIC output rate; the complex spectrum ranges rom - AMP / to AMP /. Aliased images in CIC old back towards the edge o the desired ilter passband. It is the level o these aliases as they move into the desired passband that are o concern. The improved rollo o CIC over CIC can be seen when these plots are compared to those shown previously or CIC. 3 4 6 7 8 9 3 4 6 7 8 9.4.3.....3.4 / samp.4.3.....3.4 / samp CIC Alias Rejection, M CIC =4 4
The set o plots below represents a decimation o 3 in the CIC ilter. It can be seen that the lobes o the ilter drop as the decimation rate increases, but the aliased requencies increase due to the reduction o the output rate. 3 4 6 7 8 9 3 4 6 7 8 9.4.3.....3.4 / samp.4.3.....3.4 / samp CIC Alias Rejection, M CIC = 3 Passband Droop Correction ince the CIC ilters orm low pass ilters with a pole at DC, they immediately roll o rom that point. This is especially true when stages are cascaded. In order to minimize pass band droop and generate a minimum ripple passband or the net ilter operation, the roll o generated in the CIC stages must be countered in the RCF stage. By designing the RCF response so that it counters the roll o, the net pass band perormance can be lat. The correction shown below is the required correction or protection o +/- khz with a decimation o 6 in the CIC stage. As shown, nearly db o correction is required. DEDROOP( ) 4 3 3 4 pass / samp CIC Passband Droop Correction RCF peciication The RCF stage o the AD66 orms a sum o products FIR ilter. The chip contains 6 words o data memory as well as 6 words o coeicient memory. The ilter designed must it in this memory space. There are several guidelines on the ilter speciication.. Maximum number o taps is 6/number o channels (i.e. 6 or 8 taps).. Maximum number o taps is M_tot*clk/data_rate. M_tot is the total decimation, clk is the requency o the clock provided to the AD66, and data_rate is the sample rate per channel supplied to the AD66. 3. The maximum clock rate is 6 MP. 4. The maximum data rate is 6 MP/number o channels.. There must be an integer relationship between clock rate and data rate. The conditions above deine the number o taps that can be speciied or the RCF ilter. As indicated, the hardware limitation is either 6 or 8. Otherwise, the total decimation rate and the ratio between the clock rate and the data rate solely determine the number o ilter taps. ince the AD66 perorms complex MAC per clock (one I and one Q), the higher the over clocking ratio, the more taps that can be processed. The AD66 dual channel ADC or example, has a x clock output. The use o this clock as the main clock to the AD66 allows twice as many taps to be perormed. I higher clock ratios can be made available, then larger ilters can be designed. The upper limit on the clock rate is 6 MP. AD66 Filter Design otware With this said, the ilter design sotware provided with the AD66 takes all the hard work out o designing the ilter program. The ollowing sections will explain how the sotware works and explain the unctions o the sotware. Once the reader has read through this material, the ilter design process will be quick and interactive. Installation The AD66 ilter design sotware requires Windows 9 or later 3-bit operating system. Approximately megabytes o disk space are required or the installation. Run the ETUP.EXE program and the program will be installed under the Program Files directory. When the installation is complete, the program may be run by using the tart Programs AD66 ltrdsgn sequence. everal other utility programs are installed in this path, but they should not be executed directly, as they are part o the ilter design sequence. The evaluation board sotware is also loaded at this time. For details on operation o the evaluation board, see the document covering that sotware. The irst time the program is run, the ollowing message appears. This message indicates that a design ile must be speciied. ince this is the irst time run, simply select one o the iles supplied or run the wizard to create a new ilter design.
Click OK to move on to the main program screen. The main screen appears here. There are several sections to the main program screen. When File is selected, the ollowing choices are provided. Choose Filter peciication File allow an existing ilter design ile to be loaded through the Common Dialog Box. Once a ilter ile has been loaded, it may be designed and examined using the various eatures o the sotware. The AD66 design program consists o a menu bar, three text windows and two graph windows. The let side o the screen has the three text windows. The top screen provides details o various ilter designs, including decimation rates in each o the stages and details o ilter perormance. ince no ilter design has been perormed, the screen in blank. Once a ilter has been designed, this screen will provide details. The second window provides cursor inormation when placed over the top graph, the Composite Frequency Response o the ilter. The bottom text window provides program status as program execution continues. The top graphic window provides the Composite Frequency Response o the ilter selected. This window may be zoomed so that small details can be closely examined. To change the view o this window, place the mouse cursor at the top let corner o the desired window. Depress the let mouse button and slide the mouse to the lower right corner o the desired window. Release the mouse button. Click the H-Zoom and/or the V-Zoom button to execute the new view. Both buttons do not have to be selected; only the desired view. To restore the original view, click restore. The values entered in the zoom process are saved in short term memory and need not be reset between ilter designs as long as the program is not exited. This can be useul to examine ine details between ilter designs. I this window is double clicked, the rejection characteristics are displayed in the bottom text window. The bottom graphic window is the impulse response. This window can not be changed and displays the current impulse response. I this window is double clicked, the number o taps in the ilter are displayed. Menu Bar The menu bar has 4 items. Through the menu bar, the various eatures o the design sotware are accessed. File 6 ave Filter Response allows completed designs to be saved with the aid o the common dialog box. Once a ilter has been saved, the sotware or the AD66 evaluation board can read the data stored in the ile and load the data into the appropriate registers. The ormat or this ile is quite simple and shown below. This ormat includes the decimation rates and chip setup. This allows all design parameters to be automatically loaded when the impulse ile is loaded. 6& 4& 6& 3888..4...4. In this ile ormat, the 6, 4 and 6 are the decimation rates or the CIC, CIC and the RCF respectively. The & is required to tell the sotware that these are decimation rates. The 3888 is the data rate used. The irst is the chip mode, or single channel real, or dual channel real and 3 or single channel complex. The second is the clock multiplier. In this case, the clock rate is equal to the data rate. The remaining data in the ile is the impulse response. This program scales the data between +/- using double precision representation. It can also be represented in using any convenient numerical range as the evaluation board sotware can automatically rescale the data to it the +/- ^9 ormat used by the AD66. Load Filter Response loads a previously saved ilter design or observation within the program. This data can not be changed. Exit terminates the program.
Design earch Requested Decimation Rate searches or ilter designs that meet only the speciied decimation rates. Rates above and below that which is speciied are ignored. earch All Decimation Rates searches all decimation rates or which the AD66 is designed. This can be time consuming but will show all possible designs using the AD66 Forced Decimation allows you to try only one decimation combination. When this option is selected, the program asks what decimation should be used in each o the three stages. Then it computes the optimal ilter. Edit Filter Table allows the selected ilter design to be changed. The ilter could have been selected using the File Choose Filter peciication File or through the use o the ilter wizard. Either way, the ilter speciication could be tweaked. For more details about editing a ilter, see Edit Filter Table below. Filter Wizard Filter Wizard walks the user through the design process. A quick walk through will give a lavor or the possibilities and explain what each are. The ilter wizard utilizes Cancel, Next and Back buttons so that the design can be navigates smoothly i mistakes are made. Data is not saved until the last entry is made, thereore, a cancel will abort the data entry process. It is recommended that the program be started and the user ollow through the ollowing steps in order to understand how the wizard works. The wizard is very helpul and easy to use. To this end, we will work on an example that is close to the requirements or AMP. During installation, other sample iles were placed in the target directory and may be viewed or edited at any time. Feel ree to browse through these at any time. The irst entry required is the ile name where the ilter will be stored. The deault extension or a ilter is DAT; however, any extension may be used. For this discussion enter the ilename o AMP.DAT. The second entry is the data rate in Hertz. This is not necessarily the same as clock rate. In the case o products such as the AD66 dual channel ADC, a x clock is provided. The value entered is the actual sample rate per channel. For our example, enter 644. Next the sotware must be told i the chip will be operated in dual or single channel mode. Normal data converters are run in the single channel mode while products such as the AD66 could be used in the dual channel mode. A simple y or n is required or this entry. For this example, select n. This design is targeted or a single channel ADC such as the AD664. The next entry is the ratio between the data rate and the AD66 clock. For most applications this will be a but applications such as the AD66, a x clock is generated and should be entered here. I acilities are available or dierent rates, they too can be entered here; however, it should be remembered that the maximum clock rate is 6 MHz. Enter or our example. The next input is the decimation rate. This is the rate or which the data is reduced. Enter 4 as the decimation or our example. The next input is whether an IF ilter is used. A y should be entered i an analog ilter is used that appreciably shapes the channel characteristics. I used, this inormation will be used in designing the digital ilter or this channel. I not, the input is ignored. I a y is entered, the program will prompt you or ilter inormation. First it requests the number o bands. Usually, this is two, a pass band and a stop band. A higher number may be entered which will allow multiple stop bands to be entered. Only one pass band is deined. In any case, the ollowing sequences o questions deine the pass and stop band. The irst will be the start o the pass band. This is always. The second entry is the edge o the pass band. The next number is the start o the stop band. Together these last two numbers entered deine the transition band o the ilter. The ollowing inputs are the ollowing stop band zones. The last entry is always the Nyquist requency. Once the requency terms are entered, the rejections are entered. The irst is the pass band, which should be. The stop bands should have the required rejection. Our application will not have channel iltering outside o our digital application, so enter n. The next main section o the design process is the composite response. There are two option here. A raised root cosine ilter design can be used. I so, the next entry should be a y. I yes is selected, the parameters are requested including alpha and the symbol rate. I the symbol rate is unknown, an auto-calculate eature is provided. Next the stop band rejection is requested. Finally, the number o ilter taps is requested. Again, an auto-calculate eature is provided that determines the maximum number o taps available within the AD66. I a RRC ilter is not selected then the program requests the composite perormance speciication. As with the IF ilter speciications, the number o bands is requested ollowed by the pertinent requencies and the required rejection. For details on entering an IF ilter speciication. For our application enter n when asked about an RRC ilter. For composite bands, enter ; a pass band and a stop 7
band. Next, the pass and stop bands must be deined as outlined about. Enter a or the let corner o band. All o the ilters designed with this program a reerenced to the center o the channel. Next enter or the right corner o band. This deines a passband o +/- Hertz. Next enter 3 or the let corner o band. This deines the start o the stop band. The inal entry is the right corner o band. ince we have only deined bands, the last entry is the Nyquist requency o the data rate or 3.7 MHz in this case. This is presented as the deault. Any other entry will be ignored. The next two entries deine the band rejections. Enter or band, the pass band and - 9 or band, the stop band. elect File Choose Filter peciication File and load one o the ilters provided with the sotware. In order to see the perormance o the ilter, select Design earch Requested Decimation Rate. This launches the another application called Decim.exe. This program computes the ilter perormance or each o the possible ilters by actoring the decimation rate and distributing it between each o the stages. Once the ilter wizard is complete, it launches the Filter edit window. This allows the ilter design to be edited or tweaked. All requencies are entered in Hertz. ince the above ilter above does not use an IF ilter, the speciication has been disabled. When designing a ilter, it is best to speciy decimation rates that are easily and robustly actored. Although not required, decimation rates that have small actors such as, 3, 4 or When the editing is complete, select the OK button. This saves the inormation or later use. Once a design is ready to test, the ilter can be design can be initiated by earching Requested Decimation Rate. This will cause the program to search all possible ilter designs. Once complete, the top text box will contain inormation about all possible ilter designs. As shown three good ilter designs can be perormed with the required ilter speciication. Double clicking on the ilter in the upper text box will display the ilter perormance. I you wish to save the ilter perormance, select File ave Filter Response and the data will be written to the ile o the users choice or loading into the evaluation board. For evaluation, each o the good ilter designs could be saved under dierent names and loaded into the evaluation board or comparison. It should be noted that the test or ilter quality is pessimistic and some o the ilters listed as ailures may actually be good. Thereore the rule is to try the ilters that pass irst. Ater that, it is always a good idea to check some the ilters that are listed as ailures. To examine details o any ilter, including those that ail, single click on the ilter table. Filter details are available in the lower lethand text box. are preerable. I the decimation rate has actors no smaller than, then the program will ail to generate any ilters at all. When the Decim application is complete, the ilter table will appear with ilter details. ingle click or text details or double clicking or a ilter design. Double clicking launches another application called RCF.exe. This application examines the ilter speciications and actually designs the ilter request with result displayed on the two graphs within the Filter Design Program. Loading and Using a Filter File Once a ilter has been speciied, a ilter ile is created. This ile may be reerenced by Choose Filter peciication File. 8
9 I the ilter meets the application, then the ilter can be saved using the File ave Filter Response option. This will write all pertinent data to a ile or use by the AD66 evaluation board sotware or or inclusion as a data ile in the DP code o the inal application.