First enter in the discrete data for the desired transfer function To do this we will create two vectors f Hd f contains the discrete frequency points and Hd contains the ideal transfer function To create the vector f first type f then The colon will give for an assignment Then choose Matrix from the insert menu Enter in the of rows that you need and 1 column to form the vector Enter in the value for each and hit the tab key to move to the next block nf 12 40 60 100 200 400 600 fd 1000 2000 4000 6000 8000 10000 0 2 0 31 0 579 1 487 0 618 0 329 Hd 0 421 0 107 0 455 1 069 1 995 1 387 Next calculate Hd in dB To create the looping index first type i for the assignment then 0 13 Note that the semicolon give the range symbol of Also note that the vector is indexed from 0 to 13 not 1 to 14 Also to get the subscript for Hdb or Hd type i 0 nf 1 i Hdb 20 log Hd i Plot Hdb as a check Choose the graph toolbar from the right hand side of the MathCad window Then select the X Y plot icon On the vertical axis type Hdb i On the horizontal axis type i then enter 10 0 Hdbi 10 20 0 5 10 i 15 Define a function representing an ideal bandpass filter The variables of the function are p complex freq Av voltage gain fo resonant freq and Q Note when entering equations use the spacebar to control the underscore location This determines the active area Secondly to raise something to a power use i e p square would be entered as p 2 then hit the spacebar to complete the task and continue entering in data When entering a quotient use the spacebar to underscore all the variables that will be in the numerator Then hit to establish the quotient When done use the space bar to move out of the denominator and back up to the main line Hbp p Av fo Q Av 2 fo Q p 2 p 2 fo Q p 2 fo 2 Define the top level design as a superposition of three parallel bandpass filters combined through a summing amp Note that the gains are controlled via the filter as well as the summing amp itself Htop p A1 f1 Q1 A2 f2 Q2 A3 f3 Q3 Hbp p A1 f1 Q1 Hbp p A2 f2 Q2 Hbp p A3 f3 Q3 From the data set our group decides to use a summing amp of two band pass filters with resonant frequencies at 200 Hz and 8 kHz A simple loop is created to alter the gains and the Q s of the filters and the mean is computed To do this initially determine the bounds of the gains and the Q s Here we will vary the gain of filter 1 from 1 1 to 1 6 over 6 steps the gain of filter 2 from 1 8 to 2 3 the Q of filter 1 from 1 to 3 5 over 6 steps and the Q of filter 2 from 1 to 3 5 again over 6 steps f1 200 f2 1000 f3 8000 A10 1 4 dA1 0 1 Q10 1 5 dQ1 0 5 A20 0 2 dA2 0 05 Q20 12 dQ2 0 5 A30 1 8 dA3 0 1 Q30 1 dQ3 0 5 Next define a program block to scan through the values of the voltage gains and Q s The program block will scan through all the values then find the minimum variance error note this can be modified to find the minimum mean error For the minimum variance error store the values of A1 A2 Q1 and Q2 that resulted in that error To enter in this program block first type vmin for the assignment Next select the Programming Toolbar On the programming toolbar select Add line A program block will come up With the cursor in the first placeholder select Add line a few more times to add more lines to the program block Note that with MathCad always create more lines than you need You can come back and delete them later Now move the cursor to the first placeholder of the program block and then enter A1m 0 where the arrow is from the programming toolbar to intialize A1m Continue on to initialize the other variables Note here vm will be the minimum variance error However it has been assigned a very large value intially Once this is entered in the loops need to be entered To this end select for from the programming toolbar Then type 0 5 in the right hand place holder and the variable i1 in the left hand place holder Next move the cursor to the placeholder in the indented line of the for loop Add a few lines here by clicking Add Line from the programming toolbar Then enter A1 A10 dA1 i1 This assigns a value to A1 that is incremented by i1 dA1 Note that again the arrow is selected from the toolbar Continue with this process to enter in all the loops scanning successively through A1 A2 Q1 and Q2 In the inner most loop In the inner most loop we will compute the transfer function of the sum of our two band pass filters Also the mean and then the variance are calculated Finally conditional statements are added in Note that the if here must be selected from the programming toolbar Effectively these statements assign a new value to the variables A1m A2m Q1m Q2m if the current variance error is less than the current minimum error The value of vm the minimum variance error is also updated Finally a vector is created containing the values of A1m A2m Q1m and Q2m that resulted in the minimum variance error Also the variance error and the mean error are also included in this vector This vector is assigned to vmin Note that this only finds the minimum within your specified bounds Thus we have to be careful in properly specifying the bounds of the computation and the stepsize vmin A1m 0 A2m 0 Q1m 0 Q2m 0 vm 9999 for i1 0 5 A1 A10 dA1 i1 for i2 0 5 A2 A20 dA2 i2 for j1 0 5 Q1 Q10 dQ1 j1 for j2 0 5 Q2 Q20 dQ2 j2 for i3 0 5 A3 A30 dA3 i3 for j3 0 5 Q3 Q30 dQ3 j3 0 for k1 0 nf 1 ht Htop 2j fd k1 A1 f1 Q1 A2 f2 Q2 A3 f3 Q3 htm ht htdb 20 log htm htdb Hdb k1 nf sv 0 for k2 0 nf 1 ht Htop 2j fd htdb 20 log ht k2 A1 f1 Q1 A2 f2 Q2 A3 f3 Q3 sv sv htdb Hdb sv k2 2 sv nf A1m A1 if sv vm A2m A2 if sv vm A3m A3 if sv vm Q1m Q1 if sv vm Q2m Q2 if …
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