1
#include <PWM.h>
int led = 9; 
void setup()
{
  InitTimersSafe();
  Serial.begin(115200);
  Serial.println();
  variable_freq();
  pinMode(A0,INPUT);
}
void variable_freq()
{
   while(true)
 {
   a=analogRead(A0);
   float p = (a/1024)*5;
   int Vi = p/0.143;
   float Vo = 12;
   float Po=100;
   float n=1, ni=0.9, Ntr=1, Vf=0.7, Rf=0.018, rc=0.025, Mvs=0.9;
   float Rl=(Vo*Vo)/Po;
   float fo = 70000;
   float Mv = Vo/Vi;
   float Qo=6;
   float pi = 3.14159;
   float g ;
   g= (1+(2*(Vf/Vo))+((Rf*pi*pi)/4*Rl)+(rc/Rl)*(((pi*pi)/8)-1));
   float Ri=((8*Rl*n*n)/(Ntr*pi*pi))*g;
   float Mvr, MVR, h;
   Mvr=(pi*Ntr)/(2*n*sqrt(2)*g);
   MVR=Mv/(Mvs*Mvr);
   h=(sqrt((pow((ni/MVR), 2))-1))/Qo;
   float f_sw;
   f_sw = ((fo*h)/2) + (sqrt(pow(fo*h,2) + 4*pow(fo,2)))/2;
   
   SetPinFrequency(led,f_sw);
   
   float T = 0.5;
   
   pwmWriteHR(led,T*65536);
 } 
}

I am working on a project where I have to find a required frequency from a varying DC input voltage. I am using Arduino Nano to produce a PWM signal of this required freqeuncy.

From the code, once the frequency f_sw is calculated, I have used the setPinFrequency function to set the frequency of pin D9 to f_sw. I want a PWM signal of duty cycle 50% with f_sw as the frequency.

Does pwmWriteHR(led,T*65536) accomplish this? As per this website, pwmWrite()'s 2nd argument is the duty cycle. Given that pwmWriteHR() is just the higher resolution version of pwmWrite(), will this output the signal as per my requirements?

I cannot test this on a board yet, so I simulated it in Proteus, but the frequency of the signal I obtained there does not match, although the duty cycle was 50%.

8
  • What frequency are you getting, and what frequency are you expecting?
    – Nick Gammon
    Apr 24, 2023 at 21:51
  • The frequency calculated for a certain input voltage value is 76 kHz. But I am not even getting 100 Hz. Apr 25, 2023 at 0:32
  • Can you please print the value f_sw just prior to doing this line: SetPinFrequency(led,f_sw);
    – Nick Gammon
    Apr 25, 2023 at 5:06
  • @NickGammon imgur.com/a/2sRb40c I modified the code without analogRead() as I didn't have the setup ready. Apr 26, 2023 at 14:13
  • The image shows the frequency as 76441.25.
    – Nick Gammon
    Apr 26, 2023 at 22:02

1 Answer 1

1

Let's look at what's possible using the Atmega328P (which is on the Nano).

The timers are really just counters, with the input to the counter being the system clock, possibly after being divided down by a prescaler.

Timers 0 and 2 are 8-bit timers which means they can count to 256 before wrapping around. Timer 1 is a 16-bit timer which means it can count to 65536 before wrapping. The inputs to the timers are zero-relative, so the actual counter limits are 255 (0xFF) and 65535 (0xFFFF).

Your desired frequency of 76441 means the period is 1/76441 seconds, namely 13.082 µs.

With no prescaler, the period of the system clock is 1/16000000, namely 0.0625 µs.

Divide 13.082 by 0.0625 and you get 209.312 which means 209 counts are going to roughly get you the frequency you want.

However then we have to divide by 2 because each time the counter counts up we toggle the output, and it takes two toggles to do one period (one up, one down).

So we need to set up a timer of 209/2 which is 104.5. Since we can't count up to half a count we actually count up to 104. The code to do that, without needing any libraries, is:


Example code

void setup() 
  {
  pinMode (9, OUTPUT);  // output pin is fixed (OC1A)

  unsigned long Hz = 76441;

  // it takes two toggles for one "cycle"
  unsigned long ocr = (F_CPU / Hz / 2) - 1;
  
  // stop timer
  TCCR1A = 0;
  TCCR1B = 0;
  // reset counter
  TCNT1H = 0;
  TCNT1L = 0;
  
  // what to count up to
  OCR1AH = highByte (ocr);
  OCR1AL = lowByte (ocr);
  
  TCCR1A = bit (COM1A0);              // toggle output pin
  TCCR1B = bit (WGM12) | bit (CS10);  // start timer, CTC mode
  }  // end of setup

void loop() { }

The results on pin 9 were measured as 76.805 kHz which is slightly out, partly because of the fact that the resolution is in increments of 62.5 ns, and partly because the Nano has resonator* rather than a crystal, so its clock might not be exactly 16 MHz.

* I'm not sure about that.


Duty cycle

In this particular example we have a 50% duty cycle because each time the timer reaches its count it toggles the output. Thus it does it symmetrically. That is, the on portion will be the same length as the off portion.

There are other timer modes which can be used for PWM generation where the duty cycle is not 50%. See the datasheet for more information.


Prescaler

The prescalers (not used in this particular example) are used to extend the length of time that a timer can count for.

Possible prescalers are 1, 8, 32, 64, 128, 256, and 1024. Prescalers of 32 and 128 are only available on timer 2.

So, for example, if you use a prescaler of 8 then each "tick" of the timer will be 8 * 62.5 ns, so it can count for 8 times as long before it overflows. However each count will only have a resolution of 500 ns rather than 62.5 ns, so you can get a less precise time measurement.

Choosing prescalers is a compromise between resolution and the available time period you can time for.


See my page about timers for more discussion about the Atmega328P timers.


List of possible frequencies

From my page above I reproduce this list which shows what frequency and period you get for various timer counts, and prescalers.

  n  -- Prescale 1   --  -- Prescale 8   --  -- Prescale 64  --  -- Prescale 256 --  -- Prescale 1024--
     Freq (Hz) Per (µs)  Freq (Hz) Per (µs)  Freq (Hz) Per (µs)  Freq (Hz) Per (µs)  Freq (Hz) Per (µs)
  1: 8,000,000*   0.125  1,000,000    1.000    125,000    8.000     31,250   32.000      7,813  128.000  
  2: 5,333,333    0.188    666,667    1.500     83,333   12.000     20,833   48.000      5,208  192.000  
  3: 4,000,000    0.250    500,000    2.000     62,500   16.000     15,625   64.000      3,906  256.000  
  4: 3,200,000    0.313    400,000    2.500     50,000   20.000     12,500   80.000      3,125  320.000  
  5: 2,666,667    0.375    333,333    3.000     41,667   24.000     10,417   96.000      2,604  384.000  
  6: 2,285,714    0.438    285,714    3.500     35,714   28.000      8,929  112.000      2,232  448.000  
  7: 2,000,000    0.500    250,000    4.000     31,250   32.000      7,813  128.000      1,953  512.000  
  8: 1,777,778    0.563    222,222    4.500     27,778   36.000      6,944  144.000      1,736  576.000  
  9: 1,600,000    0.625    200,000    5.000     25,000   40.000      6,250  160.000      1,563  640.000  
 10: 1,454,545    0.688    181,818    5.500     22,727   44.000      5,682  176.000      1,420  704.000  
 11: 1,333,333    0.750    166,667    6.000     20,833   48.000      5,208  192.000      1,302  768.000  
 12: 1,230,769    0.813    153,846    6.500     19,231   52.000      4,808  208.000      1,202  832.000  
 13: 1,142,857    0.875    142,857    7.000     17,857   56.000      4,464  224.000      1,116  896.000  
 14: 1,066,667    0.937    133,333    7.500     16,667   60.000      4,167  240.000      1,042  960.000  
 15: 1,000,000    1.000    125,000    8.000     15,625   64.000      3,906  256.000        977 1024.000  
 16:   941,176    1.063    117,647    8.500     14,706   68.000      3,676  272.000        919 1088.000  
 17:   888,889    1.125    111,111    9.000     13,889   72.000      3,472  288.000        868 1152.000  
 18:   842,105    1.187    105,263    9.500     13,158   76.000      3,289  304.000        822 1216.000  
 19:   800,000    1.250    100,000   10.000     12,500   80.000      3,125  320.000        781 1280.000  
 20:   761,905    1.313     95,238   10.500     11,905   84.000      2,976  336.000        744 1344.000  
 21:   727,273    1.375     90,909   11.000     11,364   88.000      2,841  352.000        710 1408.000  
 22:   695,652    1.438     86,957   11.500     10,870   92.000      2,717  368.000        679 1472.000  
 23:   666,667    1.500     83,333   12.000     10,417   96.000      2,604  384.000        651 1536.000  
 24:   640,000    1.562     80,000   12.500     10,000  100.000      2,500  400.000        625 1600.000  
 25:   615,385    1.625     76,923   13.000      9,615  104.000      2,404  416.000        601 1664.000  
 26:   592,593    1.688     74,074   13.500      9,259  108.000      2,315  432.000        579 1728.000  
 27:   571,429    1.750     71,429   14.000      8,929  112.000      2,232  448.000        558 1792.000  
 28:   551,724    1.813     68,966   14.500      8,621  116.000      2,155  464.000        539 1856.000  
 29:   533,333    1.875     66,667   15.000      8,333  120.000      2,083  480.000        521 1920.000  
 30:   516,129    1.938     64,516   15.500      8,065  124.000      2,016  496.000        504 1984.000  
 31:   500,000    2.000     62,500   16.000      7,813  128.000      1,953  512.000        488 2048.000  
 32:   484,848    2.062     60,606   16.500      7,576  132.000      1,894  528.000        473 2112.000  
 33:   470,588    2.125     58,824   17.000      7,353  136.000      1,838  544.000        460 2176.000  
 34:   457,143    2.188     57,143   17.500      7,143  140.000      1,786  560.000        446 2240.000  
 35:   444,444    2.250     55,556   18.000      6,944  144.000      1,736  576.000        434 2304.000  
 36:   432,432    2.313     54,054   18.500      6,757  148.000      1,689  592.000        422 2368.000  
 37:   421,053    2.375     52,632   19.000      6,579  152.000      1,645  608.000        411 2432.000  
 38:   410,256    2.438     51,282   19.500      6,410  156.000      1,603  624.000        401 2496.000  
 39:   400,000    2.500     50,000   20.000      6,250  160.000      1,563  640.000        391 2560.000  
 40:   390,244    2.563     48,780   20.500      6,098  164.000      1,524  656.000        381 2624.000  
 41:   380,952    2.625     47,619   21.000      5,952  168.000      1,488  672.000        372 2688.000  
 42:   372,093    2.687     46,512   21.500      5,814  172.000      1,453  688.000        363 2752.000  
 43:   363,636    2.750     45,455   22.000      5,682  176.000      1,420  704.000        355 2816.000  
 44:   355,556    2.812     44,444   22.500      5,556  180.000      1,389  720.000        347 2880.000  
 45:   347,826    2.875     43,478   23.000      5,435  184.000      1,359  736.000        340 2944.000  
 46:   340,426    2.938     42,553   23.500      5,319  188.000      1,330  752.000        332 3008.000  
 47:   333,333    3.000     41,667   24.000      5,208  192.000      1,302  768.000        326 3072.000  
 48:   326,531    3.063     40,816   24.500      5,102  196.000      1,276  784.000        319 3136.000  
 49:   320,000    3.125     40,000   25.000      5,000  200.000      1,250  800.000        313 3200.000  
 50:   313,725    3.188     39,216   25.500      4,902  204.000      1,225  816.000        306 3264.000  
 51:   307,692    3.250     38,462   26.000      4,808  208.000      1,202  832.000        300 3328.000  
 52:   301,887    3.313     37,736   26.500      4,717  212.000      1,179  848.000        295 3392.000  
 53:   296,296    3.375     37,037   27.000      4,630  216.000      1,157  864.000        289 3456.000  
 54:   290,909    3.437     36,364   27.500      4,545  220.000      1,136  880.000        284 3520.000  
 55:   285,714    3.500     35,714   28.000      4,464  224.000      1,116  896.000        279 3584.000  
 56:   280,702    3.562     35,088   28.500      4,386  228.000      1,096  912.000        274 3648.000  
 57:   275,862    3.625     34,483   29.000      4,310  232.000      1,078  928.000        269 3712.000  
 58:   271,186    3.688     33,898   29.500      4,237  236.000      1,059  944.000        265 3776.000  
 59:   266,667    3.750     33,333   30.000      4,167  240.000      1,042  960.000        260 3840.000  
 60:   262,295    3.813     32,787   30.500      4,098  244.000      1,025  976.000        256 3904.000  
 61:   258,065    3.875     32,258   31.000      4,032  248.000      1,008  992.000        252 3968.000  
 62:   253,968    3.938     31,746   31.500      3,968  252.000        992 1008.000        248 4032.000  
 63:   250,000    4.000     31,250   32.000      3,906  256.000        977 1024.000        244 4096.000  
 64:   246,154    4.063     30,769   32.500      3,846  260.000        962 1040.000        240 4160.000  
 65:   242,424    4.125     30,303   33.000      3,788  264.000        947 1056.000        237 4224.000  
 66:   238,806    4.188     29,851   33.500      3,731  268.000        933 1072.000        233 4288.000  
 67:   235,294    4.250     29,412   34.000      3,676  272.000        919 1088.000        230 4352.000  
 68:   231,884    4.313     28,986   34.500      3,623  276.000        906 1104.000        226 4416.000  
 69:   228,571    4.375     28,571   35.000      3,571  280.000        893 1120.000        223 4480.000  
 70:   225,352    4.437     28,169   35.500      3,521  284.000        880 1136.000        220 4544.000  
 71:   222,222    4.500     27,778   36.000      3,472  288.000        868 1152.000        217 4608.000  
 72:   219,178    4.563     27,397   36.500      3,425  292.000        856 1168.000        214 4672.000  
 73:   216,216    4.625     27,027   37.000      3,378  296.000        845 1184.000        211 4736.000  
 74:   213,333    4.688     26,667   37.500      3,333  300.000        833 1200.000        208 4800.000  
 75:   210,526    4.750     26,316   38.000      3,289  304.000        822 1216.000        206 4864.000  
 76:   207,792    4.813     25,974   38.500      3,247  308.000        812 1232.000        203 4928.000  
 77:   205,128    4.875     25,641   39.000      3,205  312.000        801 1248.000        200 4992.000  
 78:   202,532    4.938     25,316   39.500      3,165  316.000        791 1264.000        198 5056.000  
 79:   200,000    5.000     25,000   40.000      3,125  320.000        781 1280.000        195 5120.000  
 80:   197,531    5.062     24,691   40.500      3,086  324.000        772 1296.000        193 5184.000  
 81:   195,122    5.125     24,390   41.000      3,049  328.000        762 1312.000        191 5248.000  
 82:   192,771    5.188     24,096   41.500      3,012  332.000        753 1328.000        188 5312.000  
 83:   190,476    5.250     23,810   42.000      2,976  336.000        744 1344.000        186 5376.000  
 84:   188,235    5.312     23,529   42.500      2,941  340.000        735 1360.000        184 5440.000  
 85:   186,047    5.375     23,256   43.000      2,907  344.000        727 1376.000        182 5504.000  
 86:   183,908    5.438     22,989   43.500      2,874  348.000        718 1392.000        180 5568.000  
 87:   181,818    5.500     22,727   44.000      2,841  352.000        710 1408.000        178 5632.000  
 88:   179,775    5.563     22,472   44.500      2,809  356.000        702 1424.000        176 5696.000  
 89:   177,778    5.625     22,222   45.000      2,778  360.000        694 1440.000        174 5760.000  
 90:   175,824    5.687     21,978   45.500      2,747  364.000        687 1456.000        172 5824.000  
 91:   173,913    5.750     21,739   46.000      2,717  368.000        679 1472.000        170 5888.000  
 92:   172,043    5.813     21,505   46.500      2,688  372.000        672 1488.000        168 5952.000  
 93:   170,213    5.875     21,277   47.000      2,660  376.000        665 1504.000        166 6016.000  
 94:   168,421    5.937     21,053   47.500      2,632  380.000        658 1520.000        164 6080.000  
 95:   166,667    6.000     20,833   48.000      2,604  384.000        651 1536.000        163 6144.000  
 96:   164,948    6.063     20,619   48.500      2,577  388.000        644 1552.000        161 6208.000  
 97:   163,265    6.125     20,408   49.000      2,551  392.000        638 1568.000        159 6272.000  
 98:   161,616    6.188     20,202   49.500      2,525  396.000        631 1584.000        158 6336.000  
 99:   160,000    6.250     20,000   50.000      2,500  400.000        625 1600.000        156 6400.000  
100:   158,416    6.313     19,802   50.500      2,475  404.000        619 1616.000        155 6464.000  
101:   156,863    6.375     19,608   51.000      2,451  408.000        613 1632.000        153 6528.000  
102:   155,340    6.438     19,417   51.500      2,427  412.000        607 1648.000        152 6592.000  
103:   153,846    6.500     19,231   52.000      2,404  416.000        601 1664.000        150 6656.000  
104:   152,381    6.562     19,048   52.500      2,381  420.000        595 1680.000        149 6720.000  
105:   150,943    6.625     18,868   53.000      2,358  424.000        590 1696.000        147 6784.000  
106:   149,533    6.688     18,692   53.500      2,336  428.000        584 1712.000        146 6848.000  
107:   148,148    6.750     18,519   54.000      2,315  432.000        579 1728.000        145 6912.000  
108:   146,789    6.813     18,349   54.500      2,294  436.000        573 1744.000        143 6976.000  
109:   145,455    6.875     18,182   55.000      2,273  440.000        568 1760.000        142 7040.000  
110:   144,144    6.938     18,018   55.500      2,252  444.000        563 1776.000        141 7104.000  
111:   142,857    7.000     17,857   56.000      2,232  448.000        558 1792.000        140 7168.000  
112:   141,593    7.063     17,699   56.500      2,212  452.000        553 1808.000        138 7232.000  
113:   140,351    7.125     17,544   57.000      2,193  456.000        548 1824.000        137 7296.000  
114:   139,130    7.187     17,391   57.500      2,174  460.000        543 1840.000        136 7360.000  
115:   137,931    7.250     17,241   58.000      2,155  464.000        539 1856.000        135 7424.000  
116:   136,752    7.313     17,094   58.500      2,137  468.000        534 1872.000        134 7488.000  
117:   135,593    7.375     16,949   59.000      2,119  472.000        530 1888.000        132 7552.000  
118:   134,454    7.437     16,807   59.500      2,101  476.000        525 1904.000        131 7616.000  
119:   133,333    7.500     16,667   60.000      2,083  480.000        521 1920.000        130 7680.000  
120:   132,231    7.563     16,529   60.500      2,066  484.000        517 1936.000        129 7744.000  
121:   131,148    7.625     16,393   61.000      2,049  488.000        512 1952.000        128 7808.000  
122:   130,081    7.687     16,260   61.500      2,033  492.000        508 1968.000        127 7872.000  
123:   129,032    7.750     16,129   62.000      2,016  496.000        504 1984.000        126 7936.000  
124:   128,000    7.813     16,000   62.500      2,000  500.000        500 2000.000        125 8000.000  
125:   126,984    7.875     15,873   63.000      1,984  504.000        496 2016.000        124 8064.000  
126:   125,984    7.938     15,748   63.500      1,969  508.000        492 2032.000        123 8128.000  
127:   125,000    8.000     15,625   64.000      1,953  512.000        488 2048.000        122 8192.000  
128:   124,031    8.063     15,504   64.500      1,938  516.000        484 2064.000        121 8256.000  
129:   123,077    8.125     15,385   65.000      1,923  520.000        481 2080.000        120 8320.000  
130:   122,137    8.188     15,267   65.500      1,908  524.000        477 2096.000        119 8384.000  
131:   121,212    8.250     15,152   66.000      1,894  528.000        473 2112.000        118 8448.000  
132:   120,301    8.313     15,038   66.500      1,880  532.000        470 2128.000        117 8512.000  
133:   119,403    8.375     14,925   67.000      1,866  536.000        466 2144.000        117 8576.000  
134:   118,519    8.438     14,815   67.500      1,852  540.000        463 2160.000        116 8640.000  
135:   117,647    8.500     14,706   68.000      1,838  544.000        460 2176.000        115 8704.000  
136:   116,788    8.563     14,599   68.500      1,825  548.000        456 2192.000        114 8768.000  
137:   115,942    8.625     14,493   69.000      1,812  552.000        453 2208.000        113 8832.000  
138:   115,108    8.688     14,388   69.500      1,799  556.000        450 2224.000        112 8896.000  
139:   114,286    8.750     14,286   70.000      1,786  560.000        446 2240.000        112 8960.000  
140:   113,475    8.812     14,184   70.500      1,773  564.000        443 2256.000        111 9024.000  
141:   112,676    8.875     14,085   71.000      1,761  568.000        440 2272.000        110 9088.000  
142:   111,888    8.938     13,986   71.500      1,748  572.000        437 2288.000        109 9152.000  
143:   111,111    9.000     13,889   72.000      1,736  576.000        434 2304.000        109 9216.000  
144:   110,345    9.063     13,793   72.500      1,724  580.000        431 2320.000        108 9280.000  
145:   109,589    9.125     13,699   73.000      1,712  584.000        428 2336.000        107 9344.000  
146:   108,844    9.188     13,605   73.500      1,701  588.000        425 2352.000        106 9408.000  
147:   108,108    9.250     13,514   74.000      1,689  592.000        422 2368.000        106 9472.000  
148:   107,383    9.313     13,423   74.500      1,678  596.000        419 2384.000        105 9536.000  
149:   106,667    9.375     13,333   75.000      1,667  600.000        417 2400.000        104 9600.000  
150:   105,960    9.437     13,245   75.500      1,656  604.000        414 2416.000        103 9664.000  
151:   105,263    9.500     13,158   76.000      1,645  608.000        411 2432.000        103 9728.000  
152:   104,575    9.563     13,072   76.500      1,634  612.000        408 2448.000        102 9792.000  
153:   103,896    9.625     12,987   77.000      1,623  616.000        406 2464.000        101 9856.000  
154:   103,226    9.688     12,903   77.500      1,613  620.000        403 2480.000        101 9920.000  
155:   102,564    9.750     12,821   78.000      1,603  624.000        401 2496.000        100 9984.000  
156:   101,911    9.813     12,739   78.500      1,592  628.000        398 2512.000        100 10048.000  
157:   101,266    9.875     12,658   79.000      1,582  632.000        396 2528.000         99 10112.000  
158:   100,629    9.938     12,579   79.500      1,572  636.000        393 2544.000         98 10176.000  
159:   100,000   10.000     12,500   80.000      1,563  640.000        391 2560.000         98 10240.000  
160:    99,379   10.062     12,422   80.500      1,553  644.000        388 2576.000         97 10304.000  
161:    98,765   10.125     12,346   81.000      1,543  648.000        386 2592.000         96 10368.000  
162:    98,160   10.188     12,270   81.500      1,534  652.000        383 2608.000         96 10432.000  
163:    97,561   10.250     12,195   82.000      1,524  656.000        381 2624.000         95 10496.000  
164:    96,970   10.313     12,121   82.500      1,515  660.000        379 2640.000         95 10560.000  
165:    96,386   10.375     12,048   83.000      1,506  664.000        377 2656.000         94 10624.000  
166:    95,808   10.438     11,976   83.500      1,497  668.000        374 2672.000         94 10688.000  
167:    95,238   10.500     11,905   84.000      1,488  672.000        372 2688.000         93 10752.000  
168:    94,675   10.563     11,834   84.500      1,479  676.000        370 2704.000         92 10816.000  
169:    94,118   10.625     11,765   85.000      1,471  680.000        368 2720.000         92 10880.000  
170:    93,567   10.687     11,696   85.500      1,462  684.000        365 2736.000         91 10944.000  
171:    93,023   10.750     11,628   86.000      1,453  688.000        363 2752.000         91 11008.000  
172:    92,486   10.813     11,561   86.500      1,445  692.000        361 2768.000         90 11072.000  
173:    91,954   10.875     11,494   87.000      1,437  696.000        359 2784.000         90 11136.000  
174:    91,429   10.938     11,429   87.500      1,429  700.000        357 2800.000         89 11200.000  
175:    90,909   11.000     11,364   88.000      1,420  704.000        355 2816.000         89 11264.000  
176:    90,395   11.063     11,299   88.500      1,412  708.000        353 2832.000         88 11328.000  
177:    89,888   11.125     11,236   89.000      1,404  712.000        351 2848.000         88 11392.000  
178:    89,385   11.188     11,173   89.500      1,397  716.000        349 2864.000         87 11456.000  
179:    88,889   11.250     11,111   90.000      1,389  720.000        347 2880.000         87 11520.000  
180:    88,398   11.312     11,050   90.500      1,381  724.000        345 2896.000         86 11584.000  
181:    87,912   11.375     10,989   91.000      1,374  728.000        343 2912.000         86 11648.000  
182:    87,432   11.438     10,929   91.500      1,366  732.000        342 2928.000         85 11712.000  
183:    86,957   11.500     10,870   92.000      1,359  736.000        340 2944.000         85 11776.000  
184:    86,486   11.563     10,811   92.500      1,351  740.000        338 2960.000         84 11840.000  
185:    86,022   11.625     10,753   93.000      1,344  744.000        336 2976.000         84 11904.000  
186:    85,561   11.688     10,695   93.500      1,337  748.000        334 2992.000         84 11968.000  
187:    85,106   11.750     10,638   94.000      1,330  752.000        332 3008.000         83 12032.000  
188:    84,656   11.813     10,582   94.500      1,323  756.000        331 3024.000         83 12096.000  
189:    84,211   11.875     10,526   95.000      1,316  760.000        329 3040.000         82 12160.000  
190:    83,770   11.937     10,471   95.500      1,309  764.000        327 3056.000         82 12224.000  
191:    83,333   12.000     10,417   96.000      1,302  768.000        326 3072.000         81 12288.000  
192:    82,902   12.063     10,363   96.500      1,295  772.000        324 3088.000         81 12352.000  
193:    82,474   12.125     10,309   97.000      1,289  776.000        322 3104.000         81 12416.000  
194:    82,051   12.188     10,256   97.500      1,282  780.000        321 3120.000         80 12480.000  
195:    81,633   12.250     10,204   98.000      1,276  784.000        319 3136.000         80 12544.000  
196:    81,218   12.313     10,152   98.500      1,269  788.000        317 3152.000         79 12608.000  
197:    80,808   12.375     10,101   99.000      1,263  792.000        316 3168.000         79 12672.000  
198:    80,402   12.437     10,050   99.500      1,256  796.000        314 3184.000         79 12736.000  
199:    80,000   12.500     10,000  100.000      1,250  800.000        313 3200.000         78 12800.000  
200:    79,602   12.562      9,950  100.500      1,244  804.000        311 3216.000         78 12864.000  
201:    79,208   12.625      9,901  101.000      1,238  808.000        309 3232.000         77 12928.000  
202:    78,818   12.688      9,852  101.500      1,232  812.000        308 3248.000         77 12992.000  
203:    78,431   12.750      9,804  102.000      1,225  816.000        306 3264.000         77 13056.000  
204:    78,049   12.813      9,756  102.500      1,220  820.000        305 3280.000         76 13120.000  
205:    77,670   12.875      9,709  103.000      1,214  824.000        303 3296.000         76 13184.000  
206:    77,295   12.938      9,662  103.500      1,208  828.000        302 3312.000         75 13248.000  
207:    76,923   13.000      9,615  104.000      1,202  832.000        300 3328.000         75 13312.000  
208:    76,555   13.062      9,569  104.500      1,196  836.000        299 3344.000         75 13376.000  
209:    76,190   13.125      9,524  105.000      1,190  840.000        298 3360.000         74 13440.000  
210:    75,829   13.187      9,479  105.500      1,185  844.000        296 3376.000         74 13504.000  
211:    75,472   13.250      9,434  106.000      1,179  848.000        295 3392.000         74 13568.000  
212:    75,117   13.313      9,390  106.500      1,174  852.000        293 3408.000         73 13632.000  
213:    74,766   13.375      9,346  107.000      1,168  856.000        292 3424.000         73 13696.000  
214:    74,419   13.438      9,302  107.500      1,163  860.000        291 3440.000         73 13760.000  
215:    74,074   13.500      9,259  108.000      1,157  864.000        289 3456.000         72 13824.000  
216:    73,733   13.563      9,217  108.500      1,152  868.000        288 3472.000         72 13888.000  
217:    73,394   13.625      9,174  109.000      1,147  872.000        287 3488.000         72 13952.000  
218:    73,059   13.687      9,132  109.500      1,142  876.000        285 3504.000         71 14016.000  
219:    72,727   13.750      9,091  110.000      1,136  880.000        284 3520.000         71 14080.000  
220:    72,398   13.812      9,050  110.500      1,131  884.000        283 3536.000         71 14144.000  

* = may not work reliably, testing shows.

Space restraints preclude including the entire list, see the page mentioned above for a few more rows.

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