Dynometer project data acquisition filtering

27
Dynamometer Project Data Acquisition Filtering Name: Rauf Tailony Rocket number:R01368594 Supervisor: Prof.Sorin cioc

Transcript of Dynometer project data acquisition filtering

Page 1: Dynometer project data acquisition filtering

Dynamometer  Project  Data  Acquisition  Filtering    

 Name:  Rauf  Tailony    Rocket  number:R01368594    Supervisor:  Prof.Sorin  cioc    

                                                                         

Page 2: Dynometer project data acquisition filtering

1.  Introduction:    Data  acquisition  is  used  in  this  project  to  give  an  indication  of  the  engine  power  by  extracting   data   from   a   load   cell   and   then   convert   the   load   data   into   torque   and  power  using  relevant  equations.    Data  acquisition  is  a  very  sensitive  part  of  this  project  and  any  project  because  the  more   clear   the   data   the   more   clear   the   decisions   could   be   made   related   to   the  project  success.    Collecting  data  is  usually  a  process  that  uses  sensor  of  different  types  to  collect  data  for  certain  parameter  in  order  to  compare  the  result  produced  by  these  parameters  with  the  existing  ones.    Analog  sensor  reading  are  usually  accompanied  with  a  lot  of  noise  of  different  types,  that  could  lead  to  a  non  clear  vision  for  the  parameters  that  we  are  trying  to  answer  some  questions  about,  so  in  order  to  eliminate  any  unwanted  noise  or  unwelcomed  data  its  necessary  to  use  filters  depending  on  what  kind  of  data  we  want  present  on  the  output  screen.    2.  Objective:    In  this  section  of  the  project  we  are  trying  to  do  the  following  objectives:    

1. filtering  and  fine-­‐tuning  the  data  acquisitioned  from  the  sensor   ;which   is   in  our  case  a  load  cell  that  measures  the  force  delivered  through  a  beam  by  the  alternator  that  is  connected    by  a  belt  with  the  engine.  

2. Comparing  the  filtered  and  non  filtered  force  data  using  graph  indicators.  3. Presenting  the  torque  generated  using  graph  indicator  after  passing  the  force  

data  through  related  equations.                                  

Page 3: Dynometer project data acquisition filtering

3.  Procedure:    3.1  Engine  power  delivery:    engine  power  is  delivered  to  the  alternator  through  a  belt  and  the  alternator  varies  the   load  on  the  engine  depending  on  a   lighting  system  connected  to  the  alternator  which   is   power   by   a   latching   button   ,   reflected   as   a   load   on   the   engine   which  changes  engine  power  produced  relating  to  the  load,  this  load  fluctuation  leads  to  a  angular  force  produced  by  the  alternator  ,  and  this  force  in  delivered  via  arm  to  be  applied  on  the  load  cell  located  at  the  end  of  the  arm,  as  shown  in  figure1.      

   Figure1,  connecting  arm  between  Alternator  and  Load  cell          3.2    sensor  connection  and  reading:    the  used  sensor  is  load  cell  (omegadyne),Figure  2,  and  connected  in  full  bridge  mode  through  an  NI9949  module  as  shown  in  figure  3,  and  this  module   is  connected  via  serail  port(RJ50)  through  analog  input/output  module  NI9237,Figure4,  and  fixed  on  NI   cDAQ-­‐9172,Figure   5,   and   connected   to   a   lab   view   software   of   custom  design(designed  by  Rauf  Tailony).      

Page 4: Dynometer project data acquisition filtering

   Figure  2,Omegadyne  load  cell          

   Figure3,NI9949        

Page 5: Dynometer project data acquisition filtering

   Figure4,NI9237      

   Figure5,NI  cDAQ-­‐9172            

Page 6: Dynometer project data acquisition filtering

3.3  Terminals  connection  tables  and  technical  information:    Load  cell-­‐NI9949  connections  table:    Terminal  name   Load  cell  colour  code   NI9949  pin  number  Signal  +(AL+)   Green   2  Signal  –  (AL-­‐)   White   3  Excitation  +(EX+)   Red   6  Excitation  –(EX-­‐)   Black   7      *Note:  previously   the   students  where   converting   the  wires  of  AL+  and  AL-­‐,  which  was  causing  the  data  to  be  in  minus.(fixed)      NI9949  –  NI9237  connection  table:    Device   Channel  NI9949   Single  channel  NI9237   CH0            *  Technical  data:    Load  cell  excitation  voltage  range(3-­‐10mv)    Used  excitation  voltage  (5mv)    Load  cell  Load  range(0-­‐20  LB)    Arm  length  (connecting  between  alternator  and  load  cell)  =  6  in        3.4  Filtering  and  Fine-­‐tuning:        The  filtering  procedure  we  are  using  is  software  dependent,  which  means  we  didn’t  use  any  physical  filters  or  data  conditioning  modules,  we  used  the  LV  express  filters  in  the  Block  diagram  mode  ,Figure6,  to  filter  the  data  extracted  from  the  load  cell.    We  used  Butterworth  low  pass  filter  with  cutoff  frequency  of  25  HZ,  and  the  order  of  the  filter  to  be  5,  with    signals  view  mode,  and  the  data  have  been  peak  limited  using  

Page 7: Dynometer project data acquisition filtering

mask  and  limit  testing,  and  these  filtered  signals  are  transferred  to  graph  indicators  to  be  presented  to  the  user,Figure6.    Filtered   data   are   sent   to   spectral  measurement   tools,   to   have   an   idea   about  what  kind  of  peaks  we  get  from  the  readings,  and  sent  to  a  spectral  indicator  to  be  read  by  the  user,Figure  7.    We  adjusted   the  Butterworth   filter   ,   in   the   sotware   to  have  a   slider   to   control   the  cutoff   frequency   in   real   time   mode   during   the   data   presentation   on   the   graph  indicator,Figure  8,  so  we  give  a  better  control  and  understanding  of  the  signal  form.              

     Figure6,Block  Diagram  Mode.  

Page 8: Dynometer project data acquisition filtering

 Figure7,Spectrum  graph      

 Figure8,Cutoff  frequency  Slider      

Page 9: Dynometer project data acquisition filtering

   3.5  Lab  view  Software’s  design  detailed  information:    since  we  are  using  NI  cDaQ-­‐9172  as  interface  between  the  sensor  and  the  Lab  view  software,  we  started  the  design  in  the  block  diagram  mode  by  adding  DAQ  assistant  block,   and   then   passing   the   data   line   to   subtracter   to   apply   the   data   offset  compensation  of  15   lb,after   that   the  data   line  passed   to  a   low  pass  analogue   filter  with  cutoff  frequency  of  10HZ  and  Butterworth  type  filter  of  order  5,and  connected  a  graph  indicator  on  the  line  to  represent  the  force  with  time  and  after  that  the  data  line   passed   to   a   multiplier   with   a   magnitude   of   (6in)   which   is   the   arm   length  between  the  alternator  and  the  load  cell  in  order  to  calculate  the  torque(Lb.  In)  after  filtering  ,  and  in  order  to  fine-­‐tune  the  data  more  precisely  we  passed  the  data  line  to  a  mean(averaging)  block  to  make  the  signal  more  smooth,  and  at  last  data  passed  to  a  data  recording  block(write  to  measurement  file)  to  save  the  data  on  hard  disk  depending   on   user   command,   all   the   previously   reported   blocks   are   shown   in  Figure9.      

   Figure9,  Block  diagram  design.  

Page 10: Dynometer project data acquisition filtering

                               The   graphical   user   interface   mode,   is   only   a   representation   of   the   output   tools  inserted  in  the  block  diagram,  which  contains  a  force-­‐time  graph,  and  Torque-­‐time  graph,   and   timer,   stop   button   and   cutoff   frequency   slider   and   sampling  rate,sampling  frequency  boxes,  as  shown  in  figure  10.        

   Figure10,GUI  mode      

Page 11: Dynometer project data acquisition filtering

 *  Sensor  calibration  and  reset:    Since   our   load   cell   sensor   is   a   bridge   circuit   ,   we   need   to   enter   for   the   lab   view  software   and   assign   the   first   two   values   of   calibration   provided   by   the  manufacturing  company  of  the  load  cell,  in  the  load  cell  we  are  using  we  could  find  some  calibration  data  on  the  manufacturer’s  website(Omegadyne.com),  and  we  can  find   the   place   to   calibrate   the   bridge   by   clicking   right   on   DAQ   assistant   in   block  diagram  mode  and  in  properties,  you  will  find  configure  scale,Figure11,  and  then  the  table  of  calibration  data,Figure12.    

 Figure11,DAQ  assistant  properties  window.    

Page 12: Dynometer project data acquisition filtering

 Figure12,Configure  scale  window      Note:  electrical  values  are  0.0000  and  0.9668  respectively,  and  physical  values  are  0  and  2.5  respectively.    Physical  sensor  calibration:      To  make  sure  that  the  data  we  are  getting  in  the  software  are  real  and  there  is  no  error  in  the  reading  ,  we  made  physical  calibration  for  the  sensor  side  by  side  with  the  sensor  software  calibration.      We  made  the  calibration  using  (0.25,0.65,1.3,5lb)  weights  ,  and  loading  it  on  the  top  of   the   load   cell   after   isolating   it   from   the   system  and   then  observing   the   readings  presented  on   the   load  graph,   and  adjusting   the   subtraction  magnitude   in  order   to  make   the   load   cell   give   as   much   precise   data   as   it   is   capable   of,   as   described   in  figures  13,14  respectively.      Its  worth   it   to  mention  that  after   taking  the  data  on  the  graph  read  by  the  sensor  from   the  previous  weights,  we   found   that   there   is   an  offset   in   the   factor  of   (3.39)  which   we   could   deal   with   it   by   multiplying   the   data   line   with   this   factor   before  presenting  it  on  the  graph,  Figure  15.      

Page 13: Dynometer project data acquisition filtering

 

       Figure  13,  weights  used  in  calibration.      

 Figure  14,  mounted  weight  on  load  cell  structure.        

Page 14: Dynometer project data acquisition filtering

   Figure15,offset  compensation  block                        3.6  Displaying  calculated  rpm  in  the  GUI  :    As   it   is   known   ,   Torque(Lb.   IN)   has   a   relation  with   power(HP)   and  RPM  which   is  shown  the  relation  below:    Torque  (lb.in)  =  63,025  x  Power  (HP)  /  Speed  (RPM)……………………….(1)    and  using  this  relation  allows  us  to  show  the  calculated  engine  RPM  in  the  Labview  software   since   the   power   is   known   for   the   engine,   but  with   a   limitation   that   this  RPM   will   be   precise   only   for   the   engine   in   the   Idle   state,   but   after   coupling   the  engine   with   the   alternator   ,it   will   be   very   complex   to   predict   the   RPM   in   the  calculation   torque  based  method  which  will   give   correct   data   representation   only  when  engine  have  no  load  and  running  on  high  rpm(>6000rpm)  ,  Figure16.    

Page 15: Dynometer project data acquisition filtering

 Figure16,RPM  in  the  GUI  mode      Before  we  pass  the  data  line  to  RPM  indicator  we  passed  it  to  a  formula  box  ,  which  contain  the  following  formula  which  is  number  substitution  to  formula  (1)  :    (63025*0.611)/X1  ………………………….(2)      

                                                   Torque  data       Power(HP)      Eq.(1)  constant      We   got   the   power   value   of   0.611   ,by   running   the   engine   on   RPM   =   7500,   and  coupling   it  with   the  alternator,   and  Using   the  ProCal   software   to  get   the   rpm   ,  we  could  calculate  the  real  power  after  coupling  using  eq.(1),  and  you  can  trace  the  data  line  passing  through  the  formula  block  by  looking  to  figure  17.      

Page 16: Dynometer project data acquisition filtering

   Figure17,Full  block  diagram      We   compared   the   data  we   got   from   our   design   of   labview   GUI   RPM,   with   Procal  RPM,  the  results  were  almost  the  same  in  the  same  running  conditions,  as  indicated  in  Figure18.    

Page 17: Dynometer project data acquisition filtering

   Figure18,  Labview  RPM  VS.  Procal                

Page 18: Dynometer project data acquisition filtering

4.  Conclusion:    Data  filtering  can  enhance  the  data  we  extract  from  the  load  cell  sensor  even  its  not  a  physical  filtering  but  it  could  fairly  enhance  the  results  to  the  user  in  order  to  give  a  better  understanding  of  the  parameters  that  we  are  trying  to  observe  which  is  in  our  case  the  torque  and  power.      

   Figure  19,  Original  Data  with  noise    In   the  previous  graph  we  are  presenting   the  original  data   that   is   extracted   in   real  time  directly  from  the  sensor,  as  you  can  see  in  figure  13,  the  data  have  a  lot  of  noise  which  make  it  hard  for  the  observer  to  decide  of   the  torque  he   is  getting  from  the  engine  is  good  or  bad   ,  and  following  to  that  we  have  pasted  the  filtered  force  and  torque  graphs  with  time  for  the  engine  in  the  Idle  state,  so  that  you  can  observe  the  change  happened  to  the  data  after  filtering,  and  what  kind  of  enhancement  made  to  make  the  data  more  stable  and  readable.      

Page 19: Dynometer project data acquisition filtering

   Figure  20,  Filtered  Data      *  Mean  and  averaging:    even  we  have  implemented  the  averaging  property  to  the  block  diagram  as  you  saw  previously,  but  related  to  a  limitation  in  the  Labview  software  you  can’t  present  the  data   of   the   averaging   and   mean   or   RMS   as   a   graph   but   only   as   numbers,   as  presented  previously  in  the  GUI  screenshot.    5.  Recommendations:    I   would   recommend   for   the   coming   teams  who  will   work   on   this   project   for   the  software   side   to   use   FPGA   software   to   represent  more   filtered   and   averaged   and  stable  data  that  could  look  more  professional  for  future  use  of  the  project,  or  using  matlab   since   its   supporting   the   graphical   representation  more   than   lab   view,   and  also  have  a   lot  of  resources  that  could  help  researcher  do  a  better  design  than  the  Labview  do.    

Page 20: Dynometer project data acquisition filtering

6.  Index:    Filter  used  and  related  concepts:    Butterworth  Filter:      In  applications  that  use  filters  to  shape  the  frequency  spectrum  of  a  signal  such  as  in  communications  or  control  systems,  the  shape  or  width  of  the  roll-­‐off  also  called  the  “transition   band”,   for   a   simple   first-­‐order   filter   may   be   too   long   or   wide   and   so  active   filters   designed   with   more   than   one   “order”   are   required.   These   types   of  filters  are  commonly  known  as  “High-­‐order”  or  “nth-­‐order”  filters.    The   complexity   or   Filter   Type   is   defined   by   the   filters   “order”,   and   which   is  dependant  upon  the  number  of  reactive  components  such  as  capacitors  or  inductors  within   its  design.  We  also  know  that  the  rate  of  roll-­‐off  and  therefore  the  width  of  the   transition   band,   depends   upon   the   order   number   of   the   filter   and   that   for   a  simple  first-­‐order  filter  it  has  a  standard  roll-­‐off  rate  of  20dB/decade  or  6dB/octave.    Then,  for  a  filter  that  has  an  nth  number  order,  it  will  have  a  subsequent  roll-­‐off  rate  of   20n   dB/decade   or   6n   dB/octave.   So   a   first-­‐order   filter   has   a   roll-­‐off   rate   of  20dB/decade  (6dB/octave),  a  second-­‐order  filter  has  a  roll-­‐off  rate  of  40dB/decade  (12dB/octave),   and   a   fourth-­‐order   filter   has   a   roll-­‐off   rate   of   80dB/decade  (24dB/octave),  etc,  etc.  High-­‐order   filters,   such   as   third,   fourth,   and   fifth-­‐order   are   usually   formed   by  cascading  together  single  first-­‐order  and  second-­‐order  filters.  For  example,  two  second-­‐order  low  pass  filters  can  be  cascaded  together  to  produce  a  fourth-­‐order   low  pass  filter,  and  so  on.  Although  there  is  no  limit  to  the  order  of  the  filter  that  can  be  formed,  as  the  order  increases  so  does  its  size  and  cost,  also  its  accuracy  declines.      Decades  and  Octaves  One  final  comment  about  Decades  and  Octaves.  On  the  frequency  scale,  a  Decade  is  a  tenfold  increase  (multiply  by  10)  or  tenfold  decrease  (divide  by  10).  For  example,  2  to  20Hz  represents  one  decade,  whereas  50  to  5000Hz  represents  two  decades  (50  to  500Hz  and  then  500  to  5000Hz).  An  Octave   is   a   doubling   (multiply   by   2)   or   halving   (divide   by   2)   of   the   frequency  scale.   For   example,   10   to   20Hz   represents   one   octave,   while   2   to   16Hz   is   three  octaves   (2   to   4,   4   to   8   and   finally   8   to   16Hz)   doubling   the   frequency   each   time.  Either   way,   Logarithmic   scales   are   used   extensively   in   the   frequency   domain   to  denote  a  frequency  value  when  working  with  amplifiers  and  filters  so  it  is  important  to  understand  them.          

Page 21: Dynometer project data acquisition filtering

Logarithmic  Frequency  Scale  

     Since   the   frequency   determining   resistors   are   all   equal,   and   as   are   the   frequency  determining   capacitors,   the   cut-­‐off   or   corner   frequency   (  ƒC  )   for   either   a   first,  second,  third  or  even  a  fourth-­‐order  filter  must  also  be  equal  and  is  found  by  using  our  now  old  familiar  equation:  

     As  with  the  first  and  second-­‐order  filters,  the  third  and  fourth-­‐order  high  pass  filters  are   formed   by   simply   interchanging   the   positions   of   the   frequency   determining  components  (resistors  and  capacitors)  in  the  equivalent  low  pass  filter.  High-­‐order  filters  can  be  designed  by   following   the  procedures  we  saw  previously   in   the  Low  Pass  and  High  Pass  filter  tutorials.  However,  the  overall  gain  of  high-­‐order  filters  is  fixed  because  all  the  frequency  determining  components  are  equal.    Filter  Approximations  So  far  we  have  looked  at  a  low  and  high  pass  first-­‐order  filter  circuits,  their  resultant  frequency   and   phase   responses.   An   ideal   filter   would   give   us   specifications   of  maximum  pass  band  gain  and  flatness,  minimum  stop  band  attenuation  and  also  a  very  steep  pass  band  to  stop  band  roll-­‐off   (the  transition  band)  and   it   is   therefore  apparent   that   a   large   number   of   network   responses   would   satisfy   these  requirements.  Not  surprisingly  then  that  there  are  a  number  of  “approximation  functions”  in  linear  analogue   filter   design   that   use   a  mathematical   approach   to   best   approximate   the  transfer  function  we  require  for  the  filters  design.  Such  designs  are  known  as  Elliptical,  Butterworth,  Chebyshev,  Bessel,  Cauer  as  well  as  many  others.  Of  these  five  “classic”  linear  analogue  filter  approximation  functions  only  the  Butterworth  Filter  and  especially  the  low  pass  Butterworth  filter  design  will  be  considered  here  as  its  the  most  commonly  used  function.    Low  Pass  Butterworth  Filter  Design    The   frequency   response   of   the   Butterworth   Filter   approximation   function   is   also  often  referred  to  as  “maximally  flat”  (no  ripples)  response  because  the  pass  band  is  designed  to  have  a   frequency  response  which   is  as   flat  as  mathematically  possible  from   0Hz   (DC)   until   the   cut-­‐off   frequency   at   -­‐3dB   with   no   ripples.   Higher  frequencies   beyond   the   cut-­‐off   point   rolls-­‐off   down   to   zero   in   the   stop   band   at  20dB/decade   or   6dB/octave.   This   is   because   it   has   a   “quality   factor”,   “Q”   of   just  

Page 22: Dynometer project data acquisition filtering

0.707.  However,   one  main   disadvantage   of   the   Butterworth   filter   is   that   it   achieves   this  pass   band   flatness   at   the   expense   of   a  wide   transition   band   as   the   filter   changes  from  the  pass  band  to  the  stop  band.  It  also  has  poor  phase  characteristics  as  well.  The   ideal   frequency  response,  referred  to  as  a  “brick  wall”   filter,  and  the  standard  Butterworth  approximations,  for  different  filter  orders  are  given  below.    Ideal  Frequency  Response  for  a  Butterworth  Filter  

     Where   the  generalised  equation  representing  a   “nth”  Order  Butterworth   filter,   the  frequency  response  is  given  as:  

 Where:  n  represents   the   filter  order,  Omega  ω   is  equal   to  2πƒ  and  Epsilon  ε   is   the  maximum  pass  band  gain,  (Amax).  If  Amax  is  defined  at  a  frequency  equal  to  the  cut-­‐off  -­‐3dB  corner  point  (ƒc),  ε  will  then  be  equal  to  one  and  therefore  ε2  will  also  be  one.  However,  if  you  now  wish  to  define  Amax  at  a  different  voltage  gain  value,  for  example  1dB,  or  1.1220  (1dB  =  20logAmax)  then  the  new  value  of  epsilon,  ε  is  found  by:  

 

•  Where:  •    H0  =  the  Maximum  Pass  band  Gain,  Amax.  •    H1  =  the  Minimum  Pass  band  Gain.  

Transpose  the  equation  to  give:  

     The  Frequency  Response  of   a   filter   can  be  defined  mathematically  by   its  Transfer  

Page 23: Dynometer project data acquisition filtering

Function  with  the  standard  Voltage  Transfer  Function  H(jω)  written  as:  

 

•  Where:  •    Vout  =  the  output  signal  voltage.  •    Vin    =  the  input  signal  voltage.  •          j      =  to  the  square  root  of  -­‐1  (√-­‐1)  •        ω    =  the  radian  frequency  (2πƒ)  

   Note:   (  jω  )   can   also   be  written   as   (  s  )   to   denote   the   S-­‐domain.   and   the   resultant  transfer  function  for  a  second-­‐order  low  pass  filter  is  given  as:  

     Normalised  Low  Pass  Butterworth  Filter  Polynomials  To  help  in  the  design  of  his  low  pass  filters,  Butterworth  produced  standard  tables  of  normalised  second-­‐order  low  pass  polynomials  given  the  values  of  coefficient  that  correspond  to  a  cut-­‐off  corner  frequency  of  1  radian/sec.  n   Normalised  Denominator  Polynomials  in  Factored  Form  1   (1+s)  2   (1+1.414s+s2)  3   (1+s)(1+s+s2)  4   (1+0.765s+s2)(1+1.848s+s2)  5   (1+s)(1+0.618s+s2)(1+1.618s+s2)  6   (1+0.518s+s2)(1+1.414s+s2)(1+1.932s+s2)  7   (1+s)(1+0.445s+s2)(1+1.247s+s2)(1+1.802s+s2)  8   (1+0.390s+s2)(1+1.111s+s2)(1+1.663s+s2)(1+1.962s+s2)  9   (1+s)(1+0.347s+s2)(1+s+s2)(1+1.532s+s2)(1+1.879s+s2)  10   (1+0.313s+s2)(1+0.908s+s2)(1+1.414s+s2)(1+1.782s+s2)(1+1.975s+s2)  Filter  Design  –  Butterworth  Low  Pass  Find   the   order   of   an   active   low   pass   Butterworth   filter   whose   specifications   are  given  as:  Amax  =  0.5dB  at  a  pass  band  frequency  (ωp)  of  200  radian/sec  (31.8Hz),  and  Amin  =   -­‐20dB  at  a  stop  band   frequency  (ωs)  of  800  radian/sec.  Also  design  a  suitable  Butterworth  filter  circuit  to  match  these  requirements.  Firstly,   the   maximum   pass   band   gain   Amax   =   0.5dB   which   is   equal   to   a   gain   of  1.0593  (0.5dB  =  20log  A)  at  a  frequency  (ωp)  of  200  rads/s,  so  the  value  of  epsilon  ε  is  found  by:  

     Secondly,  the  minimum  stop  band  gain  Amin  =  -­‐20dB  which  is  equal  to  a  gain  of  -­‐10  (20dB  =  20log  A)  at  a  stop  band  frequency  (ωs)  of  800  rads/s  or  127.3Hz.  Substituting  the  values  into  the  general  equation  for  a  Butterworth  filters  frequency  response  gives  us  the  following:  

Page 24: Dynometer project data acquisition filtering

     Since  n  must  always  be  an  integer  (  whole  number  )  then  the  next  highest  value  to  2.42   is  n  =  3,   therefore  a   “a   third-­‐order   filter   is   required”  and   to  produce  a   third-­‐order  Butterworth  filter,  a  second-­‐order  filter  stage  cascaded  together  with  a  first-­‐order  filter  stage  is  required.  From  the  normalised  low  pass  Butterworth  Polynomials  table  above,  the  coefficient  for  a  third-­‐order  filter  is  given  as  (1+s)(1+s+s2)  and  this  gives  us  a  gain  of  3-­‐A  =  1,  or  A  =  2.  As  A  =  1  +  (Rf/R1),  choosing  a  value  for  both  the  feedback  resistor  Rf  and  resistor  R1  gives  us  values  of  1kΩ  and  1kΩ  respectively,  (  1kΩ/1kΩ  +  1  =  2  ).  We  know  that  the  cut-­‐off  corner  frequency,  the  -­‐3dB  point  (ωo)  can  be  found  using  the  formula  1/CR,  but  we  need  to  find  ωo  from  the  pass  band  frequency  ωp  then,  

Page 25: Dynometer project data acquisition filtering

     So,   the   cut-­‐off   corner   frequency   is   given   as   284   rads/s   or   45.2Hz,   (284/2π)   and  using   the   familiar   formula   1/CR   we   can   find   the   values   of   the   resistors   and  capacitors  for  our  third-­‐order  circuit.  

 Note  that  the  nearest  preferred  value  to  0.352uF  would  be  0.36uF,  or  360nF.                    

Page 26: Dynometer project data acquisition filtering

Third-­‐order  Butterworth  Low  Pass  Filter    and  finally  our  circuit  of  the  third-­‐order  low  pass  Butterworth  Filter  with  a  cut-­‐off  corner  frequency  of  284  rads/s  or  45.2Hz,  a  maximum  pass  band  gain  of  0.5dB  and  a  minimum  stop  band  gain  of  20dB  is  constructed  as  follows.  

                                                   

Page 27: Dynometer project data acquisition filtering

7.  Acknowledgment:    Very   big   thanks   for   Prof.   Sorin   Cioc,   Assistant   professor,UT,   for   giving   me   the  opportunity  to  use  his  Internal  combustion  lab,  and  giving  me  a  solid  pathway  to  use  it  in  order  to  reach  the  goal  in  this  work  using  the  shortest  road.    Special   thanks   for   Sabin   Bati,Masters   student,MIME,UT,   for   his   help   in   practical  work,  and  for  his  bright  Ideas  that  he  shared  with  me  in  order  to  make  the  data  look  and  behave  more  precise.      8.  References:      

1. http://www.ni.com/community/  2. http://www.omegadyne.com/nav/entry.html  3. http://www.electronics-­‐tutorials.ws