======================Q_FACTOR======================


Q_factor              QualityFactor       cycles to settle 
                      ( Impedance_L )/R   cycles to settle 
                      ring freq           where Impedance_L = Impedance_C       
                      2*PI()*Freq*L       equals 1/(2*PI()*Freq*C)                                                         
                            _                                 
                           | |  _                                     
                           | | | |  _                                         
                           | | | | | |  _    PULSE RESPONSE                  
                           | | | | | | | |  _                       
                           | | | | | | | | | |  _                          
                           |_|_|_|_|_|_|_|_|_|_|_|_____\                     
                           | | | | | | | | | |_|       / Time    
                           | | | | | | | |_|                     
                           | | | | | |_|                             
                           | | | |_|                                  
                           | | |                                      
                           | |_|                                      
                                  L                                           
                                  _  _  _                                      
                        __  R    / \/ \/ \       __                        
                       |  |_  /\_| () () |______|  |                
                       |__| \/              |   |__|            
                                           _|_                     
                                           ___  C                  
                        __                  |     __                        
                       |  |_________________|____|  |        
                       |__|                      |__|     


-------------------------------------------------------------------------------------  

                       20dB|................................................   
                           |           .           .           .           .  
                           |           .           b   Q=10    .           .   
                           |           .           .           .           .  
                           |           .        b  .           .           .  
                           |           .      b    .b          .           .
                        0dB|..........a..a...a..............................
                           |           .        a  . b         .           .  
                           |           .           .           .           .  
                           |           .           a  b        .           .   
                           |           .           . a         .           .  
                           |           .           .   a       .           .   
                      -20dB|.............................a..................
                           |           .           .                       .   
                           |           .           .           .           .    
                           |           .           .           .           .   
                           |           .           .           .           .  
                           |           .           .           .           .  
                           |______________________________________________ .  
                           100KHz      1MHz      10MHz        100MHz      1GHz


-------------------------------------------------------------------------------------  


impedance C           _|_                      Z(S) = 1/s*C
                      ___
                       |
                             _  _  _        
                            /*\/ \/ \          Z(S) = s*L
                      ___   | () () |   ___       
impedance L          |   |__|       |__|   |    
                     |___|             |___|

-------------------------------------------------------------------------------------- 
                      
                                  L   Z(S) =s*L                                          
                                  _  _  _                                      
                        __  R    / \/ \/ \       ___                        
                       |IN|_  /\_| () () |______|OUT|                
                       |__| \/              |   |___|            
                                           _|_                     
                                           ___  C  Z(S)= 1/s*C                
                        __                  |     __                        
                       |  |_________________|____|  |        
                       |__|                      |__|     


Transfer Function     OUT = IN*( 1/s*C)/( R + s*L +1/s*C )
                      OUT = IN*1/(a*s^2 +b*s +c ) 

-------------------------------------------------------------------------------------- 
                     
Complex_Poles         1/(a*s^2 +b*s +c)  = 1/(s^2 +(wo/Q)*s +wo^2)

Quadratic formula     a*x^2 +b*x +c = 0 
roots                 (-b +/-sqrt(b^2-4ac))/2a

                      1/(a*s^2 +b*s +c)  =1/(( s +alpha +jwo )*( s +alpha -jwo ))


                         IMAGINARY      
                            ^
                           /|\
                            |
                         X  | ^
                            | | jw0
                      ______|_v_____\ REAL
                            |       /
                            |
                         X  |
                         <->
                         alpha
----------------------------------------------------------------------------
SciLab_Templates      Cut and paste into a SciLab command window to run
                      plots of gain_dB and Phase_deg
Low_Pass_Q10          =================SciLab_Template=========================
                      w0=2*%pi*10                                     // Freq = 10Hz
                      Q=10                                            // Q    = 10
                      freqmax=100                                              
                      freqstep=.005
                      freqmin=.1
                      dBmax=20
                      dBmin=-60
                      Phmax=20
                      Phmin=-180
                      s=poly(0,'s')                                    // define s as a poly symbol
                      h=syslin('c', w0^2/(s^2+ w0*s/Q +w0^2))          // trans func'c'= cont
                      [frq,rf]=repfreq(h,freqmin,freqmax,freqstep);    // create complex frq response
                      [db,phi]=dbphi(rf);                              // extact db phase vectors
                      subplot(211)                                     // 2X1 window first plot
                      xgrid();
                      plot2d(frq,db,logflag="ln",rect=[freqmin,dBmin,freqmax,dBmax]) 
                      xtitle("Gain_vs_Freq","Freq_Hz","Gain_DB");
                      subplot(212)                                     // 2X1 window second plot
                      xgrid();
                      plot2d(frq,phi,logflag="ln",rect=[freqmin,Phmin,freqmax,Phmax])
                      xtitle("Phase_vs_Freq","Freq_Hz","Phase_deg");
High_Pass_Q10         =================SciLab_Template=========================
                      w0=2*%pi*10                                     // Freq = 10Hz
                      Q=10                                            // Q    = 10
                      freqmax=100
                      freqstep=.005
                      freqmin=.1
                      dBmax=20
                      dBmin=-60
                      Phmax=180
                      Phmin=-20
                      s=poly(0,'s')                                    // define s as a poly symbol
                      h=syslin('c', s^2/(s^2+ w0*s/Q +w0^2))           // transfer funct 'c'= cont
                      [frq,rf]=repfreq(h,freqmin,freqmax,freqstep);    // create complex frq response
                      [db,phi]=dbphi(rf);                              // extact db phase vectors
                      subplot(211)                                     // 2X1 window first plot
                      xgrid();
                      plot2d(frq,db,logflag="ln",rect=[freqmin,dBmin,freqmax,dBmax]) 
                      xtitle("Gain_vs_Freq","Freq_Hz","Gain_DB");
                      subplot(212)                                     // 2X1 window second plot
                      xgrid();
                      plot2d(frq,phi,logflag="ln",rect=[freqmin,Phmin,freqmax,Phmax])
                      xtitle("Phase_vs_Freq","Freq_Hz","Phase_deg");                      
Band_Pass_Q10         =================SciLab_Template=========================
                      w0=2*%pi*10                                     // Freq = 10Hz
                      Q=10                                            // Q    = 10
                      freqmax=100
                      freqstep=.005
                      freqmin=.1
                      dBmax=10
                      dBmin=-60
                      Phmax=100
                      Phmin=-100
                      s=poly(0,'s')                                    // define s as a poly symbol
                      h=syslin('c', (w0*s/Q)/(s^2+ w0*s/Q +w0^2))      // transfer funct 'c'= cont
                      [frq,rf]=repfreq(h,freqmin,freqmax,freqstep);    // create complex frq response
                      [db,phi]=dbphi(rf);                              // extact db phase vectors
                      subplot(211)                                     // 2X1 window first plot
                      xgrid();
                      plot2d(frq,db,logflag="ln",rect=[freqmin,dBmin,freqmax,dBmax]) 
                      xtitle("Gain_vs_Freq","Freq_Hz","Gain_DB");
                      subplot(212)                                     // 2X1 window second plot
                      xgrid();
                      plot2d(frq,phi,logflag="ln",rect=[freqmin,Phmin,freqmax,Phmax])
                      xtitle("Phase_vs_Freq","Freq_Hz","Phase_deg")
Band_Reject_Q10       =================SciLab_Template=========================
                      w0=2*%pi*10                                     // Freq = 10Hz
                      Q=10                                            // Q    = 10
                      freqmax=100
                      freqstep=.005
                      freqmin=.1
                      dBmax=10
                      dBmin=-60
                      Phmax=100
                      Phmin=-100
                      s=poly(0,'s')                                    // define s as a poly symbol
                      h=syslin('c', (s^2 +w0^2)/(s^2+ w0*s/Q +w0^2))   // transfer funct 'c'= cont time,
                      [frq,rf]=repfreq(h,freqmin,freqmax,freqstep);    // create complex frq response
                      [db,phi]=dbphi(rf);                              // extact db phase vectors
                      subplot(211)                                     // 2X1 window first plot
                      xgrid();
                      plot2d(frq,db,logflag="ln",rect=[freqmin,dBmin,freqmax,dBmax]) 
                      xtitle("Gain_vs_Freq","Freq_Hz","Gain_DB");
                      a=get("current_axes");
                      t=a.title;
                      t.font_size=3;
                      subplot(212)                                     // 2X1 window second plot
                      xgrid();
                      plot2d(frq,phi,logflag="ln",rect=[freqmin,Phmin,freqmax,Phmax])
                      xtitle("Phase_vs_Freq","Freq_Hz","Phase_deg")
                      a=get("current_axes");
                      t=a.title;
                      t.font_size=3;