General time- and transfer constant analysis

<p>The general time- and transfer-constants (TTC) analysis is the generalized version of the Cochran-Grabel (CG) method, which itself is the generalized version of zero-value time-constants (ZVT), which in turn is the generalization of the <a href="/facts/Open-circuit_time_constant_method/4pu9XcJd">open-circuit time constant method</a> (OCT). While the other methods mentioned provide varying terms of only the denominator of an arbitrary transfer function, TTC can be used to determine every term both in the numerator and the denominator. Its denominator terms are the same as that of Cochran-Grabel method, when stated in terms of time constants (when expressed in Rosenstark notation). however, the numerator terms are determined using a combination of <a href="/facts/Transfer_constant/qlgtxs79">transfer constants</a> and <a href="/facts/Time_constant/5na4AbzV">time constants</a>, where the time constants are the same as those in CG method. Transfer constants are low-frequency ratios of the output variable to input variable under different open- and short-circuited active elements.
</p><p>In general, a transfer function (which can characterize gain, admittance, impedance, trans-impedance, etc., based on the choice of the input and output variables) can be written as:
</p>

H
        (
        s
        )
        =
        
          
            
              
                a
                
                  0
                
              
              +
              
                a
                
                  1
                
              
              s
              +
              
                a
                
                  2
                
              
              
                s
                
                  2
                
              
              +
              …
              +
              
                a
                
                  m
                
              
              
                s
                
                  m
                
              
            
            
              1
              +
              
                b
                
                  1
                
              
              s
              +
              
                b
                
                  2
                
              
              
                s
                
                  2
                
              
              +
              …
              +
              
                b
                
                  n
                
              
              
                s
                
                  n
                
              
            
          
        
      
    
    {\displaystyle H(s)={\frac {a_{0}+a_{1}s+a_{2}s^{2}+\ldots +a_{m}s^{m}}{1+b_{1}s+b_{2}s^{2}+\ldots +b_{n}s^{n}}}}

General time- and transfer constant analysis open-in-new

General time- and transfer constant analysis