FREQUENCY RESPONSE / NORMALISATION AND FILTER CIRCUITS
First Order Systems 

First order systems are systems that involve only a single energy storage element like a capacitor or an inductor. These single energy storage elements may lay alone in a first order system or in combination with resistors either in series or in parallel. These systems are called first order systems because the differential equation that characterises these systems is of first order. The transfer function of figure H below is :

......(1)

figure H : first order system circuit

From equation (1) above =>

let

                               

There is a pole at :

            

from the above equation it can be seen that when the frequency w becomes very small (w= 0), then :

For large w the gain becomes :

                 =>                  =>      

   

the gain at a frequency w1 is :            

..........(2)

the gain now at the double frequency is :        

.......(3)               subtracting (3) from (2)  =>     

  =>                       

           

A(dB) = 20 log (2) = 6dB/octave or 20dB/decade

When w = a

     ,