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Block diagram representation and reduction
  To draw the block diagram for a system, first write the equation which describe the dynamic behaviour of each components. Take the laplace transform of these equations, assuming zero initial conditions and represent each laplace transformed equation individually in the form of block. Finally assemble the elements into a complete block diagram.

As an example consider the Rc circuit shown in the below figure. The equations for the circuit shown are

Equation (1) becomes

Laplace transforms of equations (2) & (3) are

Equation(5) represents a summing operation and the corresponding diagram is shown in below figure(b). Equation(4) represents the block as shown in below figure(c). Assembling these two elements, the overall block diagram for the system shown in below figure(d) is obtained.



Signal flow graph representation and reduction using Mason's gain formula