Nikola Šerman, prof. emeritus                                                                                  Linear Theory
nserman@fsb.hr                                                                                                         Transfer Function Concept Digest

### 7. BLOCKS ALGEBRA

All the interactions within any SISO blocks system regardless of its complexity can be described by a combination of the elementary interactions presented in fig. 7.1. Fig. 7.1 Elementary interactions between blocks

In the time domain relationship between system input x(t) and output y(t)  is described by a differential equation.  When mapped into the frequency domain it turns into a simple algebraic relation (4.5).

By applying elementary blocks algebra from Fig 7.1 the following relations between transfer function components and respective system transfer functions take place:

For blocks in series: For blocks in parallel: For blocks in negative feedback closed loop: The numerator in (7.3) depends on the system’s output.  The denominator is always  a sum of 1 plus a product of all the transfer functions within the closed loop.

The product in the denominator can be understood as a serial connection of the block HA(s) and HB(s).  We call it open-loop transfer function W(s): 