**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 * H_{A}(s)* and

*. We call it*

**H**_{B}(s)*open-loop*transfer function

*:*

**W(s)**