**Nikola Šerman,**prof. emeritus

*Linear Theory*nserman@fsb.hr

*Transfer Function Concept Digest*

**10. ELEMENTARY BLOCKS**

Let us remind on *“poles and zeros”* annotation of the transfer function (4.4), where poles *s _{1}…s_{n}* are the roots of the denominator and zeros

*s*are the roots of the nominator of transfer function

_{I}… s_{m}*H(s)*.

In the chapter 7 there has been shown that the transfer function of serially connected blocks equals a product of the individual transfer functions. Therefore, transfer function of any dynamic system under consideration (i.e. *linear, lumped parameters, time invariant*) can be presented as a serial connection of components described by transfer functions of the following form:

where *C* is a constant, *p* denotes pole and *z* denotes zero of the respective transfer function.

This fact offers an opportunity to formulate some ready-to-use packages of knowledge, which are suitable to be learned by heart and have proven themselves as very useful tool in closed-loop dynamics qualitative analyses.

These packages that are called Elementary Blocks are dealt with in the following chapters.

It is assumed that Elementary Blocks are stable i.e. there are no poles falling into the right-hand side of the complex plane. For real poles that means that *p ≤ 0*. For complex poles that appear in conjugate pairs the stability is ensured by * Re p ≤ 0*.

The main Elementary Blocks are specified in the following pages:

**10.1 Static Gain**

**10.2 Integrator**

**10.3 First-Order Lag****10.4 Differentiator**

**10.5 First-Order Lead****10.6 Second Order Oscillator**