**Nikola Šerman,**prof. emeritus

*Linear Theory*nserman@fsb.hr

*Transfer Function Concept Digest*

**10. ELEMENTARY BLOCKS**

#### 10.1 Static Gain

The elementary block described by (10.1) is presented in fig 10.1 as an autonomous system which is commonly referred to as* static gain.*

**Fig 10.1** Block presentation of **static gain**

Dependence of the output *y(t)* on input *x(t)* is defined in the time domain by a zero-order differential equation which contracts to algebraic equation:

where *K* is a constant with dimension: [brackets denote *‘dimension of’*].

When *x* and *y* are relative, i.e. dimensionless variables, *K* is dimensionless as well. The use of relative variables is assumed throughout the following paragraphs.

Static gain maps input function* x(t)* into the output *y(t)* without any dynamical distortion, as it is demonstrated in fig. 10.2 using the step response as an example.

**Fig 10.2** Step response of **a static gain** (unity step at input)

The equation (10.4) is mapped into the frequency domain as the transfer function:

For *s = j ω* the transfer function (10.5) defines frequency response presented in Bode diagram in fig. 10.3 and in Nyquist diagram in fig. 10.4.

**Fig 10.3** Frequency response of a **static gain** (three different values of *K*) in Bode diagram

**Fig 10.4** Frequency response of a static gain in Nyquist diagram (*K* is a real number)