## Bode Diagram

### General

The  Bode Diagram (according to Hendrik Wade Bode) is a special funcion's graph consisting of one graph for the amount (the gain of the amplitude), and of one for the argument (the phase shift) of a complex transfer function.

Bode Diagrams are used to represent linear time - invariant (LTI) systems in electronics/electrical engineering, control engineering, and mechatronics, as well as in impedance spectroscopy.

Bode Diagrams describe the stationary reactions  at a system's entrance to a harmonic impulse ("sinus oscillation") given at a system's exit. Thus, to completely describe an LTI system with n entrances and m exits you need n times m diagrams.

Bode Diagrams serve to represent the dynamic system's behaviour, also called frequency response. Das Bode Diagram is deduced and calculated from mathematical descriptions of the system by means of differential equations.

### Characteristics

• On the x - axis (abscissa), the frequency, resp. the radian frequency is represented logarithmically. Thus, the the behavior over a large frequency sector can be observed.
• On the y - axis (ordinate) of the first graph the amplification of the amplitude, i. e., the complex contribution of the transmission function, is represented in in decibel which means, it is represented logarithmically as well. This graph is called "amplitude response."
• On the y - axis of the second graph the phase displacement, i. e., the argument of the phase displacement, is applied linearly. Ths graph is called "phase displacement."

Amplitude response and phase response are applied on top of each other, so that the amplification and the phase of a frequency are placed vertically on top of each other.

As the gains are represented in decibel, the advantage of Bode Diagrams is that complex Bode Diagrams can be drawn up by superposing simple sub-diagrams. For this purpose, the complex function is separated by factorizing to first- and second - class partial transmission functions. By applying the gain logarithmically the multiplication of the partial transmission functions is converted into the sum of its amplitude responses represented in decibel. Also without logarithmical scaling the phase responses  are additive.

### Bode Diagrams in servo amplifiers

The servo amplifiers S300 and S700 both offer Bode Plot functions for current control, speed control, and for position control.