derivative

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derivative

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Library

Signal\Block Diagram

Implementations

FO

Pure

Use

Domains: Continuous. Size: 1-D. Kind: Block Diagrams.

Description - Pure

This model calculates the derivative of an input signal. The initial value of the output is equal to the parameter "initial".

 

output = ddt(input,initial);

 

A pure derivative requires special integration methods like the BDF method (default in 20-sim). Therefore 20-sim will try solve pure derivatives during compilation. If symbolic solving of a derivative fails, the Process Tab will show that the model contains 1 or more dependent state. To prevent dependent states, it is better to use the first order (FO) approximation of a derivative.

Interface - Pure

Inputs

Description

input

 

Outputs

 

output

 

Parameters

 

initial

The initial value of the output.

Description - FO

This model is a first order (FO) approximation of a derivative. For low frequency signals, the model gives a good approximation of  a pure derivative. The transfer function is:

Derivative-FO

The parameter fh is the derivative bandwidth. This is the maximum frequency or which this model gives a good approximation of a pure derivative. This is clear from the bode plot below which show the lines for a pure derivative (dotted) and the first order approximation.

Differentiate-FO2

Interface - FO

Inputs

Description

input

 

Outputs

 

output

 

Parameters

 

fh

Differentiation bandwidth [Hz]

Initial Values

 

output_initial

The initial value of the output.