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# Ferroelectricity and voltage-capacitance behaviour

6th December 2023
Sheryl Miles
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Würth Elektronik has implemented the voltage-capacitance behaviour of ferroelectric multilayer ceramic capacitors (MLCCs) in the LTspice files of its products, which significantly improves the accuracy of simulations.

The Application Note "ANP114" published by the supplier of electronic and electromechanical components describes the model development for ferroelectric class-2 multilayer ceramic capacitors, explaining their dependence on voltage and frequency. The use of MLCCs, e.g., in filtering circuits, is thus significantly simplified for the developer.

Ferroelectric multilayer ceramic capacitors (MLCCs) are electronic components that exhibit the property of ferroelectricity. They can maintain stable electric polarisation even in the absence of an external electric field and therefore have a voltage-dependent capacitance.

The Application Note gives an in-depth explanation of the voltage and frequency dependence of ferroelectric MLCCs. The AppNote starts with an introduction into the world of ferroelectricity, before going on to derive a mathematic model for the capacitance-voltage behaviour of ceramic MLCCs from a dipole polarisation model, in which the parameters of the model are reduced to two fitting parameters.

### Model tested by measurements

To demonstrate the practical applicability, the model was tested by comprehensive measurements on a selection of MLCCs from Würth Elektronik's portfolio. Since the integral of the capacitance-voltage model mathematically contains only basic trigonometric expressions, it can be easily implemented in software that requires functions of charge instead of capacitance, such as the simulation software LTspice. Furthermore, it is shown that the model is extremely useful in describing the capacitance spectra of MLCCs at different DC voltages.

Contents:

• Introduction to the ferroelectricity of capacitors
• Interpretation of capacitance-voltage measurements
• Mathematical model of ferroelectric polarisation
• Experimental measurements and boundary conditions
• Implementation of a frequency- and voltage-dependent model

The AppNote is part of a comprehensive collection of publications on the complex of issues regarding multilayer ceramic capacitors and can be directly downloaded from the internet at WE online.