Ferroelectric multilayer ceramic capacitors (MLCCs) are electronic devices that exhibit the property of ferroelectricity, which means they can maintain stable electric polarization even in the absence of an external electric field and therefore have a voltage-dependent capacitance. Würth Elektronik has implemented the voltage capacitance behavior in the LTSpice files. The underlying model development is explained in this appnote. The use of the MLCC, e.g. for filtering, is thus significantly simplified for the developer. MLCCs are widely used in various electronic devices for energy storage and filtering.

This application note explains the voltage and frequency dependence of ferroelectric MLCCs. After an introduction to ferroelectricity, a mathematical model for the capacitance-voltage behavior of ceramic MLCCs is derived from a dipole polarization model. The parameters of the model are reduced to two fitting parameters. To demonstrate the practical applicability, the model is tested by 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 Spice. Furthermore, it is shown that the model can be used to describe the capacitance spectra of MLCCs at different DC voltages.

Content:

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

Download: ANP114