BS EN 62562:2011 pdf download – Cavity resonator method to measure the complex permittivity of low-loss dielectric plates

The object of this International Standard is to describe a measurement method of dielectric properties in the planar direction of dielectric plate at microwave frequency. This method is called a cavity resonator method. It has been created in order to develop new materials and to design microwave active and passive devices for which standardization of measurement methods of material properties is more and more important.

This method has the following characteristics:

• the relative permittivity ε ‘ and loss tangent tanδ values of a dielectric plate sample can be measured accurately and non-destructively;

• temperature dependence of complex permittivity can be measured;

• the measurement accuracy is within 0,3 % for ε ‘ and within 5×1 0 –6 for tanδ ;

• fringing effect is corrected using correction charts calculated on the basis of rigorous analysis.

This method is applicable for the measurements on the following condition:

– frequency : 2 GHz < f < 40 GHz;
– relative permittivity: 2 < ε ' < 1 00;
– loss tangent : 1 0 –6 < tanδ < 1 0 -2 .
2 Measurement parameters
The measurement parameters are defined as follows:
ε r = ε '− jε"= D /(ε 0 E)
tanδ = ε" /ε'
where
D is the electric flux density;
E is the electric field strength;
ε is the permittivity in a vacuum;
ε and ε '' are the real and imaginary components of the complex relative permittivity ε r ;
TCε is the temperature coefficient of relative permittivity;
ε and ε ref are the real parts of the complex relative permittivity at temperature T and reference temperature T ref (= 20 °C to 25 °C), respectively.
3 Theory and calculation equations
3.1 Relative permittivity and loss tangent A resonator structure used in the nondestructive measurement of the complex permittivity is shown in Figure 1 a. A cavity having diameter D and length H = 2M is cut into two halves in the middle of its length. A dielectric plate sample having ε ' , tanδ and thickness t is placed between these two halves.
The TE 01 1 mode, having only the electric field component tangential to the plane of the sample, is used for the measurement, since air gaps at the plate-cavity interfaces do not affect the electromagnetic field. Taking account of the fringing field in the plate region outside diameter of the cavity on the basis of the rigorous mode matching analysis, we determine ε ' and tanδ from the measured values of the resonant frequency f 0 and the unloaded Q-factor Q . This numerical calculation, however, is rather tedious. u Therefore,
a) approximated values ε' a and tanδ a from the f 0 and Q u values by using simple formula for a resonator structure shown in Figure 1 b, where a fringing effect for Figure 1 a is neglected, will be determined;
b) then, accurate values ε ' and tanδ from ε' a and tanδ a using charts calculated from the rigorous analysis will be obtained.
3.2 Temperature dependence of ε′ and tanδ Temperature dependence of ε′ and tanδ also can be measured using this method. Temperature coefficient of relative permittivity TCε is calculated by equation (3). When the temperature dependences of ε′ is linear, particularly, ε′ ( T ) is given by ε ′ ( T ) = ε ′ ( T 0 )[ 1 +TCε(T −T 0 ) ] (20) where T and T 0 are the temperatures in measurement and the reference temperature, respectively. In this case, TCε can be determined by the least squares method for many measurement points against T .
The thermal linear expansion coefficient of the dielectric plate α and that of the conductor cavity α c should be considered in the TCε measurement. Furthermore, the temperature coefficient of resistivity TCρ should be considered in the temperature dependence measurement of tanδ . Using these parameters, temperature dependent values of t ( T ) , D ( T ) , H ( T ) , and ρ ( T ) are given by
t = + α − (21 )
( T ) t ( T 0 )[ 1 (T T 0 ) ]