Microwave Design Notes - What are 
and Qo
This is the relative permittivity of the material
sometimes referred to as the dielectric constant. This is a fundamental material characteristic and
is determined by the composition and processing of the materials - as such there are small
variations in
from batch to batch and also if
the composition of the material is varied to achieve different TCF values.
The
is effectively a measure of the ‘polarisation’ of the crystal structure. The
can be measured both at low and high frequency. There is effectively little or no change in the
of the materials listed from kHz to GHz values. The difference between the
of the material and the
of free space gives a ‘discontinuity’ at the surface of the material which allows a
standing wave to propagate within the material at a frequency dependant on the value of the
and the dimensions of the component. The value of
contributes directly to the dimensions of ceramic components for Microwave applications.
The higher the value the smaller the size of the component.
Frequency of a cylindrical dielectric resonator can be estimated using the following equation
where K is a constant, d and t are the diameter and thickness of the resonator respectively.
The
is calculated directly from frequency values measured using a parallel plate fixture
similar to a Courtney Jig.
The
is measured on each batch of ceramic material manufactured by Morgan Electro
Ceramics as part of the initial material qualification prior to release to manufacturing.
Qo
and QL
Q is a term which relates to the Quality Factor of the
dielectric. Q is a measure of the energy lost or dissipated compared to the energy stored within the
component. There are 2 Q values that have to be considered.
- Loaded Q (
QL ) - This is a measure of the Quality Factor of the ‘system’ that comprises of the
component, the cavity, the coupling probes and other devices that will dissipate energy
- Unloaded Q
(QO) – This is the Quality Factor obtained by considering only the component in an
‘ideal’ environment where all other loss mechanism can be discounted.
- QL can be directly measured from a frequency
trace according to
The parameters involved in these equations can be
assessed easily from the frequency output from most Network analysers. See trace example below.
Higher Q values lead to much greater selectivity
and isolation in many filter designs.
The Q of each batch of material is measured on
standard components prior to material release. Q may also be measured on individual parts.
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