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The AT- cut crystal resonator, which is most commonly used for filters, has a
family of unwanted anharmonic responses at frequencies slightly above the
desired resonance and harmonic (overtone) responses at approximately odd integer
multiples of the fundamental resonance. The
location of the overtones and the major anharmonics can be calculated in
advance. The overtone responses can
be suppressed by additional LC filtering which, given adequate package
dimensions, can be accommodated inside the filter package if required.
The near-by anharmonic responses cannot normally be suppressed by LC
filtering. Here suppression of
spurious responses is accomplished by a combination of resonator design,
resonator processing and filter circuit design.
As the crystal resonator electrode area is increased, more unwanted
anharmonic responses will be excited (assuming a constant operating frequency)
and the motional inductance will decrease. In order to reduce insertion loss and/or retain a narrow band
design, it may be necessary to increase the electrode dimensions at wider
bandwidths. Therefore, wider bandwidth filters can be expected to have more and
stronger spurious responses. However,
one can always take advantage of narrow band design by operating the crystal
filter at a higher frequency with the reduced percentage bandwidth, such that
the spurious response will be improved for a given bandwidth requirements.
14. Group Delay Distortion
Group delay, also called envelope delay, is the time taken for a narrow-band
signal to pass from the input to the output of a device.
Group delay distortion is the difference between the maximum and the
minimum group delay within a specified pass band region or at two specific
frequencies. For most bandpass
filters, the delay response will have a peak close to each passband edge, where
the filter attenuation begins to increase rapidly.
Filter delay and attenuation characteristics are interdependent.
The more rapidly the filter attenuates, the larger the delay peaks. In general, large delay peaks are associated with filters
having many poles or filters that have close-in stopband poles (such as elliptic
function filters). On the other
hand, the MCFs have a very small group delay distortion, typically less than 10
ms.
15. Inter-modulation (IM)
Inter-modulation occurs when a filter acts in a nonlinear manner causing
incident signals to mix. The new
frequencies that result from this mixing are called inter-modulation products,
and they are normally third-order products, which means that a one dB increase
in the incident signal levels produces a 3 dB increase in IM.
The IM can be classified in the following two types:
Out-of-band inter-modulation occurs when two incident signals (typically -20
to -30 dBm) in the filter stopband produce an IM product in the filter passband.
This phenomenon is most prevalent in receiver applications when signals
are present simultaneously in the first and second adjacent channels.
This IM performance of crystal filters at low signal levels is primarily
determined by surface defects associated with the resonator manufacturing
process and is not subject to analytical prediction.
In-band inter modulation occurs when two closely spaced signals within the
filter passband produce IM products that are also within the filter passband.
It is most prevalent in transmit applications where signal levels are
high (typically -10 dBm and +10 dBm). This
IM performance at high signal levels is a function of both the resonator
manufacturing process and the nonlinear elastic properties of quartz.
The latter is dominant at higher signal levels, and can be analyzed.
16. Phase Shift and Minimum Phase Transfer Function
The change in phase of a signal as it passes through a filter. A delay in
time of the signal is referred to as phase lag and in normal networks, phase lag
increases with frequency, producing a positive envelope delay.
The great majority of crystal filters are minimum phase shift filters.
Mathematically, this means that there is a functional relationship
between the attenuation characteristic and the phase characteristic of the
filter. The transfer function of
such a two-port network is said to have the minimum phase shift property, which
means that its total phase shift from zero to infinite frequency is the minimum
physically possible for the number of poles that it possesses.
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