6. Frequency and Bandwidth of Crystal Filters

      Crystal filters can be built with center frequencies ranging from a few kilo Hertz to several hundred Mega Hertz, but the best operating regions fall where the dimensions and operating parameters of the crystals are near their optimum.

      The best operating range for "Low" frequency filters is from about 100 kHz to 800 kHz and with bandwidths that lie within the following chart.

      The best operating range for "Mid" frequency crystals falls between about 2 MHz and 50 MHz.  It is noted that this leaves a band of frequencies between 800 kHz and 2 MHz not covered.  This does not mean that crystal filters cannot be built within this range; it only means that it is more difficult, and therefore more costly.

      Crystal filters with center frequencies above 30 MHz can be built using either overtone mode crystals or high frequency fundamentals.  The overtones have much higher Qs and are suitable for the narrower bandwidths, while the fundamentals have much lower impedance and are used for the wider bandwidths.  However, all crystals have spurious responses, and the spurs normally occur on the high side of the passband.  This spurious characteristic limits the maximum bandwidth that a filter can be achieved.

7. Center Frequency and Nominal Frequency

      Center frequency is a given frequency in the specification, to which other frequencies may be referred, while nominal frequency is the nominal value of center frequency and is used as the reference frequency for specifying relative levels of attenuation.  In bandpass and bandstop filters F_on denotes the nominal center frequency; F_o denotes the actual or measured center frequency of an individual filter and is usually defined as:

                      F_o = (f_l × f_u)^½

       Where f_l and f_u are measured lower and upper passband limits, usually the 3 dB attenuation frequencies.  Sometimes it is more convenient to specify frequency relative to the actual or measured filter center frequency.  The value of F_o will, of course, vary from unit to unit and within the same unit as function of temperature and time.  Therefore, there must be a tolerance associated with F_o, making allowance for temperature, aging, and manufacturing tolerances.

8. Passband, Stopband & Bandwidth

     Passband is the frequency range in which a filter is intended to pass signals.  It is expressed as a range of frequencies attenuated less than the specified value, typically specified at 3 dB.

    Stopband is a band of frequencies in which the relative attenuation of a filter is equal or great than specified values.  It is expressed as a range of frequencies attenuated by more than some specified minimum, such as 60 dB.

    For a bandpass or bandstop filter, the width (frequency difference) between lower and upper points having a specified attenuation, such as the 3 dB bandwidth or the 80 dB bandwidth.  For a lowpass filter, bandwidth is simply the frequency at which the attenuation has the specified value.