9. Ripple and Passband Ripple

      Generally referring to the wavelike variations in the amplitude response of a filter with frequency.  Ideal Chebychev and elliptic function filters, for example, have equal-ripple characteristics, which means that the differences in peaks and valleys of the amplitude response in the pass band are equal.  Butterworth, Gaussian, and Bessel functions, on the other hand have no ripple.  Ripple is usually measured in dB.

     The pass band ripple is defined as the difference between the maximum and minimum attenuations within a pass band.

10. Shape Factor

      Shape factor is the ratio of the stopband bandwidth to the passband bandwidth, typically the ratio of 60 dB bandwidth to the 3 dB bandwidth.  It is a critical parameter that determines the number of poles and complexity required to meet the specification.

11. Insertion Loss

     The frequency response of filters is always considered as relative to the attenuation occurring at a particular reference.  The actual attenuation at this reference is commonly called insertion loss.  It is referenced at the minimum attenuation point within the pass band.  Insertion loss can be defined as the logarithmic ratio of the power delivered to the load impedance before insertion of the filter to the power delivered to the load impedance after insertion of the filter.  In other words, it is the decrease in power delivered to the load when a filter is inserted between the source and the load.  The insertion loss is given by:

                    IL_dB = 10log (P_L1 / P_L2)

      Where P_L1 is the power delivered to the load with filter bypassed and P_L2 is the output power with filter inserted into the circuit.  The equation above can also be expressed in terms of a voltage ratio as:

                    IL_dB = 20log (V_L1 / V_L2)

     This allows insertion loss to be measured directly in terms of output voltage.

12. Insertion Loss Linearity

     The insertion loss of a filter may change with drive level.  At high power levels, quartz resonators become non-linear causing the filter loss to increase, and this phenomenon is primarily determined by properties of the quartz, not by processing of the filters.  However, at low drive levels resonator processing becomes critical in maintaining constant insertion loss.  With the application of proper design, stringent processing and rigid controls, filters have been being produced with no more than ± 0.005 dB change in insertion loss for a 40 dB change in drive level.

13. Spurious Responses

      All resonators, whether they are LC tuned circuits, cavity resonators or crystal resonators have unwanted resonance modes.  Quartz crystals have an harmonic resonance normally occurring just above the desired resonance as well as near- harmonic overtone responses.  Consequently, almost all crystal filters will exhibit unwanted responses in their amplitude and phase characteristics. The deviations are often, but not always, of narrow bandwidth.  Normally they occur in the filter stopband and appear as narrow, unwanted regions of reduced attenuation.  Spurious response usually appears at a higher frequency than the center frequency.  Occasionally in wider bandwidth filters a spurious response may occur in the filter passband, causing undesirable ripple.

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