Thus far in this chapter, we have assumed the inductors and capacitors used in the designs to be lossless. Indeed, all of the response curves presented in this chapter are based on that assumption. But we know from our previous study of Chapters 1 and 2 that even though capacitors can be approximated as having infinite Q, inductors cannot, and the effects of the finite- Q inductor must be taken into account in any filter design.

The use of finite element Q in a design intended for loss-less elements causes the following unwanted effects (refer to Fig. 3-33):

1. Insertion loss of the filter is increased whereas the final stopband attenuation does not change. The relative attenuation between the two is decreased.

2. At frequencies in the vicinity of cutoff ( f _c), the response becomes more rounded and usually results in an attenuation greater than the 3 dB that was originally intended.

3. Ripple that was designed into the passband will be reduced. If the element Q is sufficiently low, ripple will be totally eliminated.

4. For band-reject filters, the attenuation in the stop-band becomes finite. This, coupled with an increase in passband insertion loss, decreases the relative attenuation significantly.

FIG. 3-33: The effect of finite-Q elements on filter response.

Regardless of the gloomy predictions outlined above, however, it is possible to design filters, using the approach outlined in this chapter, that very closely resemble the ideal response...