Filtering in the Time and Frequency Domains

Except for a brief discussion in Section 5.4.5, we have dealt only with lossless filter elements. In practice losses are always present, however, and they cause the frequency- and time-domain responses to deviate from those predicted by theory. In addition to the response distortion, losses introduce a flat passband loss referred to as insertion loss, which often directly influences system performance. For example, the insertion loss of preselectors in the receiver (front-end filters) is required to be less than 0.5 dB, for such loss adds directly to the system noise figure. Also filters used at the transmitter output for achieving spectral purity are required to have low insertion loss. The seemingly small value of 1-dB insertion loss indicates that 20.6% of the power is dissipated in the filter. This figure is better appreciated by noting that for a 100-kW transmitter, 20.6 kW is dissipated in the filter. For such applications, even 1-dB insertion loss is too large!
In this chapter we determine the effect of losses on the attenuation and transient responses, establish for easy reference the insertion loss of the popular filter types, and introduce the technique of predistorting the responses so that with losses present, the responses "return" to the theoretically predicted ones.
Filter losses can be represented by a resistor in series with each inductor and a resistor in parallel with each capacitor, but as is commonly done, we represent the element loss by its quality factor ( Q). Thus lossless elements...