TABLE OF CONTENTS The ideal inductor and capacitor exhibit the above terminal circuit behavior and have no dissipated energy. With ideal elements, filter design would be pure mathematics and far simpler than it is in practice. Unfortunately, components exhibit loss and other parasitics. Loss occurs with electric fields in lossy dielectrics, with current flowing in lossy conductors and via radiation. Various component technologies have significantly different loss mechanisms and magnitudes. Just as importantly, the circuit configuration influences how a given component performs. For example, the midband loss in a bandpass filter is not only a function of component quality but also the design bandwidth. Circuit configuration effects are discussed in a later chapter.
Component Q, also referred to as unloaded Q, is defined as the ratio of the stored to dissipated energy in the element. Energy is stored in fields [1] and dissipated in resistance. For lumped elements, if the loss resistance is modeled as being in series with the reactance, X, the unloaded Q is
| (5) |  |
From the above reactance expressions, Q u for the inductor is
| (6) |  |
and for the capacitor is
| (7) |  |
If the loss resistance and reactance are modeled in parallel, the unloaded Q is
| (8) |  |
which for the inductor and capacitor are, respectively,
| (9) |  |
Unloaded Q is a measure of component quality. The maximum available unloaded Q varies among component technologies. Finite unloaded Q results in filter passband insertion loss, heating in power applications, amplitude...
