Synthesis of 4th order lossy filters with uniform Q distribution

Planar lossy filters for satellite transponders

“…The previous approach is extended in [4] and [5] considering different attenuation factors Kij <1 for transfer and reflection functions. In this general case, several methods for direct synthesis of the lossy coupling matrix have been developed in the literature [4]- [6], [17] [18]. A special case is to consider a constant attenuation (K11 = K21 = K22 = K < 1).…”

“…The introduction of resistive cross-couplings (RCCs) in the network allows adjusting the flatness in the passband [22], [17]. The number of RCCs in the network is an important parameter, which impacts the performance of the filter directly, in particular its insertion loss and flatness.…”

A Microstrip Lossy Diplexer With Flat Channel Passbands

“…Fortunately, this additional insertion loss can be readily compensated for by amplification in many applications. It is worth noting that 'lossy filter' is an established terminology to describe the type of filters that achieve flatter insertion loss over the passband using resonators with ununiform quality factors [12,13] or by deliberately introducing lossy elements such as coupling resistors [14,15]. This terminology has been used to distinguish from conventional filters with inherent finite quality factors (and therefore losses) without any extra resistive elements.…”

Microwave Filters in Planar and Hybrid Technologies with Advanced Responses

“…In most of the reported works on lossy techniques, lters are implemented using waveguide-cavity resonators or mixed technologies, but only a few of them are fully done in planar technology. Nevertheless, these fully microstrip-planar designs presented in [36], [38] and [39] normally require RCCs that are dicult to implement. For an easier fabrication, an entire microstrip lossy lter without any resistive coupling, considering an extended doublet conguration as well as a non-uniform Q distribution is described in [40].…”

“…Similarly, in [38] and in [39], SMD resistors have been used for introducing resistive couplings and implement simple hairpin microstrip lossy lters of uniform Q (Figure 1.14). Specically, in [39] a fair comparison between dierent lossy approaches is provided considering the same specications and the same technology (i.e.…”