Direct Synthesis of Parallel-Connected Symmetrical Two-Port Filters

Abstract

This brief presents a general technique for the synthesis of parallel-connected two-port networks. This is based on the even-and odd-mode admittances of a standard Chebyshev network. The expressions for the even/odd-mode admittance are used to synthesize the low-pass network into branches of subnetworks connected in parallel between the source and the load. These together will have the same characteristics as a ladder network. It is also shown how a filter of a particular order will have the same parallel branch topology regardless of how many transmission zeros are used in the filter's transfer function. This design technique can be beneficial for various implementation techniques such as multilayer substrate and dual-mode resonators. Examples of fourth-and sixth-order degree networks with various numbers of transmission zeros are presented.

Modular implementation of transversal filter using transversal matrices and multi‐mode resonators

“…In this section, a fourth-order transversal bandpass filter will be synthesised in four cases to fully illustrate the modularity property of transversal filters. The configurations of filters in four cases are dissimilar, but their filtering responses are the same (see (14)) . The specification of the fourth-order transversal bandpass filter with Chebyshev response is centre frequency f 0 = 5 GHz, FBW = 5%, in-band RL≥20 dB, two TZs at 4.8 and 5.2 GHz.…”

“…The corresponding coupling matrix could be synthesised as shown in (14) [8]. From (14), it could be seen that the filter constrained in 14is constituted by four resonators, and the properties of the four resonators have been summarised in Table 1 using 2and 3. Among the four resonators, R1 and R3 are even-mode resonators resonating at 4.8446 and 5.0951 GHz, respectively.…”

“…To start with, the first case realises the specified fourth-order transversal filter in (14) in a simple and straightforward way, as shown in Fig. 2.…”

“…It is found that a transversal filter with high order could be decomposed into a group of sub-filters with the lower order, namely modules, and each module could be individually synthesised on different multi-mode resonators (MMRs). Compared to the above modular techniques and other reported transversal filters [9][10][11][12][13][14][15][16][17][18][19][20][21], the proposed modular technique reveals the following advantages in synthesising filters: i. Flexibility: For a high-order filter, arbitrary number and order of resonators could be grouped to individually form a module.…”

A type of lumped-element-based analog filters based on transversal circuit networks

“…1(b) with M = 1 and N = 4 was used. To initially find the values of its associated inductances and capacitances elements, design equations analogous to (5) and (6) but for the lowpass filter case were employed in (1)-(4) [4]. Subsequently, a final optimization of the whole circuit was performed to finely fulfill the prefixed specifications.…”