Analysis of wire-bonded multiconductor transmission line-based phase-shifting sections

Abstract

The theoretical analysis of wire-bonded multiconductor transmission lines (MTL) for synthesizing phase shifters is accomplished and generalized in order to extend the traditional theory where 3-dB quarter-wavelength directional couplers are usually employed. In this paper, it is demonstrated that this kind of reflection phase shifters, where the coupled and direct ports are terminated with reactive loads, can be designed for any coupling level. Therefore, analytical design equations are derived to compute both the insertion and return losses as well as the operating frequency band as a function of the coupling factor of the MTL. Furthermore, two general equivalent circuits as a function of the number of strips are derived for two particular arrangements, when both coupled and direct ports are open-or short-circuited. These simple equivalent circuits provide some insight into the physical behavior of the MTL and are expedient to the design of filtering structures and 90 • and −90 • phase shifters. Finally, the validity of the developed theory is assessed by means of measurements. Two critical-and over-coupling open-circuited and short-circuited wire-bonded MTLs and a broadband balun with an operating fractional bandwidth higher than 92% and excellent output isolation are designed, manufactured, and measured.

Analytical Design of Compact Multiband Bandpass Filters with Multiconductor Transmission Lines and Shunt Open Stubs

“…In short, the S-parameters from the transmission line equivalent model are computed and considered to obtain a proper filtering function, and finally, the circuit design parameters. The exact analysis of the short-circuited multiconductor transmission lines was thoroughly carried out in [13]. On the one hand, the transmission-line equivalent model consists of a transmission-line section and two shunt short-circuited stubs with characteristic impedances Z 0 a and Z sc a , respectively.…”

Synthesis of Dual-Band Bandpass Filters With Short-Circuited Multiconductor Transmission Lines and Shunt Open Stubs

“…Two symmetrical prototypes are considered in order to design first-and second-order dual-band BPFs. The analysis of both filters can be directly carried out by using the equivalent circuit for a short-circuited MTL [25], consisting of a transmission-line section and two shunt short-circuited stubs with characteristic impedances Z 0 a and Z sc a , respectively. The equivalent circuit models based on transmission-line for both prototypes are depicted in Fig.…”

“…Given the prescribed transmission zeros in the low-pass domain as ω z = {0, ∞, j, −j} (25) the filtering function in the normalized frequency ω for a fourth-order Chebyshev filter is obtained as follows [31] F I (ω) = t 4 ω 4 + t 2 ω 2 + t 0 ω δ 2 + ω 2 .…”

Analytical Design of Wire-Bonded Multiconductor Transmission-Line-Based Ultra-Wideband Differential Bandpass Filters

“…From (1), the image impedance of the two-port short-circuited wire-bonded MTL [see Fig. 1(b)] is computed as (4) where and are defined as [25] (5)…”