I. INTRODUCTION

Microwave 3-dB directional couplers or hybrid couplers are four-port reciprocal passive networks that distribute the inputsignal energy between their direct and coupled ports whereas the remaining terminal is isolated [1]. They find use in various RF applications, such as the design of feeding networks for antenna beamforming or reflection-type phase shifters. Recently, 3-dB couplers are being co-integrated with other RF analogsignal-processing actions-e.g., filtering or amplificationin the same device. Benefits of this multi-functional design approach include reduced circuit size/volume, lower insertion loss, and optimized RF performance with the co-synthesis [2].

In the case of 3-dB bandpass filtering couplers with out-ofphase signals in their direct and coupled ports, some exponents to be highlighted are those in [3]- [8]. They include moderateand high-order schemes for single-and multi-band designs with static and frequency-tunable response developed in different technologies-e.g., planar and 3-D substrate-integrated cavity resonators. All of them feature a reflective-type BPF behavior, so that the RF-input-signal energy that is not distributed to their direct and coupled ports within the bandstop regions is reflected back at the input. However, these unwanted RF-signal-power reflections may produce adverse effects into the preceding active stages, such as frequency-conversion modules-e.g., generation of additional unwanted intermodulation products through the remixing of such RF power reflections with the local oscillator-or power amplifierse.g., instability issues [9]. This may lead to the malfunctioning of the overall RF front-end chain. Note also that the use of inter-block isolation stages to alleviate this problem may be an inefficient alternative as they are bulky and hard to integrate.

In this work, a type of input-reflectionless out-of-phase 3-dB filtering bandpass couplers with input-reflectionless character- istics are reported by the first time. They exploit the reflectionless bandpass-filter (BPF) concept in [10] for this class of filtering couplers, by inserting a quasi-absorptive bandstopfilter (BSF) section at the input terminal that consumes in its loading resistor the RF-input-signal energy not transmitted by the coupler filtering electrical paths. The operational foundations and optimization-based theoretical design examples for this RF tri-functional circuit-i.e., 180 o 3-dB coupling, bandpass filtering, and out-of-band isolation-are provided. Furthermore, for practical-validation purposes, a second-order microstrip prototype at 2 GHz is manufactured and measured.

II. THEORETICAL FOUNDATIONS

The circuit detail of the engineered input-reflectionless outof-phase 3-dB bandpass-filtering coupler architecture is shown in Fig. 1(a). For a Kth-order implementation, it is composed of a 180 o 3-dB directional coupler in which Kth-order filtering sections are co-integrated as follows:

• Two identical Kth-order BPF sections are combined with the out-of-phase 3-dB coupler signal-propagation paths from its input to its direct and coupled ports, respectively, where the admittance inverters of the coupler are also exploited as source-to-first-resonator admittance inverters of the BPF sections. As a result, a Kth-order bandpass-filtering functionality is realized in the coupler. Furthermore, a perfect output power isolation between the direct and coupled ports is attained at all frequencies.

• A resistively-terminated Kth-order BSF section exhibiting a complementary filtering response with regard to the one of the BPF sections is connected to the coupler input port. In this manner, instead of being reflected back at the input, the RF-signal energy that is not distributed to the direct and coupled ports in the bandstop regions of the bandpass transmission responses is routed to the loading resistor of the input BSF section that dissipates it. Therefore, an input-reflectionless behavior is obtained. For illustration purposes, several examples of theoretical power transmission and input-reflectionless parameters of the input-reflectionless out-of-phase 3-dB bandpass-filtering coupler topology in Fig. 1(a) for first-to-third-order cases are depicted in Fig. 1(b). They were derived by means of an inspection/optimization-based procedure in which: (i) the power transmission response was imposed have the desired 3-dB transmission bandwidth and the degree of selectivity expected for such order, and (ii) the input-powerreflection parameter was minimized as much as possible. The resulting values for the admittance-inverter constants are summarized in Table I. As can be seen in Fig. 1(b), perfectlyzero input power reflection at any frequency is obtained for the first-order case whereas an input-quasi-reflectionless behavior is derived for the second-and third-order examples. In particular, as the order of the filtering functionality increases, both the filtering selectivity and the minimum input-power reflection level are augmented as a trade-off between selectivity/out-ofband rejection levels and input-reflectionless property. Note also that, at the normalized center frequency Ω = 0, a perfect 3-dB power-division factor between the direct and coupled ports along with full power isolation between these terminals and total power matching at all ports is attained for all cases. The phase difference between the transfer functions from the input to the direct and coupled ports is 180 o at all frequencies.

III. EXPERIMENTAL RESULTS

To validate the practical viability of the proposed concept of input-reflectionless out-of-phase 3-dB bandpass-filtering coupler, the second-order example in Fig. 1(b) was manufactured in microstrip technology and characterized. For its design, a 2-GHz center frequency and a 3-dB absolute bandwidth of 385 MHz-i.e., equal to 19.3% in relative terms-were selected.

The transmission-line-based schematic of this circuit is represented in Fig. 2(a). The admittance inverters were realized

as quarter-wavelength-at-2-GHz transmission-line segments whose characteristic impedances were finely adjusted from the theoretical ones-given by Z = Z 0 /J-for performance optimization. Their final values are as follows (Z 0 = 50 Ω):

, and Z D2 = 11Z 0 /10note that the A2 and Z B3 inverters not shown in Fig. 2(a) absorbed into the resistor and direct/coupled ports. The resonators were implemented as open-ended half-wavelengthat-2-GHz transmission-line segments with characteristic impedance Z r = 2Z 0 /5 to fulfill the bandwidth requisite. The theoretical S-parameters in amplitude are depicted in Fig. 2(b). As can be seen, owing to the frequency dependance of the admittance inverters, the input-reflectionless bandwidth is reduced to be more than twice the 3-dB transmission one. Fig. 2(c) demonstrates how the operational bandwidth can be flexibly adjusted through Z r while maintaining the inputreflectionless behavior of the bandpass filtering coupler.

A photograph of the fabricated prototype is provided in Fig. 3(a). Its simulated-with Ansys HFSS-and measuredwith an Agilent-E8361A network analyzer-S-parameters in amplitude are drawn in Fig. 3(b). The simulated and measured amplitude-and phase-imbalance curves between the direct and coupled ports are plotted in Fig. 3(c). As shown, a close agreement between simulations and measurements is obtained. The main measured characteristics of the built circuit are as follows: center frequency of 1.96 GHz, 3-dB absolute bandwidth equal to 345 MHz-i.e., 17.6% 3-dB relative bandwidth-, minimum in-band insertion-loss level of 3.63 dB and 3.93 dB for the direct and coupled ports-i.e., 0.63-dB and 0.93-dB excess loss with regard to the ideal 3-dB power-division factor-, minimum input-power-matching levels of 9.45 dB within the 1.59-2.28-GHz frequency range-i.e., twice the 3-dB transmission bandwidth-, and in-band power isolation above 23.1 dB. The measured in-band amplitude difference between the transmissions at the direct and coupled ports is in the range (-0.31 dB, +0.15 dB), whereas the in-band variation of their phase difference-with regard to the value at the center frequency-is in the interval o , +5.3 o ).