A New Coupled-Line Based Dual-Band Branch-Line Coupler with Port-Extensions

|In this paper, a coupled-line based dual-band branch-line coupler with port-extensions is presented. The con(cid:12)guration of the coupler consists of a single coupled-lines section, two transmission lines, and an easy to analyze L-section impedance matching network at all four ports of the coupler. A detailed theoretical analysis is carried out to obtain the closed-form design equations to determine the design parameters of the coupling structure. It is observed that the proposed dual-band coupler can support wide band-ratio and arbitrary power division. To validate the proposed design concept, a prototype working at 0.9 GHz and 1.8 GHz is fabricated on a 60 mil Rogers 4003C substrate exhibiting excellent match between the simulated and measured results. Therefore, in this paper, a novel coupled-line based dual-band branch-line coupler is proposed to attain wider band-ratio range and arbitrary power division capability at the coupled and through port of the coupler.This paper will begin with developing the design theory of the proposed coupler. Then, a prototype following the proposed circuit topography is fabricated and measured for comparison with the simulated response of the coupling structure. Finally, a comparison table of state-of-the-art port-extended BLCs is presented to demonstrate the novelty of the proposed structure.


INTRODUCTION
Branch-line coupler (BLC) is one of the fundamental blocks in the field of microwave engineering [1]. Multi-band operation of a BLC enables its spectrum aggregation capability [2,3] which is a primary technique to ensure real-time high-speed communication.
Conventional single band BLCs are implemented using quarter wavelength long branches resulting in spurious responses only at the odd harmonics of the fundamental frequency [1]. In contrast, multi-band designs are implemented by adding additional stubs [4] and half-wavelength sections [5] to the conventional structure, modifying the coupled-lines structures [6] or some other unique BLC structures [7,8], by port-extension techniques [9][10][11], etc. Over the years, numerous works have been reported on different aspects of dual-band coupler performance, for example, bandwidth control [12] and enhancement [13], miniaturization [14], wider band-ratio support [15], arbitrary port impedance [11], and arbitrary power division [9-11, 16, 17].
For any dual-band coupler, two major design criteria are the band-ratio and arbitrary power division. All of the dual-band branch-line couplers mentioned in the literature either achieve a wide band-ratio [15] or support arbitrary power division [9-11, 16, 17]. In practice, a combination of both of these capabilities in a single structure would be useful in the design stage of a complex structure. Therefore, in this paper, a novel coupled-line based dual-band branch-line coupler is proposed to attain wider band-ratio range and arbitrary power division capability at the coupled and through port of the coupler.
This paper will begin with developing the design theory of the proposed coupler. Then, a prototype following the proposed circuit topography is fabricated and measured for comparison with the simulated response of the coupling structure. Finally, a comparison table of state-of-the-art port-extended BLCs is presented to demonstrate the novelty of the proposed structure.

DESIGN OF PROPOSED DUAL-BAND PORT EXTENDED COUPLED-LINES COUPLER
In Fig. 1, we have proposed a special type of branch-line coupler where the vertical transmission line sections of a conventional branch-line coupler are replaced by a single coupled-lines section having even and odd mode impedances Z e and Z o , respectively. The electrical length of the coupled transmission line is 2θ. Horizontal transmission line sections have a characteristic impedance of Z t with the same electrical length of 2θ. The configuration has two axes of symmetry XX ′ and Y Y ′ . Based on these axes of symmetry, four different configurations of even-odd mode circuits are shown in Figs. 1 The variable Y denotes the characteristic admittance of the transmission line which is inversely related to the Z variables. Hence, Equivalent admittances for each even-odd mode circuits can be derived as According to [18], the equivalent input admittance looking at any port of the coupler of Fig. 1(a) is denoted by Y eq = G eq + jB eq . Here, G eq and B eq are the equivalent input conductance and susceptance of the coupler, respectively. Their expressions can be derived as Once the value of Y eq is calculated using Eqs. (5) and (6), dual-band port-extended impedance matching networks can be implemented to realize a functioning dual-band coupler. It follows from Eq. (6) that to make G eq a positive real value, the following inequality must be met In a dual-band design, the electrical length and design frequencies are interdependent [9]. If the two design frequencies are f 1 and f 2 , where f 2 > f 1 and the dual-band frequency-ratio is r = f 2 /f 1 , then for a dual-band operation, the electrical length θ at f 1 can be obtained as Equation (9) gives the value of θ at f 2 as Here m can be any integer value. The relation of θ at f 1 and f 2 given in Eq. (9) dictates the complex conjugate relationship in Eqs. (1)- (6). In other words, Equations (6) and (5) are plotted in Fig. 2(a) and Fig. 2(b), respectively. Both the plots validate Eq. (10) by showing that for a fixed set of Z e , Z o , and Z t , G eq has an even symmetry whereas B eq has an odd symmetry with respect to the same asymptote at θ = 90 • . The ratio of S 21 and S 31 of the coupler is related to the power division parameter k, (k > 0) as below Here, 20 log(k) denotes the power division ratio in dB. The definitions of S 21 and S 31 for a symmetrical four-port network reduce to the following [10] Here, the reflection coefficients for the even-even (Γ ee ) and odd-odd (Γ oo ) cases are given by  6) and (5), respectively. Now using Eqs. (12) and (13) in Eq. (11), the power division ratio can be derived as Using Eqs. (14) and (15) into Eq. (16) yields: plots calculated G eq and B eq using Eqs. (6) and (5) for different (Z e , Z o ) pairs with respect to frequency ratio r. It is apparent from Fig. 4(b) that as the value of r increases, G eq decreases and converges to a lower value whereas B eq at first decreases, reaches a minimum, and then increases. This indefinite increase of B eq limits the use of port impedance matching network (IMN) at each input port of the core of the coupler shown in Fig. 1. The purpose of IMN is to match the resulting Y eq from Eqs. (5) and (6) to port termination impedance, Z p (normally equal to Z 0 = 50 Ω). From the plot of Fig. 4(b), it is evident that the IMN must be capable of transforming this wide range of Y eq to port termination impedance, Z p . As r increases, different IMN configurations need to be considered to match the ports to the core of the coupler. In this paper, a simple L-section matching network is employed, shown in Fig. 5, to match the complex valued admittance, Y eq , to real valued port termination impedance, Z p . The (Z 1 , θ 1 ) line transfers Y eq to Y ex using Eq. (19) where Z ex is given in Eq. (20).    Fig. 4(a). These plots are for k = 0 dB.
Here, a = tan(θ 1 ). For dual-band operation, the value of θ 1 is determined using Eq. (22) which is similar to Eq. (8), and p can be any positive integer. The purpose of the characteristic impedance Z 1 is to transfer Y eq to Y ex so that its real part G ex given in Eq. (21) becomes equal to port termination admittance, Y p (= 1/Z p ). This leads to a quadratic equation in Z 1 as given in Eq. (23).
A summary for the design flow is shown in the flowchart of Fig. 6(a). A combination of flowcharts shown in Fig. 3 and Fig. 6(a) is used to obtain a set of design parameters, namely, (Z e , Z o ) pair, Z t , Z 1 , and Z s for different r and k values for the novel port-extended coupling structure shown in Fig. 5. The novelty of the structure is two-fold. It supports an extremely wide range of both frequency ratio, r, and power division ratio, k. To show this wide supporting range, a set of plots and tables are generated. At first, the value of k is fixed at 0 dB, and the calculated design parameters are plotted in Fig. 6(b) with respect to dual-band frequency ratio, r. It is evident from the plot that for k = 0 dB, the port-extended branch-line coupler supports the dual-band ratio of 1.5-8.  Table 1 displays the calculated design parameters for extreme band-ratio cases. It dictates the capability of the proposed coupling structure in supporting high r and k values. For example, the first row of the table is for r = 1.5 where all the design parameters are in practical range for different k values, namely, 2 dB, 8 dB, and 11.76 dB. It is also clear that, for k = 2 dB, the proposed coupler supports the r value of 1.5-7. For k = 8 dB, the r value ranges from 1.5 to 11 whereas for k = 11.76 dB, the r value ranges from 1.5-12.

SIMULATION AND MEASUREMENT RESULTS
To validate the proposed design concept for the port-extended branch-line coupler, a prototype has been designed, simulated, and fabricated using the proposed design configuration. A dual-band port-   Fig. 7(a). The physical dimensions are shown in mils (thousandth of an inch). The scattering parameters of the designed prototype are measured using a Tektronix TT506A Vector-Network Analyzer (VNA). The measurement setup is shown in Fig. 7(b) where the VNA display on the computer screen shows the measured |S 21 |. The EM simulated results obtained using the Keysight ADS vs the measured Sparameter magnitude response are shown in Fig. 8(a). It is apparent from the plots that the measured and simulated data correlate well with each other having return loss and isolation loss better than 20 dB at both design frequencies. For a 10 dB reference, the return loss bandwidths are 143 MHz @f 1 / 118 MHz @f 2 , and the isolation loss bandwidths are 150 MHz @f 1 / 180 MHz @f 2 . The transmission bandwidths in this region are 120 MHz @f 1 / 100 MHz @f 2 . Although the overall magnitude responses of S 11 and S 41 shift slightly from the intended second center frequency of 1.8 GHz due to fabrication tolerances, the 10 dB bandwidth still supports the proposed/simulated regions of operation. If desired, this shift can be fixed with post-fabrication tuning coupled with simulation. In Fig. 8(b), the simulated and measured phase differences between port 2 and port 3 of the coupler are plotted. The measured result is in correlation with the simulated results at both the design frequencies. The measured phase differences are found to be 89.60 • @f 1 / − 90.10 • @f 2 .
A comparison table between the proposed coupler and the state of the art port-extended couplers is presented in Table 2. It is shown in the table that the proposed coupling structure supports wide range of band-ratios of 1.5-8 at k = 0 dB, 1.5-7 at k = 2 dB, 1.5-11 at k = 8 dB, and 1.5-12 at k = 11.76 dB. The fabricated device size is comparable to the state-of-the-art port-extended branch line couplers. Therefore, in the design of microstrip line based planar port-extended coupling structures, the proposed design configuration can support extensively large band ratio at arbitrary power division values.

CONCLUSION
In this paper, a novel port-extended dual-band branch-line coupler has been designed for the first time which supports extensively high band-ratio and arbitrary power division. The closed-form analytical design equations are derived, and a simple flow chart is presented to obtain the set of design parameters for arbitrary band-ratio and power division values. To prove the design concept, a prototype has been designed, fabricated, and measured. The measured and simulated results match quite well supporting the design theory of the proposed coupler.