Three-line coupled structure analysis

Figure 1 shows the layout of the proposed multilayer balanced-to-balanced PD with bi-symmetric structure, which is designed by using two layers of RO4003C substrates (permittivity ε _r = 3.38, the loss tangent tan δ = 0.0027, and the thickness h = 0.508 mm). A λ _g/2 microstrip line in the middle layer is fed by a pair of ports (i.e. port 1 and port 1′), which is used as the balanced input. The top layer involves four λ _g/4 microstrip lines with one short-circuited end, while two pairs of ports (i.e. ports 2 and 2′, 3 and 3′) are used as two in-phase balanced outputs. The red portion represents the loaded lumped resistor R, which is used to realizing good isolation between the two balanced outputs.

Fig. 1.

Layout of the proposed balanced-to-balanced PD. (a) 3-D view. (b) Cross view.

Figure 2(a) shows the transmission-line model of the proposed PD. The resistor R for isolating the balanced output ports has no effect on signal transmission from input to outputs. As a result, the balanced-to-balanced PD can be treated as a pair of back-to-back Marchand baluns (shown in Fig. 2(b)) [Reference Marchand8]. Accordingly, the design method of the traditional Marchand balun can be referred in the PD design, and the coupling strength between the transmission lines is the key parameter to the bandwidth of the PD [Reference Ang and Robertson9]. Therefore, the strong multi-layer coupling scheme is adopted, as shown in Fig. 1.

Fig. 2.

Transmission-line model. (a) Proposed balanced-to-balanced PD. (b) Marchand balun.

Figures 3(a) and 3(b) show the CM and DM equivalent circuits of the transmission-line model, respectively. It is obvious that the CM equivalent circuit is an all-stop structure [Reference Pozar10] so that the CM suppression in this design does not need to be considered. And then the DM equivalent circuit is analyzed to achieve the desired power division. The three-line coupled structure in Fig. 3(b) can be fully analyzed using the fundamental modes of operation, i.e. even–even (EE), odd–odd (OO), and odd–even (OE) modes [Reference Pavlidis and Hartnagel11], as shown in Fig. 4.

Fig. 3.

Equivalent circuits of transmission-line model. (a) CM. (b) DM.

Fig. 4.

Sketches of the electric-field lines for the fundamental modes existing in a three-line coupled structure. (a) EE-mode, (b) OO-mode. (c) OE-mode.

PD design

To achieve good matching at the input and outputs, there must be [Reference Abbosh12]

(1)$$Z_{\rm 0} = \sqrt {Z_{1oo}Z_{1ee}} = \sqrt {Z_{2oo}Z_{2ee}} = Z_{2oe}$$

where Z _ee, Z _oo, and Z _oe are EE-, OO-, and OE-mode impedance, respectively. In this case, the coupling factor (F) from the center line to each of the side lines can be accurately calculated by using Z _oo and Z _ee:

(2)$$F = \displaystyle{{Z_{2ee}-Z_{2oo}} \over {\sqrt {(Z_{1ee} + Z_{1oo})(Z_{2ee} + Z_{2oo})}}} $$

For a PD with equal power division, i.e. power division ratio 1:1, F is equal to$\sqrt {{\rm 1/2}} $. As shown in Fig. 1(a), the lengths of the coupled structure are l ₁ = λ _g/2 (λ _g is the effective wavelength calculated at the center frequency f ₀ = 1.95 GHz) and l ₂ = λ _g/4. The value of R is selected to achieve perfect matching for the two output ports at the centered frequency when the power division ratio is 1:1, thus it can be calculated from [Reference Guo, Zhu and Abbosh13] as $R = 2Z_{2oe}^2 / Z_0 = 100\,\Omega$.

After optimization using Ansoft HFSS, the structure parameters of the proposed balanced-to-balanced PD are as follows: l ₁ = 40 mm, l ₂ = 20 mm, w ₁ = 3.3 mm, w ₂ = 2.5 mm, w ₃ = 1.15 mm, w ₀₁ = 1.1 mm, w ₀₂ = 2.6 mm, s = 1 mm, g = 0.6 mm, and the overall size of the PD is 40.6 mm × 8.4 mm, corresponding to the electrical size is 0.44λ _g × 0.09λ _g. Figure 5 shows the comparison results of the equivalent circuit and EM simulation of the PD. The fabricated balanced-to-balanced PD is shown in Fig. 6.

Fig. 5.

The extracted S parameters of equivalent circuit (ADS) and EM simulation (HFSS).

Fig. 6.

Photograph of the fabricated PD.

Result and discussion

Figure 7 shows the simulated and measured DM results of the proposed balanced-to-balanced PD centered at f ₀. The simulated and measured results exhibit good agreement. As shown in Fig. 7(a), the measured DM return loss S _dd11 shows fractional bandwidth (FBW) of 16% better than 15 dB over the frequency range from 1.75 to 2.1 GHz, and the best DM isolation S _dd23 between the two balanced output ports is 34 dB. Figure 7(b) shows that the measured DM phase difference between the two output ports is from −0.4 to 0.36° over the frequency range. It can be seen from Fig. 8 that the CM suppression is better than 20 dB over the frequency range, achieving FBW of 100%. Meanwhile, the differential-to-CM results are better than 40 dB for the whole measured frequency band.

Fig. 7.

The simulated and measured DM results. (a) S-parameters. (b) Phase differences between two balanced output ports.

Fig. 8.

The simulated and measured CM and differential-to-CM S-parameters of the PD.

Table 1 gives the performance comparison of the proposed balanced-to-balanced PD with the previously reported counterparts. It is clear that the proposed PD is very compact due to the back-to-back Marchand balun configuration, as compared with the designs using the Wilkinson topology [Reference Xia, Wu and Mao4] and Gysel topology [Reference Xia, Wu, Ren and Mao5]. Meanwhile, the proposed PD has wideband CM suppression resulting from the all-stop structure. In addition, the bandwidth of the proposed PD is extended by using the strong multi-layer coupling scheme and it is comparable with that of the designs in [Reference Xia, Wu and Mao4, Reference Xia, Wu, Ren and Mao5].

Table 1.

Performance comparison with the previous designs.