Ultracompact isolated multilayer broadside-coupled balun with arbitrary isolation bandwidth

Abstract

An isolated low-profile multilayer all-ports-matched broadside-coupled balun (BCB) with arbitrary isolation bandwidth is presented. Analytical relations are derived and provided for the isolation circuit (IC) design in terms of electrical and physical parameters. Accordingly, instructions are given on obtaining optimum bandwidth and isolation responses for the IC. Design procedure for the BCB is presented together with a case study for power amplifier application. The BCB is validated theoretically, analytically, and experimentally, and results are in good agreement. The fabricated balun has insertion loss of 0.27 dB, input and output return losses of 19 dB, isolation of 20 dB at f_c, and phase and magnitude imbalance better than 2° and 0.2 dB across the Bandwidth (BW), respectively. The realized isolated balun has dimensions of 0.06λ_g × 0.03λ_g.

Introduction

Baluns are used to divide an unbalanced signal into a pair of out-of-phase (balanced) signals and transform impedance; and thus, they find application in diverse microwave circuits, such as power amplifiers (PAs) [1–5], balanced mixers [6], frequency multipliers, and antenna feeding networks [7]. Microwave baluns have been realized using coaxial cables [8], multilayer coupled structures [9], and spiral coils [10].

Planar Marchand balun (MB) seems to be the most popular balun due to its simplicity, wideband performance and manufacturing benefits. However, MB structure occupies large circuit area [11, 12]. Unlike MB, the broadside-coupled balun (BCB), which relies on inductive coupling, reduces balun size considerably [9]. The low-profile and step-down impedance transformation of the latter makes it extremely suitable for power division/combining, particularly in push-pull PAs. However, for PAs, isolation and output matching are very crucial to improve reliability. In fact, without isolation circuit (IC), the reflected power at output ports of transistors would damage the transistor as a result of amplitude imbalance at output ports. Regardless of the type of balun, research on microwave baluns has mainly focused on techniques to reduce size [13, 14], broaden bandwidth [15], and lower insertion loss [16], but little has been written on isolation of baluns.

The isolation of a MB was first addressed in paper [12], where the IC included a λ/2 transmission line (TL), making it both narrowband and lengthy. Later, wideband and compact ICs were proposed [11, 17]. Nevertheless, to the best of authors’ knowledge, isolation in BCBs is not well-explored.

In this paper, a multilayer highly isolated BCB is designed that benefits from new embedded compact wideband IC. The novelty and contribution of this work includes: (a) offering new simple compact IC with arbitrary isolation bandwidth, (b) providing analytical relations for synthesis of the IC as well as systematic approach for designing the balun itself, (c) offering analytical relations and instructions on obtaining optimum bandwidth and isolation responses for the IC, and validating it numerically, through full-wave simulation, and experimentally via fabrication, and (d) presenting a worked example through a case study for PA application. In doing so, “Analysis of the isolated BCB” presents the analysis of isolated BCB and the IC.“Design of the isolated BCB” offers design procedure and synthesis through a case study. Closed-form formula and considerations for design of the isolated BCB are also presented. This section also evaluates balun power handing capability (PHC) constrains and tunability in design of such balun. Simulation and measurement results are given in “Simulation and measurement” and conclusions are drawn in “Conclusion”.

Analysis of isolated BCB

Theory of operation

As seen in Fig. 1, a BCB is formed of two conductors sandwiched by a substrate, with l_P, l_S, w_P, and w_s as lengths and widths of primary (bottom) and secondary (top) conductors, respectively. In addition, h is the substrate thickness. When port 1 is excited, power is transferred from the bottom conductor to the top conductor into ports 2 and 3 [18]. BCB, however, suffers from poor isolation between output ports [19]. Therefore, an IC is placed between ports 2 and 3 to achieve good isolation response.

Figure 1. Broadside-coupled balun with isolation circuit.

Figure 2 represents the equivalent circuit model of the BCB of Fig. 1 [20]. The BCB can be modelled by a transformer comprised of primary inductor, L_P, secondary inductor, L_s, and mutual inductance and capacitance denoted by L_m, and C_m, respectively. In addition, Z ₀: port 1 impedance, Z ₁: ports 2 and 3 impedances, I _P: current of primary inductor, I _S: current of secondary inductor, and I ₀: current at input port. Ohmic and dielectric losses are neglected for simplicity.

Figure 2. Equivalent circuit model of balun of Figure 1.

Mutual inductance, L_m, can be determined as a function of self-inductances, L_P and L_S, such that ${L_m} = {K_m}\sqrt {{L_p}{L_s}} $, where K_m is the magnetic coupling coefficient. Equation (1) expresses impedance transformation ratio (2Z ₁/Z ₀) in terms of primary and secondary inductors.

(1)\begin{equation}\frac{{2{Z_1}}}{{{Z_0}}} = {K_m}^2\frac{{{L_s}}}{{{L_p}}} = \frac{1}{{{n^2}}} \cong {\left( {\frac{{{N_s}}}{{{N_p}}}} \right)^2}\end{equation}

where N_P and N_s are number of turns for primary and secondary windings, respectively. Also, n is the ratio of primary to secondary turns [21].

Extracting the S-matrix of isolated balun

Under the lossless condition and neglecting magnetic flux leakage, the S-matrix of the balun of Fig. 1, without the IC, can be given by [19]:

(2)\begin{equation}\left[ S \right] = \left[ {\begin{array}{*{20}{c}} 0&{j/\sqrt 2 }&{ - j/\sqrt 2 } \\ {j/\sqrt 2 }&{1/2}&{1/2} \\ { - j/\sqrt 2 }&{1/2}&{1/2} \end{array}} \right]\end{equation}

As equation (2) implies, while the input port is matched, the output ports are not matched without the IC. Return losses of output ports (S ₂₂, S ₃₃) and isolation between them (S ₃₂) are 6 dB; emphasizing the need for an IC. The S-matrix of the balun with IC can be obtained if admittance matrix (Y-matrix) of the balun without IC is calculated based on port designations in Fig. 1, as:

(3)\begin{align}{\left[ {\text{Y}} \right]_{{\text{without IC}}}}& = \left( {{y^*}{\text{ - y}}{{\text{k}}^{{\text{ - 1}}}}{\text{S}}{k^*}} \right){\left( {{{\text{k}}^{{\text{ - 1}}}}{\text{S}}{k^*}{\text{ + }}{{\text{U}}_{\text{n}}}} \right)^{{\text{ - 1}}}} \nonumber\\ &= \left[ {\begin{array}{*{20}{c}} {\text{0}}&{\frac{{{\text{ - j}}}}{{\sqrt {{\text{2}}{{\text{Z}}_{\text{0}}}{{\text{Z}}_{\text{1}}}} }}}&{\frac{{\text{j}}}{{\sqrt {{\text{2}}{{\text{Z}}_{\text{0}}}{{\text{Z}}_{\text{1}}}} }}} \\ {\frac{{{\text{ - j}}}}{{\sqrt {{\text{2}}{{\text{Z}}_{\text{0}}}{{\text{Z}}_{\text{1}}}} }}}&{\text{0}}&{\text{0}} \\ {\frac{{\text{j}}}{{\sqrt {{\text{2}}{{\text{Z}}_{\text{0}}}{{\text{Z}}_{\text{1}}}} }}}&{\text{0}}&{\text{0}} \end{array}} \right]\end{align}

where U_n is the identity matrix, and k ⁻¹, k*, y = y* are given by:

(4)\begin{align}{k^{ - 1}} &= \left[ {\begin{array}{*{20}{c}} {\sqrt {{Z_0}} }&0&0 \\ 0&{\sqrt {{Z_1}} }&0 \\ 0&0&{\sqrt {{Z_1}} } \end{array}} \right] \nonumber\\ {k^*} &= \left[ {\begin{array}{*{20}{c}} {{1 \mathord{\left/ {\vphantom {1 {\sqrt {{Z_0}} }}} \right. } {\sqrt {{Z_0}} }}}&0&0 \\ 0&{{1 \mathord{\left/ {\vphantom {1 {\sqrt {{Z_1}} }}} \right. } {\sqrt {{Z_1}} }}}&0 \\ 0&0&{{1 \mathord{\left/ {\vphantom {1 {\sqrt {{Z_1}} }}} \right. } {\sqrt {{Z_1}} }}} \end{array}} \right] \nonumber\\ {y^*} &= \left[ {\begin{array}{*{20}{c}} {{1 \mathord{\left/ {\vphantom {1 {{Z_0}}}} \right. } {{Z_0}}}}&0&0 \\ 0&{{1 \mathord{\left/ {\vphantom {1 {{Z_1}}}} \right. } {{Z_1}}}}&0 \\ 0&0&{{1 \mathord{\left/ {\vphantom {1 {{Z_1}}}} \right. } {{Z_1}}}} \end{array}} \right]\end{align}

Now, the admittance matrix of the IC with input impedance Z _IC can be given as:

(5)\begin{equation}{\left[ Y \right]_{{\text{IC}}}}{\text{ = }}\left[ {\begin{array}{*{20}{c}} {\text{0}}&{\text{0}}&{\text{0}} \\ {\text{0}}&{\frac{{\text{1}}}{{{Z_{{\text{IC}}}}}}}&{\frac{{\text{1}}}{{{Z_{{\text{IC}}}}}}} \\ {\text{0}}&{\frac{{\text{1}}}{{{Z_{{\text{IC}}}}}}}&{\frac{{\text{1}}}{{{Z_{{\text{IC}}}}}}} \end{array}} \right]\end{equation}

Therefore, Y-matrix of the isolated balun can be calculated from equations (3) and (5) as:

(6)\begin{equation}{\left[ {\text{Y}} \right]_{{\text{with IC}}}}{\text{ = }}{\left[ {\text{Y}} \right]_{{\text{without IC}}}}{\text{ + }}{\left[ {\text{Y}} \right]_{{\text{IC}}}}{\text{ = }}\left[ {\begin{array}{*{20}{c}} {\text{0}}&{\frac{{{\text{ - j}}}}{{\sqrt {{\text{2}}{{\text{Z}}_{\text{0}}}{{\text{Z}}_{\text{1}}}} }}}&{\frac{{\text{j}}}{{\sqrt {{\text{2}}{{\text{Z}}_{\text{0}}}{{\text{Z}}_{\text{1}}}} }}} \\ {\frac{{{\text{ - j}}}}{{\sqrt {{\text{2}}{{\text{Z}}_{\text{0}}}{{\text{Z}}_{\text{1}}}} }}}&{\frac{{\text{1}}}{{{{\text{Z}}_{{\text{IC}}}}}}}&{\frac{{\text{1}}}{{{{\text{Z}}_{{\text{IC}}}}}}} \\ {\frac{{\text{j}}}{{\sqrt {{\text{2}}{{\text{Z}}_{\text{0}}}{{\text{Z}}_{\text{1}}}} }}}&{\frac{{\text{1}}}{{{{\text{Z}}_{{\text{IC}}}}}}}&{\frac{{\text{1}}}{{{{\text{Z}}_{{\text{IC}}}}}}} \end{array}} \right]\end{equation}

which in S-parameters reads as:

(7)\begin{align}{\left[ {\text{S}} \right]_{{\text{with IC}}}} &= -{\text{ k}}{\left( {{\text{Y + y}}} \right)^{{\text{ - 1}}}}\left( {{\text{Y - }}{y^*}} \right){{\text{k}}^{{\text{ - 1}}}} \nonumber\\ & = \left[ {\begin{array}{*{20}{c}} {\text{0}}&{\frac{{\text{j}}}{{\sqrt {\text{2}} }}}&{\frac{{{\text{ - j}}}}{{\sqrt {\text{2}} }}} \\ {\frac{{\text{j}}}{{\sqrt {\text{2}} }}}&{\frac{{\text{1}}}{{{\text{2}}{{\text{Z}}_{\text{1}}}/{{\text{Z}}_{{\text{IC}}}}}}{\text{ - 1}}}&{\frac{{\text{1}}}{{{\text{2}}{{\text{Z}}_{\text{1}}}/{{\text{Z}}_{{\text{IC}}}}}}{\text{ - 1}}} \\ {\frac{{{\text{ - j}}}}{{\sqrt {\text{2}} }}}&{\frac{{\text{1}}}{{{\text{2}}{{\text{Z}}_{\text{1}}}/{{\text{Z}}_{{\text{IC}}}}}}{\text{ - 1}}}&{\frac{{\text{1}}}{{{\text{2}}{{\text{Z}}_{\text{1}}}/{{\text{Z}}_{{\text{IC}}}}}}{\text{ - 1}}} \end{array}} \right]\end{align}

Comparison of equations (2) and (5) shows that the IC does not, theoretically, have any effect on the balun insertion losses (S ₂₁, S ₃₁). Moreover, from equation (7) “perfect” output match and isolation can be achieved if 2Z ₁ = Z _IC is satisfied.

Analysis of the wideband IC

Given the 180° phase difference between ports 2 and 3 in the balun, the IC can be realized by a λ/2 TL as depicted in Fig. 3(a). For this phase difference, a single λ/2 TL offers a limited bandwidth (see Fig. 3), and so we try here to provide analysis that results into a wideband IC. Figure 3 shows two different ICs; one with a TL of length l ₀ = λ ₀/2 (Fig. 3(a)), and the other with two TLs of lengths l ₁ = λ ₁/2, and l ₂ = λ ₂/2 (Fig. 3(b)).

Figure 3. (a) Conventional IC and (b) the proposed IC.

In Fig. 3(a), input impedance Z_in of the IC’s constituent TL with characteristic impedance ${Z_s}$ can be calculated using equation (8):

(8)\begin{align}{Z_{in}}& ={Z_s}\frac{{{Z_{\text{1}}}{\text{ + }}j{Z_s}{\text{tan}}\frac{{{\text{2}}\pi {l_{\text{0}}}}}{\lambda }}}{{{Z_s}{\text{ + }}j{Z_{\text{1}}}{\text{tan}}\frac{{{\text{2}}\pi {l_{\text{0}}}}}{\lambda }}}{\text{ = }}{Z_s}\frac{{{Z_1}{\text{ + }}j{Z_s}{\text{tan}}\frac{{\pi {\lambda _{\text{0}}}}}{\lambda }}}{{{Z_s}{\text{ + }}j{Z_i}{\text{tan}}\frac{{\pi {\lambda _{\text{0}}}}}{\lambda }}} \nonumber\\ & = {Z_s}\frac{{{Z_{\text{1}}}{\text{ + }}j{Z_s}{\text{tan}}\frac{{\pi \omega }}{{{\omega _{\text{0}}}}}}}{{{Z_s}{\text{ + }}j{Z_{\text{1}}}{\text{tan}}\frac{{\pi \omega }}{{{\omega _{\text{0}}}}}}}\end{align}

where ω ₀ is the center frequency, and ω is operating frequency.

The input impedance of the single-TL IC, Z _IC-S, can be given by:

(9)\begin{equation}{Z_{{\text{IC - S}}}}{\text{ = }}{Z_1} + {Z_{in}}\end{equation}

Now for very small bandwidth, Δω ₀, around ω ₀, let ω = ω ₀ + Δω ₀. Thus, bandwidth of the IC of Fig. 3(a) can be derived by calculating Z _IC-S:

(10)\begin{equation}{Z_{{\text{IC - S}}}} \cong \frac{{{Z_s}^{\text{2}} - {Z_{\text{1}}}^{\text{2}}{\text{ + }}{Z_{\text{1}}}{Z_s}}}{{{Z_s}}}{\text{ + }}j\left( {\frac{{{Z_s}^{\text{2}} - {Z_{\text{1}}}^{\text{2}}}}{{{Z_s}}}} \right)\frac{{\pi \left( {\omega - {\omega _{\text{0}}}} \right)}}{{{\omega _{\text{0}}}}}\end{equation}

Fractional bandwidth (FBW) of IC in Fig. 3(a) can be obtained from equation (10) as:

(11)\begin{equation}\frac{{{\text{2}}\Delta {\omega _{\text{0}}}}}{{{\omega _{\text{0}}}}} = \frac{{\text{2}}}{\pi }\left( {{\text{1 + }}\frac{{{Z_{\text{1}}}{Z_s}}}{{{Z_s}^{\text{2}} - {Z_{\text{1}}}^{\text{2}}}}} \right)\end{equation}

Therefore, to obtain maximum bandwidth in a single-TL IC, according to equation (11), one has to choose Z_S close to Z ₁. For the case of a PA, where Z ₁ (and in turn Z_S) is small, realizing correspondingly thick TL proves almost impractical.

Now, assuming ω = ω ₁ + Δω ₁ and ω = ω ₂ + Δω ₂, Z_inm (where m = 1, 2), Z_inm for the double-TL IC can be given by:

(12)\begin{equation}{Z_{in}}_m{\text{ = }}{Z_s}\frac{{{Z_i}{\text{ + }}j{Z_s}{\text{tan}}\frac{{\pi {\lambda _m}}}{\lambda }}}{{{Z_s}{\text{ + }}j{Z_i}{\text{tan}}\frac{{\pi {\lambda _m}}}{\lambda }}} = {Z_s}\frac{{{Z_{\text{1}}}{\text{ + }}j{Z_s}{\text{tan}}\frac{{\pi \omega }}{{{\omega _m}}}}}{{{Z_s}{\text{ + }}j{Z_{\text{1}}}{\text{tan}}\frac{{\pi \omega }}{{{\omega _m}}}}}\end{equation}

(13)\begin{equation}{Z_{in}}_m \cong \frac{{{Z_s}^{\text{2}} - {Z_{\text{1}}}^{\text{2}}{\text{ + }}{Z_{\text{1}}}{Z_s}}}{{{Z_s}}}{\text{ + }}j\left( {\frac{{{Z_s}^{\text{2}} - {Z_{\text{1}}}^{\text{2}}}}{{{Z_s}}}} \right)\frac{{\pi \left( {\omega - {\omega _m}} \right)}}{{{\omega _m}}}\end{equation}

Therefore, Z _IC-D for Fig. 3(b) can be calculated as:

(14)\begin{equation}{Z_{{\text{IC - D}}}}{\text{ = ((}}{Z_1} + {Z_{in1}}){\text{(}}{Z_1} + {Z_{in2}}))/\left( {2{Z_1} + {Z_{in1}} + {Z_{in2}}} \right)\end{equation}

Substituting equation (13) into (14) gives:

(15)\begin{align}{Z_{{\text{IC - D}}}} &\cong \frac{{{Z_{\text{0}}}}}{{\text{2}}}\left( {\text{1 + }}j\pi \left( {\frac{{\left( {\omega - {\omega _{\text{1}}}} \right)}}{{{\omega _{\text{1}}}}}{\text{ + }}\frac{{\left( {\omega - {\omega _{\text{2}}}} \right)}}{{{\omega _{\text{2}}}}}} \right) \right. \nonumber\\ &\quad \times \left.\left( {\frac{{{Z_s}^{\text{2}} - {Z_{\text{1}}}^{\text{2}} - {Z_{\text{1}}}{Z_s}}}{{{\text{2}}\left( {{Z_s}^{\text{2}} - {Z_{\text{1}}}^{\text{2}}{\text{ + }}{Z_{\text{1}}}{Z_s}} \right)}}} \right) \right)\end{align}

Assuming Δω ₁ ≈ Δω ₂, the resonance frequency of the IC of Fig. 3(b) and its FBW can be determined as equation (16):

(16)\begin{align}{ }\frac{{{{2\Delta \omega }}}}{{{{{\omega }}_{\text{r}}}}} &= \frac{{\text{4}}}{{t{\pi }}}\frac{{{{\text{Z}}_{\text{s}}}^{\text{2}}{\text{ - }}{{\text{Z}}_{\text{1}}}^{\text{2}}{\text{ + }}{{\text{Z}}_{\text{1}}}{{\text{Z}}_{\text{s}}}}}{{{{\text{Z}}_{\text{s}}}^{\text{2}}{\text{ - }}{{\text{Z}}_{\text{1}}}^{\text{2}}{\text{ - }}{{\text{Z}}_{\text{1}}}{{\text{Z}}_{\text{s}}}}}{\text{ = }}\frac{{\text{4}}}{{t{\pi }}}\left( {{\text{1 + }}\frac{{{{\text{Z}}_{\text{1}}}{{\text{Z}}_{\text{s}}}}}{{{{\text{Z}}_{\text{s}}}^{\text{2}}{\text{ - }}{{\text{Z}}_{\text{1}}}^{\text{2}}{\text{ - }}{{\text{Z}}_{\text{1}}}{{\text{Z}}_{\text{s}}}}}} \right){\text{, }} \nonumber\\ {{{\omega }}_{\text{r}}}& = \frac{{{\text{2}}{{{\omega }}_{\text{1}}}{{{\omega }}_{\text{2}}}}}{{{{{\omega }}_{\text{1}}}{\text{ + }}{{{\omega }}_{\text{2}}}}}\end{align}

Now, the bandwidth advantage of the proposed IC of Fig. 3(b) over IC of Fig. 3(a) becomes clear by dividing FBWs such that:

(17)\begin{equation}\frac{{{\text{B}}{{\text{W}}_{{\text{Double - TL }}}}}}{{{\text{B}}{{\text{W}}_{{\text{Single - TL }}}}}}{\text{ = 2}}\left( {{\text{1 + }}\frac{{{{\text{Z}}_{\text{1}}}{{\text{Z}}_{\text{s}}}}}{{{{\text{Z}}_{\text{s}}}^{\text{2}}{\text{ - }}{{\text{Z}}_{\text{1}}}^{\text{2}}{\text{ - }}{{\text{Z}}_{\text{1}}}{{\text{Z}}_{\text{s}}}}}} \right)\end{equation}

Let $A = {Z_s}^{\text{2}} - {Z_{\text{1}}}^{\text{2}} - {Z_{\text{1}}}{Z_s}$; provided that A > 0, then, the FBW of double-TL IC of Fig. 3(b) will be at least twice that of the single-TL IC of Fig. 3(a). For A > 0 to be true, Z_S is derived in terms of Z ₁ (see equation (18)) and plotted against it in Fig. 4. The hatched area shows the region that permits positive sign for A. That is, for the proposed double-TL IC and for a given Z ₁, the corresponding Z_S can be obtained in this area, which guarantees at least doubled bandwidth compared to a single-TL IC. Note that the red line indicates the minimum values that Z_S can take for given Z ₁ under this condition.

(18)\begin{equation}{\text{(}}{Z_s} - {\text{(}}\frac{{{\text{1 + }}\sqrt {\text{5}} }}{{\text{2}}}{\text{)}}{Z_{\text{1}}}{\text{)(}}{Z_s} - {\text{(}}\frac{{{\text{1}} - \sqrt {\text{5}} }}{{\text{2}}}{\text{)}}{Z_{\text{1}}}{\text{)0}}\end{equation}

Figure 4. The hatched region indicates the permitted values of Z_S and Z ₁ for the IC of Figure 3(b).

Let’s for a PA application, assume Z ₁ = 6 Ω; then according to Fig. 4, ${{\text{Z}}_{\text{s}}}{\text{ - (}}\frac{{{\text{1 + }}\sqrt {\text{5}} }}{{\text{2}}}{\text{)}}{{\text{Z}}_{\text{1}}}{\text{0}}$ is forced (above the red line within the hatched area), which for the given Z ₁ translates into Z_S > 9.7 Ω. This means that according to equation (17), in principle, for practical Z_S values (between 10 Ω and 100 Ω), a double-TL IC can offer a BW around 2.1–96.83 times the BW of the single-TL IC.

Here, a practical case of Z_S = 25 Ω is selected for the sake of argument. Equation (17) ensures that the bandwidth of IC of Fig. 3(b) is approximately 2.7 times larger than that of the IC of Fig. 3(a). Now, we can verify this numerically. If we calculate Z _IC-S, and Z _IC-D from equations (9) and (14) and substitute for isolation (S ₃₂ = S ₂₃) in the matrix of equation (7), then we can plot isolation versus frequency for single-TL IC of Fig. 3(a) against double-TL IC of Fig. 3(b). As is evident in Fig. 5, the double-TL IC (red starred solid line) offers 3.2 times (with reference to −20 dB return loss (RL) level) larger bandwidth than single-TL IC (blue circled solid line). To further verify the results, both ICs of Fig. 3 are simulated in AWR Microwave Office software and isolation results are plotted in Fig. 5. Note that the results are in very good agreement. Furthermore, S ₂₃ of the classical BCD balun (i.e. without an IC) is also plotted in Fig. 5 against single-TL and double-TL cases, and as seen below, the S ₂₃ of balun without IC is very poor throughout the band, and in particular around the center frequency (and upward). Adding a single-TL IC improves this response and evidently, the double-TL IC improves the S ₂₃ significantly.

Figure 5. Isolation of single-TL IC against the proposed double-TL IC.

From a design perspective, the λ/2 length of the IC compared to the compact size of the balun itself, poses a size challenge, and so, it is essential to make the IC compact. This is done by using the equivalent T-network of the IC TLs loaded with shunt capacitors as shown in Fig. 6.

Figure 6. Equivalent circuit of double-TL ICs formed of shunt loaded capacitors.

Design of the isolated BCB

Design procedure

Now that different blocks of the isolated BCB are analyzed, design of the proposed balun can be elaborated through a simple straightforward procedure, depicted in the flowchart of Fig. 7.

Figure 7. Design procedure for the proposed isolated broadside-coupled balun.

Note that the actual design involves much more details to be seen, and that since an all-ports-matched balun suitable for PA applications is intended, the procedure is presented by means of a balun that satisfies the PA requirements.

Case study: isolated balun design for PA applications

Design formulas and considerations for isolated BCB is illustrated through an example based on balun in Fig. 8.

Figure 8. (a) 3D view of the BCB without isolation circuit: primary (blue), and secondary (red) windings sandwiching the substrate, and (b) associated geometrical parameters of spiral inductor.

For the BCB balun of Fig. 8(a) at f_c, the constitutive parameters of Fig. 2 are derived by:

(19)\begin{equation}{f_c}{\text{ = }}\frac{{\text{1}}}{{{\text{2}}\pi \sqrt {{\text{(}}{C_m}/2)\left( {{L_P}{\text{ + }}n{L_m}} \right) - \left( {1/4} \right){{\left( {{Z_{\text{1}}}{C_m}} \right)}^{\text{2}}}\left( {{\text{1 + }}n} \right)} }}\end{equation}

where $n = \sqrt {{Z_0}/2{Z_1}} $, and L_P and L_S in nH can be found from [22]:

(20)\begin{equation}{L_{{\text{spiral}}}}{\text{ = }}{L_P}{\text{ = }}{L_S} = \frac{{{\text{1}}{\text{.27}}{\mu _{\text{0}}}{N^{\text{2}}}{d_a}}}{{\text{2}}}\left( {{\text{ln}}\left( {\frac{{{\text{2}}{\text{.07}}}}{{{\rho }}}} \right){\text{ + 0}}{\text{.18}}\rho {\text{ + 0}}{\text{.13}}{\rho ^{\text{2}}}} \right)\end{equation}

where ${d_a} = \frac{{{d_o} + {d_i}}}{2}$, $\rho = \frac{{{d_o} - {d_i}}}{{{d_o} + {d_i}}}$, N is the number of turns, and d_o, d_i are the outer and inner diameters of the coil, respectively (see Fig. 8(b)). In addition, for the stacked overlay spiral, C_m which is proportional to the area occupied by the transformer can be found by [23]:

(21)\begin{equation}{C_m}{\text{ = }}\frac{{\text{1}}}{{\text{2}}}\frac{{{\varepsilon _{\text{0}}}{\varepsilon _r}}}{h}{\text{.}}\left( {{d_o}^{\text{2}} - {d_i}^{\text{2}}} \right)\end{equation}

where h, and ${\varepsilon _r}$ are the substrate thickness, and dielectric constant, respectively.

Also, according to equation (1), L_m can be determined in terms of K_m, L_S, and L_P as ${L_m}{\text{ = }}{K_m}\sqrt {{L_P}{L_S}} $. The value of K_m mostly depends on the geometry of windings and h. While K_m for perfect coupling is unity, it is less than unity in practice. The value of K_m for broadside-coupled structures, which can be calculated from K_m ≈ 0.9 − h/AD for average diameter of AD, is empirically reported to be mostly between 0.7 and 0.9 for strong coupling [24].

In PAs, large step-down impedance transformation ratio is desirable. For one thing, most PAs have low output resistance; in most cases, less than 10 Ω (depending on device voltage and power rating). Here, an isolated balun is designed to have 4:1 impedance transformation, i.e. n = 2. At f_c = 97 MHz and for Z ₀ = 50 Ω and 2Z ₁ = 12.5 Ω, number of turns for primary and secondary windings can be calculated from equation (1) as N_P = 2, N_S = 1. In other words, assuming perfect coupling, K_m = 1, based on equation (2), L_P/L_S = 4. Moreover, assuming d_o = 38 mm, d_i = 10 mm, geometrical and circuit model parameters are calculated using equations (19)–(21) to be L_P = 108.4 nH, L_S = 27.11 nH, C_m = 26.4 pF, w_P = 12 mm, w_S = 5.5 mm, S = 0.7 mm. At this stage, the IC is designed and added to the balun. The optimized IC parameters are obtained using Fig. 4 and equation (18) as Z _S = 80 Ω, C ₁ = 18 pF, C ₂ = 1.3 nF, C ₃ = 68 pF, C ₄ = 1.2 pF, R ₁ = 6.25 Ω. The final schematic of the proposed isolated BCB is depicted in Fig. 9.

Figure 9. Schematic of the final isolated broadside-coupled balun.

There are also some PHC constraints in choosing design parameters. More specifically, increasing substrate thickness, h, will improve PHC. Moreover, tracks should be wide enough to have suitable current-handling for the transistor. Maximum power rating of the isolation resistors (R ₁–R ₄) should be taken into account when determining the balun output power. For instance, here for a 100 W PA, each resistor should at least withstand 25 W for a robust design. Furthermore, tuning capacitors are used at input and output of the balun to improve phase and amplitude imbalance, insertion loss, and input return loss; though frequency shifting effect of such capacitors cannot be neglected.

Simulation and measurement

To validate the proposed approach, the balun designed in the previous section is simulated in HFSS and fabricated on Rogers RO4003C substrate with ε_r = 3.55, h = 0.8 mm, and loss tangent TanD = 0.0027. Figure 10(a) shows the top view of the balun layout, and Fig. 10(b) and (c) illustrate photographs of top and bottom sides of balun PCB. The very close agreement between calculated, simulation and measurement results demonstrate the validity of the proposed approach and accuracy of the computation and design.

Figure 10. (a) Top view of the layout of balun, and photograph of (b) top and (c) bottom views of the fabricated balun.

Figure 11 shows the result of HFSS full-wave simulation against measurement, which covers the frequency range of the balun in 84–110 MHz, with input and output return losses of better than 11 dB, magnitude imbalance (|S ₃₁| − |S ₂₁|) of less than 0.2 dB, and phase imbalance better than 2°.

Figure 11. Comparison of full-wave simulation, and measurement results of balun in terms of (a) transmission, (b) isolation, (c) reflection, and (d) phase difference.

At this stage, it is essential to provide a comparative analysis of benefits and deficiencies of the proposed balun against other similar reported works. However, in this particular case, the variety in balun topologies for different applications and operating frequencies makes it quite challenging to do an analogous comparison. Therefore, performance of the balun presented here is compared to similar published works in Table 1.

Table 1. Comparison with other similar published works

Note: BCB = broadside-coupled balun; LDB = lumped-distributed balun; MB = Marchand balun; MLB = microstrip line balun, NR = not reported.

As is evident, the proposed isolated balun outperforms other similar works in almost all design parameters. For instance, in terms of sizes versus bandwidths, the fabricated prototype can be claimed as the best and the smallest ever recorded using microstrip technology (even 50% smaller than [25]). Moreover, the 10 dB FBW of isolation, S ₂₃, of 108%, and the amplitude imbalance, $| S_{21}-S_{31} |$, of 0.2 dB for the fabricated prototype are unbeatable in the literature. Furthermore, fabricated balun has the highest step-down impedance conversion desirable in PA applications compare to similar reported works. This is significant because the conversion rate greatly limits the bandwidth, while a reasonable bandwidth has been achieved with the proposed balun.

Conclusion

In this paper, an all-ports-matched multilayer BCB with arbitrary impedance transformation ratio was presented. Analysis of the isolated BCB and that of its constituent wideband IC was demonstrated. Frequency response of the proposed IC is evaluated analytically and verified numerically, confirming its wide FBW. In addition, a simple straightforward procedure for design of the isolated multilayer balun was presented that offers a guaranteed optimum design through clear steps. The proposed low-profile balun is fabricated and measured using E5071C VNA. The performance of the balun, and particularly the isolation between output ports (S ₂₃) at FBW = 118%, not only confirms the validity of the proposed approach, but also makes the balun a competent alternative to the existing ones, particularly for PA applications.