Ka-Band Marchand Balun with Edge- and Broadside-Coupled Hybrid Configuration

Abstract

This article presents a novel Ka-band Marchand balun implemented in 0.13-μm SiGe bipolar complementary metal–oxide–semiconductor (BiCMOS) process. By combining both edge- and broadside-coupled structures, the new hybrid balun is able to increase the coupling and minimize the balun insertion loss. As compared with conventional edge-coupled or broadside-coupled structures, the proposed balun achieves the lowest insertion loss of 1.02 dB across a wide 1-dB bandwidth from 29.0 GHz to 46.0 GHz, with a core size of 270 μm $\times$ 280 μm.

1. Introduction

Balun, which converts single ended signals into balanced signals is widely used in RF front-end modules, such as frequency multipliers, mixers which utilize differential signals for common-mode signal cancellation, and to improve port isolations. Key performance specifications of a balun include insertion loss, amplitude/phase balance, and chip size. These parameters are important in the design of millimeter-wave (MMW) circuits and systems [1]. Marchand balun [2,3,4,5,6,7,8,9,10], which utilizes two coupled line sections, is widely used in MMW frequency circuit design, due to its wide operating bandwidth and easy implementation.

In [2], an asymmetric broadside coupled Marchand balun based on the modified off-center frequency method was proposed. It achieves a bandwidth of 34–110 GHz; however, it suffers from high insertion loss averaging around 3 dB. Another 30 GHz to 60 GHz transformer balun [11] with offset radii coils was designed to address imbalance performance. Results show a low-amplitude imbalance of 0.12 dB and phase imbalance of less than 1°; however, the maximum insertion loss is around 3 dB. A miniaturized on-chip Marchand balun [12], based on a stacked-spiral-coupled (SSC) structure with a self-coupled compensation line and center-tapped ground-shield with deep trench, was designed for wideband operation from 6.5 GHz to 28.5 GHz, but a maximum of 3 dB insertion loss was measured. Wideband operation and amplitude/phase imbalance had been the focus of previous reported literature, with the trade-off of balun insertion loss. In this article, the design of a novel Ka-band Marchand balun with low insertion loss is presented, while achieving wideband operation with acceptable imbalance performance. The proposed balun employs both edge- and broadside-coupled combined structures to enhance the coupling between the primary and secondary signals and, thus, achieves a measured low insertion loss of 1.02 dB across a 1 dB bandwidth from 29.0 GHz to 46.0 GHz. Section 2 presents the detailed balun analysis and proposed balun design, Section 3 discusses the experiment results and makes a comparison with the state-of-the-art, and Section 4 draws the conclusion.

2. Design of the Proposed Balun

2.1. Technology

A high-performance bipolar complementary metal–oxide–semiconductor (BiCMOS) technology (SG13G2) with a 0.13-μm complementary metal–oxide–semiconductor (CMOS) process from innovations for high performance microelectronics (IHP) has been used for designing the balun. The backend of the line offers 5 thin metal layers, metal 1 (M1) to metal 5 (M5), two thick metal layers, top metal 1 (TM1, 2 μm thick) and top metal 2 (TM2, 3 μm thick), and a metal–insulator–metal (MIM) layer.

2.2. Balun Analysis

Figure 1 shows the schematic of the conventional Marchand balun, which consists of two identical coupled line sections, where a single section coupler with electrical length of θ, is shown in Figure 2, and its four-port S-parameter matrix can be represented by Equation (1), as given in [13].

$${\left[\begin{array}{c}S\end{array}\right]}_{\mathrm{coupler}}=\left[\begin{array}{cccc}0& \raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$z$}\right.& \raisebox{1ex}{$y$}\!\left/ \!\raisebox{-1ex}{$z$}\right.& 0\\ \raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$z$}\right.& 0& 0& \raisebox{1ex}{$y$}\!\left/ \!\raisebox{-1ex}{$z$}\right.\\ \raisebox{1ex}{$y$}\!\left/ \!\raisebox{-1ex}{$z$}\right.& 0& 0& \raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$z$}\right.\\ 0& \raisebox{1ex}{$y$}\!\left/ \!\raisebox{-1ex}{$z$}\right.& \raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$z$}\right.& 0\end{array}\right]$$

(1)

where $x=\sqrt{1-k^2}$, $y=jk\sin \theta$, and $z=\sqrt{1-k^2}\cos \theta +j\sin \theta$, and $k$ is the coupling coefficient.

Figure 1. Block diagram of the conventional Marchand balun.

Figure 2. A single section coupler.

Then from [9], the insertion loss of the Marchand balun can be derived as

$$S_{21}=-S_{31}=\frac{x^{3}y-xy{z}^2-x{y}^3}{z^2\left(z^2+y^2\right)}$$

(2)

Ideally balanced output ports P₂ and P₃ should be of equal magnitude and exactly 180° out of phase. The plot of the insertion loss S₂₁ as a function of electrical length θ, for different values of coupling coefficient $k$, is shown in Figure 3. It is observed that the insertion loss initially decreases as $k$ increases; further increasing $k$ beyond 0.7 will increase the insertion loss at the center frequency $\theta =\pi /2$, while the flattest frequency response occurs for $k$ between 0.6 and 0.7. Based on the above observation, the balun insertion loss can be minimized through optimizing the coupling coefficient $k$, as presented in this work. Figure 4 shows the schematic of the designed Marchand balun with a capacitor C₁ added to connect the open circuit (O.C.) port to ground, so as to reduce the coupled transmission line length, as well as achieve good in-band matching.

Figure 3. Plot of insertion loss versus the coupled line electrical length θ, for different coupling coefficient $k$.

Figure 4. Block diagram of the designed Marchand balun with capacitive termination.

Meander lines with a 45° bend have been used to save chip area. To reduce the insertion loss, the top two thick metal layers, TM1 and TM2, with low sheet resistance and low parasitic capacitances to substrate are used. A Metal 1 to TM2 guard-ring surrounding the balun is drawn and shorted by internal Vias to ground and is connected to the substrate through contact Vias, as shown in Figure 5a.

Figure 5. (a) Cross-section view of the metal stack and proposed balun; (b) 3D view of the balun.

2.3. Proposed Balun

The proposed balun structure is shown in Figure 5. Broadside-coupling between TM1 and TM2 layers and edge-coupling in both TM1 and TM2 layers is formed between primary and secondary signals. Further optimization using Keysight Advanced Design System’s (ADS) Momentum Electromagnetic (EM) simulator was performed to obtain the optimum metal width and spacing, with a 6 μm metal width and a 6 μm metal spacing obtained for both TM1 and TM2 layers, as shown in Figure 5a. Detailed analysis for the proposed balun is given in Figure 6 with the cross-sectional view shown in Figure 6a, where $C_{S1}$ and $C_{S2}$ are the TM1 and TM2 conductor capacitance to ground, respectively. $C_{m1}$ and $C_{m2}$ are the mutual capacitances for the edge-coupled TM1 and TM2, respectively, and $C_{m12}$ is the mutual capacitance between the broadside-coupled TM1 and TM2. Figure 6b shows the equivalent simplified model of the balun, and the corresponding even/odd mode models are given in Figure 6c, Figure 6d, respectively.

Figure 6. (a) Cross-section of the proposed balun; (b) simplified model of the proposed balun; (c) even mode analysis; (d) odd mode analysis.

Then from [13], the coupling coefficient $k$ can be expressed as

$$k=\frac{C_m}{\sqrt{C_a+C_m}\sqrt{C_b+C_m}}$$

(3)

where $C_m=2\left(C_{m1}+C_{m2}+2C_{m12}\right)$, and $C_a=C_b=C_{s1}+C_{s2}$. Therefore, $k$ increases as $C_m$ increases. Compared with the edge-coupled structure, where either $C_{m1}$ or $C_{m2}$ exists, or the broadside-coupled structure with only mutual capacitance $C_{m12}$, using the proposed edge- and broadside-coupled hybrid configuration, a higher $C_m$ can be obtained, hence maximizing coupling $k$.

Using 6 μm metal width for both primary and secondary coupled lines, for the edge-coupled structure, the coupling $k$ is limited by the minimum metal spacing rule defined by the foundry process, with a highest simulated $k$ of 0.57; for the broadside-coupled structure, it is limited by the vertical distance between TM1 and TM2, with a highest simulated $k$ of 0.61. With the proposed edge- and broadside-coupled hybrid structure, a coupling $k$ of 0.62 is achieved. Further optimizing the capacitive termination, $C_1$ capacitance in Figure 4 with 30 fF for both edge- and broadside-coupled structures and 74 fF for the proposed hybrid balun, the simulated insertion loss is shown in Figure 7. It can be seen that the proposed balun has achieved the lowest minimum insertion loss among all the designs.

Figure 7. Plot of insertion loss.

By transforming the three-port balun into a two-port network, the minimum insertion loss IL_min [14] can be calculated by Equations (4) and (5), and the calculated IL_min is shown in Table 1. Simulation and calculation results correlate well, showing that the proposed hybrid structure gives the minimum insertion loss.

$$I{L}_{min}=\frac{1}{1+2\left(x-\sqrt{x^2+x}\right)}$$

(4)

$$x=\frac{\mathrm{Re}\left({\mathrm{Z}}_{11}\right)·\mathrm{Re}\left({\mathrm{Z}}_{22}\right)-{\left[\mathrm{Re}\left({\mathrm{Z}}_{12}\right)\right]}^2}{{\left[\mathrm{Im}\left({\mathrm{Z}}_{12}\right)\right]}^2+{\left[\mathrm{Re}\left({\mathrm{Z}}_{12}\right)\right]}^2}$$

(5)

Table 1. Simulated and calculated IL_min *.

Topology	Edge Coupled	Broadside Coupled	Proposed
Simulated ILmin (dB)	1.616	1.190	0.816
Calculated ILmin (dB)	1.212	1.046	0.791

* Excluding the balun theoretical 3 dB loss.

From [13], the equivalent even/odd mode characteristic impedance $Z_{0e}$ and $Z_{0o}$ can be expressed as

$$Z_{0e}=\sqrt{\frac{R+j\omega L}{G+j\omega C}}=\sqrt{\frac{R+j\omega \left(L_0+L_m\right)}{G+j\omega C_0}}$$

(6)

$$Z_{0o}=\sqrt{\frac{R+j\omega L}{G+j\omega C}}=\sqrt{\frac{R+j\omega \left(L_0-L_m\right)}{G+j\omega \left(C_0+2C_m\right)}}$$

(7)

where $L_m$ is the mutual inductance, and $C_m$ is the mutual capacitance and is equal to $2\left(C_{m1}+C_{m2}+2C_{m12}\right)$ in the proposed balun.

Then from [15], the amplitude imbalance of the balun can be written as

$$AmplitudeImbalance=\mathrm{d}\mathrm{B}\left(\left|S_{21}\right|/\left|S_{31}\right|\right)=\mathrm{d}\mathrm{B}\left(\frac{Z_{0e}-Z_{0o}}{Z_{0e}+Z_{0o}}\right)$$

(8)

From Equations (6)–(8), it can be seen that, as the coupling coefficient $k$ increases, both the mutual inductance, $L_m$ and mutucal capacitance, $C_m$ increase, and thus, $Z_{0o}$ decreases, $Z_{0e}$ increases, and the amplitude imbalance shifts towards the ideal 0 dB. Figure 8 shows the simulated amplitude and phase imbalance, where phase imbalance is defined as

$$PhaseImbalance=abs\left(\angle S_{21}-\angle S_{31}\right)-{180}^{°}$$

(9)

Figure 8. Plot of amplitude and phase balance.

From Figure 8, it can be seen that the proposed balun shows significant improvement over the conventional edge-coupled and broadside-coupled structures in terms of amplitude/phase balance, where the amplitude and phase imbalance are −0.18 dB to 0.20 dB and −3.23° to 0.81°, respectively across a 1-dB frequency bandwidth.

3. Experiment Results

The proposed balun is fabricated using the IHP 0.13-μm SiGe BiCMOS process with a core size of 270 μm $\times$ 280 μm. The on-wafer measurement is carried out using the Keysight PNA-X network analyzer N5247A (Keysight, Santa Rosa, CA, USA) with a four-port Hybrid Line–Reflect–Reflect–Match (LRRM) and Short–Open–Load–Thru (SOLR) calibration. The measurement setup and die photo is shown in Figure 9. A minimum insertion loss of 1.02 dB with a 1-dB bandwidth of 29.0 GHz to 46.0 GHz is measured, as shown in Figure 10.

Figure 9. Measurement setup.

Figure 10. Simulated and measured performance of the proposed balun.

Figure 11 shows the simulated and measured amplitude and phase imbalances. A ±0.83 dB amplitude imbalance and −3.8° to −7.3° phase imbalance is measured across the band from 29.0 GHz to 46.0 GHz. The small difference between the simulated and measured data is primarily due to the imbalance introduced between the output differential ports during the calibration phase. In addition, the measured frequency shift is due to the process variation of the capacitor C₁.

Figure 11. Simulated and measured amplitude and phase imbalance.

Common mode rejection ratio (CMRR), defined as the ratio between the differential-mode insertion loss over the common-mode insertion loss as shown in Equation (10), is plotted in Figure 12. CMRR more than 25 dB has been measured for the proposed hybrid structure. The difference between simulated and measured data is due to higher amplitude and phase imbalance, as the CMRR is dependent on the amplitude and phase balance of the balun. Poor amplitude or phase balance will result in higher common-mode signal pass through and, thus, low CMRR.

$$CMRR=\mathrm{d}\mathrm{B}\left(\frac{S_{21}-S_{31}}{S_{21}+S_{31}}\right)$$

(10)

Figure 12. Simulated and measured common mode rejection ratio (CMRR).

Finally, Table 2 shows the measured performance comparison with the reported SiGe baluns. Compared with the reported standalone broadside-coupled baluns, the proposed hybrid structure has achieved a lowest insertion loss of 1.02 dB.

Table 2. Performance comparison with reported baluns.

Reference	[11]	[12]	[16]	Proposed
Process	0.13-μm SiGe BiCMOS	0.13-μm SiGe BiCMOS	0.18-μm SiGe BiCMOS	0.13-μm SiGe BiCMOS
Topology	Broadside coupled	Broadside coupled	Broadside coupled	Broadside and edge coupled
Frequency (GHz)	30.0–60.0	6.5–28.5	40.0–60.0	29.0–46.0
Insertion loss * (dB)	<3	<3	1.9	1.02
Amplitude Imbalance (dB)	<0.14	<±1.0	<0.2	<±0.83
Phase Imbalance (deg.)	<1	<±1.65	<2.7	−3.8 to −7.3
Chip area (μm2)	200 × 145	360 × 150	200 × 180	270 × 280

* Excluding the balun theoretical 3 dB loss.

4. Conclusions

In this article, the influence of the coupling coefficient $k$ on the Marchand balun insertion loss has been studied. As coupling $k$ for the stand-alone edge-coupled and broadside-coupled structures has reached the process limitation, a new structure combining both edge-coupled and broadside-coupled configurations is proposed to enhance the coupling and therefore increase $k$ to minimize the insertion loss. With that, a good amplitude imbalance of ±0.83 dB and measured insertion loss of 1.02 dB has been obtained across a 1-dB bandwidth from 29.0 GHz to 46.0 GHz.