Compact and Digitally Controlled D-Band Vector Modulator for Next-Gen Radar Applications in 130 nm SiGe BiCMOS

Radar systems got very popular in sensing applications in the last two decades besides the traditional military sector. Nowadays, many applications favor multiple-input multiple-output (MIMO) radar over phased-array radar. Here, time-division multiplexing (TDM) and code-division multiplexing (CDM), like a phase-modulated continuous wave (PMCW), are well-known techniques. However, every method needs special components on the MMIC. In this article, a <inline-formula><tex-math notation="LaTeX">$\text{125}\,\text{GHz}$</tex-math></inline-formula> vector modulator (VM) circuit is presented, which can operate as a switchable amplifier in TDM systems, as a binary-phase modulator in CDM systems, and as a phase-shifter in phased-array systems. Based on simulations and <inline-formula><tex-math notation="LaTeX">$S$</tex-math></inline-formula>-parameter measurements, the VM itself and the three different operating modes are analyzed. We also present a technique to separate coupler imperfections from the <inline-formula><tex-math notation="LaTeX">$S$</tex-math></inline-formula>-parameter measurements to analyze the VM separately. We designed the VM with the B11HFC silicon-germanium technology (<inline-formula><tex-math notation="LaTeX">$f_{t} / f_{max} = 250/370\, \text{GHz}$</tex-math></inline-formula>), using both HBTs (heterojunction bipolar transistors) and CMOS transistors. Inside the VM, two cross-connected power amplifiers (PAs) are fed by an in-phase (I), and two cross-connected PAs are fed by a quadrature-phase (Q) signal. The four PAs are controlled by a 4-bit interface to switch them on or off, thus generating output signals in the range of <inline-formula><tex-math notation="LaTeX">$0^\circ$</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">$360^\circ$</tex-math></inline-formula>.


FIGURE 1. 125 GHz vector modulator circuit diagram, which is based on two pairs of cross-connected PAs and on a CMOS-based control circuit. Each pair uses the same input signal (I or Q), and all use the same inductive load.
applications where large bandwidth is required [8], [9], [10], [11].
The presented vector modulator circuit targets future Dband FMCW radar systems to enable more flexibility. It provides a fully digital interface similar to [65], [66]. Hereby, fast phase state changes are possible to enable PMCW radar operation to enhance interference mitigation properties. TDM MIMO radar operation is enabled by switching the VM on/off such that only one radar transmitter is enabled at a given time, and phased-array operation is enabled by controlling the VM's output phase. For all three operation types, the same 4-bit interface is used. Therefore, no DAC is needed to produce these different modulation schemes.
The article is divided into several sections. First, Section II presents the circuit design of the VM and the architecture of the breakout MMIC. In Section III, the simulation results are shown. Afterward, the measurement results and a technique to isolate the coupler's imperfections are presented in Section IV. To show the vector modulator's capabilities, phased-array, and PMCW properties are examined in Sections V and VI, respectively. The article is concluded in Section VII.

II. 125 GHZ VECTOR MODULATOR DESIGN
The complete circuit diagram of the 125 GHz VM is shown in Fig. 1. All external signals are shown in red and relevant internal signals in black. The vector modulator is based on four parallel PAs, where every PA is working on a common load. Two PAs share the in-phase (I) input signal U I and two PAs share the quadrature-phase (Q) input signal U Q (cf. Fig. 2). The HBT's base signals i, i, i , and i and the circuitry of the collectors of the common-base stage are arranged in such a way that a 180 • inversion of the I signal can take place.  The same applies to the transistors in the Q path. By using the common output (U O ), it is possible to achieve eight phase states in the range of 0 • to 360 • . For this, the control signals D SI , D I , D Q , and D SQ are used. In summary, eight different phase states can be generated, and a ninth state is possible, where the VM is turned off.
Inside the VM, HBTs with an emitter length of 4 μm are used for RF amplification and 3.3 V compatible CMOS transistors for controlling the phase states. The input matching network consists of a series capacitance, a parallel capacitor connected to signal ground, and a splitting structure. The split I and Q signals are fed to the four differential amplifiers. Each differential amplifier has its own current mirror that can be switched off, a common-emitter stage, and a common-base stage. Between the two stages, transmission lines (TRL) are used for interstage matching to enhance RF performance [67].
The differential inductive load consists of two short (< λ/4) TRLs connected to the 5 V node, which are utilized as inductors. The inductive load can be trimmed with a laser by cutting laserfuses in the top metal layer. Up to three fuses can be removed, which leads to four different inductive loads (cf. Fig. 3). The output TRL and capacitance, connected to U O , are designed to provide a good matching to Z diff = 100 .
While the RF HBTs are supplied with 5 V, the CMOS part is supplied with 3.3 V. Here, the signals D SI and D SQ are used to turn on or off the I and Q path inside the VM, respectively. The D I and D Q signals are used to invert the I and Q signals, respectively. In this case, one amplifier inside the I or Q path is switched off completely, and the cross-connected one is turned on. A corresponding CMOS inverter circuit ensures that only one amplifier is active within the I or Q path of the VM. In summary, only a maximum of two of the four amplifiers are active at the same time.
The rectangular size of the VM is 260 μm by 330 μm (0.085 mm 2 ). After the input stage, the width shrinks from 260 μm to 160 μm. Therefore, the non-rectangular size is 160 μm · 330 μm + 2 · 50 μm · 80 μm = 0.0608 mm 2 . For a compact design, differential TRLs for the input matching are designed in a meander structure. The interstage matching between the common-emitter and the common-base stage also uses differential TRLs. The signal combination, the inductive load, and the output matching are designed with single-ended TRLs.

A. ARCHITECTURE OF THE BREAKOUT MMIC
The block diagram of the MMIC and the breakout chip are shown in Figs. 2 and 3, respectively. Here, the single-ended pads, two baluns implemented as compact rat-race couplers, a TRL-based branchline coupler, and the vector modulator circuit are shown. The MMIC's size is 1450 μm · 500 μm = 0.725 mm 2 .
Single-ended probing pads are used, which are tuned to 125 GHz by using a resonant TRL against ground. This transforms the lowpass behavior of the pads into bandpass behavior. The couplers have meander designs to achieve compact dimensions. The breakout chip has ten dc pads to supply and control the modulator. These include three ground pads, one 3.3 V pad, one 5 V pad, four digital control pads, and one pad to tune the HBT's current density by changing the 3.3 V supply voltage in the I/Q on/off path. Between the components on the breakout chip, bypass capacitors are placed to ensure a stable supply voltage.

III. SIMULATION RESULTS
The targeted center frequency of the vector modulator is 125 GHz. Therefore, all subsequent plots are aligned to this and show a bandwidth of 30 GHz. It is particularly important that the coupler's amplitude and phase errors are minimal. Phase errors, e.g. non-ideal 90 • phase difference between I and Q, have a direct effect on the performance of the VM, since a vector superposition is performed at the PA outputs. Therefore, all other constellation points will have non 45 • phase difference. Also, a difference in amplitude between the I and Q signal will tilt four out of eight constellation points (±I ± Q) towards the stronger signal.

A. COUPLER SIMULATION
For a detailed investigation of the couplers, Sonnet version 18.52 together with a 2-layer thick metal sheet model was used [68]. The simulation results of the branchline coupler and the balun are shown in Figs. 4 and 5, respectively. The branchline's best input matching is achieved at ≈ 134 GHz. The ideal phase difference of 90 • is at ≈ 139 GHz. An amplitude difference of ≈ 5 dB is achieved in the shown frequency range. Typically, IQ amplitude differences are below 2 dB in this frequency range [32], [36], [44]. Here, the slightly higher amplitude difference and center frequency are caused by the TRL width and length choice, respectively. The suboptimal  choices were detected after MMIC production, and the effects will be examined in more detail in the next Sections.
In contrast to the branchline coupler, the rat-race baluns operate closer to the targeted center frequency. The two most important characteristic values of a balun, the phase and amplitude imbalance at the balanced outputs, are shown in Fig. 5. The balun at the input of the breakout chip is analyzed as well as the balun at the output of the breakout chip. While both baluns are identical, they differ in TRL length at the balanced ports, which are also simulated (cf. Fig. 3). Both baluns have an amplitude imbalance of less than 0.5 dB in the shown frequency range. An amplitude difference of 0 dB is achieved at ≈ 115 GHz and ≈ 140 GHz. As with the branchline coupler, the ideal phase difference is achieved at a slightly higher frequency, namely ≈ 131 GHz. For both baluns, S 11 is below 20 dB, and the insertion loss is less than 1.65 dB in the range from 110 GHz to 140 GHz, respectively.

B. VECTOR MODULATOR SIMULATION
After the couplers have been described, the VM including the couplers are examined. Here, the VM's schematic (cf. Fig. 1) and extracted RC parasitics using Mentor Calibre are used. The simulations consider a device temperature of 80 • C. Two  types of simulations are performed. First, an ideal branchline coupler and differential ports are used. The ideal branchline coupler splits the input signal without additional losses, has perfect port matching, and constant 90 • IQ outputs. Second, the S-parameter data for all three couplers from the Sonnet simulations are used together with single-ended ports. Then the results of both analyses are compared in a constellation diagram (Section III-C). Fig. 6 shows the results of the harmonic balance based S-parameter simulation (−15 dBm input power), which considers non-linearity (e.g. compression effects). It can be seen that two different gain curves are obtained. The maxima are in the range of 125 GHz. The length of the TRL based inductive load was chosen as if one fuse had been removed (cf. Fig. 3). A maximum gain of 11.70 dB and a minimum gain of 8.99 dB is achieved, respectively.
The simulated phase curves are shown in Fig. 7. Here, it can be seen that the 45 • phase difference could be achieved very well. A more detailed representation can be seen later in Fig. 10. Fig. 8 shows the simulation results when Sonnet's results are used. Due to the IQ imbalance of the branchline coupler, four different gain curves are visible. In addition, the gain is reduced since the couplers have losses which Sonnet  also considers. Also, non-ideal differential signals lead to a reduced gain because of the common-mode rejection of the differential amplifiers. Therefore, a maximum gain of 8.48 dB and a minimum gain of 3.05 dB is achieved, respectively. A suppression of the input signal of ≈ 80 dB is achieved when the VM is switched off completely.
When looking at the phase in Fig. 9, it is noticeable that the spacing between the individual VM states has become irregular because the simulated branchline coupler does not generate ideal IQ signals.

C. CONSTELLATION DIAGRAM AT 125 GHZ
In the constellation diagram in Fig. 10, the differences of both simulations at 125 GHz can be compared. The coupler's losses, the IQ imbalance, and the amplitude imbalance can be determined directly. The radial axis shows the gain, and the circular axis the phase. Here, the ticks of the radial axis are shown as concentric circles starting at 0 dB and increasing in 5 dB steps.
First, it is noticeable that with the ideal couplers, a higher gain is achieved. Second, the four phase states where both I and Q are active are tilted ≈ 10 • clockwise to the states where only I or Q are active. This effect is nearly invisible when RC parasitics are ignored (not shown in Fig. 10). Also, without RC parasitics, the difference between one and two active PAs is almost 3 dB. With RC parasitics, the difference is lowered to ≈ 2 dB. Thus, RC parasitics affect the linearity of the VM negatively.
When using Sonnet's S-parameter data, the non 90 • phase difference between I and Q as well as the amplitude imbalance is visible. Because of the superposition of I and Q, constellation points with two active PAs are tilted even more. Two different metrics are important when looking at a constellation diagram: The root-mean-square (RMS) phase error (1) and the RMS amplitude error (2).
Here, N is the number of states, A(n) and ϕ(n) are the achieved amplitude and phase values, and A(n) ideal and ϕ ideal (n) are ideal amplitude and phase values for a specific state. The presented VM circuit where I and Q are superimposed should achieve an RMS amplitude error of 1.5 dB because four of the eight states have 3 dB more gain. When using the ideal couplers, an RMS phase error of 5.2 • and an RMS amplitude error of 1.21 dB is achieved, which is below the above-mentioned 1.5 dB. The reason for this is the non-ideal vector superposition at the output of the VM. When using the S-parameter files from Sonnet, an RMS phase error of 14.35 • and an RMS amplitude error of 1.81 dB is achieved. Based on the findings in Sections V and VI, these values are satisfactory for beam-steering and PMCW radar.

IV. MEASUREMENT RESULTS
S-parameter measurements of the above-mentioned circuits were performed with a Keysight PNA-X N5247B vector network analyzer (VNA) and VDI D-band extenders. An extender with an integrated attenuator was used on the input side so that the VM and its gain are not distorted by compression effects. Also, an analysis of the compression behavior is performed in Section IV-C.

A. S-PARAMETER MEASUREMENT RESULTS
To examine the gain of the VM in more detail, the losses of the pads and baluns are subtracted. For this purpose, a back-toback structure was created (Fig. 11) to measure the insertion loss of the baluns and pads [69]. Fig. 12 shows the measurement results of the back-to-back structure. After calibrating the VNA, including extenders and probes, with an off-chip SOLT calibration substrate, it can be seen that the baluns and pads cause ≈ 5 dB losses at the center frequency. The best matching of the baluns and pads is just below 120 GHz and below 20 dB.
The S-parameter measurements of the VM are performed for different fuse configurations. Up to three fuses can be removed. Therefore, four different measurement scenarios can be examined. However, since the center frequency is already below 110 GHz after removing two fuses, only three fuse configurations are discussed below. The branchline coupler's insertion loss cannot be subtracted from the S-parameter measurements since there is no back-to-back structure. Therefore, the subsequent plots focus on the S 21 -parameter because the

FIGURE 14. S 21 (dB) measurement results of the VM when one fuse is cut (compensated pad and balun losses).
S 11 -parameter is mainly determined by the branchline coupler, and the minimum of S 22 is strongly correlated with the maximum of S 21 .
Figs. 13 to 15 show the gain curves of the VM. When no fuse is removed, the center frequency is at ≈ 121 GHz. A maximum gain of 7.01 dB and a minimum gain of 0.03 dB is achieved at this frequency. When one laserfuse is removed from the inductive load, the center frequency drops, and is about ≈ 110 GHz. As already shown in Section III-B, four different gain curves are measured due to the IQ imbalance of the couplers.
The power consumption of the VM depends on the used state, i.e., on the number of active amplifiers. This results in 60 mW when all amplifiers are switched off, 145 mW when one amplifier is active and 225 mW when two amplifiers are active.
In phased-array applications, the phase differences between the antennas are important. While the absolute phase changes when fuses are removed, the phase difference stays nearly constant. Therefore, only the curve with no removed fuses is shown in Fig. 16. It can be seen that the phase curves are not equidistant to each other, as we saw with the simulation results.

B. CONSTELLATION DIAGRAM AT 125 GHZ AND CORRECTION TECHNIQUE
As seen in the previous Section, the coupler's influence is not negligible. Therefore, theoretical investigations are performed here to determine the coupler's influence on the measurement results. For this purpose, a circuit simulation (similar to Fig. 2) is performed using the coupler's simulation results and an ideal VM with the S-parameter matrix shown in (3).
Here, a 6 × 6 linear-scaled matrix is used to describe an ideal VM, according to the circuit diagram in Fig. 1, with its four input ports and two output ports. Because it's a theoretical investigation, the return loss of the four input ports  swapped entries. Each of the four theoretical amplifiers has the same gain, namely G I,Q .
For every VM phase state, one touchstone S-parameter file is created. Inside the Cadence Virtuoso circuit diagram, the S-parameter data from the Sonnet simulations and one of the eight ideal VM touchstone files are used. Therefore, eight harmonic balance based S-parameter simulations must be performed. Here, G I,Q is set to 1 (unity-gain). With the sonnet simulation results and (3), the vector v coupler is created, which contains only the non-ideal balun and branchline properties. Also, the vector v ideal is created, which contains the ideal results when perfect couplers are used. With perfect IQ signals and G I,Q = 1, the ideal vector is Now, the correction vector v corr can be created (cf. Eq 5). With the correction vector, the measured data will be adjusted to separate coupler imperfections from VM imperfections.
The gain correction with the back-to-back structure (cf. Fig. 11) is not applicable since the baluns would be compensated twice. Therefore, only pad losses can be removed. Based on an additional measurement with back-to-back RF pads, the pad losses are ≈ 1.5 dB at 125 GHz. Fig. 17 shows the constellation diagram. On the one hand, it contains the measured S-parameter data at 125 GHz from the previous Section, and on the other hand, the corrected values.
Here, the constellation points are arranged such as the RMS phase error is minimal. Therefore, state 1 is not aligned to 0 • .
The key parameters of the constellation diagram are listed in Table 1.
It can be seen that the measured gain decreases with each removed fuse. Furthermore, it can be seen that the correction method turns the constellation points in the right angular direction and corrects the IQ imbalance. The corrected values and especially their phases are now in very good agreement with the simulation results from Section III-C. Before the correction, the RMS deviations are ≈ 2.5 dB and ≈ 17 • , respectively. After correction, the values have improved to ≈ 1.2 dB and ≈ 7 • , respectively. By applying the correction method, the average gain drops by 0.29 dB because the measured pad losses and simulated coupler losses are lower than the measured losses of the back-to-back balun structure. Nevertheless, the corrected RMS values give a much better impression of the VM's performance and its usability in a radar system. In addition, now they fit well to the simulated RMS values (cf. Fig. 10).

C. COMPRESSION BEHAVIOR
Another aspect of a vector modulator is the compression behavior. To measure this, a slightly different VNA setup was used. This time, a Keysight extender (N5295AX03) with coaxial cables and a power sensor (Keysight U8489 A) are used. The calibration was performed up to 110 GHz. The recorded compression data are shown in Fig. 18.
At 110 GHz, the maximum gain is achieved with one cut fuse and is almost 10 dB, when I and Q are active. When two fuses are cut, ≈ 6 dB can be achieved, and ≈ 3 dB when no fuse is cut. The 1-dB input compression points are at −0.63 dBm, −1.74 dBm, and 0.45 dBm input power for the cases when no, one, or two fuses are removed. The compression points are plotted as vertical lines in Fig. 18.  area, power consumption, input compression point, control interface, and the RMS amplitude and phase error are compared. The column with the area data shows that some designs use a lot of area. For example, structures are used where couplers and PA stages alternate. When comparing the core area, the VM presented here performs competitively. Also, it stands out in terms of gain (7.01 dB at ≈ 121 GHz and 6.55 dB at 125 GHz). Therefore, the VM creates no losses compared to others. While some VMs generate more gain, they use additional PA stages, which are not necessary for the basic functionality of the VM. Nevertheless, they can keep the power dissipation low. When looking at the compression points, the presented VM achieves the second-highest value.

D. COMPARISON WITH OTHER D-BAND VECTOR MODULATORS
The comparison of RMS errors is a bit difficult since the other VMs use analog control voltages. With high-resolution DACs, it is possible to achieve high accuracy. This is not achievable with a digital approach since no analog retuning is possible. Nevertheless, deviations of 2.57 dB and 16.91 • or 1.27 dB and 7.12 • , after removing the coupler imperfections, can be achieved.

V. PHASED-ARRAY INVESTIGATIONS AT 125 GHZ
Nowadays, the concept of virtual antennas ensures that a large virtual array can be created with only a few physical Tx and Rx antennas. This means that the detection performance can exceed that of a phased-array system with the same number of antennas [70], [71]. However, the phased-array approach offers a distinct advantage. By combining the Tx antennas, the radiated power can be increased proportionally with the number of antennas. Phase-shifters are required for beam-steering, where accurate angular resolution is often desired.
The presented VM has only eight phase states with a phase difference of ≈ 45 • . The ninth state, where the VM is turned off, is not considered. Nevertheless, the VM can be used to perform finely resolved beam steering. In Fig. 19, the array factor is shown for three different scenarios where the antenna count N is 2, 4, or 6.
The antennas are arranged linearly at a spacing of λ/2, i.e., as a uniform linear array (ULA) at the locations r. The antennas are fed by identical VMs, which have the same  design parameters and, therefore, the same imperfections. The uncorrected and measured S-parameter data at 125 GHz in the form of linear amplitude A and the phase ψ are used (cf. Fig 17) to calculate the array factor according to (6) Here, k 0 is the wavenumber, and j is the imaginary number. For the elevation angle θ , a step size of θ = 2 • is used. The azimuth angle ϕ 0 is fixed at 0 • . All combinations m ∈ M for N antennas and S = 8 VM states are evaluated. In the simulation, the number of combinations increases exponentially and starts at M = N S = 2 8 = 256 for two antennas and increases to 1,679,616 for six antennas. Eq. (6) is used to calculate the array factor for the angle range from −90 • to 90 • for each combination. In Fig. 19, the maximum value and its angular position, i.e., the array factor of the main lobe, is entered as a point. All calculated main lobes (points) are removed that are 3 dB below the maximum at θ = 0 • to keep the plot readable. The beam-steering capabilities improve significantly with the number of antennas. With two antennas, the ≈ 45 • phase resolution is visible. But when increasing the antenna count to four antennas, the beam can be continuously steered in the whole angular spectrum. Increasing the number of antennas from four to six shows minor improvements in the variation of the array factor (< 2 dB).

VI. PHASE-CODED RADAR INVESTIGATIONS AT 125 GHZ
Besides FMCW radar, research on PMCW radar increases because it has improved interference properties [19], [73], [74], [75]. This is important in environments with many radar sensors, such as the automotive industry. However, this increases the effort for signal sampling and digital demodulation [17], [18].
The PMCW performance is simulated using RC parasitics and the coupler's S-parameter because the breakout MMIC has no mixer. We focus on the phase states I + Q and −I − Q as they have ≈ 180 • phase difference (cf. Sec. IV-B), and the same power consumption. The digital interface of the VM (D I , D Q ) is driven with a pseudo-noise bit sequence with a chip rate of B c = 0.25 GHz, and the output of the VM is connected to an ideal mixer with 10 dB conversion gain. The mixer and the VM share the same mono-frequent 125 GHz LO signal.   [18]. But, this leads to a reduction of the eye size and to signals that can no longer be detected properly.

VII. CONCLUSION
This article presented a 125 GHz SiGe-based vector modulator that is characterized by its simple digital interface, and by its high gain in the D-band of up to 10 dB at 110 GHz and up to 6.55 dB at 125 GHz. In comparison, most other VMs produce only losses in the D-band. In addition, a technique to isolate the coupler's imperfections was presented, which leads to an RMS phase error of 7.12 • , and an RMS amplitude error of 1.27 dB.
Besides the simulation and measurement results, its applicability in phased-array FMCW and phased-coded CW systems were also shown. A variance of the array factor of less than 2 dB was achieved while having full coverage of the elevation angle. Here, the measured S-parameter data and an ULA with six antennas were used. Even with only four antennas, very good coverage is achieved. In addition, the VM can also be used in a phase-coded system and operated with a modulation frequency of 0.25 GHz. For both types of operation, no DAC is needed, which reduces PCB size, power consumption, and the system's complexity and cost when large-scale arrays are used. These two modes are possible in addition to the classic TDM method without changing the hardware by fuses or a complete replacement.
Future research should focus on higher switching speeds to enhance the PMCW capabilities, and on investigating the DDMA properties. In summary, the VM adds significantly more flexibility to current radar systems to achieve the best possible detection accuracy in a wide range of environmental conditions.