Investigation of Coupling Mechanisms for Efficient High Power and Low Phase Noise E-Band Quadrature VCOs in 130nm SiGe

This article compares two SiGe Colpitts quadrature voltage-controlled oscillators (QVCO) with different coupling techniques in the low E-Band, intended to be used as signal sources for push-push frequency doublers. The first QVCO is based on a cross-coupled tail-current topology, while the second is based on a fundamental active coupling network. The cross-coupled QVCO has a center frequency of 64.3 GHz and a bandwidth of 2.5 GHz. This circuit realization provides up to 12.2 dBm output power per channel and has a power consumption of 385 mW, resulting in a dc-to-RF efficiency of 8.6%. The phase noise of this oscillator at 1 MHz offset frequency is as low as −105 dBc/Hz. The fundamentally coupled QVCO has a center frequency of 67 GHz with a bandwidth of 3.9 GHz. It provides 13.1 dBm output power per channel while consuming 410 mW of power, resulting in a dc-to-RF efficiency of 9.9%. The oscillator's phase noise at 1 MHz offset frequency is as low as −105.2 dBc/Hz. In addition to the presented circuits, this article introduces a method to measure the relative phase error of quadrature signals utilizing a vector network analyzer. This method is verified with measurements of the developed QVCOs.


I. INTRODUCTION
High-quality quadrature signals are needed for modern communication and sensing systems, like vector modulators [1], [2], [3], demodulators [4], or OFDM radar systems [5].In these systems, the phase is used to encode information.Thus, the quality of those signals is crucial for the systems' performance.
In contrast to this common use of quadrature signals, we intend to use quadrature signals to drive push-push frequency doublers to generate high-quality differential signals at high frequencies.This doubler architecture loses one of the input phases because of the frequency doubling mechanism of driving a common load with differential signals [6], [7].To generate a differential, frequency-doubled output signal, two separate doublers have to be fed with differential signal pairs that have a phase shift of 90 • between them, resulting in a 180 • phase shift of the output signals.This frequency doubler approach can be used to generate output signals with frequencies above the transit frequency f T of the used semiconductor technology [8], [9], [10].
Several solutions for generating wideband quadrature signals have been demonstrated in recent years.One often implemented method for quadrature signal generation is using passive couplers, like rat-race or Lange-couplers.As these passive couplers split the input signal into an in-phase (I) and a quadrature (Q) signal path, this solution introduces a reduction of the individual signal power by at least 3 dB.Furthermore, if differential quadrature signals are needed, designing and verifying these couplers can be challenging [11].
The second widely used solution to create wideband quadrature signals is a quadrature voltage-controlled oscillator (QVCO).In these circuits, an oscillator generates output signals with a 90 • phase difference.Most commonly coupled VCOs are used, where the oscillator cores of two identical VCOs are synchronized with a phase shift of 90 • .
Different coupling architectures have been demonstrated in the last years, like coupling at the second harmonic of the generated signal or fundamental coupling.Furthermore, quadrature oscillators can also be realized as ring oscillators where several oscillator cores are coupled [12].
Generating quadrature signals with coupled oscillators has multiple advantages.A quadrature VCO, realized by two coupled oscillators, can achieve a higher output power and a lower phase noise (PN) compared to a realization with a VCO and a coupler [13], [14], [15], [16].One disadvantage of this solution is the higher power consumption, as two oscillators are needed.
This work demonstrates two separate QVCOs with a center frequency ( f c ) of 64 GHz and 67 GHz, respectively.These QVCOs were developed to compare different coupling mechanisms of coupled oscillators to generate quadrature signals.The first of these QVCOs is based on cross-coupled current sources, while the second is based on active fundamental coupling between the oscillators.Both QVCOs achieve high output power, high efficiency, and good phase noise performance.
In [17], we introduced and demonstrated a 67 GHz quadrature VCO utilizing an active coupling network to couple two VCOs at their fundamental frequency, generating quadrature signals.This article is an extended version, highlighting the requirements of the developed quadrature VCO and comparing the original QVCO with a second QVCO implementation using a different coupling technique.In this article, we begin by evaluating the requirements for the implemented quadrature VCOs in Section II.Then we discuss the circuit implementation of two QVCOs (Section III) and the measurement setup used to obtain the measurement results (Section IV).Afterward, we analyze the measurement results and compare the implemented QVCOs with the state of the art in Section V.The article is concluded in Section VI.

II. CIRCUIT REQUIREMENTS
The phase and amplitude imbalance of quadrature signals play a significant role in the performance of communication systems [18], [19].However, to define requirements for the proposed quadrature VCO, the impact of phase and amplitude imbalances on the intended use case as a signal source for a frequency doubler was investigated in preceding simulations.A simulated 67 GHz to 134 GHz push-push frequency doubler, as depicted in Fig. 1, was used to perform this investigations.
To determine the required output power of the QVCOs, we simulated the influence of the total input power, i.e., the power of both coupled VCOs, on the differential output power at the doubled frequency of 134 GHz.The simulations were conducted at a temperature of 80 • C, using HICUM transistor models using ideal quadrature signals with 90 • phase between the input signals, generated by simulation ports with a differential impedance of 100 .The transmission lines in this simulation are based on wideband RLGC transmission models provided by the technology manufacturer and verified with EM simulation models using Sonnet 18.52.The microstrip transmission line L 1 with a length of 135 μm and a width of 8 μm achieves an inductance of 46.5 pH with a quality factor Q of 16.5.The output transmission line with a length of 95.5 μm and a width of 2.4 μm achieves an inductance of 47.1 pH with a quality factor of 13.1.All of these values are evaluated for the output frequency of 134 GHz.The results of the simulation of the input compression point and conversion gain can be seen in Fig. 2.
It is essential to drive the push-push doubler into saturation to generate a high output power at the doubled frequency.The conversion gain of this frequency doubler is negative for input powers up to −3.4 dBm and reaches its peak with a conversion gain of 2.6 dB at a total input power of 2 dBm.Even though the conversion gain drops below 0 dB for input powers of more than 9 dBm, the output power still rises up to total input powers of 15 dBm.
To evaluate the influence of the input phase on the output power and the harmonic rejection of this frequency doubler architecture, the simulated push-push doubler was driven by two sources with an output power of 12 dBm each, i.e., 15 dBm total input power, and an ideal phase difference of 90 • .This phase difference was varied from 60 • to 120 • in this simulation.The simulated output power and common-mode rejection is depicted in Fig. 3.This simulation shows, that the differential output power and common-mode rejection is best for an ideal quadrature phase of 90°.For non-ideal input phases the harmonic rejection is decreasing for higher absolute phase errors, resulting in a loss of available output power of around 1 dB for input phase errors of 30 • .At this input phase error the common-mode rejection is 0 dB, meaning the common-mode power at the output is as large as the differential output power.The harmonic rejection for the third to sixth harmonic (201 − 402 GHz) can be seen in Fig. 4. Furthermore, the rejection of the input signal at 67 GHz, i.e. the first harmonic rejection, is depicted in this figure as well.The rejection of the first harmonic is better than 65 dB for the investigated input phase range.
These results show a minor influence of phase error on the output power of this doubler architecture.Even phase errors of 35 • show only a reduction of the output power of 1 dB.On the other hand, the phase error greatly influences the harmonic rejection of this circuit.Especially the fourth harmonic is rejected by more than 90 dB for input phases of 90°.This can be attributed to the common-mode rejection of the differential frequency doubler, as the fourth harmonic of the input signal appears as a common-mode signal at the output of the doubler [20].Although the rejection of the fourth harmonic is heavily dependent on an ideal input phase, the harmonic rejection is still better than 20 dB for phase errors of up to 35 • .The sixth harmonic is the next relevant harmonic that can be generated at the output of this doubler architecture.The harmonic rejection of this signal is still better than 25 dB over the simulated range of input phases.
Concluding these simulation results, the requirements for the QVCOs were defined.The QVCOs were designed to generate an output power of at least 13 dBm, i.e., 10 dBm per differential VCO, so they can drive the frequency doubler into saturation and provide a high output power at the doubled frequency.Furthermore, the requirements for phase error were relaxed compared to those on a QVCO for communication systems.As the influence of the phase error on the output power of the frequency doubler is small for phase errors below 30 • , this value was set as the maximum acceptable phase error for the QVCOs.Although this error significantly impacts the harmonic rejection of the fourth harmonic of the input signal, more than 20 dB of suppression will still be sufficient for a high-quality output signal, for example for the use in a FMCW radar system [21].Furthermore, as this simulation was performed using ideal circuit elements, the rejection of higher harmonics, especially the fourth harmonic and sixth harmonic is likely to be higher in a real scenario due to the frequency dependent behaviour of the output network of the push-push frequency doubler.Additional low-pass filtering stages in the output network of the doubler can improve the rejection of higher harmonics even more.

III. QVCO IMPLEMENTATION
In recent years several different realizations of coupling structures to couple oscillators for generating quadrature signals were demonstrated.One of the most often used approaches is to superharmonically couple two oscillators with a phase shift of 180 • to generate a phase shift of 90 • at the fundamental frequency.Here a suitable circuit node has to be identified where a second harmonic signal is present and where the oscillator can be influenced to generate a stable coupling.In differential circuits, the common-mode nodes at the symmetry plane of the oscillator can be used at different locations, like the symmetry plane of a differential common-base output amplifier [22] or the symmetry plane at the current source of a differential oscillator [23], [24], [25], [26].
An alternative approach to couple oscillators for quadrature operation is, for example, using a coupling network at the oscillator's fundamental frequency.Different realizations have been demonstrated with both passive coupling networks [27], where the required phase shift is introduced by capacitive coupling, and also active coupling networks [28], [29], [30], where amplifiers shift the phase.
To compare different coupling mechanisms of quadrature VCOs, two QVCOs based on the same VCO circuit were realized.The proposed VCO is based on the well-known differential Colpitts architecture [31].Common-base amplifiers are used as output amplifiers for signal amplification and decoupling of the oscillator core from external influences, like load pulling by the measurement setup.To provide a reliable load for the output amplifiers, integrated 50 termination resistors R T were implemented on the MMIC directly placed at the output pads, which can be removed by cutting laser fuses F 1 .The VCO core is realized with a varactor diode C var , which can be tuned by applying a tuning voltage between 1-9 V, and a microstrip transmission line, which is used as the resonator inductor.The length of this transmission line can be extended by cutting laser fuses to shift the center frequency f c of the oscillator to lower frequencies.A current mirror with resistive emitter degeneration provides the bias current I 0 for the oscillators.
To achieve good phase noise performance, good efficiency and high output power, the signal transistors T 3 and T 4 are biased close to their respective optimal emitter current density for maximum transit frequency.For the common-base amplifier transistors T 4 three parallel transistors with a length l of 10 μm and an effective width w eff of 130 nm in a CBEBC configuration, with each transistor having two base and two collector contacts, were chosen.For the oscillation transistor T 3 two parallel transistors with a length l of 8 μm and an effective width w eff of 130 nm with a CBEBEBC contact configuration were chosen.This configuration was chosen because of its increased number of base contacts, reducing the effective base resistance of the transistor, resulting in an improved phase noise.As this transistor also has an increased number of emitter contacts compared to T 4 , they operate at a similar effective emitter current despite the size difference, as the effective emitter area of both transistors is similar.To achieve a high efficiency with this circuits, we mainly used inductive circuit elements, realized by microstrip transmission lines, to implement the output network and the degeneration inductors connecting the oscillator core to the current source.The inductors for the degeneration were carefully tuned to maximize the achievable tuning range of the oscillator.
Two static divide-by-16 frequency dividers are placed on the MMIC for measurement purposes.As these are only used for measurement, they have a separate supply voltage and are not included in the power consumption measurements described in Section IV.A photograph of one of the two MMICs is depicted in Fig. 5.
The measurement MMIC has a size of 1900 × 1900 μm and consists of the respective realization of quadrature VCO and the two frequency dividers for characterization purposes.
We used Infineons B11HFC SiGe:C BiCMOS technology to realize the developed circuits [32].This technology offers devices with a f T of 250 GHz and f max of 370 GHz, RF-MIM capacitors and RF-TAN resistors.Furthermore, the manufacturer offers a metal stack consisting of six copper layers and one aluminum layer used for laser fuses and pads.

A. SUPERHARMONICALLY COUPLED QVCO (QVCO 1)
The first of the two implemented quadrature VCOs is based on the concept of a cross-coupled-pair [33], [34], [35], where a signal in one half of the cross-coupled-pair introduces an inverted signal in the other half of the cross-coupled-pair.Applying this concept to a coupling mechanism for quadrature VCOs, the common-mode current i 1 at the second harmonic of the oscillator, generated at the common-mode circuit nodes of the differential VCO, is used to introduce a 180 • phase shifted current i 2 into the second oscillator.As the phase of the second harmonic of the oscillators is shifted by 180 • , the phase of the fundamental frequency of the two VCOs has to be shifted by 90 • .This concept can be applied at every common-mode node of the differential circuits.However, we chose the common current source node at the end of the degeneration transmission lines, as with this concept, the current mirrors that set the dc-current and bias point for the oscillators can also be utilized for the coupling of the VCOs.Furthermore, this means that the circuit layout of the manufactured QVCO 1 can utilize two symmetry planes, improving the device matching between the oscillators.One additional advantage of the coupling at this circuit node is that the coupling does not lead to any additional power consumption of the QVCO compared to two individual, uncoupled VCOs.A schematic of the cross-coupled current mirror coupling concept is depicted in Fig. 6.
The coupling capacitors C 1 and C 2 are used to feed the common-mode current i 1 at the second harmonic frequency of one oscillator to the current mirror of the other oscillator, where a 180 • phase shifted current i 2 at the second harmonic is generated.This 180 • phase shift at the common-mode nodes of the oscillators leads to a 90 • phase shift at the fundamental frequency of the VCO.
The performance of this type of implementation of quadrature VCOs relies on the matching between the two VCOs.Therefore, the layout of QVCO 1 was realized with two symmetry planes for the best possible performance.Linear symmetry is utilized between the two halves of the differential VCO, as well as between the two individual VCOs forming the presented QVCO 1.For the circuit layout of the crosscoupled current mirrors point symmetry was utilized.
The manufactured layout of QVCO 1, utilizing the crosscoupled current source coupling mechanism, is shown in Fig. 5.The QVCO itself has a size of 295 × 1400 μm.The complete schematic of the implemented superharmonically coupled QVCO can be seen in Fig. 7.

B. FUNDAMENTALLY COUPLED QVCO WITH ACTIVE COUPLING NETWORK (QVCO 2)
The fundamentally coupled QVCO 2 with an active coupling network is the second implemented coupling mechanism.In contrast to the coupling concept described in Section III-A, where the oscillators are coupled at the second harmonic of the VCO, this concept directly couples the two oscillators at the fundamental frequency.
To fundamentally couple two of these oscillators into one quadrature oscillator, a coupling network (CN) must be implemented to introduce the 90 • phase shift necessary for quadrature operation.The low pass characteristic of the current gain of a common-emitter amplifier T 1 is used to create this phase shift.
The current gain β( jω) is nearly equal to β 0 for frequencies ω ω β .The current gain is lowered for frequencies above ω β , which corresponds to a first-order low pass.For higher frequencies, the current gain has an imaginary part.For frequencies ω ω β the common-emitter current gain can be simplified to For these frequencies, the imaginary part of the current gain dominates, corresponding to a 90 • phase shift between the base and emitter-collector current of the common-emitter amplifier.This phase shift can be used to create the coupling between the two VCO cores of the QVCO.To achieve efficient coupling, a solution was developed to couple the cores of the two oscillators directly at the varactor diode instead of coupling the oscillators' output signals.As this oscillator node is highly susceptible to external influences, only a minimal coupling current is needed to couple the two oscillators.This solution requires an additional current of only 3.2 mA for quadrature operation.
A schematic diagram of the implemented coupling network, including the phases of the currents passing through this coupling network, is depicted in Fig. 8.The complete schematic of QVCO 2 based on this coupling mechanism, including a circuit block depicting the coupling network consisting of four coupling paths, can be seen in Fig. 9.
As it proved impossible to directly couple the cores of the two oscillators next to each other while still using a symmetric differential circuit layout, the half-wavelength microstrip line L 1 was used to connect the two oscillator cores.The emitterfollower amplifier T 2 was used to decouple the varactor from the long transmission line, as it otherwise would have significantly lowered the achievable bandwidth of the oscillators.
The performance of this type of implementation of quadrature VCOs also relies on the matching between the two VCOs.Therefore, the layout of QVCO 2 was also realized with two symmetry planes for the best possible performance.Linear symmetry was utilized between the two halves of the differential oscillator and between the two differential VCOs forming the presented QVCO 2. Because of this symmetry the coupling lines L 1 of QVCO 2 have multiple crossings to connect the correct circuit nodes of the VCO cores to each other.
The coupling of this QVCO implementation can be interpreted as a coupling concept forming a closed loop.A voltage at circuit node A leads to an introduction of a current with 270°phase difference to the original voltage at circuit node C. The voltage at node C is introducing a phase shifted current into circuit node B. This concept is completed by circuit node

B driving node D and node D introducing a current into circuit node A, which results in a closed loop.
A photograph of the realized fundamentally coupled QVCO 2, which has a size of 620 × 1400 μm, can be seen in Fig. 10.

IV. MEASUREMENT SETUP
The experimental results, which will be discussed in Section V, are composed of three separate measurements, as described in [17].
The phase noise of the presented oscillator was determined in the first measurement.The phase noise of the QVCOs was measured using a Rohde & Schwarz FSWP phase noise analyzer (PNA) at the output of the divide-by-16 frequency divider with an offset frequency f of 1 MHz.These measurement results were corrected by 24.1 dB to compensate for the frequency translation of the frequency divider.
The output power of the QVCOs was measured using an Agilent E4418B power meter (PM) with a corresponding V8486 A waveguide power sensor at one of the four output pads.At this output pad, the integrated 50 termination was removed by cutting a laser fuse to measure the output power with a 50 interface.All other terminations were left in place to load the outputs of the VCOs evenly.
The measurement of the phase of the output signals was conducted with a Keysight PNA-X vector network analyzer (VNA).The four input ports of the network analyzer were SOLT calibrated on a calibration substrate.The output signals were disabled to use the VNA as a 4-channel receiver, measuring the incoming waves b 1 to b 4 .One of the input signals (b 1 ) was configured as a reference signal I and the phase of the other signals Q, I and Q were referenced to this input signal.On the network analyzer, two simultaneous measurements were conducted on two separate measurement channels to perform the relative phase measurement.On a spectrum analyzer channel, the output spectrum of the oscillator was measured, and the fundamental frequency of the VCO was determined with a tracking marker.On a second channel, set up as a network analyzer channel, three individual traces Tr 1, Tr 3 and Tr 4, were used to determine the phase of the incoming waves b 2 to b 4 in relation to the common wave b 1 .As the markers on all four traces in this measurement setup were coupled, the relative phase of the incoming waves could be evaluated at the fundamental frequency of the QVCOs.
A screenshot of this setup during an actual measurement of one of the QVCOs is depicted in Fig. 11.In the bottom of this screenshot, the spectrum analysis of one of the input signals is depicted.In the top of this figure the relative phase measurement is shown.The y-axis of this measurement graph is only valid for the trace named Tr 3. The other traces Tr 1 and Tr 4 were offset for better visualization of the measurement data.The coupled markers in this measurement determine the  relative phase of the traced signal at the frequeny determined in the spectrum analysis, in relation to the incoming signal b 1 .In the measurement list at the top of this figure, a good agreement between the theoretical values of relative phases of 90 • , 180 • and 270 • and the actual measurements can be identified, verifying this measurement setup.

V. EXPERIMENTAL RESULTS
The experimental results obtained using the measurement setups described in Section IV are discussed in this Section.
Although Colpitts VCOs typically show much larger relative tuning ranges (rTR) in this technology [31], this VCO is limited by the intended application as a QVCO.As the coupling networks achieve coupling for quadrature operation for different tuning ranges, these frequency ranges are considered for the following discussions.The coupling of the oscillators is considered successful if the phase error of the measured output signals is below 30 • , as described in Section II.Without the frequency limitation mentioned earlier, the VCO generates an output signal with a frequency between 59.3-68.9GHz with a differential output power ranging from 10.5 to 13.1 dBm per channel.

A. SUPERHARMONICALLY COUPLED QVCO (QVCO 1)
In Fig. 12, the measured (solid lines) and simulated (dashed lines) output power and phase noise, measured at an offset frequency f of 1 MHz, of one differential channel of the superharmonically coupled QVCO is depicted for tuning voltage between 2.5-3.7 V.The differential power is depicted in black and the phase noise is given in red lines.
It can be seen that the superharmonically coupled QVCO 1 can be operated between 63.1-65.5 GHz achieving a flat output power between 10.5-12.2dBm.The phase noise, measured with an offset frequency f of 1 MHz, reaches a minimum value of −105 dBc/Hz.The phase noise is better than −103 dBc/Hz for the entire usable bandwidth.
Comparing the measurement results of this QVCO implementation to the simulation results of the same circuit, a good agreement between the two results can be seen for the output power as well as the phase noise.The simulated results were obtained using HICUM transistor models to achieve results that represent the measured circuit as close as possible.In these results a small deviation of max.1.82 dB in output power and 1.46 dB the phase noise performance was achieved.The current consumption of the QVCO 1 is 77 mA from a single 5 V supply.Considering these measurement results, a dc-to-RF efficiency of up to 8.6% can be determined.In Fig. 13, the measurement (solid lines) and simulation (dashed lines) results of the superharmonically coupled QV-COs' output phase errors, the deviation from ideal quadrature phase of 90 • , are given.The measured phase error When comparing the measurement and simulation results, it is apparent that the phase error in simulation is much lower than in the measurement results.This can be explained in part by the inaccuracy introduced by the measurement setup, explained in detail in Section V-C.Furthermore, the simulation was done without EM-simulation of the complete QVCO cell, because of the amount of simulation complexity and the resulting very long simulation time for this cell.Especially increased capacitive loading of the coupling node, introduced by parasitic capacitors between the circuit elements forming the QVCO cell and neighboring metal structures can lead to a deterioration of signal amplitude at the second harmonic at the coupling nodes, leading to a lower coupling factor between the individual VCOs.This in return can lead to a lower usable frequency range, where the QVCO is locking itself into quadrature operation, and an increased phase error.Furthermore, as the cross-coupled current mirror used as a current source in this circuit is also used as a differential amplifier for the second harmonic signal, it could be that the gain of this amplifier is not high enough at this frequency, due to parasitic capacitors, which results in an increased phase error compared to the simulation results.

B. FUNDAMENTALLY COUPLED WITH ACTIVE COUPLING (QVCO 2)
The fundamentally coupled QVCO 2 with an active coupling network can be used in the frequency range of 65-68.9GHz, providing a differential output power between 11.7-13.1 dBm.The measured phase noise in this frequency range, evaluated at an offset frequency of 1 MHz, is below −102.3 dBc/Hz for the entire tuning range, with a minimum value of −105.2 dBc/Hz at a frequency of 67 GHz.These measurement results can be seen in Fig. 12 depicted in blue and green lines.
Comparing the measurement results of QVCO 2 to the simulation results of the same circuit, a good agreement between the two results can be seen for the output power as well as the phase noise.In these results a small deviation of max.0.86 dB in output power and a deviation of around 1.72 dB the phase noise performance was achieved.
The current consumption of this QVCO implementation is 82 mA from a single 5 V supply.Considering these measurement results, a dc-to-RF efficiency of up to 9.9% can be determined for this quadrature VCO.
The measured relative phase errors of QVCO 2 are depicted in Fig. 14.The frequency range for quadrature operation, where the phase error compared to the ideal phase of 90 • is below 30 • , is between 65-68.9GHz.The phase error in this frequency range is 0.2 • −11.8 • .
When comparing these measurement results to the simulation results, it is apparent that the phase error in simulation is much lower than in the measurement results for this QVCO implementation as well.Again, this can be explained in part by the inaccuracy introduced by the measurement setup, explained in detail in Section V-C.Furthermore, the simulation was done without EM-simulation of the complete QVCO cell, because of the amount of simulation complexity and the resulting very long simulation time for this cell.Especially the length of the coupling transmission lines L 1 is critical for the performance of the cell and every crossing and turn introduces errors in electrical length for this transmission line.Because of this, for the highest agreement between simulation model and physical model, a complete EM simulation of at least the oscillator cores and the coupling network would be advised.But this results in a simulation model model of at least 600 μm × 800 μm resulting in a very large simulation model which leads to impracticable simulation times.Therefore, we simulated this cell with the given transmission line models of the PDK provided by the manufacturer.These models are based on RLGC modeling of the microstrip transmission lines.Furthermore, the idea of a coupling concept which is based on the length of a transmission line is inherently frequency limited, as the frequency shift of this transmission line is frequency dependent.As the implemented concept forms a closed loop, this phase error introduced by the non-ideal length of the transmission line for frequencies deviating from the target frequency is cancelled, as the closed loop should force the coupling at 90°.As the measured phase error is seams to be decreasing towards higher frequencies, it seems to suggest, that the length of the transmission line is too short for the intended frequency range, thus shifting the frequency range for quadrature operation towards higher frequencies.As we can not shift the frequency of the oscillator to higher frequencies after manufacturing and there are also no laser fuses in the coupling lines to lengthen the lines after manufacturing, we currently can not confirm this assumption in this hardware revision, and will investigate this further in the future.

C. COMPARISON OF THE PROPOSED COUPLING CONCEPTS
When comparing both coupling concepts, it is apparent that both circuits perform almost the same regarding phase noise and output power.This is because both circuits are based on the same Colpitts VCO design and only differ in the coupling concept.The slight difference of around 1 dB in output power can be attributed to the slightly different frequency range measured and minor differences in the measurement setup, The slight difference in output power and the difference in current consumption of around 5 mA lead to a reduction in dc-to-RF efficiency from 9.9% for the fundamentally coupled QVCO 2 to 8.6% for the superharmonically coupled QVCO 1.The higher current consumption of the fundamentally coupled QVCO 2 is based on the coupling network's additional current injected into the VCO cores.
Another benefit of the fundamentally coupled QVCO 2 concept is the generation of unambiguous phase positions.Using the superharmonically coupled QVCO 1, the second harmonic of the fundamental frequency of the oscillator is coupled by 180 • , shifting the harmonic frequency by ±90 • .This phase ambiguity is irrelevant for the use case in combination with a frequency doubler.However, it must be considered when designing a QVCO for use cases like communication, as the relation of the output phases is random at every oscillator startup.
To evaluate the phase error and to determine if the error is given by the circuit or introduced by the measurement, the phase of the differential signals I − I and Q − Q can be evaluated for both relative phase measurements.Due to the differential circuitry and the use of symmetric circuit layouts, the differential signals I and I as well as Q and Q have to show a phase shift of 180°to each other.In turn it can be assumed, that any deviation of this phase shift of 180°can be attributed to influences by the measurement setup.When looking at the example measurement depicted in Fig. 11, a phase error of 2.68°between I and I and an error of 1.32°between Q and Q was determined for this measurement.To evaluate the overall measurement uncertainty of the used measurement setups for QVCO 1 and QVCO 2, the maximum deviation from the ideal 180°phase between the differential signals was evaluated for each investigated output frequency of the QVCOs.It can be determined that the maximum measurement uncertainty in the investigated frequency range is ≤ 5.1 • for the fundamentally coupled QVCO 2 and ≤ 4.95 • for the superharmonically coupled circuit (QVCO 1).
This could be explained by the fact that the measurement probes needed to be moved after the SOLT calibration, as the distance of the opposite pads on the MMIC differs from the distance between the pads on the calibration substrate.Although cables with a high phase stability were used, this error could be introduced by the movement of the probes as 1 • of phase difference corresponds to a positioning error of just 12.4 μm.
To evaluate the measurements of VCOs, several figures of merit (FoMs) can be found in the literature.For bipolar Colpitts VCOs the following FoM VCO−PA is most widely used [43], as this FoM includes the output power of the evaluated oscillator: As parasitic effects limit the relative frequency tuning range of mmWave oscillators, an additional FoM VCO−T was introduced that includes the relative tuning range of the evaluated oscillator, but omits the output power of the circuit: To include both, the tuning range and the output power into a single FoM, the figures of merit FoM VCO−T and FoM VCO−PA , as defined in [43], can be combined to result in a new figure of merit FoM VCO−PAT , as descibed in [44]: QVCOs typically exhibit a higher power consumption than VCOs but reach a higher output power because the in-phase and quadrature output power must be considered.Because of this, the FoM has to be calculated for the total MMIC output power and total power consumption of the chip.Furthermore, for quadrature VCOs the relative frequency tuning range of the circuits is limited to the frequency range, where quadrature operation can be verified.
In Table 1, the results of a comparison of the presented QV-COs to state-of-the-art silicon VCOs and QVCOs are given.For a better comparison of the underlying VCO design, the given output power is defined as the differential output power of one VCO.For QVCOs, the output power has to be doubled (i.e.+ 3 dB) to represent the total output power.
Both implemented circuits achieve high dc-to-RF efficiencies of more than 8.6% and output powers of more than 12.2 dBm, with up to 13.1 dBm peak output power for the fundamentally coupled QVCO 2. In combination with the low minimum phase noise of less than −105 dBc/Hz for both circuits, the FoM VCO−PAT for these QVCO implementation reach values of −181.22 dBc/Hz and −186.15dBc/Hz, respectively.
Comparing the measured phase error with the state of the art, it is apparent, that the presented QVCOs do not reach values of below 5°as some of the other QVCOs in the comparison table.When comparing the output power of these QVCOs, it can be seen, that these reach output powers of max.−1.5 dBm, which is almost 15 dB lower, than the presented circuits.When comparing the presented circuit with one with comparable output power, as given in [22], it can be seen, that the presented circuits reach similar phase error values.

VI. CONCLUSION
This work presents two high-power and efficient quadrature SiGe VCOs in the E-Band.These QVCOs are implemented using two different coupling techniques, and the performance of both implementations is compared to each other and the state of the art in silicon VCO designs.As these QVCOs are designed to be used in combination with push-push frequency doublers for high-frequency differential signal generation, the requirements on the circuits' performance, especially on the output power and phase error, differ from the requirements on traditional use cases for quadrature signal generation, like communication systems.
In this work two approaches for coupling VCOs for quadrature signal generation are presented and compared to each other and with the state of the art.
The first presented QVCO is based on a concept of crosscoupled current sources.These introduce a phase shift of 180°a t the second harmonic, achieving a phase shift of 90°at the targeted output frequency.This QVCO implementation achieves an output power of 10.5-13.1 dBm in a frequency range from 63.2 GHz to 65.5 GHz with a dc-to-RF efficiency of up to 8.6 %.The measured phase error of this circuit ranges from 4.8 • to 25.1 • .This QVCO circuit achieves a phase noise between −103 dBc/Hz and −105 dBc/Hz for an offset frequency f of 1 MHz and a FoM VCO−PAT of −181.2 dBc/Hz.
The second concept is a fundamental coupling concept directly coupling the cores of two identical VCOs.It is based on the phase shift caused by the low pass characteristic of the current gain of common-emitter amplifiers introducing the 90°phase shift between the outputs of the oscillators.This fundamentally coupled QVCO achieves an output power of 11.7-13.1 dBm in a frequency range from 65 GHz to 68.9 GHz with a dc-to-RF efficiency of up to 9.9 %.The measured phase error of this circuit ranges from 0.2 • to 11.8 • .This QVCO circuit achieves a phase noise between −102.3 dBc/Hz and −105.2 dBc/Hz for an offset frequency f of 1 MHz and a FoM VCO−PAT of −186.2 dBc/Hz.In addition to the presentation of two coupling concepts for QVCOs and the demonstration of these concepts, this article also details a novel measurement setup using a vector network analyzer as a multi-channel receiver for the measurement of the relative output phases of QVCOs.This measurement setup was successfully demonstrated by the characterization of the presented quadrature oscillators.

FIGURE 1 .
FIGURE 1. Schematic of differential frequency doubler based on push-push architecture, driven by quadrature signals.

FIGURE 2 .FIGURE 3 .
FIGURE 2. Simulated differential output power and conversion gain of two push-push frequency doublers driven by ideal 67 GHz quadrature signals, depending on input power.

FIGURE 4 .
FIGURE 4. Simulated harmonic rejection of two push-push frequency doublers driven by 67 GHz (1st Harmonic) quadrature signals providing 15 dBm of input power, depending on input phase.

FIGURE 5 .
FIGURE 5. Photograph of one of the realized quadrature VCO MMICs, containing the superharmonically coupled QVCO 1 implementation and two frequency dividers for measurement purposes.

FIGURE 6 .
FIGURE 6.Schematic of the cross-coupled current mirror coupling concept.

FIGURE 9 .
FIGURE 9. Schematic of the proposed fundamentally coupled QVCO 2. Circuit nodes with the same color and designator are connected to each other.

FIGURE 11 .
FIGURE 11.Screenshot of the PNA-X network analyzer during a relative phase measurement of the fundamentally coupled QVCO 2.

FIGURE 12 .
FIGURE 12. Measured and simulated output power and phase noise of the realized superharmonically coupled QVCO (QVCO 1), depicted in black and red, and the fundamentally coupled QVCO (QVCO 2), depicted in blue and green.Simulated curves are given in dashed lines, measurement results are depicted in solid lines.Phase noise measurement and simulation data is evaluated at an offset frequency f of 1 MHz.

FIGURE 13 .
FIGURE 13.Simulated and measured output phase errors of the superharmonically coupled QVCO 1. Simulation results are depicted in dashed lines and measurement results are given in solid lines.

FIGURE 14 .
FIGURE 14. Simulated and measured output phase errors of the fundamentally coupled QVCO 2. Simulation results are depicted in dashed lines and measurement results are given in solid lines.

TABLE 1 . Comparison of State-of-the-Art VCOs and QVCOs in Silicon Technologies like
misalignment or slightly higher contact resistance of the probe.