1. Introduction

Millimeter-wave (mm-Wave) automotive radar systems are one of the essential enabling technologies in autonomous vehicles. Thanks to smaller wavelength and smaller antenna size, 77-GHz automotive radars attract much attention over the latest decade^[1-3]. These systems call for high-quality and power-efficient local oscillators (LOs). However, mm-Wave voltage-controlled oscillators (VCOs) suffer from limited tuning range and poor spectral purity due to low-Q inductors and low-capacitance-ratio varactors. As summarized in Fig. 1, the phase noise performance of recent-published mm-VCOs degrades by 24 dB from 20 to 80 GHz, which is much larger than the theoretical degradation value of 12 dB. To obtain low phase noise and wide tuning range LOs, lower frequency oscillators with their output multiplied up to the desired frequency are preferred. Therefore, a synthesizer architecture with a PLL embedded with a 20-GHz VCO, followed by frequency quadrupler is utilized to generate E-band LO signals, as shown in Fig. 2. To ensure the overall performance of the synthesizer, the quadrupler is required to be wideband, while providing high output power and robust operation. In addition, the quadrupler must suppress unwanted harmonics with low power consumption.

Fig. 1.  (Color online) Phase noise performance of recent-published VCOs at 1 MHz.

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Fig. 2.  The architecture of the proposed E-band frequency synthesizer.

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To build a frequency quadrupler, both the linear superposition technique^[8] and the direct ×4 nonlinear class-B/C stages^[9] can be employed. However, these techniques provide limited output power of the 4th harmonic. Besides, they usually rely on the accuracy of device modeling and are sensitive to process variations. Injection-locked^{[10, 11]} and single-stage phase-controlled push–push frequency quadruplers^[12] occupy compact chip area. Nevertheless, these techniques require additional buffer amplifiers due to the low conversion gain. Thus, cascading frequency doublers are preferred.

To address the above challenges, this paper introduces an E-band frequency quadrupler utilizing two push–push frequency doublers, achieving 1.7-dBm output power and over 45 dB fundamental suppression. As an extension of Ref. [13], this paper presents an in-depth analysis of the frequency quadrupler, which guides the design and optimization.

2. Design considerations

The nonlinearity of a class-B biased transistor can be employed to generate strong harmonic contents, which naturally forms a frequency multiplier. Researches on single-ended frequency doubler are mainly focused on extracting the 2nd harmonic by resonating the LC output tanks, and employing the transmission line based quarter-wavelength open stub to suppress the fundamental signal. However, the operation bandwidth is usually narrow, and the fundamental suppression is sensitive to the output frequency. Meanwhile, higher output power can be obtained via the differential swing in a balanced design. Thus, push–push topology^[14-16] is considered. As shown in Fig. 3(a), the class-B biased pair (M₁ and M₂) generates in-phase 2nd-harmonic (2f₀) signals and the phase-shifted fundamental (f₀) signals. The two 2f₀ signals are added while the f₀ signals are cancelled by each other at the combined drain. Thus, the balanced topology has the advantage of achieving wideband fundamental and high odd-harmonic suppression without using resonator tanks.

Fig. 3.  The topology of (a) push-push doubler and (b) cascode structure.

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On the basis of the push–push topology, a cascode device (M₃) is added, as shown in Fig. 3(b). It not only amplifies the 2f₀ component from the combined drain, but also reduces the Miller effect of M₁ and M₂, resulting in a higher gain-bandwidth product of the transistor. To meet the requirement of the output power, 16-μm devices are employed for the doubler pair. However, the addition of the M₃ decreases the drain voltage of the push–push pair. With a 1-V supply, the combined drain voltage decreases to 500 mV or below with a higher input power, leading to a deteriorated generation of 2f₀ component. As a trade-off between conversion gain (CG) and power consumption, the supply voltage of the cascode doubler is raised to 1.5 V. Meanwhile, the size of M₃ also influences the generation of 2f₀ component. Fig. 4 depicts the output power and CG at 77 GHz with the size of M₃ equals to 16, 24, 32, and 40 μm, respectively. It indicates that larger M₃ provides lower V_GS, raising the voltage of the combined drain, which further enhances CG. The maximum output power and conversion gain improvement gradually saturated when the size exceeds 32 μm, achieving a maximum output of –1.15 dBm with a peak CG of 1.2 dB from a 1.5-V supply. Moreover, the performance of the push–push one is also compared, which obtains a saturation power of 1.2 dBm with a limited CG of –1.5 dB. Hence, taking output power, conversion gain, reverse isolation and power consumption into consideration, the cascode topology is adopted, while a 32-μm cascode device is selected for the best performance.

Fig. 4.  (Color online) The simulation results of (a) output power and (b) conversion gain at 77-GHz.

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As indicated in Fig. 4(a), the output power of the 2nd harmonic decreases when the input signal sweeps from 0 to 5 dBm. To address this issue, the drain current of the doubler pair is analyzed. Fig. 5 plots the drain current transient waveform of M₁. With different input power (–5 and –1 dBm) and bias condition (200 and 400 mV), the operating state of the doubler pair changes, which influences the generation of the 2nd harmonic. In Fig. 5, I_max represents the maximum drain current, τ is the length of the pulse, and T is the period of the fundamental frequency. The even harmonic components at the combined drain node are controlled by the input power and the gate bias voltage. Besides, each even harmonic has a clear maximum below τ/T = 0.5^[17]. The simulated results of output power and conversion gain with the bias of 200, 250, 300, 350 and 400 mV are plotted in Fig. 6. When the input power increases to 0 dBm, I_max and the conduction duty cycle (τ/T) raises, which enhances the 2nd harmonic (see Fig. 6(a)). When increasing the input power to 5 dBm, I_max improves but τ/T becomes a bottleneck, resulting in reduction of 2nd harmonic. Meanwhile, the bias condition also influences I_max and τ/T, as indicated in Fig. 5. With a –1-dBm input, a bias of 400 mV provides higher I_max (see Fig. 5 solid-blue), while a bias of 200 mV achieves enhanced output power (see Fig. 6(a) black). Fig. 6 also suggests that a lower bias condition delivers 1.3 dB higher saturation power, while a higher bias offers compelling conversion gain. Consequently, taking dc power into account, 300 mV is the optimal choice.

Fig. 5.  (Color online) The drain current of M₁ with different input power and bias voltage.

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Fig. 6.  (Color online) The simulation results of (a) output power and (b) conversion gain at 77-GHz with different bias.

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3. Circuit implementation

The block diagram of the proposed frequency quadrupler is depicted in Fig. 7(a). Two single-stage power amplifiers (PAs) are implemented following each frequency doubler to compensate for loss. The inter-stage PA is designed to drive the second doubler into saturation and reduce the fundamental leakage from the first doubler, so as to avoid the intermixing of f₀ and 2f₀ components at the second doubler. Furthermore, each transformer is carefully optimized, so that sufficient bandwidth and high harmonic suppression can be ensured.

Fig. 7.  (a) The block diagram of the proposed frequency quadrupler. The schematic of (b) frequency doubler and (c) power amplifier.

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3.1 Frequency doubler and power amplifier

The push–push topology with cascode device is adopted, as shown in Fig. 7(b). The bias voltage (V_B1) is set to300 mV, as the optimal bias condition discussed in section 2. Therefore, the doublers produce strong harmonics and high conversion gain with low dc current. The two doublers consume 18 mW from a 1.5-V supply at 0 dBm input power. Besides, decoupling capacitors (C₂ and C₃) are implemented at both the gate and the drain terminals of the cascode device, so as to reduce the loss of single-ended-to-differential transformation.

Fig. 7(c) depicts the schematic of the power amplifier. Neutralization technique^[18] is applied to build PAs at 38.5 and 77 GHz. The interdigitated metal-oxide-metal capacitor C_neu is cross connected between the drain and the gate of the differential pair (M₄ and M₅). This method reinforces the unconditional stability and gain without additional cost of power dissipation. With a 7.4-fF neutralization capacitor and a V_B2 of 550 mV, the two PAs consume 16 mW from a 1-V supply at 0 dBm input power. Moreover, impedance matching is performed in this work, which provides higher gain and further enhances power efficiency. The two single-stage PAs offer a power gain of 13 and 8 dB, respectively.

3.2 Optimization of matching networks

In the proposed circuit, all inter-stage and output matching networks (T_1–5) are transformer-based resonators^[19]. Meanwhile, the transformer can be used as a balun to covert a single-ended signal to a differential one. Ultra-thick metal M8 and M9 are used to form all the transformers. As a trade-off among conductor resistance, Q factor and chip area, the coil width of all the transformers is designed between 3 and 4 μm.

Biasing at class-B leads to an input impedance of 432-j×1190 Ω and 133-j×610 Ω of the push–push pairs, respectively. Such a large inductance makes it challenging to perform impedance matching. Direct matching results in large inductance of each coil up to around 2 nH, which brings large insertion loss and occupies sizable area. Therefore, C₁ is added to the input matching network (see Fig. 7(b)). Large C₁ is attractive to reduce the inductance of the coils, but contributes to a narrow matching bandwidth. Thus, a trade-off should be made between conductor resistance and matching bandwidth. After optimization, C₁ is set to 60 and 22 fF for each doubler. Meanwhile, T₁ and T₃ are designed highly symmetrical to ensure odd harmonics cancellation at the combined drain, so as to improve odd harmonic rejection. The secondary coils are center-tapped in order to easily bias the gate of the doublers.

T₂ and T₄ are carefully designed at 38.5 and 77 GHz to ensure low loss and high harmonics suppression simultaneously. The primary coil of the transformer resonates with the drain capacitance of cascade device, while the secondary coil resonates with the differential input capacitance of the following amplifier. Therefore, T₂ and T₄ are used to convert the common-mode second harmonic current of the doubler to the differential output voltage. To reduce fundamental leakage, T₂ is designed narrow-band at 38.5 GHz. Moreover, to cover the whole radar bandwidth (i.e., 76–81 GHz), weakly-coupled transformer is adopted to design T₄. The transformer’s coupling coefficient (k) determines the transfer function of the coupled resonators. Fig. 8 depicts the transimpedance Z₂₁ and S₂₁ of T₄. On the one hand, a lower k flattens the response and in return introduces an insertion loss of over −8 dB. On the other hand, a higher k introduces less insertion loss as the expense of enlarged ripple. To guarantee wideband matching and strong output power of 4th harmonic, a k of 0.35 was chosen. Based on EM simulation, T₂ is implemented as a two-turn transformer with 28.1- and 23.5-μm inner radius, realizing 581 and 525 pH at 38.5 GHz. T₄ is implemented as a center-tapped one-turn transformer with 31- and 23.5-μm inner radius, realizing 164 and 152 pH at 77 GHz. Fig. 9 depicts the layout of the two transformers.

Fig. 8.  (Color online) (a) Z₂₁ and (b) S₂₁ of T₄ with different k.

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Fig. 9.  The layouts of (a) T₂ and (b) T₄.

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To further enhance harmonic suppression, T₅ is designed as a bandpass filter, especially to suppress the 2f₀ component. Fig. 10 depicts the equivalent circuit model of T₅. L₁ and L₂ form a strongly-coupled center-tapped transformer, which ensures high output power of the 4th-harmonic element. The insertion of C₁ and C₂ adjusts the passband region, while minimizing transformer insertion loss. Finally, T₅ realizes a k of 0.5. L₃ and C₃ are implemented to form a transmission zero around the 2nd harmonic. After EM simulation, T₅ realizes a frequency response as a third-order two-pole/one-zero bandpass filter, as indicated in Fig. 11(a). Note that a sharp rejection around 2f₀ occurs and the higher frequency is shaped in order to reduce the intermixed product of 5f₀ and 6f₀ components. With a input signal of 19.25 GHz, the simulated harmonics with and without the bandpass filter at the output of the proposed quadrupler is presented in Fig. 11(b). As expected, the filter reduces 2f₀ harmonic by 7 dB. It has little effect on 3f₀ harmonic but still helps in harmonic suppression for 5f₀ and 6f₀ components by 5 dB.

Fig. 10.  The equivalent circuit model of T₅.

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Fig. 11.  (Color online) Simulated (a) S₂₁ of T₅ and (b) harmonics at the output node with and without the bandpass filter.

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4. Measurement results

The frequency quadrupler is implemented in 40-nm CMOS technology. The chip microphotograph of the E-band frequency quadrupler is shown in Fig. 12. It consumes 34 mW with 1.5-V supply for the doublers and 1-V supply for the PAs. The core chip size is 930 × 250 μm², including G–S–G pads. The chip has been measured on a high-frequency probe station. The S-parameters are measured by a vector network analyzer operating up to 86 GHz.

Fig. 12.  (Color online) Chip micrograph.

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As depicted in Fig. 13, the measured S₁₁ maintains less than –10 dB across 17.5–19.7 GHz and S₂₂ is below –10 dB across 75–86 GHz, indicting good impedance matching across the automotive radar band (i.e., 76–81 GHz). In Fig. 14, the simulated and measured output power and conversion gain are plotted. The measured saturated output power is around 1.7 dBm from 76 to 78 GHz (see Fig. 14(a)) with a peak conversion gain of 3.4 dB at 76 GHz (see Fig. 14(b)). Fig. 15 presents the frequency response of the quadrupler with a 1-dBm input. As revealed by the 4th harmonic, the quadrupler has a 1.5-dB bandwidth of more than 6 GHz (74–80 GHz). Note that the quadrupler achieves a fundamental and 2nd-harmonic suppression above 45 and 20 dB, respectively, over the measured band.

Fig. 13.  (Color online) Measured S-parameters: (a) S₁₁ and (b) S₂₂.

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Fig. 14.  (Color online) Measurement results of (a) output power and (b) conversion gain.

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Fig. 15.  (Color online) Measured output power of the E-band quadrupler.

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In further research, an VCO and frequency quadrupler link is designed. In Fig. 16, the measured phase noise spectrum of the multiplier output at 77 GHz and the VCO output at 19.25 GHz are depicted. As expected, the phase noise increases by 12 dB, which matches the theoretical result well. It proves that the proposed multiplier does not introduce significant noise penalties. Therefore, it is suitable as a building block of the automotive radar systems.

Fig. 16.  (Color online) Measured phase noise at 77 GHz (red) and VCO phase noise at 19.25 GHz (blue).

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In Table 1, the performance of the proposed frequency quadrupler is summarized and compared with prior-art designs. Occupying a competitive core chip area, this work exhibits sufficient output power and conversion gain with the highest fundamental suppression and relatively low power dissipation.

Table 1.  Performance comparison.

Parameter	MWCL 2020[20]	MWCL 2021[21]	TMTT 2020[22]	This work
Technology	90 nm CMOS	40 nm CMOS	120 nm SiGe	40 nm CMOS
Output frequency (GHz)	71–81	65.6–75.2	70–110	74–82
Output power (dBm)	3.1	–0.2	3	1.7
Conversion gain (dB)	N/A	–8.9	–1.5	3.4
Fundamental suppression (dB)	>36	>33	>30	>45
PDC (mW)	70	11.3	240	34
Core area (mm2)	0.52	0.1	1.9	0.23

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5. Conclusion

An E-band CMOS frequency quadrupler with 1.7 dBm output power and 3.4 dB conversion gain has been demonstrated in a 40-nm CMOS process. The chip consumes 34 mW and occupies 0.23 mm² silicon area. This design utilizes two push-push cascode frequency doublers and two single-stage power amplifiers with well-optimized transformer-based matching networks. Besides, it achieves compelling conversion gain (3.4 dB) and excellent fundamental and 2nd-harmonic suppression over the spectrum from 74 to 82 GHz.

Acknowledgements

This work was supported in part by the National Key Research, Development Program of China under Grant 2018YFB1802100 and the Major Key Project of PCL (PCL2021A01-2).