Millimeter-Wave Voltage-Controlled Oscillators

• Millimeter-wave VCOs are tunable oscillators operating in the 30–300 GHz band, essential for modern communications, quantum processing, and sensing.
• They combine charge-based designs (using varactors in LC tanks) and spintronic approaches (using VCMA) to achieve high VCO gain, broad tuning range, and low phase noise.
• Recent advances include sub-100 nm integration, cryogenic operational stability, and novel phase-noise suppression strategies that enhance performance for next-gen electronics.

A millimeter-wave voltage controlled oscillator (mm-wave VCO) is a tunable electronic source that generates an output signal within the 30–300 GHz frequency range, with frequency selectivity governed by an input control voltage. Millimeter-wave VCOs are foundational for modern wireless communication systems (notably 5G), scalable quantum computing architectures, and frequency-agile radar and sensor networks. They encompass diverse physical mechanisms: charge-based electronic devices (e.g., LC tanks with FET or bipolar negative resistance) as well as spintronic nano-oscillators utilizing voltage-controlled magnetic anisotropy. The critical performance metrics for mm-wave VCOs are tuning range, phase noise, power efficiency, and integration compatibility, with tuning mechanisms and phase-noise suppression strategies being central research topics. Millimeter-wave VCOs have recently achieved sub-100 nm gate patterning, order-of-magnitude frequency tuning, and cryogenic operational stability.

1. Fundamental Architectures and Tuning Principles

Millimeter-wave VCOs are realized via two main device classes: charge transport (cross-coupled L–C tanks, including FET and bipolar topologies) (Bui et al., 11 Nov 2025, Hollmann et al., 2018) and spin-based voltage-gated nano-constriction oscillators (González et al., 2022).

Charge-based VCOs employ an L–C resonant circuit whose center frequency $f_0 = (2\pi\sqrt{L C_{\rm tot}})^{-1}$ is modulated by varying the total tank capacitance $C_{\rm tot}$, commonly by biasing a varactor. The negative resistance required to sustain oscillation is synthetic, implemented via cross-coupled transistor pairs. Start-up necessitates $g_m\,Z_{LC} > 2$, where $g_m$ is the transconductance and $Z_{LC}$ the loaded tank impedance. CASCODE topologies further increase effective negative resistance and improve oscillation robustness.

Spintronic VCOs utilize the voltage-controlled magnetic anisotropy (VCMA) effect in W/CoFeB/MgO nano-constriction spin Hall nano-oscillators (SHNOs). Magnetization dynamics are described by the Landau–Lifshitz–Gilbert equation with spin–orbit torque (SOT) and voltage-dependent uniaxial anisotropy:

$$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$

The voltage-tunable anisotropy field $H_K(V_G)$ modulates the local effective field, shifting the auto-oscillation frequency over broad windows.

2. Oscillation Frequency, Tuning Range, and Sensitivity

The achievable oscillation frequency and tuning range dictate the suitability of mm-wave VCOs for applications such as 5G, high-frequency PLLs, and quantum processor control.

In LC-based charge VCOs, electronic tuning via varactor bias yields:

• Conventional cross-coupled topology: $f_{\rm min}=22.6$ GHz, $f_{\rm max}=26.8$ GHz, $\Delta f=4.2$ GHz (17.7% center frequency span).
• Cascode cross-coupled topology: $C_{\rm tot}$0 GHz, $C_{\rm tot}$1 GHz, $C_{\rm tot}$2 GHz (21.7% center frequency span), achieved via increased $C_{\rm tot}$3 and improved bias range (Bui et al., 11 Nov 2025). VCO gain ($C_{\rm tot}$4, Hz/V) quantifies voltage–frequency sensitivity:
• Conventional: $C_{\rm tot}$5 GHz/V.
• Cascode: $C_{\rm tot}$6 GHz/V.

SiGe BiCMOS VCOs operating at both 300 K and $C_{\rm tot}$7 K evidence a wide tuning window: 29.6–32.4 GHz (low-band) and 32.0–35.5 GHz (high-band), combining to a 5.9 GHz (18.1%) span via $C_{\rm tot}$8 V. Tuning sensitivity is $C_{\rm tot}$9 GHz/V (Hollmann et al., 2018).

Nano-constriction SHNOs exhibit auto-oscillation frequency tuning of 9–14 GHz ($g_m\,Z_{LC} > 2$0 MHz) in the strong-tuning regime, with reported $g_m\,Z_{LC} > 2$1 MHz/V (16 MHz/V simulated) when gate width matches constriction width (González et al., 2022).

3. Phase Noise, Damping, and Noise Management

Phase noise performance critically impacts VCO suitability for coherent communications and qubit manipulation.

Leeson's model describes single-sideband phase noise as:

$g_m\,Z_{LC} > 2$2

where $g_m\,Z_{LC} > 2$3 is the noise factor, $g_m\,Z_{LC} > 2$4 the loaded tank Q, $g_m\,Z_{LC} > 2$5 temperature, and $g_m\,Z_{LC} > 2$6 oscillator output power.

Measured/simulated phase noise (offset from carrier):

• Conventional LC VCO: $g_m\,Z_{LC} > 2$7 dBc/Hz (10 MHz), $g_m\,Z_{LC} > 2$8 dBc/Hz (800 MHz).
• Cascode LC VCO: $g_m\,Z_{LC} > 2$9 dBc/Hz (10 MHz), $g_m$0 dBc/Hz (800 MHz); the cascode topology slightly lowers both close-in and wide-offset noise (Bui et al., 11 Nov 2025).
• SiGe HBT VCO: $g_m$1 dBc/Hz (100 kHz, 300 K), $g_m$2 dBc/Hz (100 kHz, 4 K); $g_m$3/$g_m$4 dBc/Hz (1 MHz, 300 K/4 K) (Hollmann et al., 2018). Observed flicker corners occur near $g_m$5 kHz, after which noise falls as $g_m$6, limited ultimately by $g_m$7.

Nano-constriction SHNOs leverage VCMA-driven damping to modulate linewidth and phase noise: in the voltage-tuning regime, effective damping, $g_m$8, rises five-fold ($g_m$9) over a $Z_{LC}$0 range of $Z_{LC}$1 V to $Z_{LC}$2 V (González et al., 2022).

4. Design Trade-Offs, Integration, and Operating Conditions

Cascode cross-coupled LC VCOs present increased negative resistance, larger $Z_{LC}$3, and higher $Z_{LC}$4, improving phase noise at the expense of headroom and possible increased parasitic capacitance. Larger $Z_{LC}$5 facilitates easier PLL loop-filter design but elevates spurious signal sensitivity. Inductor $Z_{LC}$6 and varactor series resistance must be maximized to suppress noise, and layout must minimize tank-bias line coupling (Bui et al., 11 Nov 2025).

SiGe HBT VCOs are functional from 300 K to 4 K, with power consumption rising from $Z_{LC}$7 mW to $Z_{LC}$8 mW and output power increasing from $Z_{LC}$9 dBm to $$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$0 dBm. Efficiency is low ($$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$1% at 300 K, $$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$2% at 4 K), compatible with control electronics near but not directly on the qubit chip (Hollmann et al., 2018). Magnetic field shifts are negligible ($$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$30.02% at $$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$4 T).

Spin Hall nano-oscillators leverage sub-100 nm gates compatible with CMOS, offering $$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$5W-level control, ultra-broadband tuning, and compact integration into dense electronics (González et al., 2022).

5. Gating Regimes and Performance Optimization

Spin Hall nano-oscillators, with VCMAs, exhibit three distinct gating regimes depending on gate width $$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$6 and voltage $$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$7 (González et al., 2022):

• Separation ($$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$8): Increased PMA expels mode from gate, forming lobes outside constriction. Frequency and damping are voltage-independent.
• Tuning ($$\frac{\partial\mathbf{\hat{m}}}{\partial t} = -\gamma \mathbf{\hat{m}} \times \mathbf{H}_{\rm eff} + \alpha_0\, \mathbf{\hat{m}} \times \frac{\partial \mathbf{\hat{m}}}{\partial t} + \tau_{\rm SHE}$$9): Spin-wave delocalization enables maximal frequency/damping tuning ($H_K(V_G)$0 MHz, five-fold damping change).
• Confinement ($H_K(V_G)$1): PMA reduction localizes the mode. Frequency slope reverses, damping becomes flat.

Optimal tuning is realized for $H_K(V_G)$2 (gate matches constriction width), maximizing $H_K(V_G)$3 and damping control. Gating outside this range produces mode decoupling and saturates tuning/damping effects. Enlarging VCMA coefficients extends frequency tuning into the mm-wave band (20–40 GHz baseline), with $H_K(V_G)$4 up to 0.1 GHz/V possible.

6. Performance Metrics Comparison

The following table summarizes key performance metrics from the primary device topologies (Bui et al., 11 Nov 2025, Hollmann et al., 2018, González et al., 2022).

Metric	Cascode LC VCO (Bui et al., 11 Nov 2025)	SiGe HBT VCO (Hollmann et al., 2018)	SHNO (González et al., 2022)
Frequency Range	21.0–26.1 GHz (5.1 GHz)	29.6–35.5 GHz (5.9 GHz)	9–14 GHz (0.8 GHz)
VCO Gain $H_K(V_G)$5	8.0 GHz/V	0.93 GHz/V	~0.016 GHz/V
Phase Noise (typical)	–116.5 dBc/Hz (10 MHz offset)	–115 dBc/Hz (1 MHz, 300K)	<VCMA-dependent>
Power Consumption	Not reported (VDD = 1.0 V)	60–75 mW (VCC = 3V)	μW regime
Tuning Mechanism	Varactor voltage	Varactor voltage	VCMA gate voltage

The data establish that cascode LC VCOs achieve superior VCO gain and phase noise performance at lower supply voltages, SiGe HBT VCOs provide wideband operation and cryogenic stability, and nano-constriction SHNOs enable low-power, broadband voltage control suitable for CMOS integration.

7. Application Domains and Outlook

Millimeter-wave VCOs impact high-speed telecommunications (5G/6G), quantum computing (cryogenic on-chip sources), and spintronic integration. The combination of wide tuning span (up to 21.7%), sub-μW voltage control, and integration-ready footprints positions both advanced LC (FET/bipolar) and SHNO VCOs as key mm-wave frequency-agile sources for next-generation electronics. For quantum computing, low-temperature operation and minimal field-dependent drift ($H_K(V_G)$60.03%) are critical, while for mobile networks, phase-noise floor, tuning sensitivity, and power efficiency remain main optimization levers.

Ongoing research aims to further expand tuning coefficients (e.g., $H_K(V_G)$7 in VCMA), reduce phase noise via topology modifications, and optimize integration for dense, low-power electronic systems compatible with advanced process nodes.