A 25% Tuning Range 7.5-9.4 GHz Oscillator With 194 FoM T and 400 kHz 1/f Corner in 40nm CMOS Technology

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I. INTRODUCTION
Modern wireless transceivers have a stringent requirement for spectral purity.For example, RF receivers working under coexistence scenarios suffer from noise figure degradation due to reciprocal mixing between the LO signal and the interferer at a mixer input [1], [2], [3], [4], [5], [6], [7], [8].Interferes could be several MHz or tens of MHz away from the wanted signal.In order to reduce the effect of reciprocal mixing, it is desirable to suppress interferes before the mixer and to have an LO with very low phase noise.However, methods are very challenging with the decrease in the offset frequency.For frequency ranges in the order of several or tens of MHz, the LO phase noise is usually dominated by the phase noise from the oscillator [9].Therefore it is desired to lower the VCO phase noise so that the reciprocal mixing causes negligible impact.
The associate editor coordinating the review of this manuscript and approving it for publication was Harikrishnan Ramiah .
In conventional voltage-controlled oscillator design, the close-in phase noise (PN) is usually degraded by 1/f flicker noise up-conversion and varactor's AM to FM conversion [10], [11].Even though technology scaling improves capacitor density and effective maximum and minimum capacitance ratio, the inductor quality factor is degraded.It is even worse in a digital library due to the lack of ultrathick metal, which further deteriorating the performance.An additional tank with resonance at the second harmonic can significantly reduce the 1/f 3 flicker noise corner [11].However, it requires extra area and extra tuning on the 2 nd resonant frequency to cover a wide tuning range.Other recent works on oscillator [12], [13], [14] achieve low phase noise by using a transformer-based LC tank with additional resonance at the third harmonic frequency (class-F 3 ).It benefited from accurate capacitor matching for accurate control on resonant frequency ratio and a transformer implemented with ultrathick metal.
In this work, we propose a oscillator with class-F 23 operation to achieve low PN and low 1/f 3 corner frequency by enabling additional resonance at the 2 nd and 3 rd harmonic frequencies with a transformer-based LC tank.The transformer is realized with pattern shielding to improve the quality factor.The capacitor bank is composed of a combination of varactor and binary-weighted MoM capacitor array, minimizing PN degradation due to varactor AM-FM conversion.And this capacitor array combination achieves a 25% tuning range.
This paper is organized as the following.Section II shows the schematic of the proposed transformer-based class-F 23 VCO and analyses the condition for the class-F 23 operation.Section III describes the detailed realization of a high-Q transformer and capacitor bank with large tuning and high linearity.The details of circuit implementation and measurement results are discussed in section IV. Conclusions and a comparison to other state-of-arts are drawn in Section V.

II. PROPOSED VCO SCHEMATIC WITH CLASS-F 23 OPERATION
The schematic of the proposed class-F 23 oscillator is shown in Fig. 1.In this class-F 23 oscillator, a 2-wing transformerbased LC tank has multiple impedance peaks in differentialmode (DM) and common-mode (CM) operations [13].This is explained in Fig. 2.
In the DM operation, the tank has an auxiliary impedance magnitude peak ideally at the third harmonic frequency.A pseudo-square waveform oscillation is created with an extended region of the waveform where its impulse sensitivity function (ISF) is close to zero.The fundamental resonant frequency is ω 2 1 = 1/(L P C P,tot + L S C S,tot ), where L P and L S is the inductance at the transformer's primary and second winding.C P,tot and C S,tot is the total capacitance at each winding.The ratio between two DM resonant frequencies, ω 3 /ω 1 , is given in (1), which is controlled by the magnetic  coupling factor, k m,DM and ratio X .The X is defined as X = L S C s,tot /L P C p,tot .
In the CM mode, the resonance only sees the CM inductance L P + 2L CT and CM capacitor C P,tot on the primary winding, due to low magnetic coupling.L CT is the inductance on the center tap connection.The CM resonant frequency is The ratio between CM resonant frequency ω 2 and DM fundamental frequency ω 1 is in (2).In the CM mode, the second harmonic components are forced to flow into the resistive path of the tank by having a tank impedance peak at the second harmonic frequency.In this way, it reduces: (i) flicker noise up-conversion, (ii) the DC value of the effective ISF [15], (iii) the close-in PN degradation by varactor nonidentities.
However, as shown in ( 1) and ( 2), class-F 23 operation depends on the parameters of L P , L CT , X .Therefore it is very sensitive to mismatch between these parameters.The sensitivity of resonance frequency ratio ω 2 /ω 1 and ω 3 /ω 1 to capacitance mismatch between the primary and secondary winding is shown in Fig. 3. Therefore, the realization of the transformer and capacitor bank is highly critical.

III. REALIZATION OF TRANSFORMER-BASED LC TANK A. TRANSFORMER REALIZATION
Realization of the transformer with a turn ratio of 1:2 is shown Fig. 4. Due lacking the ultra-thick metal layer, the transformer was constructed by stacking the aluminum layer (AP layer) on top of the top copper layer (M 8 layer) to increase the metal thickness and reduce metal line resistance.The metal width is 10 µm for the primary and secondary winding, and the gap is kept at 8 µm.A customized pattern shielding with M 1 , OD and PO layers are placed on top of the substrate to terminate the electric field and provide better shielding from the substrate to further improve its Q factor.The simulated transformer performance is shown in Fig. 5.The performance is compared between using different shielding patterns, one with the proposed shielding pattern on M 1 , OD and PO layers, and the other is using shielding pattern on M 1 layer only.In differential mode, the primary and secondary inductance are around 0.5 nH and 1.2 nH, respectively.The quality factor at 8 GHz of the primary and secondary winding are 11.6 and 15.6, respectively.The coupling factor is 0.64.Compared with shielding using M 1 layer only, the transformer with proposed pattern shielding achieves a higher quality factor over a larger bandwidth, without affecting the inductor value and coupling factor.Under common-mode operation, the inductance on the primary winding center-tap is modelled precisely to the point  where decoupling capacitors are placed.The common-mode inductance on the primary winding is around 0.2 nH.

B. CAPACITOR BANK REALIZATION
The realization of the capacitor bank should be considered together with the transformer characteristics to meet (1) and (2) for class-F 23 operation, while at the same time to achieve a wide tuning range of oscillation frequency.The varactor effective capacitance not only depends on the tuning voltage, but also on the oscillation waveform.The varactor nonideality leads to two undesired side affects.Firstly, the matching between the varactor capacitance on different transformer windings is sensitive to the different oscillation waveform on the two windings.Secondly, it also introduces AM-FM conversion.Both side effects degrade the oscillator phase noise.
In order to reduce these side affects, a small varactor with a small tuning range of 25 fF is used on the primary side.A 4-bit binary-weighted MoM capacitors is used in parallel with the varactor to have a large tuning range of oscillation frequency.The LSB MoM capacitor is 18 fF.Fig. 6 shows the comparison of normalized capacitance tuning range between the solution of using capacitor bank of varactor-and-MoM capacitors, and using varactor bank only.To achieve the same capacitance tuning range, the varactor bank consists of multiple small varactor units and shows strongly nonlinear capacitance tuning behavior.The capacitor bank however, is more linear as only one small varactor unit is used.Therefore, it is less sensitive to varactor mismatch due to the dependence on oscillation waveform.Furthermore, the phase noise degradation due to varactor AM-FM conversion is much alleviated.With this combination, the quality factor of the capacitor array is kept above 30 at 8 GHz for the whole tuning range.Therefore the quality factor of the LC tank is mostly limited by the quality factor of the transformer.
In order to meet class-F 23 operation condition, the capacitance ratio between the primary and the secondary winding is kept as 1.8.As the transformer and capacitor bank characteristics have been settled, the simulated tank impedance over the tuning range is given in Fig. 7.The minimum and maximal resonant frequencies are 7.5 GHz and 9.4 GHz, respectively.The accuracy of the ratio between resonance frequencies is limited by the matching of varactor and MoM capacitance between transformer windings, as well as transformer characteristics to meet (1) and (2).Ideally, the varactor on the secondary winding could use a separate tuning voltage for a perfect matching for class-F 23 operation.

IV. MEASUREMENT
The proposed class-F 23 VCO is implemented in a 40-nm CMOS technology without an ultra-thick metal layer.The g m devices are thick-oxide devices to handle the large voltage swing at the gate and drain node of the cross-coupled pair.The current source is implemented with a resistor at the drain to further reduce the flicker noise contribution to phase noise conversion at the close-in region.The center tap of the primary winding is connected to the supply, and the center tap of the secondary winding is connected to the bias voltage.The varactors on the transformer primary and secondary winding are connected to the same tuning voltage for simplicity.The oscillator is followed by a resistor-feedback buffer and a /4 divider.It drives the output 50 load by a differential buffer.The die micrography is shown in Fig. 8 and the core die area is 0.1 mm 2 .The results are measured by the Keysight E5052A signal source analyzer after on-chip /4 divider and buffer circuits.The measured tuning range over the 4-bit digital steps and the analog tuning range is shown in Fig. 9.After /4 divider, the measured oscillator tuning range is from 1.85 to 2.37 GHz.The oscillator core is from 7.4 to 9.48 GHz.The current consumption of the core oscillator is 9.8 mA from a 1.2 V supply.
The measured phase noise is shown in Fig. 10  The measured 1/f 3 corner frequency over the entire digital and analog tuning range is shown in Fig. 11.The 1/f 3 corner frequency is mostly between 400 kHz and 632 kHz across the whole tuning range.It is limited by the mismatch between inductance and capacitance characteristics between the primary and secondary windings.This can be caused by the imperfect EM modeling of varactor mismatch, layout matching, or parasitic capacitance.The solid line in Fig. 11 shows some of the 1/f 3 corner frequencies experience abrupt changes during the analog tuning range, while most of them are constant.This result verifies the concept in most conditions that by using the combination of a small varactor unit and MoM capacitor array, the capacitance tuning range is linearized so that capacitance matching is accurate, and varactor AM-FM conversion is much alleviated.Ideally, a separate varactor tuning voltage can be used to fine tune the capacitance ratio to further reduce the 1/f 3 corner frequency.
Table 1 compares the measured performance with other recent works on oscillators.This VCO work achieves good phase noise, low 1/f 3 corner frequency and a wide tuning range.It proves that VCO can benefit from class-F 23 operation to achieve low phase noise and low 1/f 3 corner frequency by novel design and implementation of a transformer-based LC tank, even without the ultra-thick metal layer.

V. CONCLUSION
This paper presents an 8 GHz VCO with class-F 23 in a 40-nm digital CMOS technology.The class-F 23 operation was enabled by having a transformer-based tank with auxiliary resonant frequency at 2 rd harmonic in CM mode and at 3 rd harmonic in DM mode in order to achieve low phase noise and low 1/f 3 corner frequency.A patterned shielding and stacked metal method are applied to increase the on-chip inductor quality factor.The resonant frequency ratio is accurate controlled by the capacitor matching on the primary and secondary of the transformer.With the mixed capacitor bank architecture, the 1/F 3 is 400 kHz.The VCO with a /4 divider buffer prototype measured a PN of -131 dBc/Hz at 1 MHz offset and -151 dBc/Hz at 10 MHz offset.The measured frequency is from 1.85 to 2.37 GHz with on-chip /4 divider, while the oscillator core covers from 7.4 to 9.48 GHz.With on-chip /4 divider, its FoM T reach a 194, which kept a stateof-art performance.

FIGURE 1 .
FIGURE 1.The schematic of the proposed class-F 23 oscillator core.

FIGURE 2 .
FIGURE 2. Transformer-based resonator under differential-mode (DM) and common-mode (CM) operation, and its magnitude of the input impedance respectively.

FIGURE 4 .
FIGURE 4. The layout of the transformer with proposed patterned shielding using M1, PO and OD layer.

FIGURE 5 .
FIGURE 5. Transformer primary and secondary (a) inductance in CM and DM excitation (b) inductance quality factor and coupling factor in DM excitation, solid lines refer to shielding with M1, OD and PO, dashed lines refer to shielding with M1 only.

FIGURE 6 .
FIGURE 6.Comparison of capacitance tuning range between a capacitor bank of varactor and 4-bit MoM capacitor array, and a varactor bank.

FIGURE 7 .
FIGURE 7. Transformer-based tank input impedance magnitude over oscillator tuning range frequency.

FIGURE 8 .
FIGURE 8. Die micrography of the proposed F 23 oscillator with a on-chip /4 divider.

FIGURE 11 .
FIGURE 11.Measured 1/f 3 corner frequency over analog and digital tuning range.
at the minimum and maximum oscillation frequency, after /4.At the minimum oscillation frequency, the measured phase noise at 100 kHz, 1 MHz and 10 MHz offset are −105, −131 and −151 dBc/Hz, achieving a FoM of 180, 185 and 186 dB/Hz, respectively.The 1/f 3 corner frequency is 400 kHz.At the maximum oscillation frequency, the phase noise at 100 kHz, 1 MHz, and 10 MHz offset are −101, −127 and −148 dBc/Hz, achieving a FoM of 178, 184, and 185 dB/Hz, respectively.The 1/f 3 corner frequency is 632 kHz.

TABLE 1 .
Comparison of state-of-the-art low phase noise oscillators.