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Some applications must generate their signals when only low supply voltages are available, such as in battery-powered systems. Fortunately, a quadrature voltage-controlled oscillator (QVCO) has been developed that can be fabricated with p-type metal-oxide-semiconductor (PMOS) solid-state technology. It features low phase noise and low power consumption over a moderate tuning range (5% from 2.325 to 2.440 GHz).

Quadrature coupling is achieved by a direct coupling technique for a reduction in power consumption, phase noise, and chip size. Suitable for a variety of wireless communications applications, the Colpitts-topology QVCO adds capacitive feedback to achieve an enhanced voltage swing over its tuning range. The prototype QVCO boasts phase noise of -128.2 dBc/Hz offset 1 MHz from a 2.34-GHz carrier while consuming only 0.535 mW power from a +0.55-VDC supply.

Quadrature signals play an important role in both wireless and wireline communication systems. They are used in a variety of different analog and digital modulation schemes, and several techniques can be employed to produce quadrature signals. For example, a VCO with a doubled frequency followed by a divide-by-two circuit can be used, as can a polyphase filter or a QVCO.^{1} QVCOs have been shown to be critical components in applications that require high-fidelity quadrature signals—certain communications transceivers, for example—since they can generate quadrature signals with superior phase noise and low power consumption. But designing a source capable of high-spectral-purity quadrature signals with low power consumption is still a challenge.

The simplest and most convenient way to implement a QVCO is by coupling two symmetric inductive-capacitive (LC) tank VCOs.^{2-4} The main drawback to this approach is the typically poor phase noise that results. In 2008, a Class-C VCO topology was proposed with a theoretical phase-noise improvement of 3.9 dB for the same current consumption as a standard differential-pair LC tank oscillator.^{5 }Following that approach, several new Class-C VCO topologies have been proposed.^{5-10} However, all of these designs are based on a single differential pair configuration, similar to a traditional VCO topology.^{5}

In quest of quadrature signals with low noise at low power levels, a new oscillator configuration was explored. In contrast to VCOs with traditional cross-coupled differential-pair LC-tank topologies, this new approach is a PMOS Colpitts QVCO. By employing a direct bulk coupling technique, this novel QVCO topology enables quadrature coupling without requiring additional transistors. In addition, it provides an enhanced voltage swing under a low supply voltage by means of a capacitive feedback technique.

*Figure 1(a)* shows a cross-coupled, differential-pair, Class-C oscillator. Bias current is inserted between the NMOS source and ground and, in most cases, this is accomplished by means of a tail transistor. To filter high-frequency noise from the bias current, a large tail capacitance is employed; together with an resistive-capacitive (RC) bias network, this can prevent the transistors from working in the deep triode region.^{5}

*Figure 1(b)* shows the new PMOS Colpitts VCO architecture. For a given amount of current, NMOS transistors are smaller than PMOS transistors for the same value of transconductance. However, PMOS transistors exhibit about 10-dB less 1/f noise compared with NMOS transistors. PMOS transistors also feature lower hot-carrier-induced white noise than NMOS transistors. As a result, PMOS-based VCOs can achieve better phase-noise performance than NMOS-based VCOs.^{11} Based on these considerations, a new VCO core was designed using a full PMOS transistor architecture.

Rather than using transistors (and their noise contributions) for quadrature signal coupling, direct bulk coupling is employed in this new QVCO to improve phase-noise performance while reducing power consumption and semiconductor chip area. To improve the oscillator’s voltage swing while operating with a low supply voltage, capacitive feedback is employed. The typical source of bias current has been replaced by an on-chip inductor, L_{D}, leaving maximum voltage headroom for the oscillating signal and dramatically reducing the phase noise.^{12} This technique is especially useful in low-supply-voltage topologies.

Compared to the oscillator in *Fig. 1(a)*, the proposed QVCO has eliminated bias voltage V_{bias} and the bias circuitry resistances, improving the robustness of the new oscillator’s startup functionality and reducing the thermal noise of said bias resistances. To improve QVCO startup, feedback capacitor C_{2 }has been inserted between the PMOS source and gate. The greatest difference between the new QVCO topology of *Fig. 1(b)* and the traditional topology of *Fig. 1(a)* is that the new design employs a Colpitts architecture instead of the traditional cross-coupled differential-pair LC tank topology.

The greatest difference between the proposed QVCO and the traditional cross-coupled differential-pair LC-tank configuration of *Fig. 1(a)* is the use of the Colpitts architecture in the QVCO. *Figure 2* presents a block diagram of the new PMOS QVCO. The four (quadrature) output ports are represented by parameters J+, J-, P+, and P-. Capacitive feedback is provided by capacitors C_{1} and C_{v}. Following the pioneering work of Hsieh and Lu,^{13 }a simplified expression of the QVCO voltage swing for this oscillator can be represented by Eq. 1:

A ≈ (1 + C_{1}/C_{v})V_{DD} (1)

As the simulations of the traditional VCO and the QVCO will attest, the use of capacitive feedback can greatly improve the output swing of a VCO—even when it is operating at low supply voltages.

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## A Closer Look

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Several methods are available for achieving quadrature coupling. These include parallel-coupled QVCOs, series-coupled QVCOs, and back-gate-coupled QVCOs.^{14-16} For the new QVCO, quadrature coupling was accomplished by means of a bulk coupling technique, whereby an additional transistor or capacitor was not needed to provide the coupling. The use of direct bulk coupling can reduce the supply-voltage requirements.

For a MOSFET device, the threshold voltage is governed by the body effect^{17}:

V_{t} = V_{t0 }+ γ[(|2Φ_{F }+ V_{SB}|)^{0.5} - (|2Φ_{F})|)^{0.5} (2)

where:

V_{SB} = the sideband voltage;

V_{t0} = the threshold voltage for V_{SB} = 0 V;

γ = the bulk effect parameter, with a typical value between 0.3 and 0.4 V^{0.5}; and

Φ_{F} = a physical parameter with typical value of 0.3 V.

From Eq. 2, it is known that by applying both DC and AC bulk coupling, the effective threshold voltage can be reduced; this is desirable for achieving a low-supply-voltage, low-power oscillator design. Since forward biasing of the bulk coupling also helps to reduce flicker noise in a PMOS VCO, the use of bulk coupling leads to a coupling factor of less than unity.^{18 }As a result, the direct bulk coupling technique can also improve the oscillator’s phase-noise performance. The design parameters for the QVCO are as follows: C_{1} = 429.4 fF; C_{2} = 664.9 fF; L_{S} = L_{D} = 7.1 nH; and dimensional parameters of 120/0.18 μm for M_{1}, M_{2}, M_{3}, and M_{4}.

By way of comparison, circuits for the traditional VCO and the proposed PMOS Colpitts QVCO were fabricated in monolithic form using 0.18-μm RF CMOS semiconductor technology from Taiwan Semiconductor Manufacturing Company Ltd. (TSMC). The two oscillator circuits were compared in terms of output voltage swing, frequency tuning range, and phase noise. *Figures 3 and 4* show the output voltage swings of the standard VCO and the PMOS QVCO cores, respectively.

As the plots reveal, the standard VCO circuit draws DC current of 486 μA when operating with a +0.55-VDC supply while the QVCO draws a higher 972 μA when running on the same +0.55-VDC supply voltage. From *Fig. 3*, it is known that the J- and J+ ports deliver higher output swings than the I- and I+ ports.

*Figures 5 and 6* display the tuning ranges of the two oscillator architectures. The frequency range of the standard VCO is 2.34 to 2.48 GHz when control voltage V_{ctr} sweeps from 0 to +1 VDC; the tuning range of the QVCO is 2.325 to 2.440 GHz when working with the same V_{ctr }range. *Figures 7 and 8* offer phase-noise performance levels for the two oscillator architectures. As these plots show, the best phase noise for the traditional VCO is -120.3 dBc/Hz offset far (1 MHz) from the carrier while the phase noise for the proposed QVCO is as low as -128.2 dBc/Hz offset 1 MHz from the carrier. In general, the performance of the new QVCO is superior to that of the traditional VCO, except for power consumption.

A figure of merit (FOM) was employed to evaluate the three performance parameters of frequency, phase noise, and power dissipation for the QVCO, as detailed in Eq. 3:

FOM = ELL(f_{offset}) – 20log(f_{0}/f_{offset}) + 10log(PDC/1 mW) (3)

where:

PDC = the power dissipated by the oscillator core (in mW);

ELL(f_{offset}) = the phase noise at the oscillator carrier frequency;

f_{offset} = the offset frequency from the oscillator carrier; and

f_{offset} = the center frequency.

The performance of the new QVCO is summarized in the *table*, and compared with recent work in QVCOs. The new low-voltage design exhibits the best FOM among these reported QVCOs, with higher FOM values indicating better oscillator performance.

In summary, a new PMOS Colpitts QVCO for a +0.55-VDC supply voltage has been developed and fabricated with a commercial 0.18-μm silicon CMOS technology. By using capacitive feedback and a direct bulk coupling technique, the quadratic oscillator achieves significant improvements in terms of power consumption and phase-noise performance, making it an attractive candidate for low-power RF/microwave applications requiring low supply voltages.

On the negative side, the proposed QVCO topology requires eight inductances, which leads to a larger required chip area than some other QVCO topologies. The four tail inductances, L_{S}, can be replaced by resistances or MOSFETs, but simulations show that this will degrade the phase-noise performance and power consumption. It will also require the use of a larger supply voltage, revealing the tradeoff of supply voltage, power consumption, phase noise, and chip area for this new QVCO design.

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## Acknowledgments

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This work is supported by the National Natural Science Foundation of China (No. 61274020), the natural science foundation of Hunan Province (No. 14JJ7026), and the Open Fund Project of Hunan University’s Key Laboratory (No. 13K015). The authors would like to thank the anonymous reviewers for their invaluable suggestions, which helped improve the quality of this article.

**Chunhua Wang, Professor and Doctoral Supervisor**

**Jianqun Ding, Master’s Degree Candidate**

**College of Information Science and Engineering, Hunan University, Changsha 410000, People’s Republic of China**

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