State-of-the-Art VCO with Eight-Shaped Resonator-Type Transmission Line

Abstract

A closed-loop transmission line (TL) coupled to an LCR resonator is used in this study for a fully-integrated CMOS rotary traveling wave oscillator (RTWO) based on the rotary traveling wave principle. A technique for the suppression of magnetic coupling noise is presented with eight-shaped inductors. The design and measurement of an 8.53 GHz oscillator in the TSMC 0.18 μm CMOS technology are discussed. The fully-integrated chip occupies a die area of 1.2 × 1.2 mm². The oscillator consists of four sub-oscillators and uses four 1:1 symmetric twisted transformers, with the secondary inductors connected to form a twisted closed-loop transmission line for coupling the sub-oscillators. The transformers are configured as eight-shaped structures to minimize the far-field magnetic field radiation from each transformer and the whole transformer. At a supply voltage of 1.7 V, the power consumption is 5.84 mW. The free-running oscillation frequency of the RTWO is tunable from 8.53 GHz to 10.0 GHz. The measured phase noise at a 1 MHz frequency offset is −122.4 dBc/Hz at an oscillation frequency of 8.53 GHz, and the figure of merit (FOM) of the proposed VCO with a specific inductor layout is −193.4 dBc/Hz, surpassing other similar RTWOs. The FOM with a tuning range (FOM_T) is −195.96 dBc/Hz.

1. Introduction

Voltage-controlled oscillators are used in phase-locked loops (PLLs) and dominate the noise and power consumption of PLLs. In LC oscillators, the inductor topology is an important issue in terms of dealing with coupling noise interference. Eight-shaped inductors are gaining popularity in RF circuit designs; they are used for suppressing noise interference and improving on-chip electromagnetic compatibility (EMC) susceptibility. Eight-shaped inductors are configured with a one-turn topology [1,2]. The EMC reduction results from the twisted nature of the two constitutive loops with equal magnetic field distributions and opposite polarities. A 1:1 eight-shaped transformer is configured with an asymmetric planar one-turn [3,4] and a symmetric 3D one-turn structure [5].

Among the various VCO architectures presented in the past few years, wave-based oscillators, including standing-wave oscillators (SWOs), traveling-wave oscillators (TWOs), and constructive-wave oscillators (CWOs) [6] have recently gained interest. Rotary traveling-wave oscillators (RTWOs) have drawn recent attention because they can provide multi-phase clock generation, higher oscillation frequencies, and lower phase noise [7]. RTWOs have been used in clock arrays [8], frequency quadruplers [9], frequency doublers [10], and pulse injection-locked RTWOs [11,12]. RTWOs often use twisted Möbius rings, as first presented by Wood [8], and untwisted and unfolded single-loop topologies [13,14,15]. Typical RTWO topologies are shown in Figure 1. Figure 1a shows a single-loop micro-strip RTWO. Figure 1b shows an inductor single-loop RTWO used to reduce the occupied area. The above two circuits necessitate long interconnects between the nodes and their corresponding -G_m cells. Since diagonally opposite inductors carry currents that are 180° out of phase, Figure 1c shows a folded Möbius ring RTWO, and Figure 1d shows a folded RTWO with a transformer used to reduce the occupied area [16] because the -G_m cells are placed near the oscillator nodes. In the above topologies, the area encircled by the inductive component is often sensitive to magnetic field coupling. For example, CMOS RTWO arrays [8] were utilized to generate a gigahertz clock, and the induced magnetic fields from the clock structures can be strong. In turn, the RTWO loop can pick up coupling noise and should be suppressed to avoid the frequency pulling and injection locking from a strong interference signal, such as a power amplifier. It also needs to reduce the interference radiation affecting the highly sensitive receiver or low-noise amplifier. RTWO designers require careful attention to guard against magnetic field couplings between the RTWO and other structures. The RTWO-TL can be classified into two types: resonant-type and non-resonant-type. In contrast to Figure 1b, where diagonal excitation is used, the energy excitation is directly applied in each inductor subsection uniformly in the RTWO, as shown in Figure 2a. The RTWO type shown in Figure 2b is used in this work. This paper introduces a new voltage-controlled oscillator (VCO) that uses an eight-shaped transformer as the LC resonator component and the coupling element of four sub-VCOs to form a quadrature VCO (QVCO). The unique property of this oscillator is its low EMI issue, as eight-shaped transformers are naturally noise suppressive. A high figure of merit (FOM) and FoMT (FOM with tuning range) are obtained for the designed QVCO, making the circuit suitable for RF applications.

2. Circuit Design

A schematic of the designed VCO is shown in Figure 3. The VCO is made of four complementary NP VCOs. PMOS transistor M₂ and nMOS M₁ form a cross-coupled negative resistance pair to supply the energy to the LC resonator formed with inductor L₁ and varactors (C_v1, C_v2), and the above components form the sub-VCO₁. Various negative trans-conductors (-G_m cell) can be applied, and they strongly affect the RTWO’s power consumption, phase noise, and operation voltage. The NP cross-coupled core is a low-power G_m structure. Varactor control bias V_T varies the capacitance of the varactors of sub-VCO₁ and the oscillation frequency. The same structure constructs the other three sub-VCOs as sub-VCO₁. The inductor is configured as a transformer, with the secondary as a passive coupling device for the four sub-VCOs. The four secondary inductors are connected as a closed-loop inductor ring. The sub-VCO injects an energized wave into the loop ring consisting of inductors (L_1T, L_2T, L_3T, L_4T) to form a constructive traveling wave, and the rotary traveling wave back-injects the wave into the sub-oscillator as a fundamental injection-locked oscillator (ILO) [13,14] via the transformer pair (L_iT, L_i) (i = 1, 4) to coherently generate multi-phase outputs. The transformer (L₁, L_1T) couples the wave on the closed-loop ring to sub-VCO₁. The ILO should lock to the injection signal within a limited locking range at low injection power, and the designed ILO is easy to lock to the incoming injection wave because the four ILOs are ideally generating the same frequency signals. The phase delay through each of the four subsections on the ring is approximately 90°, so the total delay around the closed traveling-wave loop ring is 360°. Distinct from a previous publication [14] without twisted inductors, the pair (L_iT, L_i) forms a twisted transformer in this work. The inductors L_Pi: (i = 1~8) are parasitic inductors caused by interconnects between transformer pairs. The coupling closed ring uses four eight-shaped inductors. Figure 4a shows the simulated oscillation frequency of the sub-VCO. Figure 4b shows the simulated oscillation frequency f_OSC of the QVCO versus the tuning range V_T. The coupling reduces the oscillation frequency. The oscillation frequency increases with the tuning voltage V_T. Increasing V_DD decreases f_OSC because of reduced V_T-V_DD. Figure 4c shows the simulated voltage waveforms of sub-VCO₃. The M₃ drain voltage is larger than the M₄ drain voltage. The -G_m cell injects current into the TL and creates two voltage waves that propagate in opposite directions. If the circuit is perfectly symmetrical, the traveling wave Vo(t, z) [17] on the TL, expressed in (1) or the standing wave as expressed in (2), exists on the TL [17].

$${\mathrm{V}}_o(t,z)={\displaystyle \sum _{n=0}^3\left[\begin{array}{l}{B}_{or}\cos \left(({\omega }_{o}t-\beta z)-\frac{n{\omega }_o{T}_o}{8}+\frac{n\beta \lambda }{8})\right)+\\ B_{ol}\cos \left(({\omega }_{o}t+\beta z)-\frac{n{\omega }_o{T}_o}{8}-\frac{n\beta \lambda }{8})\right)\end{array}\right]},$$

(1)

$${\mathrm{V}}_o(t,z)={\displaystyle \sum _{n=0}^3\left[2B_o\cos \left({\omega }_o(t-\frac{n{T}_o}{8})\right)\cos \left(\beta (z-\frac{n\lambda }{8})\right)\right]},$$

(2)

where B_or and B_ol are the same for the symmetric injection design with the wave amplitude B_or = B_ol = B_o, and they are different for the asymmetric design. β is a phase constant, λ is the wavelength, ω_o is the radian frequency, and T_o is the oscillation period.

Figure 5a shows the simulated quadrature output voltage waveforms of the QVCO. V_o3 leads V_o2 by 90°. The output waveforms rotate in a clockwise direction, and no mode ambiguity is used despite the injection waves on the coupled TL closed loop. The sub-oscillators start up the oscillation by wave traveling both clockwise and counterclockwise. This is caused by the asymmetric sub-VCO output waveform, as shown in Figure 4c. Figure 5b shows the simulated voltage waveforms on the coupling loop [13]. Figure 5c shows the current waveforms. Appendix A shows that symmetric waveforms are generated by adopting symmetric NN-core sub-VCOs. A particular frequency noise voltage gets amplified by the feedback mechanism. Then, the sub-oscillators inject the signal into the ring loop to correlate with each other in phase. Generally, low-phase noise is demanded by a VCO; however, feedback oscillators with a higher transconductance FET require a small voltage disturbance generated by thermal/flicker noise to start oscillations. Ideally, the circuit layout is symmetric. So, any location among A, B, C, and D can show the highest voltage compared to the voltages at other locations. This will not affect the time sequence of the output voltage waveforms. Figure 6a shows the simulated phase noises of the VCO and QVCO outputs; the QVCO improves the phase noise by 8.3 dBc/Hz at a 1 MHz offset frequency at the cost of more power consumption. Figure 6b shows the simulated voltage waveforms of the QVCO outputs, indicating that the QVCO exhibits a low second harmonic, and the second harmonic is obtained from the buffer. The simulation shown in Figure 6c shows that the sub-VCO also exhibits a low second harmonic. The QVCO is intrinsically harmonic-free, and common-mode resonance at twice the oscillation frequency is not necessary. Figure 6d shows the simulated output power versus V_T.

Figure 7a shows the layout of the four-port 1:1 inverting twisted transformer, and the primary and secondary inductors use one larger and a smaller inductor to form a twisted inductor. Figure 7b shows the simulated inductance and Q-factor of the transformer. At 8.536 GHz, the inductance is 0.93 nH and the Q-factor is 7.9, which is close to the maximum. A previous RTWO [13] used a 3:2 transformer could not obtain the same maximum Q-factor for the primary and the secondary inductors at the same operation frequency.

Flicker noise is a form of low-frequency device noise, and it will not be affected by the eight-shaped transformers. In each sub-VCO, flicker noise up-coverts to phase noise via the AM-FM conversion process from the varactors, so the flicker noise in one sub-VCO will not affect the phase noise in another sub-VCO. This reduces the phase noise generated by the coupling process. Each eight-shaped transformer will induce the injection pulling effect while it is subjected to a coupling noise attack. The phase noise of one sub-VCO will affect the sub-VCO phase noise via an eight-shaped transformer coupling and the phase noise wave propagation on the TL. This process reduces the phase noise, as shown in Figure 6a.

Figure 7c shows the simulated tank impedance, and the simulated phase is shown in Figure 7d for a quadrature circuit. The resonant frequency for the transformer alone is much higher than the oscillation frequency of the VCO. Hence, the varactor capacitance and MOSFET parasitic capacitance are also used in oscillation frequency determination. The resonant frequency is close to the oscillation frequency of the QVCO.

Figure 8 shows the layout of the twisted closed-loop inductor ring, which encloses a small die-empty area for low mutual coupling between the RTWO and other nearby inductive circuits. The inductor ring uses a single-loop topology, and most of the area inside the ring is occupied by the twisted transformer. The current shown by the arrow direction indicates the suppression of magnetic fields provided by each twisted transformer pair. Therefore, the net field generated by the inductive device is minimized. On the other hand, the coupling from the other aggressor is offset by the two lobes of each transformer pair. The distant spacing between the two eight-shaped transformers reduces the mutual coupling. In a traditional QVCO [13], the magnetic coupling to a sub-VCO causes the quadrature phase deviation.

Figure 9a shows the layout of the EM coupling study between the twisted transformer and an O-shaped inductor 25 μm away from the aggressor edge. The input signal is applied to the input ports of the primary and secondary inductors. The top two input ports are for the primary, which uses the external turn in the top lobe in series with the internal turn in the bottom lobe. Figure 9b shows S₂₁ versus the frequency of the input signal. The O-shaped inductor at location B receives the least coupling because the fields generated by the two lobes offset each other. The suppression ratio at 8.5 GHz is about 45 dB. Figure 10a shows the layout for the secondary inductors by quadrature phase injection. The inner diameter of the transformer is 208 μm. Figure 10b shows S₂₁ versus the frequency of the input signal. The O-shaped inductor at location C receives the least coupling because the fields generated by the two lobes offset each other.

In simplicity, Figure 3 uses a closed-loop transmission line (TL), as shown in Figure 11a, with transformer-coupled TL with four unit cells, which can be replaced by a transformer-less composite right-/left-handed (CRLH) transmission line [18], as shown in Figure 11b, with the parameters given by the following:

$$L_3=C_2{\omega }^2{M}^2$$

(3a)

$$C_3={\displaystyle \frac{L_2}{{\omega }^2{M}^2}}$$

(3b)

$$C_2={\displaystyle \frac{C_{v1}}{2}}$$

(3c)

where C₁ is the parasitic capacitance of the transmission line, ω is the radian frequency, and M is the mutual inductance between L₁ and L₂. The phase constant β as a function of ω can be derived using the CRLH TL to draw the dispersion diagram, and d is the effective length of each unit cell. The phase shift βd of the unit cell is given by the following:

$$j\beta d=\sqrt{(j\omega L_1+{\displaystyle \frac{1}{j\omega C_3+\frac{1}{j\omega L_3}}})(j\omega C_1)}$$

(4a)

$$\beta d=\sqrt{(\omega L_1+{\displaystyle \frac{\omega L_3}{1-{\omega }^2{L}_3{C}_3}})(\omega C_1)}={\displaystyle \frac{\pi }{2}}$$

(4b)

For a quadrature oscillator, the resonant frequency from (4b) is determined by the following:

$${\omega }^2={\displaystyle \frac{(C_1{L}_1+C_1{L}_3)\pm \sqrt{{(C_1{L}_1+C_1{L}_3)}^2-4(L_3{C}_3{C}_1{L}_1){\left(\frac{\pi }{2}\right)}^2}}{2L_3{C}_3{C}_1{L}_1}}$$

(5)

Figure 11. (a) Closed-loop transformer-coupled transmission line with a highlighted unit cell. (b) The unit cell is replaced by a transformer-less equivalent unit cell.

Figure 11. (a) Closed-loop transformer-coupled transmission line with a highlighted unit cell. (b) The unit cell is replaced by a transformer-less equivalent unit cell.

3. Experimental Results

Figure 12 shows a microphotograph of the fabricated 0.18 μm QVCO with a chip area of 1.2 × 1.2 mm², including all test pads and dummy metal. The QVCO was measured on a printed circuit board and tested with an Agilent E5052B signal source analyzer (Agilent, Santa Clara, CA, USA). Figure 13 shows the measured frequency tuning range from 8.53 GHz to 10.0 GHz at V_DD = 1.2 V, and it is smaller than the pre-layout simulation, but the trend is in agreement with the simulated one. Figure 14 shows the measured spectrum of the VCO at V_T = 0 V; the carrier is at 8.536 GHz with an output power of −1.32 dBm, and the second harmonic is at 17.11 GHz with an output power of −20.13 dBm. Figure 15a shows the measured phase noise of the VCO at a power consumption of 5.8464 mW. The phase noise at a 1 MHz offset from the carrier at 8.637 GHz is −122.398 dBc/Hz. The corner frequency between the 1/f³ and 1/f² phase noises is 550 kHz. The figure of merit (FOM) is calculated using the following Equation (6):

$$\mathrm{FOM}=L\left\{\Delta \omega \right\}+10·\log \left(P_{DC}\right)-20·\log \left({\displaystyle \frac{{\omega }_o}{\Delta \omega }}\right),$$

(6)

where the symbols have their usual meanings. The FOM is −193.456 dBc/Hz. The FOM_T with tuning range percentage is given by the following:

$$\mathrm{FOMT}=FOM-20·\log \left({\displaystyle \frac{Tuning Range\%}{10}}\right)$$

(7)

The FOM_T is −195.96 dBc/Hz. Figure 15b shows measured phase noise at 1 MHz and 10 MHz versus V_T = 0 V. The RTWOs suffer from flicker noise up-conversion in the sub-VCOs.

Table 1. Performance comparison of standalone CMOS RTWO.

Ref.	Tech (μm)	fosc (GHz)	Vdd(V) Pdis, mW	Area (mm2)	PN @ 1 MHz dBc/Hz	FOM dBc/Hz
[6]	0.09	15.0	1.2/12	0.45 × 0.45	−109.6	−182.0
[12]	0.18	3.26	1.0/5.33	1.07 × 1.07	−122.14	−185.11
[13]	0.18	2.79	1.1/4.78	1.2 × 1.2	−121.4	−181.8
[14]	0.18	23.6	1.8/70.2	0.8	−105.0	−164
[19]	0.13	12.2	1.2/30	0.3 × 0.35	−105.2	−171.95
[20]	0.25	18	4/54	−	−98.0	−98.0
[21]	0.18	5.28	1.8/129	1.5 × 1.5	−102.0	−155.35
[22]	0.25Bi	18.5	1/38.4	−	−103.5	−
[23]	0.022	26.2	0.8/21	0.24	−108.5	−183.6
[24]	0.022	26.2	0.8/20	0.24 core	−109.2	−184.2
[25]	0.04	19.1	1.1/16.6	0.08 core	−106.4
[26]	0.18	32	1.2/54	1.3 × 1.3	−108.0	−177.7
[27]	0.12	45	1.2/19.2	0.25	−93	−173.0
[28]	0.13	16.2	1.2/5.8	simulated	−113.7	−190.3
[29]	0.028	19.8	1.3/75	−	−101.2	−168.4
[30]	0.13	37.7	−/16.2	−	−121@10	−180.6
[31]	0.18	3.4	1.7/19.2	1.2 × 1.2	−125.7	−185.4
[32]	0.18	17.5	−/2.3	0.56 × 0.183 (core)	−110.77	−191.95
This	0.18	8.53	1.7/5.84	1.2 × 1.2	−122.4	−193.4

compares the performance of various CMOS rotary traveling wave oscillators (RTWOs). The presented design reports a high-FOM CMOS RTWO.

4. Conclusions

Rotary traveling-wave oscillators have become one element for clock generation in RF circuits and system applications. This paper verified that, experimentally, a high-FOM (FOMT) RTWO is achievable in the CMOS process. This work presents a passive inductive layout for suppressing magnetic field coupling noise, and the inductive topology was verified in the VCO at 8.53 GHz. The VCO uses four eight-shaped 1:1 transformers to suppress magnetic field coupling interference, and the secondary inductors of the transformers are wired to form a coupling line for sub-VCOs. The passive coupling reduces the coupling flicker noise from sub-VCO FETs. The primary and the secondary inductors are operated at the maximum Q-factor at the operating frequency. The four sub-VCOs are injection-locked by traveling waves on the closed-loop twisted transmission line. The signal propagation is in one direction along the closed-loop transmission line due to the NP cross-coupled FET. Compared to other similar RTWOs, the designed VCO has a higher FOM, lower phase noise, and lower EMI (electromagnetic interference). The high-FOM RTWO demonstrates that this is a good RF VCO design technique. The circuit is extendable to generate multiple phases at millimeter-wave (mm-W) frequencies.