LC-Type Digitally Controlled Oscillator
4.2. Wide Tuning Range Digitally Controlled Oscillator
4.2.1. Circuit Implementation
Short range multi-Gbps wireless interconnects has motivated marvelous research efforts recently [66]-[76]. At 60-GHz unlicensed frequency band, a 7-GHz wide spectrum is provided for up to 6-Gbps UWB applications. With the rapid developments of the VLSI process, nano-meter CMOS is considered as promising technologies to make RFICs for the broadband wireless interconnects cost effective and feasible. In the RF transceiver front-end, LC voltage-controlled oscillators (VCOs) are extensively used in frequency synthesizers to provide local carriers for up and down frequency conversion. Thus its performance is essential to the wireless transceiver. Major design issues of a VCO are focused on oscillating frequency, phase noise, output power level, and frequency tuning range. For portable devices, the power dissipation is also of special concern.
Conventionally, millimeter-wave (MMW) band LC-VCOs employ accumulation-mode MOS (A-MOS) varactors for frequency tuning [77]-[82]. For a typical LC-VCO, the loading capacitance includes the parasitic capacitance contributed by the succeeding buffer stage and path routings. In order to achieve 60-GHz operating frequency, the varactor capacitance (Cvar) and the corresponding tuning range become severely limited. This issue becomes even more critical under low supply voltage, which is required for nanometer CMOS operation.
It is well known that the phase noise performance of a VCO degrades when the VCO gain, KVCO, increases [84]. However, for a single band VCO, KVCO is proportional to its oscillating frequency for the same frequency tuning percentage. Considering an oscillator with 10% frequency tuning range and 1-V tuning voltage, its KVCO is 180 MHz/V at oscillating frequency of 1.8 GHz, but increases to 6 GHz/V if the output frequency is raised to 60 GHz. Therefore, for broadband MMW applications, multi-band VCO is necessary to degenerate VCO gain KVCO and alleviate phase noise performance degradation. However, Fig. 4.5 The front-end architecture for a 60 GHz dual-IF UWB system
42 Chapter 4. LC-Type DCO
conventional capacitor bank for multi-band operation is hardly applicable in the 60-GHz case since the Cp in the capacitance bank is too large to be tolerable. Some magnetic tuning methods have been reported [85]-[76] to increase the frequency tuning ranges of LC-tank VCOs though. Their oscillating frequencies are far less than 60 GHz.
In this section, a 40 GHz DCO employing a novel variable inductor (VID) is proposed.
Based on magnetic tuning scheme, it achieves multi-band as well as broad-band operations without sacrificing its oscillation frequency. On the other hand, measurement results show that the output frequency of a 40 GHz DCO is distributed from 37.6 GHz to 43.4 GHz corresponding to 14% tuning range. It is suitable to a dual-IF architecture for a 60 GHz UWB system shown in Fig. 4.5, and can be incorporated with digital RF processor [40]-[50] in further.
Fig. 4.6(a) illustrates the schematic of the proposed VID, which consists of a transformer T1 and a variable resistor Rv. L1 and L2 respectively represent the self inductance of the primary and secondary coils of T1, k is the coupling factor of the primary and secondary coils, and Cv is the parasitic capacitor at the secondary coil. The VID can be modeled as a variable inductor Leq in parallel with a variable resistor Req, as is illustrated in Fig. 4.6(b). Both Leq
and Req are functions of Rv and the radian frequency ω. The Leq and Req can be derived as that Fig. 4.6 (a) The proposed variable inductor (b) equivalent circuit model
If the self resonant frequencies of Cv and L2 are larger than the operating frequency ω, i.e.
ω2CvL2<1, Leq increases with the increment in Rv. Thus, the minimum equivalent inductance Lmin is equal to Leq(0,ω), and can be calculated as
(
0,)
11(
2)
Leq ω = L −k (4.6)
Contrarily, the maximum equivalent inductance Lmax is equal to Leq(∞,ω), and can be calculated as
From (4.6) and (4.7), it can be seen that only Lmax depends on the parasitic capacitance Cv, and its lower bound is L1 (i.e. Lmax > L1). In this situation, the inductance tuning ratio α, become negative if Rv is too large. This situation should be avoided in the VID design for the VCO application.
Some simulations are performed to verify the derived results. Fig. 4.7 shows the layout
25µ
Fig. 4.7 The 1:1 Transformer layout view
44 Chapter 4. LC-Type DCO
of the transformer used in the simulations. The inner radius of the primary (secondary) coil is 25 μm (37 μm); the metal width is 9 μm; and the space between the first and second coils is 3 μm. By EM simulation, the self-resonant frequency of the transformer is about 194 GHz. The self inductance of the primary (secondary) coil is about 123 pH (175 pH) and the coupling factor is about 0.45.
Fig. 4.8 shows the simulation results of Leq against Rv with different Cv around 60 GHz under the constraint of ω2CvL2 < 1. The Leq derived in (4.4) is also shown for comparison. It can be seen that Leq increases along with the increment in Rv. The inductance tuning ratio α is larger than or equal to k2 (i.e. 0.2) in all cases. Also, only Lmax is dependent on Cv as predicted by (5). The proposed lumped model shown in Fig. 4.6(a) can accurately represent its inductance. The other important parameter of the proposed VID is its quality factor Qeq. However, Qeq is strongly dependent on the parasitic resistors of the transformer which are neglected in the lumped model shown in Fig. 4.6(a). By taking the parasitic resistors into account, the Qeq can be calculated as
Fig. 4.8 Simulated and calculated Leq for ω2CvL2 < 1
Fig. 4.9 Simulated and calculated Qeq when ω2CvL2 < 1
( ) ( ) ( )
simulated and calculated Qeq with different Cv are plotted against Rv at 60 GHz in Fig. 4.9.The frequency response of the quality factor has a “V” shape, which reveals that the VID has a better quality factor in the extreme cases where Rv is nearly short or open circuit. In either case, the magnetic energy dissipated in the passive Rv can be minimized.
On the other hand, a linear operation of DCO is also proposed. The oscillating frequency of LC-tank oscillators can be derived as
( ) 1
where ωcenter is the center frequency of oscillator and Lcenter is the corresponding inductor value, ΔL denotes the deviation value from Lcenter. In the proposed VID, the inductance tuning ratio ΔL/ Lcenter is about 0.13. Hence, a linear frequency tuning of proposed VCO can be realized by a linear VID.
According to the curve of Leq shown in Fig. 4.10, it can be observed that Leq has an almost linear region when Rv is small. Therefore, we rearrange the equation (4.4) of Leq and the linear region can be approximated as
Fig. 4.10 The calculated Leq and derived Rlin of the VID
46 Chapter 4. LC-Type DCO
( )( )
2 2 2 2 2
2 1 6 1
Rlin =ω L −k k − when ω2C Lv 2 < (4.12) 1 Furthermore, the linear inductance under Rlin can be also approximated as
( )
(
2) (
2)
The above equation reveals that the linear multi-band operation can be designed by employing a linear variable resistor under Rlin. Fig. 4.10 shows the calculated results of Leq
against Rv with different Cv in solid line and the derived Rlin in dot line. Fig. 4.10 can be observed that the linear region is almost unaffected by the varied Cv. It means that the linear range of VID is nearly independent to the ω2CvL2.
In order to design a linear resistor, a reconfigurable transmission line is proposed, as shown in Fig. 4.11. The input impedance of a terminated resistance shunt with a variable length open stub and can be derived as
( ) 0 ( ) 0 0 ( )
where Z0, β and denotes the characteristic impedance, phase velocity and length of the transmission line, respectively. The ZL presents terminated resistance. When Z0 is designed to impedance match to ZL, the real part of Zin can be approximated as
Fig. 4.11 The reconfigurable transmission line
( ) ( )
It reveals that the real part of Zin is proportional to the length of open stub (
). To prevent the self resonant frequency of secondary coil approaches oscillating frequency caused by parallel open stub, the capacitive loading on imaginary part of Zin can just be compensated by the residual transmission line (
tot−
) connected to the secondary coil of transformer.According to Fig. 4.10, the influence on the imaginary part of Zin to equivalent inductance can be neglected under the linear region of VID.
The detail schematic of a 4-bits linear VID is shown in Fig. 4.12. The transmission line is divided equally into 16 segments by 16 equal MOS switches. The switches are turn one by one to reconfigure the length of open stub. One the other hand, the parasitic capacitance (Cds) of each switch can be absorbed in transmission line by nature, and the turn on resistance (ZL)
Fig. 4.12 The proposed 4-bits linear VID
(a) (b)
Fig. 4.13 (a) The EM simulated and theoretic real part of Zeq and (b) equivalent inductance and quality factor of linear VID
48 Chapter 4. LC-Type DCO
is matching with Z0. Based on EM simulation, L3, L4 and k2 of the transformer are 100 pH, 129 pH and 0.6, respectively, and ZL (Z0) and β of the transmission line are 46 Ω and 0.08 rad/
, respectively. Fig. 4.13(a) shows the theoretical approximated and EM simulated real part of Zeq. The equivalent inductance and quality factor of linear VID is distributed from 58 pH to 82 pH and 5.5 to 3.8, respectively, as shown in Fig. 4.13(b).By using the proposed linear VID, a 40-GHz DCO is designed and fabricated in a 90-nm CMOS technology for a dual-IF 60GHz UWB system. The circuit schematic is shown in Fig.
4.14, where the transformer L3 and L4 is implemented by the single-turn 1:1 transformer. In this experimental prototype, the 4 bits linear VID is controlled by digital codes Vsw1 to Vsw16
for coarse tuning, a 2-bits capacitor bank is for fine frequency tuning, and also preserves a delta-sigma inputs for frequency interpolation.
In order to reduce the parasitic capacitance at the resonator, the negative impedance converter is composed of M1 and M2 cross-coupled pair. The negative resistance provided by the cross-coupled pair M1 and M2 is denoted as –Rneg, which is approximately equal to –2/gm, and gm is the small-signal transconductance of M1/M2. Rneg must be smaller than Req to
Fig. 4.14 The circuit schematic of DCO using 4-bits linear VID
the entire frequency range. The oscillating frequency ω of the VCO can be derived as
The VCO frequency tuning range ωmax and ωmin can be calculated as
Based on (9) and (10), the frequency tuning range (β) of the VCO can be derived as
max min
2
50 Chapter 4. LC-Type DCO
4.2.2. Experimental Result
The chip micrograph of DCO is shown in Fig. 4.15. The core size is 0.5 × 0.15 mm2. The circuit is measured with on-chip probing. The DCO consumes 16 mA under a 1.2 V power supply. There are two buffers at output of DCO results in about 90 fF loading capacitance, one is for measurement and another is for next stage frequency divider. Under this condition, the measured output frequency versus digital control code is shown in Fig.
4.16. The output frequency is distributed from 37.6 GHz to 43.4 GHz which meets the requirement of dual-IF 60GHz UWB system (38.8 GHz to 43.2 GHz). The proposed DCO have 14 % tuning percentage while frequency resolution is about 100 MHz per step. A finer frequency resolution can be achieved in further by incorporating with high speed dithering
Fig. 4.15 The chip microphotograph of DCO
Fig. 4.16 Measured frequency tuning range versus input code of the DCO
as frequency interpolation. By taking instrument signal loss into account (including the loss of probes, cables and adapters), the output power varies from -15 dBm to -11 dBm due to the variation of quality factor within the entire frequency range. The measured phase noise performance at 10-MHz offset within the entire frequency tuning range is plotted in Fig. 4.17.
Fig. 4.18 shows the measured VCO output spectrums at different frequencies.
The performance benchmark of the proposed oscillator and the prior art in the literature are summarized in Table 4.1. Three different figures of merits are illustrated to investigate
where PN is the phase noise at the offset frequency Δf, fo is the oscillating frequency, Pcons is the power consumption, and TP is the frequency tuning percentage. The proposed DCO has the widest tuning range and moderate resolution but sacrificing some FOMT among the DCO beyond 40 GHz. Besides, for application in 60 GHz UWB system, the proposed DCO meets the requirement while has a finest frequency resolution.
Table 4.1 Performance comparison with MMW DCO
Reference [89] [88] This work
52 Chapter 4. LC-Type DCO
A novel variable inductor is proposed in this section. By using the variable inductor, a DCO is designed in the MMW frequency band and the DCO has a wider tuning range than the conventional VCO using varactors. Moreover, in comparison with conventional capacitor
Fig. 4.17 Measured DCO phase noise at 10-MHz offset of the DCO
(a) (b)
(c)
Fig. 4.18 Measured output spectrums with noise markers at (a) 38 GHz (b) 41.6 GHz (c) 43.3 GHz
bank, multi-band operation can be achieved without severely decreasing the oscillating frequency and increasing the chip area. The measurement results of 40 GHz DCO using proposed VID is suitable to a Dual-IF architecture for 60 GHz UWB system, and can be incorporated with digital RF processor [40]-[50] in further.