A GHz VCO using a new variable inductor for K band application

Transcription

1 Vol. 34, No. 12 Journal of Semiconductors December 2013 A GHz VCO using a new variable for K band application Zhu Ning( 朱宁 ), Li Wei( 李巍 ), Li Ning( 李宁 ), and Ren Junyan( 任俊彦 ) State Key Laboratory of ASIC & System, Fudan University, Shanghai , China Abstract: A novel transformer-type variable is proposed to achieve a wide tuning range at frequencies as high as K band. The variable is designed, and an intuitive model is built to analyze its performance by HFSS. A lot of mathematical analysis is done in detail. A VCO using the proposed variable is designed with TSMC 0.13 m technology for verification. The frequency tuning range of the VCO depends on the proposed variable. The phase noise of the VCO depends on the quality of the LC tank (including the proposed variable and varactors). So a specific AMOS varactor is implemented to improve its quality factor. The VCO is simulated at three typical TSMC fabrication corners (TT, FF, SS) to predict its measure results. The post simulation results shows that the VCO achieves a GHz continuous tuning range. Its phase noise results at 1 MHz offset are dbc/hz and dbc/hz respectively at the tuning frequencies of 19.6 GHz and 25.5 GHz. The VCO draws only 3 to 6 ma from a 1.2 V power supply. Key words: variable ; modeling; AMOS varactor; wideband DOI: / /34/12/ EEACC: Introduction A wide tuning range VCO is important for RF circuits in wideband applications. Capacitively-tuned LC-VCOs are most popular in meeting the demand of a wide tuning range Œ1. However, difficulties arise when they are used in K band because the capacitive quality factor (including DCCA and varactors) becomes a limitation. The topology of a capacitively-tuned LC-VCO is shown in Fig. 1. L P and C P are the inductance and the capacitance of the LC tank. f osc represents the oscillating frequency of the VCO. Generally, f osc is proportional to 1= p L p C p. Therefore, if the inductance is chosen to be constant, to vary the oscillating frequency by 1=k times, the capacitance must be k 2 times larger than the original value. Usually, a DCCA circuit and varactors are used for C p to realize the change of capacitance under 10 GHz. However, when the frequency is higher than 10 GHz, the quality factor of the DCCA circuit will sharply decrease, which directly causes the VCO to be unable to work. Therefore, to ensure that the quality factor of LC tank does not change with the tuning frequency, it would be better to use a variable and varactors instead of a DCCA circuit and varactors. This paper discusses the topologies of variable s, and modeling and theory analysis of the proposed transformertype variable is discussed. A wide-tuning range K- band VCO applied the proposed transformer-type variable is implemented. The design of the varactors and the output buffer are discussed respectively. Results and a performance comparison are presented. M1 Œ2 4. When M1 is off, the inductance between terminals A B is a sum of L 1, L 2, and L 3 and when M1 is on, it becomes a sum of L 1 and L 3. In Ref. [2], multilayer stacked s (MSIs) are used to realize L 1, L 2; and L 3. And a variable inductance from 8 to 23 nh at 2.4 GHz is realized with a 0.18 m one-poly-six-metal (1P6M) process. However, suppressing the degradation of the quality factor requires a large switch MOSFET, which degrades the self-resonant frequency of the. Therefore, this architecture is not suitable for high-frequency operation. A MEMS-type variable (Fig. 2(b)) consists of an and a ferromagnetic plate placed above the Œ5.The series inductance varies with the moving of the plate, which is not suitable for the process. A transformer-type variable (Fig. 2(c)) consists of two coupled s L 1 and L 2. When the current flowing through L 2 is changed by the switch MOSFET M1, the magnetic field around primary L 1 is changed. So the effective inductance of L 1 is changed. Because L 1 2. Topology of variable s In recent years, various methods have been used to realize variable s. A switch-type variable (Fig. 2(a)) consists of three s, L 1 L 3, and a switch MOSFET Fig. 1. Topology of a capacitively-tuned LC-VCO circuit. * Project supported by the National Natural Science Foundation of China (No ) and the National Twelve-Five Project (No. 513***). Corresponding author. w-li@fudan.edu.cn Received 3 May 2013, revised manuscript received 15 July Chinese Institute of Electronics

2 Fig. 3. Top view of the proposed transformer type variable. Fig. 2. Variable. (a) Switch-type variable. (b) MEMS-type variable. (c) Transformer-type. and L 2 is coupled by a magnetic field, proper design of switch MOSTET M1 can almost avoid the self-resonant frequency degradation of L 1 due to the parasitic capacitance of the switch MOSFET. Therefore, this architecture can be adapted for very high frequencies. In this paper, a transformer-type variable is designed and analyzed. Its utility in a K-band VCO is demonstrated. 3. Transformer-type variable s 3.1. Proposed transformer-type variable The structure of our proposed transformer-type variable is shown in Fig. 3. The thick top metal layer (M8) is chosen for s L 1 L 5 because of its smallest capacitance to the substrate and its smallest sheet resistance, which is 5.4 m/ in this design. The second top metal layer (M7) is used for introducing the supply terminal from primary L1, which is connected to M8 through VIA7. MOSFET M1, M2, M3 are used as switches for respectively controlling the current flowing through s L 2, L 3, L 4, L 5. The inductance of primary L 1 varies when M1, M2, M3 are ON or OFF. The left and right strips are used as one to maintain the symmetrical characteristic of the proposed variable. The quality factor of the proposed variable depends on the layer conductivity, the thickness between the signal layer and the substrate, the signal wire width W, and the metal line spacing S. In order to evaluate the performance of the proposed variable, careful simulation and modeling are strongly required. Fig. 4. The testbench of the proposed variable Modeling and simulation of the transformer-type variable The simulation test-bench is shown in Fig. 4. The terminals of every are placed with PORTs to simulate its performance. The scattering parameters (S-parameter) and the impedance parameters (Z-parameter) are obtained after EM simulation by the professional high frequency structure simulator (HFSS) from the Ansoft Corporation. S-parameters can be directly used for simulations in Cadence with N-port. Z-parameters are used to model the proposed variable. The inductances L, quality factors Q, coupling coefficients K as function of frequency can be extracted from the Z-parameters. These parameters are used to evaluate the performance of the proposed variable s. The inductance is calculated by using the following expression: L D Im.Z 11/ : (1) 2f

3 Fig. 5. The simulated inductance of L 1, L 2, L 3, L 4, L 5. Fig. 6. The simulated quality factor of L 1, L 2, L 3, L 4, L 5. Table 1. Parameters of the proposed variable. Unit: m Parameter W S H d 1 d 3 d 5 Value The quality factor is calculated by using the following expression: Q D Im.Z 11/ Re.Z 11 / : (2) The coupling coefficient K is calculated by using the following expression: s Im.Z 12 / Im.Z 21 / K D Im.Z 11 / Im.Z 22 / : (3) After several iterative designs, the dimension of the proposed variable is fixed. The metal line width W of every is 20 m. The line spacing S of s is 5 m. The metal line length d 1 of L 1 is 220 m. The metal line length d 3 of L 3 is 170 m. L 4 is the same as L 3. The metal line length d 5 of L 5 is 180 m. One side of L 2 is as long as L 3. The other side is as long as L 5. The distance H is 40 m. All these parameters are summarized in Table 1. The inductances of L 1, L 2, L 3, L 4, L 5 are shown in Fig. 5. The inductance of the primary coil is about 400 ph. The second inductance of the secondary coil is about 200 ph. The inductances of L 3 and L 4 are the same. The inductance of L 5 is the smallest. So, L 5 and L 3, L 4 can be used for fine tuning of the equivalent inductance of the primary coil. L 2 is used for coarse tuning of the equivalent inductance of the primary coil. In Fig. 6, the quality factors of L 1, L 2, L 3, L 4; and L 5 are depicted. In K band, from 18 to 26.5 GHz, the quality factors of L 1 and L 2 are higher than 30. The quality factors of L 3 and L 4 are higher than 20. The quality factor of L 5 is the lowest: it is nearly 15. In Fig. 7, the coupling coefficients between L 1 and L 2, L 3, L 4, L 5 are shown. L 1 and L 2 have the strongest coupling strength. The coupling coefficient K 12 is more than 0.4. However, the coupling strengths between L 1 and L 3, L 4, L 5 are as low as 0.3. A model of the proposed variable is shown in Fig. 8. Fig. 7. The simulated coupling coefficients between L 1, L 2, L 3, L 4, L 5. Fig. 8. Model of the proposed variable. The model and the simulated parameters such as inductance and quality factor provide an intuitive understanding of the proposed variable. In order to ensure correctness and simulation accuracy, the N-port tool is used. N-port is a simulation tool provided by Cadence. The S parameter in N-port can be directly used to run time-domain and frequency-domain simulations. The method can improve the simulation accuracy

4 Fig. 9. The basic schematic of a two-coil transformer-type variable. Fig. 10. The equivalent circuit of a basic two-coil transformer type variable when MOSFET M1 is ON Theory analysis of the proposed transformer-type variable In order to analyze the proposed variable s, a twocoil transformer-type variable is considered. The basic schematic is showed in Fig. 9. When MOSFET M1 is ON, it is equivalent as a resistance. The equivalent circuit is shown in Fig. 10. Z 1 represents the series resistance of L 1. Z 2 represents the sum of the series resistance of L 2 and on the resistance of MOS- FET M1. U 1 represents the voltage between terminals A and B. L 1 represents the inductance of the primary coil. I 1 represents the current through the L 1. L 2 represents the inductance of the second coil. I 2 represents the current through the L 2. M represents the mutual-inductance between s L 1 and L 2. K represents the coupling coefficient between s L 1 and L 2. There is: U 1 D I 1 Z 1 C j!l 1 I 1 C j!mi 2 ; (4) j!mi 1 D I 2.j!L 2 C Z 2 /: (5) The effective impedance between A and B is as follows: U 1 I 1 D Z 1 C j!l 1 C!2 M 2 j!l 2 C Z 2 : (6) If the s and MOSFET M1 is ideal, we have U 1 I 1 D j!l 1.1 K 2 /: (7) Equation (7) means that when MOSFET M1 is ON, the inductance of primary coil decreases. Fig. 11. The equivalent circuit of a basic two-coil transformer-type variable when MOSFET M1 is OFF. If the s and MOSFET M1 are not ideal, we have U 1 D Z 1 C!2 M 2 Z 2 I 1 L 2 2 C Cj! L 1!2 M 2 Z2 2 L 2 2 C L 2 : (8) Z2 2 Equation (8) means that the changes of inductance reduce because of the series resistance of L 2 and the onresistance of MOSFET M1. At the same time, the quality factor is reduced. So, a small on-resistance of MOSFET M1 is expected. When MOSFET M1 is OFF, it is equivalent as a capacitance, as shown in Fig. 11. There is: L eff D L 1 C!2 o M 2 C 2 1 o L 2C 2 : (9) In Eq. (9), L eff represents the equivalent inductance of the primary. Equation (9) means the inductance of the primary rises when MOSFET M1 is OFF. More interestingly, if the capacitance C 1 of the primary coil is considered, there is:.1 K 2 /! o 4.!2 s1 C!2 s2 /!2 o C!2 s1!2 s2 D 0: (10) In this equation, assuming L 1 C 1 D 1=! s1 2 and L 2C 2 D 1=! s2 2.! o represents the working frequency,! s1 represents the intrinsic oscillation frequency of the primary coil, and! s2 represents the intrinsic oscillation frequency of the secondary coil. Assuming n D! s2 2 =!2 s1, there is:! o D s.n C 1/ p.n C 1/ K 2 /n! 2.1 K 2 s1 : (11) / There are two solutions to Eq. (11). One is the lower oscillation frequency! o1. And the another is the upper oscillation frequency! o2. Careful design is required to determine at which oscillation frequency point the circuit works. For easily understanding this problem, the distribution relationship between! o1,! o2 and! s1,! s2 is depicted in Fig. 12. In Fig. 12, we can see that the lower oscillation frequency! o1 is lower than! s1 and the upper oscillation frequency! o2 is higher than! s1. In order to make the circuit robust and run at a high quality factor, the size of the switch MOSFET M1 should be small in order to make! s2 away from! s1. At the same time, it causes! o1 to be closer to! s1, which makes the variable work with a higher quality factor. The detailed mathematic derivation of Eq. (9) (11) and the relationship between! o and! s1 depending on n and K are described in Appendix A

5 Fig. 12. The quality factor of the variable versus the angular frequency. 4. Wide tuning range VCO Fig. 13. C V and Q V characteristics of the MOS varactor with different dimensions Varactor Generally, when frequency is lower than 10 GHz, the quality factor of the LC tank is limited by the. However, in K-band, it is the opposite. The quality factor of the capacitors (Q c 1=!R s C / decreases with frequency, while that of the depends on the design procedure. So, careful design and an optimized layout of the MOS varactor are strongly advised. Generally, the most commonly used on-chip varactors are inversion MOS (PMOS) or accumulation MOS (AMOS). Realizing the same capacitance change range, PMOS is larger than AMOS. It not only introduces more parasitic capacitance but also degrades the quality factor. As described in Ref. [6], if only the capacitance from the gate oxide and the resistance from the poly gate and the channel are considered, Q is Q Š 1!R s C D 12!C ox.r sheet; nw L 2 C R sheet; poly W 2 / ; (12) where R sheet; nw and R sheet; poly are the sheet resistances of the n-well and poly gate, W and L are the width and length of each finger,! is the working frequency, C ox is the gate-oxide capacitance per area. To increase Q, smaller W and L should be used. However, the penalty is a smaller capacitance change. Since R sheet; nw is more than 50 times R sheet; poly, L should be made smaller. At the same time, more fingers reduce the gate resistance of the varactor, which improves the high frequency performance. Figure 13 shows C V and Q V curves simulated at 25 GHz by Cadence, which is calculated by MATLAB. From Fig. 13, the gate length is 240 nm and the gate width is 500 nm, 25 fingers are preferred. A quality factor of 20 is achieved at a frequency of 25 GHz VCO and buffer design The VCO using the proposed transformer-type variable and its buffer circuit is shown in Fig. 14. M1 and M2 is an NOMS cross-couple pair, which generates a negative resistance to cancel the losses in the LC tank. M5 and M6 are the tail current sources of the VCO and the output buffer, respectively. C var1 and C var2 are the specific AMOS with a high quality factor. Fig. 14. The VCO using the proposed transformer-type variable and its buffer circuit. In this VCO design, the proposed variable is used to tune the frequency instead of using a traditional DCCA circuit. From Fig. 6, the quality factor of the proposed variable can be 30, which is almost two times that with the same inductance provided by the TSMC foundry. Besides, the specific varactor is also designed to improve the quality factor of the varactor provided by the TSMC foundry. Because of the high quality factor of the proposed transformer-type variable and the specific AMOS, the VCO shows an excellent phase-noise performance with low power consumption. The output buffer is designed with a common-source MOSFET and a transmission line, which is used as an

6 Fig. 15. The simplified equivalent circuit of the transmission line. Fig. 18. Tuning curves of the VCO. Fig. 16. The matching circuit of the output buffer. Fig. 19. Phase noise of the VCO. Fig. 17. Layout of the VCO. for matching 50 load. The transmission line is modeled by a lumped tank, as depicted in Fig. 15; a justified approximation because the total length of the line is about one-tenth of the wavelength Œ7. The matching circuit is shown in Fig. 16. Capacitor C 1 represents the sum of the PAD capacitance and other parasitic capacitances. Capacitor C 1 resonates with the transmission line at the frequency of 23 GHz, which makes the circuits match the load over the frequency from to 25.3 GHz. 5. Results and performance comparison The VCO is implemented in a TSMC 0.13 m process. Figure 17 shows the layout of the VCO. The tuning range of the VCO is obtained at the terminal V outc by changing the V TUNE of the varactors and the control bit V 3, V 2 and V 1 of the proposed variable. The phase noise of the VCO is simulated at the terminal V outc. The matching characteristic of output buffer is found through an S-parameter simulation with a 50 PORT at the terminal of V outc. The tuning characteristic of the VCO is shown in Fig. 18. Figure 19 gives the phase noise of the VCO. The matching characteristic of output buffer is depicted in Fig. 20. The quality factor of the proposed variable varies with the switch MOSFET being on or off. By means of tuning the variable, eight phase noise results at the different working frequencies can be obtained from Fig. 19. Since VCO performance is very sensitive to process variation, the VCO performances at three typical TSMC process corners TT, FF, SS are simulated and shown in Tables 2 and 3, respectively. The VCO tuning range covers the desired GHz band. The phase noise varies by less than 3.84% due to process variation, and its graphical result is depicted in Fig. 21. These results above can be used to foresee the measurement results due to the stability of TSMC process technology. The performance of the VCO is compared with other published VCOs in Table 4. Note that the VCOs presented in Refs. [3, 4] employ the switch-type variable. So, the VCOs in Refs. [3, 4] work at frequency as low as several

7 Table 2. Corner simulation results of the VCO tuning range. TT (GHz) FF (GHz) SS (GHz) K vco (MHz/V) VCO tuning range achieved GHz Table 3. Corner simulation results of the VCO phase 1 MHz offset. Phase noise variation due to process variation TT Fre. (GHz) PN (dbc/hz) FF Fre. (GHz) PN (dbc/hz) SS Fre. (GHz) PN (dbc/hz) Corner errors FF/TT (%) SS/TT (%) Fig. 20. Matching characteristics of the output buffer. Fig. 21. Phase noise variation due to process variation. gigahertz. The VCO in Ref. [8] is tuned by varactors. So, it achieves a relative narrow tuning range, which is just 12.2%. In Ref. [9], a triple-coupled transformer is used to tune the frequency. Therefore, the VCO can work at frequency as low as 100 GHz. However, it achieves an 11.2% relatively narrow band due to its varactor-less circuit structure. To compare the VCO performances, the figure of merit (FOM T / Œ10 is used in Table 4. It can be seen that because of the proposed transformer-type variable, the VCO in this work achieves a high FOM T of dbc/hz with a 22.2% tuning range at as high frequency as K-band. 6. Conclusion A novel transformer-type variable is proposed and an intuitive model is built to analyze the performance of the proposed variable. The mathematic analysis of the proposed variable is derived in detail and applied to a K-band VCO. Because of the proposed transformer-type vari- able,the VCO achieves a wide tuning range from 20 to 25.5 GHz. In addition, because of the high quality factor of the LC tank (including the proposed variable and varactors), the VCO achieves a low phase noise dbc/hz at the frequency 19.6 GHz and dbc/hz at the frequency 25.5 GHz. Appendix A This Appendix shows a detailed derivation of the two-coil transformer-type variable when the switch MOSFET M1 is off. In Eq. (6), we have U 1 D Z 1 C j!l 1 C!2 M 2 : I 1 j!l 2 C Z 2 Assuming Z 1 D 0; Z 2 D 1=j!C 2, we write (A-1) L eff D L 1 C!2 o M 2 C 2 1 o L 2C 2 : (A-2)

8 Parameter Ref. [3] MTT 2006 Ref. [4] EL 2012 Ref. [8] MWCL 2012 Ref. [9] ESSCIRC 2012 This work Process (nm) FOM T D PN 20 lg f0 Mf Table 4. Performance comparison with other works. Tuning method Tuning range Phase noise Power supply (GHz) f 1 offset f 2 carrier fre.) Switch-type variable Switch-type variable (5%) (24%) (18.8%) (19.4%) Varactor (12.2%) Power consumption (mw) Transformertype variable Transformertype variable (11.2%) (22.2%) F TR 10 C 10 lg PDC 1 mw GHz GHz GHz GHz GHz GHz GHz GHz GHz GHz FOM T * (dbc/hz) Table A-1. Relationship between! o1 and! s1 dependent on n and K. n, k L eff represents the equivalent of the primary. Equation (A-2) is the same with Eq. (9). Assuming K D p M L1, L L 2 C 2 D 1= 2 s2, we get 2 3 L eff D L C K 2 4! o! s2 1! 0! s2 : (A-3) 7 5 Multiply C 1 at both sides of Eq. (A-3) at the same time, assuming L 1 C 1 D 1=! s1 2, we get! 0! s1 D 1! 0! s2 1.1 K 2 /! 0! s2 ; (A-4).1 K 2 /! 0 4.!2 s1 C!2 s2 /!2 0 C!2 s1!2 s2 D 0: (A-5)

9 Table A-2. Relationship between! o2 and! s1 dependent on n and K. n, k Assuming n D!2 s2, the solutions of Eq. (A-5) is! s1 2 s.n C 1/ p.n C 1/! 0 D K 2 /n! 2.1 K 2 s1 : (A-6) / The relationship between the solutions and! s1 depended on n and K is shown in Tables A-1 and A-2. References [1] Berny A D, Niknejad A M, Meyer R G. A 1.8-GHz LC VCO with 1.3-GHz tuning range and digital amplitude calibration. IEEE J Solid-State Circuits, 2005, 40(4): 909 [2] Park P, Kim C S, Park M Y, et al. Variable inductance multilayer with MOSFET switch Control. IEEE Electron Device Lett, 2004, 25(3): 144 [3] Yim S M, Kenneth K O. Switched resonators and their applications in a dual-band monolithic LC-tuned VCO. IEEE Trans Microw Theory Tech, 2006, 54(1): 74 [4] Zou W, Chen X, Dai K, et al. Switched- VCO based on tapped vertical solenoid s. IEEE Electron Lett, 2012, 48(9): 509 [5] Choi D H, Lee H S, Yoon J B. Linearly variable with RF MEMS switches to enlarge a continuous tuning range. IEEE Transducers, 2009, 10(6): 573 [6] Hung C M, Ho Y C, Wu I C, et al. High-Q capacitors implemented in a process for low-power wireless applications. IEEE Trans Microw Theory Tech, 1998, 46(5): 505 [7] Razavi B. A 60 GHz receiver front-end. IEEE J Solid- State Circuits, 2006, 41(1): 17 [8] Liu S L, Tian X C, Hao Y. A bias-varied low-power K-band VCO in 90 nm technology. IEEE Microw Wireless Compon Lett, 2012, 22(6): 321 [9] Yi X, Boon C C, Lin J F, et al. A 100 GHz transformer-based varactor-less VCO with 11.2% tuning range in 65 nm technology. IEEE ESSCIRC, 2012: 293 [10] Soltanian B, Kinget P. A low phase noise quadrature LC-VCO using capacitive common-source coupling. IEEE ESSCIRC, 2006: