Analysis and Design of Differential LNAs with On-Chip Transformers in 65-nm CMOS Technology Takao Kihara, Shigesato Matsuda, Tsutomu Yoshimura Osaka Institute of Technology, Japan June 27, 2016
2 / 16 Outline Background Analysis of Differential LNAs with On-Chip Transformer Differential Common-Source (CS) LNA Differential Common-Gate (CG) LNA Design Considerations and Comparison Simulation Schematic Simulated Results Comparison Summary
Wearable devices with Bluetooth Low Energy (BLE) have required small-size RF modules Background Single-ended input/ output RF transceivers reduce PCB area RF2541 BLE Module (NiceRF Wireless Technology) Challenges: On-chip balun LNAs often employ differential topologies On-chip transformer / OUT GND Chip Transformer (balun) provides single-to-differential conversion greatly influences the LNA peformances: input impedance, gain, and noise figure Differential LNA 3 / 16
4 / 16 Objectives Analyze influences of transformer on Inductively-degenerated CS LNA (widely used) Cross-coupled CG LNA Analytical expressions Input impedance Current gain Noise figure Design considerations Required Q and L of inductors in transformer Comparison of topologies
5 / 16 Input Impedance of Transformer Loaded with LNA i 1 i 2 1 : n sl 1 sl 2 L 1 L 2 Z in,dif,lna smi 2 smi 1 Zin,dif,lna Z in,trans R 1 R 2 Input impedance of differential LNA without transformer, Z in,di f,lna Mutual inductance, M (= nkl 1 ), and coupling factor, k Parasitic resistances (R i = ω 0 L i /Q i, i = 1, 2) included ( jωnkl 1 ) 2 Z in,trans = R 1 + jωl 1 R 2 + jωn 2 L 1 + Z in,di f,lna
Input Impedance of Differential CS LNA Additional capacitors (C 1, C 2 ) resonate with inductors (L 1, L 2 and L s ) at operating frequency, ω 0 C 1 OUT_P C L L L L L V DD OUT_N C L Z in,cs = R 1 + ω2 0 n2 k 2 L1 2 R 2 + 2ω T L, s g m ω T = C gs + C 2 C 2 L 1 Z in,cs L 2 L s L s C 2 2ω T L s: Real part of input impedance of differential CS LNA without transformer, conventionally set to 50 Ω. For a larger L 1, we have to increase 2ω T L s accordingly to achieve input impedance matching. 6 / 16
7 / 16 Current Gain and NF of Differential CS LNA i 1 =v s / 2R s smi 1 / (R 2 +2w T 'L s ) sl 1 sl 2 v gs1 g m1 v gs1 smi 2 smi 1 s (C gs1 + C 2 ) 2sL s R 1 R 2 v gs2 g m2 v gs2 Current gain and noise factor: α cs = g m v gs1 v s /2R s = g m sm s(c gs + C 2 )(R 2 + 2ω T L s) = ω T nkl 1 R 2 + 2ω T L, s F cs = 1 + F R1 + F R2 + F RLs + γ 2R s g m R s + 2α 2 cs Current gain (α cs ) influences noise figure. α 2 csr eq,ll
8 / 16 Input Impedance of Differential CG LNA Additional capacitors (C 2 ) resonate with inductors (L 1 and L 2 ) at ω 0 OUT_P L L L L V DD OUT_N Equivalent resistance of LC tank (L 2, C 2 and C gs ): R eq,l2 = Q 2 2 R 2 Input admittance of CG LNA without transformer: g m + 1/R eq,l2 C L L 1 L 2 Z in,cg C 2 C C C 2 C L Z in,cg R 1 + k 2 n 2 ( g m + 1/R eq,l2 ), where k 2 1.
Current Gain and NF of Differential CG LNA i 1 =v s / 2R s sl 1 sl 2 g m1 v gs smi 2 smi 1 v gs 2s(C gs + C 2 ) R 1 R 2 g m2 v gs Current gain and noise factor: α cg = g m v gs1 sm v s /2R s = R 2 +sl 2 g m 1 R 2 +sl 2 + g m + 2s(C gs + C 2 ) F cg = 1 + F R1 + F R2 + γ 2α 2 cg g m R s + 2R s α 2 cgr eq,ll. kg m n ( g m + 1/R eq,l2 ), Dependence of α on transformer design parameters (L and Q) provides us useful information 9 / 16
10 / 16 Calculated Current Gain (α cs and α cg ) vs. L 1 and CS LNA α cs = ω T nkl 1 R 2 + 2ω T L s CG LNA kg m α cg = n ( ) g m + 1/R eq,l2 α cs, α cg 0.9 0.85 0.8 =8 0.75 =6 0.7 =4 0.65 α cs α cg =8 =6 =4 0.6 0.55 Increasing Q i results in higher current gains f 0 =2.45 GHz, g m =17 ms, γ=1 n=0.92, k=0.90, Q Ls =6 C c =10 pf, R eq,ll =380 Ω 0.5 2 2.5 3 3.5 4 4.5 5 L 1 [nh] α cs has the maximum value (around L 1 = 2.6 nh), while α cg increases as L 1 increases CG LNA obtains a higher current gain for L 1 > 3.5 nh
11 / 16 Calculated NF vs. L 1 and F cs =1 + F R1 + F R2 + F RLs + γ + 2α 2 cs 2R s α 2 csr eq,ll, F cg = 1 + F R1 + F R2 + γ g m R s + 2α 2 cg 2R s α 2 cgr eq,ll. g m R s NF [db] 6.5 6 5.5 =4 Q 5 1 =6 Q 4.5 1 =8 Increasing Q i results in lower NFs Transformer with Q > 6 provides NF < 5 db f 0 =2.45 GHz, g m =17 ms, γ=1 n=0.92, k=0.90, Q Ls =6 C c =10 pf, R eq,ll =380 Ω NF cs NF cg =4 =6 =8 4 2 2.5 3 3.5 4 4.5 5 L 1 [nh] CG LNA has a lower NF than CS LNA for L 1 > 3.5 nh
12 / 16 Schematics (Half) of Differential CS and CG LNAs OUT_P 1.0 pf 0.8 pf 0.7 V 4.1 nh 72 mm 60 nm 48 mm 120 nm 4.1 nh 1.9 ma 72 mm 60 nm 48 mm 120 nm 0.7 V OUT_P 1.0 pf 510 mv 0.7 pf 1.8 nh 0.6 pf 10 pf 510 mv 1.9 ma Renesas Silicon-on-Thin-Buried Oxide (SOTB) 65-nm CMOS Frequency=2.45 GHz; Current consumption=3.8 ma@0.70 V
13 / 16 Layout of Transformer Structure Two inter-winding symmetric octagonal inductors Stacked with top three metal layers (1.7 µm in thickness) Outer diameter (d out ): 300 µm Metal width: 10 µm To LNA Characteristics@2.45 GHz (Simulated with Momentum) L 1 = 3.6 nh, L 2 = 3.1 nh = 5.7, Q 2 = 5.4 k = 0.91 GND
14 / 16 Simulated S 21 and NF of CS and CG LNAs 18 S 21 [db] 20 10 0 NF [db] 16 14 12 10 8 CS LNA CG LNA 10 CS LNA CG LNA 20 1 2 3 4 5 Frequency [GHz] 6 4 2 1 2 3 4 5 Frequency [GHz] CG LNA achieved a slightly higher gain and a lower NF ( S 21 = 20.9 db, NF = 4.55 db) than CS LNA ( S 21 = 20.4 db, NF = 5.18 db)
15 / 16 Comparison between Simulations and Calculations Transformer Simulated Calculated LNA d out L 1 S 11 S 21 NF S 21 NF [µm] [nh] [-] [db] [db] [db] [db] [db] Spec. - - - < 10 >20 <5 >20 <5 CS 300 3.6 5.7 27.2 20.4 5.18 21.0 4.80 360 5.3 6.2 25.8 20.7 5.53 20.8 4.78 CG 300 3.6 5.7 18.8 20.9 4.55 21.0 4.68 360 5.3 6.2 25.9 21.0 4.42 21.6 4.57 f 0 = 2.45 GHz, V DD = 0.7 V, I DD = 3.8 ma. f 0 = 2.45 GHz, g m = 17 ms, γ = 1, Q Ls = Q LL = 6, C c = 10 pf. Two transformers (d out =300, 360 µm) are used Calculated NFs of CS LNAs are slightly lower than simulations, due to parasitic capacitances of transformer Calculations of CG LNAs agree with simulations, because these capacitances can be considered as C gs
16 / 16 Summary Derived analytical expressions for differential CS and CG LNAs with on-chip transformers: Calculations agree well with simulations, except for NF of CS LNA CG LNA (with L >3.5 nh) achieves a higher gain and lower NF than CS LNA Presented design considerations: Minimum requirements for Q and L of transformer: Q >6 for NF >5 db and L >3.5 nh for CG LNA Significantly reduce the design efforts to differential LNAs with on-chip transformers.