- Email: [email protected]
Power amplifier resilient design for process, voltage, and temperature variations
Microelectronics Reliability 53 (2013) 856–860
Contents lists available at SciVerse ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Power amplifier resilient design for process, voltage, and temperature variations J.S. Yuan ⇑, E. Kritchanchai Department of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA
a r t i c l e
i n f o
Article history: Received 7 November 2012 Received in revised form 7 January 2013 Accepted 7 February 2013 Available online 26 March 2013
a b s t r a c t This paper presents RF power amplifier adaptive body bias compensation technique for output power and power-added efficiency resilient to process, supply voltage, and temperature (PVT) variations. The adaptive body biasing scheme uses a current source for PVT sensing to provide resilience through the threshold voltage adjustment to maintain power amplifier performance over a wide range of variability. Analytical equations are derived for physical insight. ADS simulation results show that the resilient body biasing design improves the robustness of the power amplifier in output power and power-added efficiency over process, supply voltage, and temperature variations. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction CMOS technology continues device scaling for high integration. However, as feature sizes shrink and chip designers attempt to reduce supply voltage to meet power targets in large multi-core systems, parameter variations are becoming a serious problem. Parameter variations can be broadly classified into device variations incurred due to imperfections in the manufacturing process and environmental variations and on-die temperature and supply voltage (VDD) fluctuations [1]. Smaller feature size further makes CMOS circuits more vulnerable to process, supply voltage, and temperature (PVT) variability. Large design margin is then needed to insure circuit robustness against reliability issues. Using PVT and long-term reliability resilience design is becoming an essential design requirement for future technology nodes and may reduce overdesign, while increasing yield and circuit robustness. Recently, many papers on reliability and variability for analog, digital, and mixed circuits have been published [2–13]. Chen and Gielen [4] used post-fabrication calibration to static errors in the design of a 14-bit current steering digital-to-analog converter. Dierickx [5] and Pananikolaou [6] presented the runtime monitoring and countermeasures to compensate for variability and reliability errors. Kim et al. [7] fabricated an on-chip reliability monitor for measuring digital circuit frequency degradation. Yamauchi et al. [8] presented an X-band monolithic-microwave integrated-circuit power amplifier with a simplified on-chip temperature compensation circuit composed of diodes and a resistor. Gómez et al. [9] studied process and temperature compensation circuits for RF low-noise amplifiers and mixers. Yuan and Tang [10] used adaptive gate biasing for RF circuit design for reliability. ⇑ Corresponding author. E-mail address: [email protected] (J.S. Yuan). 0026-2714/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2013.02.003
Liu and Yuan [11] proposed resilient body biasing design to reduce the sensitivity of RF power amplifier (PA) to the transistor parametric variations. Kang et al., [12] developed on-chip variability sensor using phase-locked loop to track various sources of circuit variations. Zhang and Apsel [13] demonstrated a scalable, process-and-temperature compensated GHz ring oscillator with a low variation addition-based current source to improve temperature stability and process variation effect. In this paper, using adaptive body biasing technique to minimize PVT variations of RF class AB power amplifier is evaluated. The adaptive body bias is generated using an on-chip currentsource to track process, supply voltage, and temperature variations. The organization of this paper is organized as follows. In Section 2 the analytical equations of current-source sensing as a signature for on-chip adaptive body biasing is presented. In Section 3 the sensitivity of RF power amplifier with resilient body biasing is investigated and compared with the PA without body biasing. ADS circuit simulation results are provided. Finally, a conclusion is given in Section 4. 2. Current-source sensor An on-chip variability sensor using current source is proposed to detect process, supply voltage, and temperature variations or even reliability degradation stemming from hot electron effect. The PVT variations yield a control signal from the designed current source. In Fig. 1 the current-source circuit is made of n-channel transistors M1, M2 and M3. The transistors M1 and M2 have the same width and length and two times width of transistor M3. On the right branch in Fig. 1, a resistor R is used to set a control voltage VCtrl. The reference current Iref is dependent on the PVT fluctuations. The Kirchhoff’s current law to solve for VCtrl is given by
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J.S. Yuan, E. Kritchanchai / Microelectronics Reliability 53 (2013) 856–860
R2 R1 Vref VABB Vctrl R1 R2 Fig. 3. Level shifting circuit. Fig. 1. Current-source circuit schematic.
2
V Ctrl ¼ V DD Iref R
DV Ctrl
ð1Þ
and Iref is the reference current and can be obtained as [14]
Iref
ðV DD V T1 V T3 Þ2 ¼ qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 2L1 3 þ K2L Kn W 1 nW3
2 6eox R ðV DD V T1 V T3 Þ 7 4 Dln q ffiffiffiffiffi ffi q ffiffiffiffiffi ffi 2 5 tox 2L1 3 þ 2L W1 W3 2 3
ð2Þ
62RðV DD V T1 V T3 Þ7 þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T1 2L1 3 þ K2L Kn W 1 nW3 2 3
where VT is the threshold voltage, L is the channel length, W is the channel width, and Kn is the transconductance factor (Kn = lneox/tox). Subscripts 1 and 3 represent the transistors M1 and M3, respectively. The VCtrl shift because of supply voltage variation is derived using (1 and 2)
@V Ctrl 2RðV DD V T1 V T3 Þ ¼ 1 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 @V DD 2L1 3 þ K2L KnW1 nW3
3
2RðV DD V T1 V T3 Þ7 6 ¼ 41 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV DD 2L1 3 þ K2L KnW1 nW3 2 3
62RðV DD V T1 V T3 Þ7 þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T3 : 2L1 3 þ K2L Kn W 1 nW3
ð3Þ 2.1. Tuning for variability
The VCtrl shift due to mobility fluctuation is given by
The sensitivity of the class AB PA is evaluated in Fig. 2. The PVT variations change behaviors of the PA and also degrade the performance. In the simulation, the PVT variations are given to the PA circuit. Adaptive body biasing is used to find a range of body biasing voltage (VABB) to compensate each variation. VCtrl signal is efficiently transformed to an optimal body bias signal for power amplifier application. From a range of VABB, an operational amplifier is used as a voltage shifter and amplifier to adjust the VCtrl to meet a required VABB (see Fig. 3). Choosing appropriate size of resistor R1 and R2 using (7) provides a matched VABB for PA. For example, for a reference voltage (Vref) of 0.4 V, R1 and R2 can be designed at 500 O and 1500 O, respectively.
2
@V Ctrl eox R ðV DD V T1 V T3 Þ ¼ ffi qffiffiffiffiffiffi2 tox qffiffiffiffiffi @ ln 2L1 3 þ 2L W1 W3
ð4Þ
Furthermore, the VCtrl shift resulting from fluctuation of the threshold voltage from M1 or M3 is
@V Ctrl 2RðV DD V T1 V T3 Þ ¼ qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 : @V T1;3 2L1 3 þ K2L KnW1 nW3
ð5Þ
Combing (3)–(5) yields the overall VCtrl variation as follows:
VG
V DD
Rg
Ld Cout
RFin
ð6Þ
Input Matching
Cin Input Matching
M1
VABB
Lout
Lin
Fig. 2. A class AB PA with adaptive body biasing.
RFout
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J.S. Yuan, E. Kritchanchai / Microelectronics Reliability 53 (2013) 856–860
V ABB ¼
R2 ðV Ctrl V ref Þ R1
ð7Þ
Due to the body effect, the threshold voltage of the power amplifier transistor is described by the following expression
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi V T ¼ V T0 þ cð 2/F V ABB 2/F Þ
ð8Þ
where c is the body effect factor and /F represents the Fermi potential. The threshold voltage shift of the PA transistor is modeled by the fluctuation of VT0 and VABB as
@V T @V T DV T0 þ DV ABB @V T0 @V ABB
120 115
c
¼ DV T0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DV ABB 2 2/F V ABB
ð9Þ
From (7) the VABB shift is given by
DV ABB ¼
@V ABB R2 DV Ctrl ¼ DV Ctrl @V Ctrl R1
ð10Þ
Thus, the threshold voltage shift of the power amplifier input transistor due to PVT variations are summed as
82 3 > < 2RðV V V Þ 6 DD T1 T3 7 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 41 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV DD DV T ¼ DV T0 2R1 2/F V ABB > 2L1 2L3 : þ KnW3 KnW1 2 3 2 3
105 100 95
85 80 0.48
ð12Þ
Assume the VGS shift is proportional to the fluctuation of VDD.
DV GS ¼ aDV DD
ð13Þ
110
Kn W3
Kn W1
Kn W3
In the above equation the terms beyond DVT0 represent the VDD, mobility, and threshold voltage compensation effects. To normalized output power degradation is related to the normalized drain current degradation as follows [15]:
DPo DID Po ID
ð15Þ
3. Results and discussion The power amplifier with the current source compensation technique is compared with the PA without compensation using
after VABB compensation
105 100 95
before compensation
90 85 80
360
375
390
405
420
435
Mobility (cm2/V s) .
Fig. 5. Output power versus mobility variation.
120 before after compensation
115
Output Power (mW)
Kn W1
0.56
115
where a is a fitting parameter. Using (11)–(13) the fluctuation of drain current normalized to its fresh current is expressed as follows: DID Dln 2aDV DD 2 cR2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ þ DV T0 ID ln V GS V T V GS V T 2R1 2/F V ABB 82 3 2 3 > < 2RðV DD V T1 V T3 Þ7 6 6eox 2RðV DD V T1 V T3 Þ7 41 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV DD 4 qffiffiffiffiffiffi qffiffiffiffiffiffi2 5Dln > t ox 2L1 2L1 : 3 3 þ K2L þ 2L Kn W1 W1 W3 nW3 91 2 3 2 3 > = 62RðV DD V T1 V T3 Þ7 62RðV DD V T1 V T3 Þ7 C þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T1 þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T3 A ð14Þ > 2L1 2L3 2L1 2L3 ; þ þ
0.54
120
Output Power (mW)
@ID @ID @ID Dln þ DV GS þ DV T @ ln @V GS @V T
0.52
Fig. 4. Output power versus threshold voltage shift.
Kn W3
The drain current fluctuation subjects to key transistor parametric drifts Dln, DVGS and DVT can be modeled as
0.50
Threshold Voltage (V)
2 6eox R ðV DD V T1 V T3 Þ 7 62RðV DD V T1 V T3 Þ7 4 5Dln þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T1 q ffiffiffiffiffi ffi q ffiffiffiffiffi ffi 2 tox 2L1 2L1 3 3 þ 2L þ K2L W1 W3 KnW1 nW3 9 2 3 > = 62RðV DD V T1 V T3 Þ7 þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T3 ð11Þ > 2L1 ; þ 2L3
DI D ¼
before compensation
90
cR2
KnW1
after VABB compensation
110
Output Power (mW)
DV T ¼
ADS simulation. For the process variation effect, the output power is evaluated against threshold voltage and mobility variations as shown in Figs. 4 and 5. It is clear from Figs. 4 and 5 that the power amplifier with adaptive body bias is more robust against threshold voltage variation (see Fig. 4) and mobility fluctuation (Fig. 5). For the process variation effect, the output power of the PA has also been evaluated using different process corner models dueto inter-die variations. The simulation result of the fast–fast, slow–slow, and nominal–nominal models is shown in Fig. 6.
110 105 100 95 90 85 80 ff
tt
ss
Process Models Fig. 6. Output power versus process corner models.
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J.S. Yuan, E. Kritchanchai / Microelectronics Reliability 53 (2013) 856–860
Clearly, the PA using the adaptive body bias compensation exhibits better stability against process variation effect. Figs. 7 and 8 show the output power of the power amplifier versus temperature variation and supply voltage change, respectively. As seen in Figs. 7 and 8 the output power of the PA using the adaptive body bias compensation technique demonstrates less sensitivity over temperature and VDD variations.
In addition, the power-added efficiency of the power amplifier with or without adaptive body bias compensation is examined against semiconductor process variations effects. Figs. 9 and 10 display the improvement of power-added efficiency of the PA with ABB compensation over that without adaptive body bias for the threshold voltage shift (see Fig. 9) and mobility variation (see Fig. 10).
45
Power-added Efiiciency (%)
120
Output Power (mW)
115 110
after VABB compensation
105 100 95 before compensation
90 85
44 after VABB compensation
43 42 41
before compensation
40 39 350 360 370 380 390 400 410 420 430
80
Mobility (cm2/V s) .
0
20
40
60
80
100
o
Temperature ( C)
Fig. 10. Power-added efficiency as a function of mobility.
Fig. 7. Output power versus temperature.
45
Power-added Efiiciency (%)
120
Output Power (mW)
115 after VABB compensation
110 105 100
before compensation
95 90
before after compensation
44
43
42
41
40
85 80 2.2
39
2.3
2.4
2.5
2.6
2.7
ff
2.8
tt
ss
Process Models
Supply Voltage (V)
Fig. 11. Power-added efficiency versus process corner models.
Fig. 8. Output power versus supply voltage.
45
45 after VABB compensation
44
Power-added Efiiciency (%)
Power-added Efiiciency (%)
44 43 42 41
before compensation
40 39 0.48
0.50
0.52
0.54
0.56
Threshold Voltage (V) Fig. 9. Power-added efficiency as a function of threshold voltage.
43
after VABB compensation
42 41 before compensation
40 39 0
20
40
60
80
100
Temperature (C) Fig. 12. Power-added efficiency versus temperature.
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J.S. Yuan, E. Kritchanchai / Microelectronics Reliability 53 (2013) 856–860
References
Power-added Efiiciency (%)
45 44
after VABB compensation
43 42 before compensation
41 40 39 2.2
2.3
2.4
2.5
2.6
2.7
2.8
Supply Voltage (V) Fig. 13. Power-added efficiency versus supply voltage.
For the process corner models the power-added efficiency of the PA with ABB compensation shows less process sensitivity, as evidenced by the plot in Fig. 11. Then, the power-added efficiency is compared against temperature and supply voltage variations. The power-added efficiency is getter better for the PA with ABB compensation as shown in Figs. 12 and 13. 4. Conclusions In this paper, the PVT compensation of power amplifier using a current-source as an on-chip sensor has been presented. The adaptive body bias design using current sensing makes the output power and power-added efficiency much less sensitive to process, supply voltage, and temperature variations, predicted by derived analytical equations and verified by ADS circuit simulation results.
[1] Blish R, Dellin T, Huber S, Johnson M, Maiz J, Likins B, et al. Critical reliability challenges for the IRTS. Int Sematech, Austin, TX, Tech Rep Technol Transfer #03024377A-TR; 2003. [2] Kumar SV, Kim CH, Sapatnekar SS. Impact of NBTI on SRAM read stability and design for reliability. In: Proc. 7th int. symp. quality, electron. des.; 2006. p. 210–18. [3] Turner TE. Design for reliability. Proc Int Phys Fail Anal 2006:257–64. [4] Chen T, Gielen G. A 14-bit 200-MHz current-steering DAC with switchingsequence post-adjustment calibration. IEEE J Solid State Circ 2007;42(11): 2386–94. [5] Dierickx B. Scaling below 90 nm: designing with unreliable components; 2007. Available from http://www.imec.be/tad/IMEC_TAD_papers/2007/2007_FSA.ppt. [6] Papanikolaou A. Reliability issues in deep deep submicron technologies: Timedependent variability and its impact on embedded system design. Proc IFIP Int Conf Very Large Scale Integr 2006:342–7. [7] Kim T-H, Persaud R, Kim CH. Silicon odometer: an on-chip reliability monitor for measuring frequency degradation of digital circuits. IEEE Symp VLSI Circ 2007:122–3. [8] Yamauchi K, Iyama Y, Yamaguchi M, Ikeda Y, Urasaki S, Takagi T. X-Band MMIC power amplifier with an on-chip temperature compensation circuit. IEEE Trans Microw Theory Technol 2001(December):2501–6. [9] Gómez D, Sroka M, Jiménez J. Process and temperature compensation for RF low-noise amplifiers and mixers. IEEE Trans Circ Syst I, Reg Papers 2010:1204–11. [10] Yuan JS, Tang H. CMOS RF design for reliability using adaptive gate-source biasing. IEEE Trans Electron Dev 2008:2348–53. [11] Liu Y, Yuan JS. CMOS RF power amplifier variability and reliability resilient biasing design and analysis. IEEE Trans Electron Dev 2011(February):540–6. [12] Kang K, Park SP, Kim K, Roy K. On-chip variability sensor using phase-locked loop for detecting and correcting parametric timing failures. IEEE Trans VLSI Syst 2010:270–80. [13] Zhang X, Apsel AB, low-power A. process-and-temperature-compensated ring oscillator with addition-based current source. IEEE Trans Circ Syst I: Regular Papers 2011:868–78. [14] Baker RJ. CMOS circuit design, layout, and simulation. 3rd ed. New York: Wiley; 2010. [15] Quemerais T, Moquillon L, Huard V, Fournier J-M, Benech P, Corrao N, et al. Hot-carrier stress effect on a CMOS 65-nm 60-GHz one-stage power amplifier. IEEE Electron Dev Lett 2010(September):927–9.
Contents lists available at SciVerse ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Power amplifier resilient design for process, voltage, and temperature variations J.S. Yuan ⇑, E. Kritchanchai Department of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA
a r t i c l e
i n f o
Article history: Received 7 November 2012 Received in revised form 7 January 2013 Accepted 7 February 2013 Available online 26 March 2013
a b s t r a c t This paper presents RF power amplifier adaptive body bias compensation technique for output power and power-added efficiency resilient to process, supply voltage, and temperature (PVT) variations. The adaptive body biasing scheme uses a current source for PVT sensing to provide resilience through the threshold voltage adjustment to maintain power amplifier performance over a wide range of variability. Analytical equations are derived for physical insight. ADS simulation results show that the resilient body biasing design improves the robustness of the power amplifier in output power and power-added efficiency over process, supply voltage, and temperature variations. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction CMOS technology continues device scaling for high integration. However, as feature sizes shrink and chip designers attempt to reduce supply voltage to meet power targets in large multi-core systems, parameter variations are becoming a serious problem. Parameter variations can be broadly classified into device variations incurred due to imperfections in the manufacturing process and environmental variations and on-die temperature and supply voltage (VDD) fluctuations [1]. Smaller feature size further makes CMOS circuits more vulnerable to process, supply voltage, and temperature (PVT) variability. Large design margin is then needed to insure circuit robustness against reliability issues. Using PVT and long-term reliability resilience design is becoming an essential design requirement for future technology nodes and may reduce overdesign, while increasing yield and circuit robustness. Recently, many papers on reliability and variability for analog, digital, and mixed circuits have been published [2–13]. Chen and Gielen [4] used post-fabrication calibration to static errors in the design of a 14-bit current steering digital-to-analog converter. Dierickx [5] and Pananikolaou [6] presented the runtime monitoring and countermeasures to compensate for variability and reliability errors. Kim et al. [7] fabricated an on-chip reliability monitor for measuring digital circuit frequency degradation. Yamauchi et al. [8] presented an X-band monolithic-microwave integrated-circuit power amplifier with a simplified on-chip temperature compensation circuit composed of diodes and a resistor. Gómez et al. [9] studied process and temperature compensation circuits for RF low-noise amplifiers and mixers. Yuan and Tang [10] used adaptive gate biasing for RF circuit design for reliability. ⇑ Corresponding author. E-mail address: [email protected] (J.S. Yuan). 0026-2714/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2013.02.003
Liu and Yuan [11] proposed resilient body biasing design to reduce the sensitivity of RF power amplifier (PA) to the transistor parametric variations. Kang et al., [12] developed on-chip variability sensor using phase-locked loop to track various sources of circuit variations. Zhang and Apsel [13] demonstrated a scalable, process-and-temperature compensated GHz ring oscillator with a low variation addition-based current source to improve temperature stability and process variation effect. In this paper, using adaptive body biasing technique to minimize PVT variations of RF class AB power amplifier is evaluated. The adaptive body bias is generated using an on-chip currentsource to track process, supply voltage, and temperature variations. The organization of this paper is organized as follows. In Section 2 the analytical equations of current-source sensing as a signature for on-chip adaptive body biasing is presented. In Section 3 the sensitivity of RF power amplifier with resilient body biasing is investigated and compared with the PA without body biasing. ADS circuit simulation results are provided. Finally, a conclusion is given in Section 4. 2. Current-source sensor An on-chip variability sensor using current source is proposed to detect process, supply voltage, and temperature variations or even reliability degradation stemming from hot electron effect. The PVT variations yield a control signal from the designed current source. In Fig. 1 the current-source circuit is made of n-channel transistors M1, M2 and M3. The transistors M1 and M2 have the same width and length and two times width of transistor M3. On the right branch in Fig. 1, a resistor R is used to set a control voltage VCtrl. The reference current Iref is dependent on the PVT fluctuations. The Kirchhoff’s current law to solve for VCtrl is given by
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J.S. Yuan, E. Kritchanchai / Microelectronics Reliability 53 (2013) 856–860
R2 R1 Vref VABB Vctrl R1 R2 Fig. 3. Level shifting circuit. Fig. 1. Current-source circuit schematic.
2
V Ctrl ¼ V DD Iref R
DV Ctrl
ð1Þ
and Iref is the reference current and can be obtained as [14]
Iref
ðV DD V T1 V T3 Þ2 ¼ qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 2L1 3 þ K2L Kn W 1 nW3
2 6eox R ðV DD V T1 V T3 Þ 7 4 Dln q ffiffiffiffiffi ffi q ffiffiffiffiffi ffi 2 5 tox 2L1 3 þ 2L W1 W3 2 3
ð2Þ
62RðV DD V T1 V T3 Þ7 þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T1 2L1 3 þ K2L Kn W 1 nW3 2 3
where VT is the threshold voltage, L is the channel length, W is the channel width, and Kn is the transconductance factor (Kn = lneox/tox). Subscripts 1 and 3 represent the transistors M1 and M3, respectively. The VCtrl shift because of supply voltage variation is derived using (1 and 2)
@V Ctrl 2RðV DD V T1 V T3 Þ ¼ 1 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 @V DD 2L1 3 þ K2L KnW1 nW3
3
2RðV DD V T1 V T3 Þ7 6 ¼ 41 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV DD 2L1 3 þ K2L KnW1 nW3 2 3
62RðV DD V T1 V T3 Þ7 þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T3 : 2L1 3 þ K2L Kn W 1 nW3
ð3Þ 2.1. Tuning for variability
The VCtrl shift due to mobility fluctuation is given by
The sensitivity of the class AB PA is evaluated in Fig. 2. The PVT variations change behaviors of the PA and also degrade the performance. In the simulation, the PVT variations are given to the PA circuit. Adaptive body biasing is used to find a range of body biasing voltage (VABB) to compensate each variation. VCtrl signal is efficiently transformed to an optimal body bias signal for power amplifier application. From a range of VABB, an operational amplifier is used as a voltage shifter and amplifier to adjust the VCtrl to meet a required VABB (see Fig. 3). Choosing appropriate size of resistor R1 and R2 using (7) provides a matched VABB for PA. For example, for a reference voltage (Vref) of 0.4 V, R1 and R2 can be designed at 500 O and 1500 O, respectively.
2
@V Ctrl eox R ðV DD V T1 V T3 Þ ¼ ffi qffiffiffiffiffiffi2 tox qffiffiffiffiffi @ ln 2L1 3 þ 2L W1 W3
ð4Þ
Furthermore, the VCtrl shift resulting from fluctuation of the threshold voltage from M1 or M3 is
@V Ctrl 2RðV DD V T1 V T3 Þ ¼ qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 : @V T1;3 2L1 3 þ K2L KnW1 nW3
ð5Þ
Combing (3)–(5) yields the overall VCtrl variation as follows:
VG
V DD
Rg
Ld Cout
RFin
ð6Þ
Input Matching
Cin Input Matching
M1
VABB
Lout
Lin
Fig. 2. A class AB PA with adaptive body biasing.
RFout
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J.S. Yuan, E. Kritchanchai / Microelectronics Reliability 53 (2013) 856–860
V ABB ¼
R2 ðV Ctrl V ref Þ R1
ð7Þ
Due to the body effect, the threshold voltage of the power amplifier transistor is described by the following expression
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi V T ¼ V T0 þ cð 2/F V ABB 2/F Þ
ð8Þ
where c is the body effect factor and /F represents the Fermi potential. The threshold voltage shift of the PA transistor is modeled by the fluctuation of VT0 and VABB as
@V T @V T DV T0 þ DV ABB @V T0 @V ABB
120 115
c
¼ DV T0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DV ABB 2 2/F V ABB
ð9Þ
From (7) the VABB shift is given by
DV ABB ¼
@V ABB R2 DV Ctrl ¼ DV Ctrl @V Ctrl R1
ð10Þ
Thus, the threshold voltage shift of the power amplifier input transistor due to PVT variations are summed as
82 3 > < 2RðV V V Þ 6 DD T1 T3 7 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 41 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV DD DV T ¼ DV T0 2R1 2/F V ABB > 2L1 2L3 : þ KnW3 KnW1 2 3 2 3
105 100 95
85 80 0.48
ð12Þ
Assume the VGS shift is proportional to the fluctuation of VDD.
DV GS ¼ aDV DD
ð13Þ
110
Kn W3
Kn W1
Kn W3
In the above equation the terms beyond DVT0 represent the VDD, mobility, and threshold voltage compensation effects. To normalized output power degradation is related to the normalized drain current degradation as follows [15]:
DPo DID Po ID
ð15Þ
3. Results and discussion The power amplifier with the current source compensation technique is compared with the PA without compensation using
after VABB compensation
105 100 95
before compensation
90 85 80
360
375
390
405
420
435
Mobility (cm2/V s) .
Fig. 5. Output power versus mobility variation.
120 before after compensation
115
Output Power (mW)
Kn W1
0.56
115
where a is a fitting parameter. Using (11)–(13) the fluctuation of drain current normalized to its fresh current is expressed as follows: DID Dln 2aDV DD 2 cR2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ þ DV T0 ID ln V GS V T V GS V T 2R1 2/F V ABB 82 3 2 3 > < 2RðV DD V T1 V T3 Þ7 6 6eox 2RðV DD V T1 V T3 Þ7 41 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV DD 4 qffiffiffiffiffiffi qffiffiffiffiffiffi2 5Dln > t ox 2L1 2L1 : 3 3 þ K2L þ 2L Kn W1 W1 W3 nW3 91 2 3 2 3 > = 62RðV DD V T1 V T3 Þ7 62RðV DD V T1 V T3 Þ7 C þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T1 þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T3 A ð14Þ > 2L1 2L3 2L1 2L3 ; þ þ
0.54
120
Output Power (mW)
@ID @ID @ID Dln þ DV GS þ DV T @ ln @V GS @V T
0.52
Fig. 4. Output power versus threshold voltage shift.
Kn W3
The drain current fluctuation subjects to key transistor parametric drifts Dln, DVGS and DVT can be modeled as
0.50
Threshold Voltage (V)
2 6eox R ðV DD V T1 V T3 Þ 7 62RðV DD V T1 V T3 Þ7 4 5Dln þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T1 q ffiffiffiffiffi ffi q ffiffiffiffiffi ffi 2 tox 2L1 2L1 3 3 þ 2L þ K2L W1 W3 KnW1 nW3 9 2 3 > = 62RðV DD V T1 V T3 Þ7 þ 4 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi2 5DV T3 ð11Þ > 2L1 ; þ 2L3
DI D ¼
before compensation
90
cR2
KnW1
after VABB compensation
110
Output Power (mW)
DV T ¼
ADS simulation. For the process variation effect, the output power is evaluated against threshold voltage and mobility variations as shown in Figs. 4 and 5. It is clear from Figs. 4 and 5 that the power amplifier with adaptive body bias is more robust against threshold voltage variation (see Fig. 4) and mobility fluctuation (Fig. 5). For the process variation effect, the output power of the PA has also been evaluated using different process corner models dueto inter-die variations. The simulation result of the fast–fast, slow–slow, and nominal–nominal models is shown in Fig. 6.
110 105 100 95 90 85 80 ff
tt
ss
Process Models Fig. 6. Output power versus process corner models.
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J.S. Yuan, E. Kritchanchai / Microelectronics Reliability 53 (2013) 856–860
Clearly, the PA using the adaptive body bias compensation exhibits better stability against process variation effect. Figs. 7 and 8 show the output power of the power amplifier versus temperature variation and supply voltage change, respectively. As seen in Figs. 7 and 8 the output power of the PA using the adaptive body bias compensation technique demonstrates less sensitivity over temperature and VDD variations.
In addition, the power-added efficiency of the power amplifier with or without adaptive body bias compensation is examined against semiconductor process variations effects. Figs. 9 and 10 display the improvement of power-added efficiency of the PA with ABB compensation over that without adaptive body bias for the threshold voltage shift (see Fig. 9) and mobility variation (see Fig. 10).
45
Power-added Efiiciency (%)
120
Output Power (mW)
115 110
after VABB compensation
105 100 95 before compensation
90 85
44 after VABB compensation
43 42 41
before compensation
40 39 350 360 370 380 390 400 410 420 430
80
Mobility (cm2/V s) .
0
20
40
60
80
100
o
Temperature ( C)
Fig. 10. Power-added efficiency as a function of mobility.
Fig. 7. Output power versus temperature.
45
Power-added Efiiciency (%)
120
Output Power (mW)
115 after VABB compensation
110 105 100
before compensation
95 90
before after compensation
44
43
42
41
40
85 80 2.2
39
2.3
2.4
2.5
2.6
2.7
ff
2.8
tt
ss
Process Models
Supply Voltage (V)
Fig. 11. Power-added efficiency versus process corner models.
Fig. 8. Output power versus supply voltage.
45
45 after VABB compensation
44
Power-added Efiiciency (%)
Power-added Efiiciency (%)
44 43 42 41
before compensation
40 39 0.48
0.50
0.52
0.54
0.56
Threshold Voltage (V) Fig. 9. Power-added efficiency as a function of threshold voltage.
43
after VABB compensation
42 41 before compensation
40 39 0
20
40
60
80
100
Temperature (C) Fig. 12. Power-added efficiency versus temperature.
860
J.S. Yuan, E. Kritchanchai / Microelectronics Reliability 53 (2013) 856–860
References
Power-added Efiiciency (%)
45 44
after VABB compensation
43 42 before compensation
41 40 39 2.2
2.3
2.4
2.5
2.6
2.7
2.8
Supply Voltage (V) Fig. 13. Power-added efficiency versus supply voltage.
For the process corner models the power-added efficiency of the PA with ABB compensation shows less process sensitivity, as evidenced by the plot in Fig. 11. Then, the power-added efficiency is compared against temperature and supply voltage variations. The power-added efficiency is getter better for the PA with ABB compensation as shown in Figs. 12 and 13. 4. Conclusions In this paper, the PVT compensation of power amplifier using a current-source as an on-chip sensor has been presented. The adaptive body bias design using current sensing makes the output power and power-added efficiency much less sensitive to process, supply voltage, and temperature variations, predicted by derived analytical equations and verified by ADS circuit simulation results.
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