Energy Efficient Wireless Transmitters: Polar and Direct-Digital Modulation Architectures
Jason Thaine Stauth Seth R. Sanders
Electrical Engineering and Computer Sciences University of California at Berkeley
Technical Report No. UCB/EECS-2009-22 http://www.eecs.berkeley.edu/Pubs/TechRpts/2009/EECS-2009-22.html
February 4, 2009 Copyright 2009, by the author(s). All rights reserved.
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Energy Efficient Wireless Transmitters: Polar and Direct-Digital Modulation Architectures
by
Jason Thaine Stauth
B.A. (Colby College) 1999 B.E. (Dartmouth College) 2000 M.S. (University of California, Berkeley) 2006
A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy
in
Engineering – Electrical Engineering and Computer Sciences
in the
GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY
Committee in Charge Professor Seth R. Sanders, Chair Professor Ali M. Niknejad Professor Paul K. Wright
Fall 2008
The dissertation of Jason Thaine Stauth is approved:
Chair Date
Date
Date
University of California, Berkeley
Fall 2008
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CMOS ft and fmax (performance analog/mixed signal devices), International technology roadmap for semiconductors (ITRS) [1]...... 1 21$%`V1`VCV7 VI7 `:JI1 V`5H.:JJVC5:JR`VHV10V`8...... 5 21$%`V87IGQCHQJ VCC: 1QJ11 .R1``V`VJ J%IGV`Q`G1 L7IGQC8 ...... 6 Figure 4. Complex constellation diagram and trajectory for (a) constant envelope modulation and (b) π/4DQPSK, which uses amplitude modulation for the same constellation points as (a)...... 7 21$%`V 8``Q`0VH Q`1 .VR1``V`VJHVGV 1VVJ .V:H %:C:JR1RV:C7IGQC0VH Q`8 .... 9 21$%`V 87]1H:C `:JI1 V`R1 Q` 1QJIVH.:J1I:``VH 1J$"8 ...... 10 Figure 7. Transmitter output spectrum showing spectral regrowth...... 11 Figure 8. Direct-conversion Cartesian transmitter schematic diagram...... 12 Figure 9. Effects of I/Q and quadrature LO gain and phase imbalance...... 13 Figure 10. Kahn envelope elimination and restoration (EER) transmitter architecture [19]...... 14 Figure 11. General representation of the polar transmitter architecture...... 15 Figure 12. Phase-path circuit architectures: representative techniques ...... 17 Figure 13. Time- and frequency-domain waveform comparison: Cartesian and polar systems. Baseband I/Q waveform with two-tone zero mean sinusoid...... 18 Figure 14. Distortion mechanisms in polar systems: gain and phase vs supply voltage . 20 Figure 15. Common-source amplifier circuit showing mechanisms for AM-AM, AM-PM distortion ...... 20 Figure 16. Representative probability distribution function (PDF) for CDMA applications [31]...... 23 Figure 17. Power amplifier block diagram and schematic for a CMOS common-source PA ...... 24 Figure 18. Class-AB PA voltage and current waveforms...... 27 Figure 19. Switching PA schematic and time-domain waveforms...... 29 Figure 20. Class E PA schematic...... 31 Figure 21. Power amplifier efficiency in power backoff overlaid with a representative PDF ...... 33 Figure 22. Efficiency versus output power: i.) conventional class B PA, ii.) class B PA with dynamic supply regulation, iii.) class B PA, dynamic VDD with realistic loss mechanisms...... 38 Figure 23. Envelope tracking transmitter using traditional Cartesian architecture with a dynamic supply modulator to improve average efficiency...... 39 Figure 24. Time domain waveforms for VDS RF carrier waveform and power loss: fixed VDD and dynamic VDD...... 40 Figure 25. Time domain envelope tracking waveforms ...... 40 Figure 26. Dynamic supply polar modulation system ...... 42 List of Figures ii Figure 27. Linear regulator topologies...... 45 Figure 28. Generic voltage-mode switching regulator block diagram ...... 46 Figure 29. DC-DC conversion cells: buck, boost, and inverting buck-boost ...... 46 Figure 30. Typical battery discharge curve and power converter mode of operation ..... 46 Figure 31. Pulse-width-modulation (PWM) waveform...... 48 Figure 32. Fundamental and harmonics of pulse-width modulated waveform versus duty cycle, normalized to fundamental peak...... 48 Figure 33. Contour representation of average efficiency of the switching regulator vs gate width...... 51 Figure 34. Hybrid voltage regulator schematic: a.) Series hybrid, b.) Parallel hybrid .... 52 Figure 35. Effect of supply noise on RF amplifier output spectrum ...... 55 Figure 36. Noise sources in RF systems ...... 59 Figure 37. Self-induced power supply noise from high supply impedance at the envelope frequency...... 66 Figure 38. CMOS inductor-degenerated common source amplifier showing nonlinear elements...... 68 Figure 39. MOSFET drain current versus gate-source and drain-source voltage. Nonlinearities are extracted around the dc operating point highlighted in the figure...... 68 Figure 40. QIIQJRQ%`HV:I]C1`1V`IQRVC ...... 77 Figure 41. D:GQ`: Q`7 V V %] ...... 77 Figure 42. .Q Q$`:].Q` .VR1VGQJRVRQJ .V$QCRR]C: VR V GQ:`R8 1V:`V:1 8II8II8...... 78 Figure 43. 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Pulse-density modulator block ...... 150 Figure 89. 1-Bit polarity feedforward to reduce power from rapid phase transitions ... 152 Figure 90. Constellation diagram for 8DPSK with feedforward phase transition: π 5π → ...... 152 4 4 Figure 91. Polarity bit significantly reduces high frequency power in the RF clock signal waveform by smoothing phase transitions near origin ...... 153 Figure 92. Effect of polarity on amplitude quantization - ∆Σ process remains linear near zero...... 155 Figure 93. Error-feedback digital ∆Σ modulator ...... 156 Figure 94. Example baseband 3rd order ∆Σ modulator spectrum with a notch at ±12MHz, G(z) = −z −3 + 5.2 z −2 − 5.2 z −1 ...... 157 Figure 95. ∆Σ Modulator: 1st, 2nd, 3rd order comparison, all zeros at 2.4GHz...... 158 Figure 96. Complementary class D PA schematic...... 159 Figure 97. Schematic representation of class-D power amplifier with cascode output stage ...... 162 Figure 98. Current recycling scheme: excess current from PMOS drive stage used by digital processing ...... 163 Figure 99. Class-D PA output stage NMOS layout: gate and cascode share diffusion region to reduce junction capacitance...... 163 Figure 100. Level shift and deadtime control ...... 165 Figure 101. System-level implementation of Bluetooth transmitter...... 166 Figure 102. Die Photo of CMOS class D PA and RF pulse-density modulator circuits ...... 166 Figure 103. Block diagram of the experimental setup...... 167 Figure 104. Time-domain waveforms at transmitter output ...... 168 Figure 105. Efficiency and output power vs supply voltage ...... 169 Figure 106. Efficiency and linearity0]%CVRRVJ1 7 ...... 169 Figure 107. Power of digital processing (pulse-density modulation, clock recovery, sampling and synchronization) with and without current recycling scheme. Measured as power drawn from Vhalf regulator ...... 170 Figure 108. Measured constellation diagrams ...... 172 Figure 109. 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Representative probability distribution function (PDF) for CDMA applications [31]. /J IQ ]Q` :GCV HQII%J1H: 1QJ :]]C1H: 1QJ5 `:JI1 V` :`V `:`VC7 %VR : I:61I%I ]Q1V`8 /J HVCC%C:` 7 VI5 .V `:JI1 V` ]Q1V` CV0VC 1 HQJ 1J%Q%C7 :R=% VRRV]VJR1J$QJ .V]`Q61I1 7Q` .V.:JRV Q .VG:V : 1QJ8.11RQJV`Q` 1Q `V:QJ7 Q :0V ]Q1V` 1J .V ]Q` :GCV %J1 5 :JR Q ]`V0VJ `:JI1 V` ``QI 1J V``V`1J$11 .V:H.Q .V`1JH`Q1RVR]VH `%I8.VVHQJR`V:QJ1@JQ1J: .V JV:`R`:`V``VH :JR1:HQIIQJ]`QGCVI1JI%C 1]CVR:HHV11`VCV7 VI`a8 Figure 16.Q1 .V]`QG:G1C1 7Q` `:JI1 1J$: :$10VJQ% ]% ]Q1V``Q`: "# 7 VI`Q`%`G:J:JR`%`:CVJ01`QJIVJ 8.VI:61I%I]Q1V`1RI5Q`QJV1: 5 G% .V:0V`:$V]Q1V`1HCQV` Q RRIQ`:`Q%JRI8CV:`C75: `:JI1 V` .: 1V``1H1VJ QJC7: I:61I%I]Q1V`I:7JQ GVV``VH 10V1J:`V:C1 1HVJ01`QJIVJ 8 .V:0V`:$VV``1H1VJH7Q` .V `:JI1 V`H:JGVH:CH%C: VR%1J$ .V 27 Transmitter Fundamentals 24 ∞ g(P ) ⋅ P dP ∫ L L L η = −∞ avg ∞ , ^ _ g(P ) ⋅ P (P )dP ∫ L supply L L −∞ 1.V`V% 1 .V]Q1V`RVC10V`VR Q .VCQ:R^6R:611JFigure 16_5 g(PL ) 1 .V]`QG:G1C1 7 RVJ1 7`%JH 1QJ5:JR Psup ply (PL ) 1 .V]Q1V`R`:1J``QI .V%]]C7::`%JH 1QJQ`% 8 # `:JI1 V`RV1$JVR`Q`.1$.:0V`:$VV``1H1VJH711CC.:0VGV V`G: V`7C1`V .:J1` :0V`:$VV``1H1VJH71JQ :@VJ1J Q:HHQ%J 8 8 Q1V` :I]C1`1V` Q0V`01V17 $VJV`:C Q]V`: 1QJ :JR ]Q1V` V``1H1VJH7 Figure 17. 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Transmitter Fundamentals 26 `VQJ:J `%H %`V5.VC]1J$ .V #IVV .V`V_%1`VRQ% ]% ]Q1V``Q`:`16VR%]]C7 0QC :$V`a8 /I]VR:JHV I: H.1J$ : .V # 1J]% 1 HQJ0VJ 1QJ:C :JR 1 JQ R1H%VR 1J $`V: RV :1C1J #C1 V`: %`V8/I]VR:JHV `:J`Q`I: 1QJ: .VQ% ]% 5QJ .VQ .V`.:JR51 JQJ `101:C :JR 1:``:J : $`V: RV:C Q` HQJ1RV`: 1QJ8 D%I]VR 1I]VR:JHV `:J`Q`I: 1QJ JV 1Q`@ 1JHC%RV DRI: H.1J$ JV 1Q`@ :JR :]]VR H:]:H1 Q` `:J`Q`IV`` 5a8)VQJ:J `:J`Q`I: 1QJJV 1Q`@:`V$VJV`:CC7C1I1 VRG7CQV 1J .V ]:10V HQI]QJVJ :JR I:7 QJC7 GV %V`%C : CQ1 HQJ0V`1QJ `: 1Q8 ; .V` 1Q`@%V]Q1V`HQIG1J1J$ Q%I .VQ% ]% Q`I%C 1]CV:I]C1`1V`:H.1V01J$.1$.V` ]Q1V`CV0VC11 .HQJ `:1JVR%]]C70QC :$V1J"; VH.JQCQ$1V8#Q@1V :C81J`a ]`VVJ VI1J:C 1Q`@ QJ 1J V$`: VR `:J`Q`IV` `%H %`V .: %V 7IIV `7 Q HQIG1JV .V]Q1V`Q`I%C 1]CVR1``V`VJ 1:CR"; #5:H.1V01J$.1$.V``1H1VJH7:JR.1$. 1J V$`: 1QJ8D1%V :C8]`VVJ 1I1C:`I:$JV 1H `:J`Q`IV` .: :CCQ1 # :$V Q %`J Q``: CQ1V`]Q1V`CV0VC51I]`Q01J$I:61I%IQ% ]% ]Q1V`:JR:0V`:$VV``1H1VJH7` 5 a8 2.5.2 Linear Power Amplifiers: Class AB Transmitter Fundamentals 27 VDS IDS Imax (A) DS I ; ) (V DS V Vdsat 180o<Φ<360o Figure 18. Class-AB PA voltage and current waveforms .V`V:`VI:J7HC:VQ`]Q1V`:I]C1`1V`5R1 1J$%1.VRG7 .VIQRVQ`Q]V`: 1QJQ` .V:H 10VRV01HV5 .VH%``VJ HQJR%H 1QJ:J$CV5:JR .V Q]QCQ$7Q``VQJ:J JV 1Q`@ : .V Q% ]% 8 C:V #5 #5 5 :`V HQJ1RV`VR C1JV:` ]Q1V` :I]C1`1V`5 1JHV .V :I]C1 %RV Q` .V Q% ]% 1$J:C 1 ]`Q]Q` 1QJ:C Q .V :I]C1 %RV Q` .V 1J]% 1$J:C8 C:V5 55:JR2:`VHQJ1RV`VRJQJC1JV:`1JHV1J]% RQ% ]% :I]C1 %RVC1JV:`1 71 JQ 1J.V`VJ 5 Q` 1 1 JQ ]Q1GCV Q IQR%C: V .V Q% ]% :I]C1 %RV ``QI .V 1J]% V`I1J:C87V`V1V11CCRVH`1GV .V$VJV`:CQ]V`: 1QJQ`HC:# Q$10V:VJVQ` .V `:RVQ``1J.V`VJ 1J #RV1$J8 Figure 18.Q1 .V0QC :$V:JRH%``VJ 1:0V`Q`I`Q` .VHC:# #8.V:H 10V RV01HVQ]V`: V::H%``VJ Q%`HV5G% HQJR%H QJC7:``:H 1QJQ` .V`%CCH7HCVT1 1 :QJ;GV 1VVJ Q:JRQQ` .V 1IV8`:R1 1QJ:CHC:# #5V]VH1:CC71J:%R1Q :]]C1H: 1QJ5 VJR Q %V ]%.R]%CC Q%`HV `QCCQ1V` Q% ]% :$V `a8 # .1$.V` ``V_%VJH1V1 1IQ`VV``1H1VJ Q%V:1J$CVRV01HV11 .:]%CCR%]1JR%H Q`5 Lchoke 1J Figure 188.V`VQJ:J JV 1Q`@`1C V`%J1:J VRQ% ]% .:`IQJ1H%H. .: .VR`:1J Transmitter Fundamentals 28 0QC :$V1:]]`Q61I: VC71J%Q1R:C8.VHQJR%H 1QJ:J$CV5Q`:J$%C:```:H 1QJQ` .V`%CC ]V`1QR .: .VRV01HV1HQJR%H 1J$51GV 1VVJ ^ .VC1I1 1J$H:V`Q`HC:#_:JR ^ .V C1I1 1J$ H:V `Q` HC: _8 .V RV01HV R11]: V ]Q1V` 1.VJ :JR = ⋅ Q0V`C:]5: Ploss I DS VDS 8#HQIIQJIV `1H`Q`]Q1V`:I]C1`1V`V``1H1VJH71 .VR`:1J V``1H1VJH77 P η = L drain , ^ _ Psup ply 1.V`V % 1 .V ]Q1V` RVC10V`VR Q .V CQ:R :JR % %]]C7 1 .V ]Q1V` R`:1J ``QI .V %]]C78 `:1JV``1H1VJH7JV$CVH .V]Q1V``V_%1`VR QR`10V .V1J]% Q` .V #5G% 1 :%V`%C`1$%`VQ`IV`1 `Q` .V0:`1Q% #HC:V8 .VR`:1JV``1H1VJH7Q`HC:#:I]C1`1V`1:`%JH 1QJQ` .VHQJR%H 1QJ:J$CV5 Φ 5 :JR .V0QC :$V11J$: .VR`:1J5JQ`I:C1 vˆ η = o drain K , where VDD Φ − sin Φ ^_ K = Φ Φ Φ 4sin − cos 2 2 2 Φ 1.V`V 1 .VHQJR%H 1QJ:J$CV:RV`1JVR1J21$%`V 5 vˆo 1 .V1$J:C:I]C1 %RV: .VR`:1JQ` .V:H 10VRV01HV5:JRηR`:1J1 #R`:1JV``1H1VJH7`a8 .VC1I1 1J$H:VQ`V``1H1VJH7`Q` .VHC:# #:`V .V:IV:HC:#:JRHC: Q]V`: 1QJ8.VI1J1I%IV``1H1VJH7Q` Q.:]]VJ1J .VHC:#C1I1 1J$H:V1.VJ Φ = 0 = Φ = 0 360 :JR vˆo VDD 8 .V I:61I%I V``1H1VJH7 Q` 8 Q .:]]VJ 1.VJ 180 Transmitter Fundamentals 29 = :JR vˆo VDD 8.V`VC: 1QJ.1]1J^_:CQ.QCR`Q`HC: #8/J .VHC:H:V5: .VHQJR%H 1QJ:J$CV5 Φ 5:]]`Q:H.V Q% ]% ]Q1V` :]]`Q:H.V V``1H1VJH1V RVH`1GVR .V`V :`V G:VR QJ :`V ]%`VC7 1RV:C H1`H%I :JHV %1J$ .V H%``VJ R0QC :$V 1:0V`Q`I 1J .V RV01HV :JR RQ JQ 1JHC%RV :J7 CQV ``QI ]:10V HQI]QJVJ 8#CQ51J^_51 11I]Q` :J QJQ V .: V``1H1VJH71C1JV:`11 . .V1$J:C :I]C1 %RVT1` .V1$J:C11J$: .VR`:1JQ` .VRV01HV1`VR%HVR5V``1H1VJH711CC:CQ GV `VR%HVR8 V 11CC `V011 .V HQJHV] Q` V``1H1VJH7 : CV .:J I:61I%I Q% ]% ]Q1V`C: V`1J .1H.:] V`8 Constrained by output network Constrained VDS by switch (V) time b.) General VDS waveforms VDS IDS (A) VGATE DS I VDD ; a.) Switching PA schematic ) (V DS V c.) Class E VDS - IDS waveforms time Figure 19. Switching PA schematic and time-domain waveforms 2.5.3 Switching Power Amplifiers: Class E example Transmitter Fundamentals 30 11 H.1J$ ]Q1V` :I]C1`1V` H:J :H.1V0V .1$.V` V``1H1VJH7 .:J C1JV:` :I]C1`1V` GVH:%V .V:H 10VRV01HVQ]V`: V::11 H.8.V:H 10VRV01HV1%%:CC7R`10VJ.:`R VJQ%$. .: 1 Q]V`: V::`V1 Q`1J .V:QJ; : V:JRHQJR%H JQH%``VJ 1J .V:Q``; : V81 .]`Q]V`C7HQJ `:1JVR0QC :$V:JRH%``VJ 1:0V`Q`I511 H.1J$:I]C1`1V` H:J:H.1V0V.1$.Q% ]% ]Q1V`11 .Q1RV:CV``1H1VJH78J`Q` %J: VC7 .1%%:CC7 IV:J .: 11 H.1J$ #`Q`V$Q .VC1JV:`1J]% RQ% ]% H.:`:H V`1 1HQ`C1JV:` #:JR .:0V.1 Q`1H:CC7GVVJ%VRI:1JC7`Q`HQJ :J VJ0VCQ]VIQR%C: 1QJH.VIV8 Figure 19^:_.Q1:H.VI: 1H`V]`VVJ : 1QJ`Q`:";11 H.1J$ #8.VRV01HV1 HQJ`1$%`VR1I1C:`C7 Q .VC1JV:` #RV01HV5V6HV] .: .V$: V1$J:CR`10V .VRV01HV GV 1VVJ `1QRV:JRH% Q```V$1IV8.Q1J1JFigure 19^G_51.VJ .VRV01HV1:QJ5; .V R`:1JRQ%`HV 0QC :$V 1HQJ `:1JVR QJV:` Q%`HV 0QC :$V 1 HQJ `:1JVR G7 .V R7J:I1H Q` .V Q% ]% JV 1Q`@8 .V Q% ]% JV 1Q`@ 1 RV1$JVR Q I1J1I1 1:0V`Q`I8/RV:CC75 .V:H 10VRV01HV %`JQJ1.VJ .VR`:1JRQ%`HV0QC :$V1 :H.1V01J$ I1J1I1<1J$ .VCQ1JH%``VR``QI11 H.1J$ .VR`:1JH:]:H1 :JHVQ` .V:H 10VRV01HV8 Transmitter Fundamentals 31 Figure 20. Class E PA schematic C: # :H.1V0V GQ . H.:`:H V`1 1H8.VHC:HQJHV] .:GVVJ%VR`Q`:`:J$VQ`:]]C1H: 1QJ1JHC%R1J$ )2]Q1V`:I]C1`1V`5` 55a5:JR`VQJ:J ]Q1V`HQJ0V` V`5`5a8.Q1J1J Figure 19^H_5 .VR`:1JRQ%`HV0QC :$V1:]]`Q61I: VC7 Figure 20.Q1:H.VI: 1H`V]`VVJ : 1QJ`Q`: 7]1H:C";HC: #5:1J`a8 :JR:`V].71H:CC%I]VR]:10VHQI]QJVJ .: I:7GV1J V$`: VR: .VRV01HVQ` GQ:`RCV0VC8$VJV`:CC71JHC%RV .V]:`:1 1HR`:1JRQ%`HVH:]:H1 :JHVQ` .V:H 10V RV01HV8 .V`V:`VI:J7IV .QR QRV1$J .VQ% ]% JV 1Q`@`Q`:HC::I]C1`1V`5QIVQ` 1.1H.:`VQ% C1JVR1J` 55a8.VJV 1Q`@1$VJV`:CC7RV1$JVR1J .V 1IVRRQI:1J %H. .: .V0QC :$V:JRH%``VJ 1:0V`Q`I`1 .VH.:`:H V`1 1H `:=VH Q`1V.Q1J1J Figure 19 ^H_8 .V 1IVRRQI:1J `V]QJV Q` .V Q% ]% JV 1Q`@ 1.VJ .V 11 H. 1 Q]VJVR.Q%CRGV%H. .: .VR`:1J0QC :$V`V:H.V QJV.:C`11 H.1J$H7HCV8/J .VQ`1$1J:C]:]V`G7Q@:C5`a5 .1HQJR1 1QJ`V%C 1J .V `QCCQ11J$V6]`V1QJ`Q` .V]:10VJV 1Q`@7 π (π 2 − )4 R R L = L ≈ .1 1525 L , ^_ 16 wc wc 8 1 1 C = ≈ .0 1836 , ^_ 1 π π 2 + ( )4 wc RL wc RL 8 V 2 V 2 P = DD ≈ .0 5768 DD , ^_ L π 2 + 4 RL RL Transmitter Fundamentals 32 1.V`V wc 1 .VH:``1V```V_%VJH7555:JR :`V:RV`1JVR1JFigure 205:JR 1 .V ]Q1V`RVC10V`VR Q .VCQ:R8 # R`:1G:H@ 11 . .V HC: Q]QCQ$7 1 .: .V R`:1JRQ%`HV 0QC :$V V6HVVR .V ≈ ⋅ %]]C70QC :$VG7:%G :J 1:CI:`$1J8/J .VJQI1J:CH:V5 VDS max .3 56 VDD 8.1 H:J GV ]`QGCVI: 1H 1` .V RV01HV 1 %HV] 1GCV Q .1$.R0QC :$V G`V:@RQ1J8 /J "; VH.JQCQ$7 Q61RV G`V:@RQ1J H:J GV : I:=Q` 1%V C1I1 1J$ .V C1`V 1IV Q` .V :H 10V RV01HV8 .V .1$. ]V:@ 0QC :$V 11J$ %`J Q% Q GV : V`1Q% 1%V 11 . .V HC: RV1$J C1I1 1J$ .V I:61I%I ]Q1V` .V :I]C1`1V` H:J RVC10V` `VC: 10V Q .V %]]C7 0QC :$V8 class A class B class E Peak Efficiency 50% 78.50% 100% Supply constrained output power (W) (VDD=1V, RL=1Ω) 500mW 500mW 577mW Breakdown constrained output power (W) Ω (VDSmax=2V, RL=1 ) 500mW 500mW 182mW Table I. Comparison of power amplifier performance Table I8.Q1 .V]V``Q`I:JHVQ`HC:#:JRHC: #HQI]:`VR QHC:82Q` .V :IV %]]C7 0QC :$V5 HC: 1 GQ . IQ`V V``1H1VJ :JR .: .1$.V` Q% ]% ]Q1V` .:JHC:#:JRHC:87Q1V0V`5$10VJ .VG`V:@RQ1JHQJ `:1J Q` .V:H 10VRV01HV5 HC: I:7 Q]V`: V 11 . : CQ1V` .:J C1JV:` Q]QCQ$1V5 1$J1`1H:J C7 `VR%H1J$ Q% ]% ]Q1V`8 .V G`V:@RQ1J ]`QGCVI 1 QIV1.: :CCV01: VR %JRV` HQJR1 1QJR%V Q`VR%H 1QJQ`.Q RH:``1V`V``VH 81JHVHC::H.1V0V]V:@0QC :$V `V: JQI1J:CC7 ]V:@1J$ R 1IV .V JQI1J:C %]]C7 0QC :$V `Q` HV` :1J "; VH.JQCQ$1V ` a8 7Q1V0V`5 .V `QG% JV Q` "; HC:R :I]C1`1V` 11 . .1$. ]V:@ 0QC :$V `V 1 _%V 1QJ:GCV5V]VH1:CC71.VJ%G=VH VR QCQ:RR]%CCT0:`1: 1QJ1J .V1I]VR:JHVQ` .V Q% ]% JV 1Q`@%%:CC7`VC: VR Q0:`71J$Q]V`: 1J$HQJR1 1QJQ` .V:J VJJ:8 2.5.4 Efficiency in Power Backoff #IVJ 1QJVR1JVH 1QJ885 `:JI1 V``:`VC7Q]V`: V: I:61I%I]Q1V`5G% :`V %G=VH Q : 11RV R7J:I1H `:J$V Q` Q]V`: 1QJ .: 1 H.:`:H V`1 RVJ1 7`%JH 1QJ8#0V`:$VV``1H1VJH71:IQ`V:HH%`: V1JR1H: Q`Q`G: V`7C1`V:JRH:J GV%VR Q_%:J 1`7 .V]V``Q`I:JHVQ`:$10VJ]Q1V`:I]C1`1V`8 5% 100% class E 4% 80% PDF 3% class B 60% 2% 40% Efficiency Efficiency Probability . Probability 1% 20% class A 0% 0% -60 -50 -40 -30 -20 -10 0 dB(Pout) - dB(Pmax) Figure 21. Power amplifier efficiency in power backoff overlaid with a representative PDF PA Class: Class A Class B Class E Average 0.78%* / 14.46% 18.21% Efficiency: 9.2%** Table II. Average efficiency calculations for the curves in Figure 21 *constant bias current **variable bias current Transmitter Fundamentals 34 Figure 21.Q1 .V1RV:CR`:1JV``1H1VJH7Q`HC:#5HC:5:JRHC: #:H`Q Q% ]% ]Q1V`8.V]Q1V``:J$V1JQ`I:C1 %]]C7 0QC :$V8 .V HC: V``1H1VJH7 H%`0V :%IV .: .V HC: ]Q1V` CV0VC 1 IQR%C: VRG7`V1 10VC7CQ1V`1J$ .V%]]C70QC :$V^ .`Q%$.%VQ`:C1JV:``V$%C: Q`T .1HQJHV] 1R1H%VR1JIQ`VRV :1C1J .VJV6 H.:] V`_8#`V]`VVJ : 10V 21 Q0V`C:1R11 . .VV``1H1VJH7H%`0V8/J .1V6:I]CV5 .VIV:JQ]V`: 1J$]Q1V`1R GVCQ1 .V]V:@]Q1V`8# .VIV:J]Q1V`CV0VC5:CC]Q1V`:I]C1`1V`HC:V:`VCV .:JQV``1H1VJ 8 .VV6]`V1QJ1J^ _1%VR QH:CH%C: V:0V`:$VV``1H1VJH75G:VRQJ .V 28.V `V%C Q` .V :0V`:$V V``1H1VJH7 H:CH%C: 1QJ `Q` .V H%`0V 1J Figure 21 :`V .Q1J 1J Table II8#0V`:$VV``1H1VJH711$J1`1H:J C7CQ1V` .:J .V]V:@V``1H1VJH71J:CCH:V8 2Q` .VHC::JRHC::I]C1`1V`5:0V`:$VV``1H1VJH71IQ`V .:J:`:H Q`Q``10VCV .:J]V:@V``1H1VJH782Q` .VHC:#:I]C1`1V`11 .HQJ :J G1:H%``VJ 51 1HCQV Q: `:H Q`Q``1` 78.VH:CH%C: 1QJ1JTable II:`V`Q` .V]%`VC71RV:CH:V11 .Q% ]:`:1 1H CQV8/`:RR1 1QJ:CCQIVH.:J1I:`V1JHC%RVR5GQ .]V:@:JR:0V`:$VV``1H1VJH7:`V %G :J 1:CC71Q`V8 .V`QCCQ11J$H.:] V`11CC@1]G:H@ Q]`V01Q%1%V:JR.1$.C1$. IQ`VR1`VH C7 .V VH.J1_%V 1J ]Q1V` I:J:$VIVJ .: I:7 GV %VR Q 1I]`Q0V :0V`:$V V``1H1VJH78 ]VH1`1H:CC751V11CCR1H%%]]C7RIQR%C: VR]QC:`:`H.1 VH %`V::1:7 Q1I]`Q0V :0V`:$V V``1H1VJH7 Q` 11`VCV `:JI1 V`8 V 11CC .Q1 .: R7J:I1H 0QC :$V Transmitter Fundamentals 35 `V$%C: 1QJ H:J @VV] # V``1H1VJH7 JV:` .V 1RV:C C1I1 5 1I]`Q01J$ :0V`:$V V``1H1VJH7 %G :J 1:CC78 .1 11CC IQ 10: V .V C: V` 1Q`@ 1J H.:] V` :JR 1.1H. RVH`1GV HQJ `1G% 1QJ Q .V:`V:Q`R7J:I1H%]]C7 `:JI1 V`:`H.1 VH %`V8.:] V` 11CC RVH`1GV :J :C V`J: 10V Q %H. :`H.1 VH %`V .: H1`H%I0VJ I:J7 Q` .V ]`QGCVI :QH1: VR11 .]QC:`7 VI]`VVJ VR1J .1H.:] V`8 36 Chapter 3 Power Management for RF Transmitters and Polar Systems Q1V` I:J:$VIVJ 1 :J 1JH`V:1J$C7 1I]Q` :J 1%V 1J .1$.C7 1J V$`: VR 11`VCV 7 VI81 .H:C1J$VI1HQJR%H Q` VH.JQCQ$75]Q1V`RVJ1 7.:GVHQIV:I:=Q` HQJ `:1J QJ7 VI]V``Q`I:JHV`5a87V: :JR1J V`HQJJVH ]:`:1 1HI:7C1I1 Q :CH%``VJ CV0VC1JI:J77 VI8`:JI1 V`:JR]`QHVQ`]Q1V`CV0VC:`V:CQ HQJ `:1JVRG7G: V`7H:]:H1 71J]Q` :GCV7 VI5`V_%1`1J$1J VCC1$VJ %VQ`:0:1C:GCV VJV`$78 71 Q`1H:CC75 ]Q1V` I:J:$VIVJ .: GVVJ : 0:C%:GCV QQC Q `VR%HV 7 VI H%``VJ HQJ%I] 1QJ:JR QV6]CQ1 `:RVQ``1J7 VI]Q1V`0V`%]V``Q`I:JHV1J: `:J$V Q` VI1HQJR%H Q` :]]C1H: 1QJ ` 5 a8 .V :IV 1 `%V 11 .1J .V HQ]V Q` 11`VCV 7 VI5 V]VH1:CC7 : `VC: VR Q .V ]Q1V` :I]C1`1V` ^ #_5 1.1H.H:J GVJV`1 ``QI:HH%`: V5V``1H1VJ 0QC :$V`V$%C: 1QJ `: V$1V8 1`VCV `:JI1 V` :JR V]VH1:CC7 ]Q1V` :I]C1`1V` .:0V ]VH1`1H :JR ]Q VJ 1:CC7 `1J$VJ ]Q1V` %]]C7 `V_%1`VIVJ 8 .1 H.:] V` 11CC RVH`1GV 1Q `:JI1 V` :`H.1 VH %`V5G:VRQJ]QC:`7 VI51.1H.GVJV`1 $`V: C7``QIR7J:I1H`V$%C: 1QJQ` .V # %]]C7 0QC :$V8V 11CC R1H% R1``V`VJ Q]QCQ$1V`Q` .V 0QC :$V `V$%C: Q`5 1JHC%R1J$11 H.1J$ R HQJ0V` V`:JRC1JV:``V$%C: Q`8.V$Q:CQ` .1H.:] V`1 Q1J `QR%HV .V1%V:JR `:RVQ``Q` .VV Q]QCQ$1VQ .: .V`QCCQ11J$H.:] V`5 Power Management for RF Transmitters and Polar Systems 37 1.1H.]`Q01RVRV :1CQJ]Q1V`%]]C7`V=VH 1QJ:JR.7G`1R0QC :$V`V$%C: Q`5:`V]% 1J ]`Q]V`HQJ V6 `Q` .VR1H%1QJ8 3.1 Motivation: Efficiency #Q% C1JVR1J.:] V`5]Q1V`:I]C1`1V`Q]V`: V11 .:11RV`:J$VQ`Q% ]% ]Q1V` .: H:J GV _%:J 1`1VR .`Q%$. .V ]`QG:G1C1 7 RVJ1 7 `%JH 1QJ8 QJ1RV`1J$ .: :0V`:$V]Q1V`CV0VCI:7GV%G :J 1:CC7GVCQ1]V:@]Q1V`CV0VC5:0V`:$VQ`VJV`$7 V``1H1VJH7 1 H:CH%C: VR G:VR QJ .V Q]V`: 1J$ : 1 1H 1J .V 28 1 . `:R1 1QJ:C :`H.1 VH %`V51.V`V .V #Q]V`: V11 .:`16VR%]]C70QC :$V:JR .V]Q1V`CV0VC1 QJC7HQJ `QCCVRG7 .V1$J:C:]]C1VR Q .V$: VQ` .V:H 10VRV01HV5:0V`:$VV``1H1VJH7 I:7GV%G :J 1:CC7CV .:J]V:@V``1H1VJH78%H.:`H.1 VH %`V`V_%1`V:C1JV:` # Q :I]C1`7 .V.1$.R7J:I1H`:J$V1J]% 1$J:C Q .VQ% ]% 8/JVH 1QJ81VRVH`1GVR .Q1JQJC1JV:` #H:J:I]C1`7C1JV:`1$J:C%1J$]QC:`:`H.1 VH %`V:JR VH.J1_%V %H.:@:.J)5.Q1J1JFigure 1087Q1V0V`5GQ .C1JV:`:JR11 H.1J$:I]C1`1V` H:JGVJV`1 1$J1`1H:J C7``QIV``1H1VJ `V$%C: 1QJQ` .V%]]C70QC :$V8 Power Management for RF Transmitters and Polar Systems 38 4% 90% ii.) 80% 70% 3% 60% PDF iii.) i.) 50% 2% 40% 30% Efficiency Probability Probability 1% 20% 10% 0% 0% -60 -50 -40 -30 -20 -10 0 dB(Pmax) - dB(Pout) Figure 22. Efficiency versus output power: i.) conventional class B PA, ii.) class B PA with dynamic supply regulation, iii.) class B PA, dynamic VDD with realistic loss mechanisms. 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VH.J1_%VIQ 10: VJV1H1`H%1 :`H.1 VH %`V Q:H.1V0V.1$.V`V``1H1VJH78 3.1.1 Envelope Tracking System I 2 + Q2 Figure 23. Envelope tracking transmitter using traditional Cartesian architecture with a dynamic supply modulator to improve average efficiency. Power Management for RF Transmitters and Polar Systems 40 VDD VDS VDD VDS PLOSS PLOSS time (s) time (s) a.) Fixed VDD, low amplitude class B b.) Dynamic VDD, low amplitude class B Figure 24. Time domain waveforms for VDS RF carrier waveform and power loss: fixed VDD and dynamic VDD. Figure 25. 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1 : 2a = 10 PSRR(dBV ) dB 8 ^_ a11 2a .V%J1 Q` 10 :`V0QC GVH:%V .VV6]`V1QJ1J^_.:GVVJI%C 1]C1VRG7 .V a11 %]]C7 `1]]CV I:$J1 %RV8 .1 CV:0V .V %J1 Q` ^_ 1J R8 .V ].71H:C 1J V`]`V : 1QJ Q` 1J ^_ 17 .V 1RVG:JR 1J RH .: 1Q%CR QHH%` `Q` : QJVR0QC ^ IVIQ`7CV ]Q1V`RV`1V :J:C718 FV6 1V 11CC RVH`1GV :J:C71 Q` ]Q1V` %]]C7 1J V`IQR%C: 1QJ`Q`7 VI11 .R7J:I1H:JR``V_%VJH7RV]VJRVJ JQJC1JV:`1 1V8 88 1J$CVR J]% ^1QRQ` _QC V``:RV`1VJ:C71 QC V``: V`1V H:J GV %VR Q :J:C7 IVIQ`78#CQJ$: .V7 VI11V:@C7JQJC1JV:`5QJC7:`V1 V`IQ` .VV`1V:`V JVVRVR Q ]`VR1H 1I]Q` :J R1 Q` 1QJ ].VJQIVJQJ8 1 . : QC V``: V`1V `V]`VVJ : 1QJ5 .V 1IV RQI:1J Q% ]% Q` : 1IVR1J0:`1:J JQJC1JV:` 7 VI `Q` :J 1J]% 56^ _5H:JGV1`1 VJ: ∞ = y(t) ∑ Fn (x(t)) 5 ^ _ n=0 1.V`V ∞ ∞ F (x(t)) = ... h (τ ,...,τ )x(t −τ )...x(t −τ )dτ ...dτ 8 n ∫ ∫ n 1 n 1 n 1 n ^ _ −∞ −∞ τ Lτ . /J^ _5 .V hn ( 1 , n ) :`V@JQ1J: .VJ Q`RV`QC V``:@V`JVCQ` .V7 VI8.V !J51.1H.`V]`VVJ .VHQJ0QC% 1QJ1J V$`:C1J^ _5:`V@JQ1J: .VQC V``:Q]V`: Q` Q` QC V``: `:J`V` `%JH 1QJ ` a8 2`QI .V ]V`]VH 10V Q` ^ _ :JR ^ _5 QC V``: V`1V :]]V:` : : $VJV`:C1 QC V``:@V`JVCH:JGV%VR1J .V``V_%VJH7RQI:1J:QC V``:Q]V`: Q`Q`QC V``: `:J`V` `%JH 1QJ Q ]V``Q`I H1`H%1 H:CH%C: 1QJ ` 5 5 5 a8 /J .1 H:V .V ω ω ω QC V``: Q]V`: Q` :`V ``V_%VJH7 RV]VJRVJ `:J`V` `%JH 1QJ5 H n ( j 1 , j 2 ,..., j n )5 Power Supply Noise Analysis for RF Amplifiers 64 .: H:] %`V .V ].:V :JR :I]C1 %RV `V]QJV Q` .V H1`H%1 `Q` : $10VJ V Q` ``V_%VJH1V ` a8 ":J7 $QQR `V`V`VJHV RVH`1GV .V %V Q` QC V``:RV`1V `:J`V` `%JH 1QJ1J .VHQJ V6 Q`I16VR 1IVR``V_%VJH7RVH`1] 1QJQ`JQJC1JV:`7 VI` 5 5 5 5 5 R a8 88 %C 1]CVR Q` QC V``:J:C71 .V V6 VJ1QJ Q` R]Q` QC V``: :J:C71 Q I%C 1R]Q` 7 VI H:J GV RQJV G7 V6 VJR1J$ .V HQJ0QC% 1QJ 1J V$`:C 1J ^ _ Q .1$.V` R1IVJ1QJ8 .V `V%C 1J$ `Q`I%C: 1QJ1JHC%RVGQ .R1`VH V`IGV 1VVJV:H.1J]% :JR .VQ% ]% 5:JRH`QR V`I .: RVH`1GV1J V`IQR%C: 1QJ:IQJ$ .V1J]% 8#1J^_5 .V`1` Q`RV`H`Q V`I H:J GV %VR Q RVH`1GV I161J$ GV 1VVJ %]]C7 JQ1V :JR .V )2 H:``1V`8 .V 1JH`V:VRR1IVJ1QJ:C1 7Q`I%C 1R]Q` QC V``::J:C71HQI]C1H: V.:JR:J:C715G% .V `1` :JR VHQJR Q`RV` V`I :`V 1CC I:J:$V:GCV5 :JR H:J ]`Q01RV HQJ1RV`:GCV 1J1$. 1J Q .V%]]C7JQ1VI161J$V``VH 8 ∞ ∞ = vout (t) ∑∑ Fmn (v1 (t),v2 (t)) ^ _ m=0 n= 0 ∞ ∞ F (v (t),v (t)) = L h (τ ,...,τ )v (t -τ )...v (t -τ )v (t -τ )...v (t -τ )dτ ...dτ mn 1 2 ∫ ∫ mn 1 m+n 1 1 1 m 2 m+1 2 m+n 1 m+n ^ _ −∞ −∞ = ω o + ω ω o 2 + ω ω ω o 3 +L Sout A10 ( j a ) S1 A20 ( j a , j b ) S1 A30 ( j a , j b , j c ) S1 + ω o + ω ω o 2 + ω ω ω o 3 +L A01( j a ) S2 A02 ( j a , j b ) S2 A03( j a , j b , j c ) S2 ^ _ + ω ω o + ω ω ω o 2 + ω ω ω o 2 +L A11( j a , j b ) S1 S2 A21( j a , j b , j c ) S1 S2 A12 ( j a , j b , j c ) S1 S2 .V 1IV RQI:1J QC V``: V`1V `Q`I%C: 1QJ `Q` : 7 VI 11 . 1J]% ]Q` :JR : Power Supply Noise Analysis for RF Amplifiers 65 1J$CV Q% ]% I:7 GV 1`1 VJ : 1J ^ _5 1.V`V ^ _ 1 .V I%C 1R]Q` :J:CQ$7 Q .V HQJ0QC% 1QJ1J V$`:C1J^ _8/J^ _5.IJ1 .VI%C 1R1IVJ1QJ:CQC V``:@V`JVC50:JR 0:`V .V 1Q1J]% 1$J:C5:JRIJ1 .VI%C 1R1IVJ1QJ:CQC V``:Q]V`: Q`1J .V 1IV RQI:1J8 /J .V ``V_%VJH7 RQI:1J .V QC V``: V`1V H:J GV 1`1 VJ : 1J ^ _8 . 7V`V .VJQ : 1QJ1=RVJQ V .VQC V``:Q]V`: Q``Q` .V1 Q`RV`Q`1J]% 5:JR .V . = Q`RV`Q`1J]% 8.V=ωJ V`I:`VR%II7``V_%VJH70:`1:GCV .: H:J:%IV .V `VCV0:J ``V_%VJH7 HQJ VJ Q` .V 1J]% 1$J:C8 .V Q]V`: Q` >◦? `V]`VVJ .V ``V_%VJH7RQI:1JQ]V`: 1QJQ` .V `:J`V``%JH 1QJQJ .V1$J:C: .V:]]`Q]`1: V ``V_%VJH1V:1 :JR:`R1J].:Q` `:J`V``%JH 1QJ:J:C718.VJQ : 1QJ1J^ _1 GQ``Q1VR``QI` a8/J^ _5:JR :`V .V`1` Q`RV`^C1JV:`_QC V``:Q]V`: Q` `Q`V:H.Q` .V 1Q1J]% V`I1J:C8.VQ]V`: Q`RVH`1GV .VVHQJRQ`RV`H`Q V`I8 :JR RVH`1GV .V .1`R Q`RV` H`Q V`I8 / .Q%CR GV JQ VR .: .V QC V``:V`1V1J^ _.: `%H %`:C1I1C:`1 7 Q .VIVIQ`7CV:J:CQ$71J^_8.V I:1JR1``V`VJHV1 .: .VQ]V`: Q`1J^ _:`V:`%JH 1QJQ` .V``V_%VJH7HQJ VJ Q` .V1J]% 1$J:C:JR`V`CVH .V1V:@C7JQJC1JV:`R7J:I1HQ` .V7 VI8 Power Supply Noise Analysis for RF Amplifiers 66 Figure 37. Self-induced power supply noise from high supply impedance at the envelope frequency #J:RR1 1QJ:CQ%`HVQ`%]]C7IQR%C: 1QJI:7GVH:%VRG7 .V #1 VC`8#.Q1J 1J 21$%`V 5 .1 .:]]VJ 1` .V %]]C7 V`I1J:C 1 JQ CQ1 1I]VR:JHV Q .V )2 Q` VJ0VCQ]V1$J:C8/J .1H:V5 .V%]]C70QC :$VI:7H.:J$V11 . .V1$J:C:I]C1 %RV8 .1H:JH:%V]`QGCVI11 .VHQJRQ`RV`R1 Q` 1QJ:1VCC:.1$.V`Q`RV`8.VV V``VH :`VH:] %`VR1JHQJ0VJ 1QJ:CR]Q` QC V``:V`1V:J:C71:JR11CCGV`V`CVH VR 1J .V`Q`1:`RRR1`VH Q]V`: Q`7 A20 5 A30 5V H8.1CVVC`R1JR%HVR%]]C7JQ1VI:7GV :V`1Q%]`QGCVI1JI:J71 %: 1QJ5 .VVV``VH H:JGV:CCV01: VR11 .$QQR%]]C7 G7]:1J$:JR0QC :$V`V$%C: 1QJ VH.J1_%V8/J .1H:V1 1JVHV:`7 QH`V: V:CQ1 1I]VR:JHV%]]C7: ``V_%VJH1VHQ``VC: VR11 . .VQ]V`: 1QJQ` .V #8/J .11Q`@ 1V `QH% QJ %JHQ``VC: VR JQ1V :JR `V: .V %]]C7 V`I1J:C : : V]:`: V 1J]% 8 .V`V`Q`V .V `QH% 1 QJ .V A11 Q]V`: Q`8 / .Q%CR GV JQ VR : : ]Q1GCV 1I]C1`1H: 1QJQ` .V:J:C715 .: .VVC`R1JR%HVRJQ1VH:JGVH.:`:H V`1 :JR `V: VR : :J 1JRV]VJRVJ JQ1V Q%`HV QJ .V %]]C78 /J .1 H:V5 .V A11 Power Supply Noise Analysis for RF Amplifiers 67 Q]V`: Q`H:JGV%VR Q %R7GQ .1JRV]VJRVJ :JRHQ``VC: VRJQ1V``QI .V7 VI8 /J .11Q`@51VRV`1JV .VFR]Q` :I]C1`1V`::GC:H@GQ611 .^R_V]:`: V1J]% :JR:1J$CVQ% ]% ]Q` 8.V:I]C1`1V``V]`VVJ VR1J21$%`V 1RV`1JVR::R]Q` 7 VI1.V`V .V1J]% :`V .VHQJ0VJ 1QJ:C1$J:C1J]% :JR .V%]]C7 V`I1J:C8.V 1$J:C ]Q` I:7 GVV1 .V` 1J$CV VJRVR Q`R1``V`VJ 1:C5 1.V`V: .V %]]C7 V`I1J:C 1 7]1H:CC7`V`V`VJHVR Q$`Q%JR8/J .1H:V1Q%CRHQ``V]QJR Q .V`Q`1:`R$:1J: ω51Q%CRHQ``V]QJR Q .V`Q`1:`R%]]C7JQ1V$:1J: ω51Q%CRHQ``V]QJR Q .V `1` 1RVG:JR : ω ^ ω5 :JR :JR 1Q%CR HQ``V]QJR Q .V VHQJR 1RVG:JR: ω ^ ω:JR ω ^ ω8.V ))Q` .VH1`H%1 1 .V`V`Q`V1`1 VJ: 2A ( jω ) PSRR = dB 10 0 ω ω 5 ^_ A11 ( j 0 , j S ) 1.V`V .V :GQC% V 0:C%V 1 :@VJ Q IV:J .V I:$J1 %RV Q` .V HQI]CV6 Q]V`: Q` `: 1Q8 / .Q%CR GV JQ VR .: .V H`Q V`I :`V JQ JVHV:`1C7 7IIV `1H5 1JHV ω ω ≠ ω ω $VJV`:CC75 A11( j 1, j 2 ) A11( j 2, j 1)8 /J %1 10VC75 .1 1 GVH:%V .V 1$J:C I:7 `QCCQ1 R1``V`VJ JQR:C ]: . Q .V Q% ]% 5 .V`V`Q`V .V ``V_%VJH7 HQJ VJ Q` 1$J:C : R1``V`VJ ]Q` 1 JQ JVHV:`1C7 1J V`H.:J$V:GCV8 #7IIV `1H QC V``: `:J`V` `%JH 1QJH:JGVI:RV]:` C77IIV `1H11 . VH.J1_%V]`VVJ VR1J` a8#1J .V H:V11 .HQJ0VJ 1QJ:C7IIV `1HQ]V`: Q`5]:` C77IIV `1HQ]V`: Q`:`VRV1`:GCV Q1I]`Q0VHQI]% : 1QJ 1IV:JRHQI]CV61 78 Power Supply Noise Analysis for RF Amplifiers 68 Figure 38. CMOS inductor-degenerated common source amplifier showing nonlinear elements. Typical operating region DC operating point Figure 39. MOSFET drain current versus gate-source and drain-source voltage. Nonlinearities are extracted around the dc operating point highlighted in the figure. 8 :`$V `QGCVI :JR .:`:H V`1<: 1QJ Q` QJC1JV:`1 1V /J Q`RV` Q RVIQJ `: V I%C 1R]Q` %]]C7 `V=VH 1QJ :J:C715 1V RV1$JVR :JR `:G`1H: VR : "; ]Q1V` :I]C1`1V` 1J JI VH.JQCQ$78 21$%`V .Q1 .V G:1H :I]C1`1V`HVCC1JHC%R1J$1JR%H :JHV: .VQ%`HV:JRR`:1J QIQRVC .VV``VH Q` .V GQJR11`V:JR)2H.Q@VVCVIVJ 8VH.QV .VHQIIQJRQ%`HV Q]QCQ$7GVH:%V1 1 .V `%JR:IVJ :C $:1J :$V `Q` I:J7 )2 %G7 VI 1JHC%R1J$ #5 :JR CQ1RJQ1V Power Supply Noise Analysis for RF Amplifiers 69 :I]C1`1V`8 21$%`V :CQ .Q1 .V I:=Q` Q%`HV Q` JQJC1JV:`1 7 1J .V "; :I]C1`1V`8 /J .1 V6:I]CV5 .V RQI1J:J Q%`HV Q` JQJC1JV:`1 7 :`V .V `:JHQJR%H :JHV ^$I_5 Q% ]% HQJR%H :JHV ^$Q_ :JR R`:1JRG%C@ =%JH 1QJ H:]:H1 :JHV ^=R_8; .V`R1 Q` 1QJHQJ `1G% Q`1JHC%RV .VGQR7RV``VH `:JHQJR%H :JHV:JR$: V H:]:H1 Q`5:C .Q%$. .VV 7]1H:CC7.:0V:I:CCV``VH QJ%]]C7JQ1V%]HQJ0V`1QJ8 FQJC1JV:`1 1V`Q` .V7 VI1J21$%`V 1V`VV6 `:H VR``QI/"0IQRVC`Q` : 1H:JRR7J:I1HJQJC1JV:`1 1V821$%`V .Q1 .V`V%C Q`]VH `V1I%C: 1QJQ` .V R`:1J H%``VJ 0V`% $: VRQ%`HV :JR R`:1JRQ%`HV 0QC :$V8 .V ]C:J:` `V]`VVJ : 1QJQ`H%``VJ .Q1R1`VH RV]VJRVJHVQJ`1` :JR.1$.V`Q`RV` V`IQ` × vgs :JR vds 8/I]Q` :J C75 .V`V1:CQH`QRV]VJRVJHVQJ V`I`VC: VR Q vgs vds 8 .VV H`Q V`I `V%C 1J I161J$ V``VH GV 1VVJ .V 1$J:C :JR %]]C7 :JR :`V 1I]Q` :J QH:] %`V`Q`JQ1V:J:C71821$%`V :CQ.1$.C1$. .VRHQ]V`: 1J$]Q1J `VC: 10V Q .V /R ]C:JV8 .V 7]1H:C Q]V`: 1J$ `V$1QJ `QCCQ1 .V CQ:RC1JV `Q` .V :I]C1`1V`5 G% RV01: V ``QI : `:1$. C1JV 1J .V /R ]C:JV GVH:%V Q` JQJC1JV:`1 75 `V:H 10V R7J:I1H5 :JR 0QC :$V `1]]CV QJ .V %]]C78 QC :$V `1]]CV V6 VJR .V Q]V`: 1J$`V$1QJ1J .V0V` 1H:C^0R _R1IVJ1QJG711J$1J$ .V0QC :$V: .VR`:1JQ` .V:H 10VRV01HV8 .VJQJC1JV:`H%``VJ :JRH.:`$V`VC: 1QJ.1]1V`VI: H.VR Q:]QC7JQI1:C`1 11 . CV: R_%:`V`V$`V1QJ:J:C71` 5 5 a8.V]QC7JQI1:CV6]:J1QJ1`1 Q].71H:C RV01HV ]:`:IV V` %H. : `:JHQJR%H :JHV :JR =%JH 1QJ H:]:H1 :JHV %1J$ GQ . H%``VJ :JRH.:`$V`VC: 1QJ.1]7 Power Supply Noise Analysis for RF Amplifiers 70 = + 2 + 3 +L id gm1vgs gm2vgs gm3vgs − − 2 − 3 −L gmb1vsb gmb2vsb gmb3vsb 8 + gmo vds ⋅vgs + gmo vds ⋅vgs2 + gmo vds2vgs +L 11 12 21 ^_ + + 2 + 3 +L go1vds go2vds go3vds d C d C d + C vdb + 2 vdb2 + 3 vdb3 +L 1 dt 2 dt 3 dt /J ^_5 $I1 `V]`VVJ .V `Q`1:`R `:JHQJR%H :JHV5 $IG1 1 .V GQR7 `:JHQJR%H :JHV5$IQ1=1 .VQ% ]% R `:JHQJR%H :JHVH`Q V`I::`%JH 1QJQ` .V . . 1 Q`RV` Q` 0R :JR .V = Q`RV` Q` 0$5 $Q1 1 .V Q% ]% HQJR%H :JHV5 :JR 1 1 .V Q% ]% H:]:H1 :JHV8 :`:IV V` 1 `V]`VVJ .V `1` :JR .1$.V` Q`RV` ]:`:IV V`1<: 1QJQ` .VQ% ]% H:]:H1 :JHV V`I^`V]`VVJ VR:Q1J21$%`V _8.V JQJC1JV:`1 71V6 `:H VR``QI .VJQI1J:CC7C1JV:`H.:`$VR0QC :$V`VC: 1QJ.1]5:1J` 5 JR `R a5`V%C 1J$1J .V`:H Q`Q`L:JRL1J .V :JR Q`RV`]Q1V`V`1V V`I8 8 QC% 1QJ Q` QC V``: ]V`: Q` QQC0V`Q` .VQC V``:Q]V`: Q`1J^ _5JQR:CV_%: 1QJ:`V1`1 VJ:JR .V7 VI 1QC0VRV_%VJ 1:CC7`Q`V:H.Q`RV`Q` .V]QC7JQI1:CV6]:J1QJ1J^_5GV$1JJ1J$11 . .V`1` Q`RV` V`I8.1]`QHVR%`V11VCCRVH`1GVR1J` 5 5 a8#%J1_%VQC V``: V`1V 1 1`1 VJ `Q` V:H. 1JRV]VJRVJ JQRV 1J .V 7 VI5 JQ 1JHC%R1J$ .V 1J]% V`I1J:C1.1H.51J .1V6:I]CV51HQJ `QCCVRG7:0QC :$VQ%`HV8.VJQ : 1QJ`Q` .V I%C 1RJQRV 7 VI H:J GV 1I]C1`1VR 11 . : %]V`H`1] 1JR1H: 1J$ `Q` 1.1H. JQRV .V V`1V 1 1J VJRVR8 2Q` .V Q%`HVRRV$VJV`: VR :I]C1`1V` 1J 21$%`V 5 .V`V :`V 1Q 1JRV]VJRVJ JQRV7QJV: .VQ%`HVQ` .V:H 10VVCVIVJ 5:JRQJV: .VR`:1JQ` .V Power Supply Noise Analysis for RF Amplifiers 71 :H 10VVCVIVJ 5:%I1J$ .VGCQH@1J$H:]:H1 Q`1:.Q` : .V``V_%VJH1VQ`1J V`V 8 1J$ .1 V`I1JQCQ$75 .VQC V``:V`1V1J^ _H:JGV1`1 VJ: ∞ ∞ = n ω ω o i j S n ∑∑ Aij ( j a ,..., j k ) S1 S 2 5 ^_ i=0 j= 0 n . . 1.V`VJQ : 1QJ Aij 1JR1H: V .VQ]V`: Q``Q` .V1 Q`RV`Q`].:Q`1J]% :JR .V= . Q`RV`Q`].:Q`1J]% `Q` .V .VJ 1JRV]VJRVJ JQRV1J .VH1`H%1 82Q`V:H.JQRV J5 :CC Q` .V `1` Q`RV` V`I :`V QC0VR 11 .Q% 1J1 1:CC7 1JHC%R1J$ .V V``VH Q` .V .1$.V` Q`RV` V`I8 / .Q%CR GV JQ VR .: .V `1` Q`RV` V`I .Q%CR I: H. HQJ0VJ 1QJ:C I:CC 1$J:C :J:C718 .V VHQJR Q`RV` V`I :`V QC0VR G:VR QJ .V JQR:CHQJ `:1J Q` .VH1`H%1 5 .VVHQJRQ`RV`JQJC1JV:`H%``VJ 5:JR .V`1` Q`RV` V`I8 .1 ]`QHV `V]V: 5 QC01J$ .V 7 VI Q` V_%: 1QJ `Q` V:H. 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L ∫ o o DC DC ^ _ T 0 2 QRV`10V:JV6]`V1QJ`Q` .V:0V`:$V]Q1V`R`:1J``QI .V%]]C75:1J^ _5 .V 0:C%V `Q` iLR 1 QC0VR G7 :%I1J$ .: iSR 1 HQJ :J R%`1J$ .V ]V`1QR Q` .V Optimum Operating Strategies for Hybrid Voltage Regulators 98 VJ0VCQ]V 1$J:C5 :JR `1JR1J$ .V HQ``V]QJR1J$ HQJR%H 1QJ :J$CV5 X5 .: .V C1JV:` `V$%C: Q`HQJR%H H%``VJ ``QI .V%]]C78 1 iSR 0.8 iLoad 0.6 iDC 0.4 Φ current current (A) 2 0.2 0 Φ Φ - + 1$%`V 8QJR%H 1QJ:J$CVRV`10: 1QJ71J%Q1R:CIQR%C: 1QJ5JQ`I:C1 21$%`V .Q1:R1:$`:IQ` .VH%``VJ 1:0V`Q`I1J .V.7G`1R`V$%C: Q`8/` .V 11 H.1J$`V$%C: Q`%]]C1V .V H%``VJ 5 .VHQJR%H 1QJ:J$CVQ` .VC1JV:``V$%C: Q` Q 1 V6:H C7 8 .1 1Q%CR IV:J .: 1J .V ]%.R]%CC Q% ]% :$V5 .V RV01HV .: HQ%]CV .VQ% ]% Q .V%]]C7HQJR%H .:C`Q` .V 1IV87Q1V0V`51J .VV6:I]CV .Q1J1J21$%`V 5 .V11 H.1J$`V$%C: Q`%]]C1VIQ`V .:J .V H%``VJ %H. .: Q X\ 8.VJV V``VH 1 .: .V:0V`:$VC1JV:``V$%C: Q`H%``VJ 1`VR%HVRG7 .V 11 H.1J$`V$%C: Q`H%``VJ 82Q` .V1:0V`Q`I1J^ _5 Φ H:JGVQC0VR`Q`: i − i Φ = −1 SR DC cos 8 ^ _ ia :VRQJ^ _5 .V:0V`:$VC1JV:``V$%C: Q`%]]C7H%``VJ H:JGV1`1 VJ1J V`IQ` HQJR%H 1QJ:J$CV: Optimum Operating Strategies for Hybrid Voltage Regulators 99 Φ 1 i = ()i + i ⋅ cos(φ) − i dφ LR π ∫ DC a SR 2 −Φ ^ _ i = a []sin Φ − Φ cosΦ . π 7V`V5 .V:0V`:$VC1JV:``V$%C: Q`H%``VJ 1QJC7:`%JH 1QJQ` .V:I]C1 %RVQ` .VCQ:R H%``VJ 11J$:JR .VHQJR%H 1QJ:J$CV8.V:0V`:$VV``1H1VJH7`Q` .V1RV:C7 VI5: 1J21$%`V 5H:JGV1`1 VJ1J V`IQ` .V]`Q]V` 1VQ` .VVJ0VCQ]V1:0V`Q`I%1J$ ^ _5 ^ _5 :JR ^ _5 ]VH1`1H:CC7 JQ 1J$ .: .V H%``VJ .V 11 H.1J$ `V$%C: Q` R`:1 ``QI .V%]]C71`VR%HVRG7HQJ0V`1QJ`: 1Q5R8/ .Q%CRGVJQ VR .: ^ _:%IV :J 1RV:C 11 H.1J$ `V$%C: Q` 11 . JQ CQ8 #0V`:$V V``1H1VJH7 `Q` .V 1J%Q1R:C #" VJ0VCQ]V`QCCQ1: v ⋅i v ⋅i + a a DC DC 2 η = 8 i ^ _ i ⋅ v +V a []sin Φ − Φ cos Φ SR DC dd π /J ^ _5 :0V`:$V V``1H1VJH7 1 1`1 VJ ]%`VC7 1J V`I Q` ]`Q]V` 1V Q` .V VJ0VCQ]V 1:0V`Q`I5 .V %]]C7 0QC :$V5 :JR .V HQJR%H 1QJ :J$CV5 X5 Q` .V C1JV:` `V$%C: Q`8 %G 1 % 1J$^ _1J Q^ _5:0V`:$VV``1H1VJH71V6]`VVR::`%JH 1QJQ` .VH%``VJ %]]C1VRG7 .V11 H.1J$`V$%C: Q`5iSR 81J$ .1`V%C 5:J:C$VG`:1HI1J1I1<: 1QJH:J GV RQJV Q `1JR .V 11 H.1J$ `V$%C: Q` H%``VJ .: ]`Q01RV I:61I%I :0V`:$V d η V``1H1VJH78.11 .VQC% 1QJ Q = 0 5:JRH:JGV`Q%JR: diSR v * = + ⋅ π DC iSR iDC ia cos 5 ^ _ Vdd Optimum Operating Strategies for Hybrid Voltage Regulators 100 * 1.V`V iSR 1 .V Q] 1I%I _%:1R : 1H 11 H.1J$ `V$%C: Q` H%``VJ 8 .V I:61I%I η * * :0V`:$VV``1H1VJH75 5`Q` .10:C%VQ`iSR 1V6]`VVR: v ⋅i ⋅ + a a vDC iDC * 2 η = 5 i ^ _ v ⋅i +V a sin()Φ* DC DC dd π 1.V`V Φ* 1 .VQ] 1I%IHQJR%H 1QJ:J$CV`Q` .VC1JV:``V$%C: Q`5:JRH:JGV1`1 VJ : * vDC Φ = π 8 ^ _ Vdd # VVJ 1J ^ _5 .V Q] 1I%I H%``VJ %]]C1VR G7 .V 11 H.1J$ `V$%C: Q` 1 JQ JVHV:`1C7V_%:C Q .V H%``VJ %]]C1VR Q .VCQ:R5G% 11J`:H :`%JH 1QJQ` .V :JRR7J:I1HH.:`:H V`1 1HQ` .VVJ0VCQ]V1$J:C:1VCC: .V%]]C70QC :$V8.1 1 : RV]:` %`V ``QI .V HQJ `QC H.VIV ]`VVJ VR 1J ` 5 a5 1.V`V .V IV:J 11 H.1J$`V$%C: Q`H%``VJ 1 .V CQ:RH%``VJ 8 .V H:CH%C: 1QJ 1 1I1C:` `Q` 1QR QJV 1$J:C5 V6HV] R1``V`VJ V6]`V1QJ :`V QG :1JVR`Q` .VHQJR%H 1QJ:J$CV:JRQ] 1I%IG1:1J$HQJR1 1QJ82Q` .VH:V .: .V )2 H:``1V` HQJ1 Q` 1Q QJV : R1``V`VJ ``V_%VJH1V5 w2 :JR w1 5 G% V_%:C I:$J1 %RV5 0:5 .V VJ0VCQ]V 1 : `%CCR1:0V `VH 1`1VR 1J%Q1R 11 . : ]V:@ 0:C%V Q` 2× va 5:1J` a5 w − w = ⋅ 2 1 venv 2 va cos t 8 ^ _ 2 /J .1H:V5 .VHQJR%H 1QJ:J$CV::`%JH 1QJQ` .V11 H.1J$`V$%C: Q`H%``VJ 1 Optimum Operating Strategies for Hybrid Voltage Regulators 101 i Φ = −1 SR cos 5 ^ _ 2ia v = a 1.V`V ia 1 .V:I]C1 %RVQ` .VH%``VJ 11J$Q`QJVQ` .V 1Q QJV1$J:C8 Rload 2QCCQ11J$ : 1I1C:` ]`QHVR%`V Q .V 1J%Q1R:C VJ0VCQ]V 1$J:C5 .V Q] 1I%I _%:1R : 1H11 H.1J$`V$%C: Q`H%``VJ HQJ `1G% 1QJ`Q` .V 1QR QJVH:V1 v * = ⋅ ⋅ a iSR 2 ia cos2 5 ^ _ Vdd 1.V`V Vdd 1 .V %]]C7 Q`G: V`7 0QC :$V8 .V I:61I%I :0V`:$V V``1H1VJH7`Q` .V 1QR QJVVJ0VCQ]V1$J:C1QC0VR`Q`: * π v ⋅i η = a a ⋅ + ⋅ ⋅[]Φ − Φ Φ 8 ^ _ 2 va iSR Vdd ia sin( ) cos( ) 2Q` .V 1QR QJVH:V51RV:CQ% ]% V``1H1VJH71GQ%JRVRGV 1VVJ 8Q`Q``:1CR`:1C π → IQR%C: 1QJ5:JR 8 Q^ L_: va 0 8/J .VQ`71` .V11 H.1J$`V$%C: Q`%]]C1VR .V H%``VJ 5V``1H1VJH71Q%CRGVGQ%JRVRG7 8 Q QQ8.1`:J$V`1 11 . .V V``1H1VJH7Q` Q`Q`: 1QR QJVVJ0VCQ]V:`V]Q` VR1J` a8 8 .VQ`V 1H:C ]`VR1H 1QJ :JR 1H%1QJ Optimum Operating Strategies for Hybrid Voltage Regulators 102 1 0.9 0.8 0.7 0.6 0.5 0.4 Sin-AM isr=isr* Efficiency 0.3 Sin-AM isr=idc 0.2 2-tone isr=isr* 0.1 2-tone isr=idc 0 0 0.1 0.2 0.3 0.4 0.5 Modulation Amplitude, Normalized (V) 1$%`V 8.VQ`V 1H:C V``1H1VJH7 0 0QC :$V :I]C1 %RV7 1JR :JR 1Q QJV H:V5 `QCCQ11J$ ^ _ :JR ^ _ 1 0.9 0.8 0.7 0.6 0.5 0.4 Efficiency 0.3 isr = idc 0.2 0.1 isr = isr* 0 0.0 5.0 10.0 15.0 20.0 25.0 Average Output Power (dBm) 1$%`V 8!``1H1VJH7 0 JQ`I:C1 21$%`V .Q1 .V .VQ`V 1H:C :0V`:$VV``1H1VJH7 `Q` .V 1J%Q1R:CR#" :JR 1QR QJVIQR%C: VRH:``1V`: .VIQR%C: 1QJ:I]C1 %RV1`VR%HVR8.V%]]C70QC :$V1 JQ`I:C1 JV:`C7 = .: va vDC 8.V 1QR QJVH:V:%IV 1Q1$J:C: R1``V`VJ ``V_%VJH1V11 . .V :IV :I]C1 %RV5 0:5 : 1J ^ _8 /` .V 11 H.1J$ `V$%C: Q` HQJ `1G% V .V CQ:R Optimum Operating Strategies for Hybrid Voltage Regulators 103 H%``VJ 5 :0V`:$V V``1H1VJH7 `:CC Q`` Q Q : .V IQR%C: 1QJ :I]C1 %RV 1 `VR%HVR8 * 7Q1V0V`51` .V11 H.1J$`V$%C: Q`%]]C1V .VQ] 1I%IH%``VJ 5iSR 5:RV`10VR1J^ _ :JR^ _5 .V:0V`:$VV``1H1VJH7H:JGV@V] .1$.V`:H`Q .VVJ 1`V`:J$VQ`Q]V`: 1QJ5 :`QCCQ1``QI^ _:JR^ _8.V`V`Q`V5 .V]`V`V``VR:]]`Q:H.1 Q`V$%C: V .V 11 H.1J$`V$%C: Q`H%``VJ Q .VQ] 1I%I0:C%V`: .V` .:J .V 0:C%V8/J %1 10VC75 .1H:JGVV6]C:1JVRG:VRQJ .VQ]V`: 1QJQ` .VC1JV:``V$%C: Q`7 • # .1$.Q% ]% 11J$CV0VC5 .V11 H.1J$`V$%C: Q`%]]C1V .V H%``VJ 8/J .1H:V .VC1JV:``V$%C: Q`Q]V`: 1QJ:]]`Q:H.VHC:5Q`1800 HQJR%H 1QJ :J$CV`Q`V:H.]%.R]%CCQ% ]% RV01HV8.1H:%V .VH%`0V1J21$%`V Q HQJ0V`$V`Q`.1$.:I]C1 %RV8 • # CQ1Q% ]% 11J$ .V11 H.1J$`V$%C: Q`Q%`HVIQ`V .:J .V H%``VJ 5 = + limiSR iDC ia %H. .: 5`Q` .V1J%Q1R:CR#"H:V5 ia→0 8/JQ .V`1Q`R5 .V .1$.1RV]: `:J1 Q`Q]V`: V1JHC:R11 . .V `:J1 Q`HQJR%H 1J$`Q` CV .:J1800 8#C V`J: 10VC75 .VCQ11RV]: `:J1 Q`:]]`Q:H.VHC:R# Q]V`: 1QJ5R`:11J$H%``VJ QJC7``QI .V11 H.1J$`V$%C: Q`Q% ]% 8 .V `VJR .Q1J 1J 21$%`V 1 :CQ QGV`0VR `Q` `V:C 11`VCV HQII%J1H: 1QJ :JR:`R8 21$%`V .Q1 V``1H1VJH7 0V`% Q% ]% ]Q1V` `Q` VJ0VCQ]V 1:0V`Q`I .: HQ``V]QJR Q /R HQRVRR1011QJ I%C 1]CVR:HHV ^ "#_8 /J .1 H:V .V VJ0VCQ]V1:0V`Q`I`QCCQ1:G:JRC1I1 VR]V%RQ`:JRQI `:=VH Q`7:JR1R1``1H%C Q _%:J 1`7 `Q` .:JR :J:C718 .V`V`Q`V5 1J 21$%`V 5 .V H%`0V :`V 1I%C: VR 11 . 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R 8:L$ 1J%Q1R:C 1QR QJV ! * + ⋅ (Φ* ) ⋅ ⋅ (Φ* ) R R iSR iDC ia cos 2 ia cos v v Φ* π DC 2 a R R Vdd Vdd v ⋅i v ⋅i + a a DC DC π v η * 2 a R R i 2 V sin()Φ* v ⋅i +V a sin()Φ* dd DC DC dd π 3π π η = 91 7. % = 93 3. % Q Q max 2π + 4 4 ⋅sin( )1 3 π η = 75% = 78 5. % Q Q min 4 4 %IV`%CCIQR%C: 1QJ7 = %IV 1Q QJV11 .:IV:I]C1 %RV50: va vDC ``1H1VJH7GQ%JR:`1V`Q%JR11 .1I%C: 1QJ :GCV HQJ QC1R: V .V Q] 1I%I G1: ]Q1J V6]`V 1QJ :JR 0:C%V `Q` :0V`:$V V``1H1VJH7`Q` .V 1J% Q1R:CR:JR 1QR QJVH: V 8.V:0V`:$VV``1H1VJH7GQ%JR:`1V `Q` :JR 8: VJ0VCQ]V 1:0V`Q`I :`V :C Q .Q1J8 $Q` .V HVCC%C:` :JR 11`VCV 1J V`JV :JR:`R 5 V``1H1VJH7 GQ%JR:`1V :JR Q] 1I%I 11 H.1J$ `V$%C: Q` * H%``VJ HQJ `1G% 1QJ5 iSR 5 :`V `Q%JR .`Q%$. 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VRG7 .V`:H Q`5R5: 1J^ _5 Q`V`CVH CQ CV R 0QC :$V HQJ0V` 1QJ8 /Q CV HQJ0V` 1QJ 1: : %IVR Q 0V`1`7 .V 1RV:C I:61I%IV``1H1VJH7H: V8Q`%` .V``V`CVH .V1RV:CH: V5 .VG1: H%``VJ Q` IQ` .VC1JV:``V$%C: Q`1: JQ 1JHC%RVR1J .VH:CH%C: 1QJ8 .Q1J1J$1$%`V 5 .V1J]% 1$J:C`V]`V VJ 1J$ .VR7J:I1HVJ0VCQ]V `:=VH Q`7 1: RVC10V`VR G7 : 7: 1QJ:C J `%IVJ L HQJ0V` V` `%JJ1J$ : &L 8 .V /:G01V1 Q` 1:`V1J V``:HV1: % VR Q$VJV`: V:JR %]]C7VJ0VCQ]V1:0V`Q`I 1$J:C 11 .%] Q:8<G:JR11R .51JHC%R1J$&R :JR 8:/71:0V`QI 8 Optimum Operating Strategies for Hybrid Voltage Regulators 108 .V 11 H.1J$`V$%C: Q`H%``VJ HQII:JR1: :R=% VRI:J%:CC7 Q:H.1V0V .V.1$.V :0V`:$V V``1H1VJH7 `Q` : $10VJ 1J]% 1$J:C8 Q 1I]C1`7 .V V6]V`1IVJ :C V %]5 : `V 1 10VCQ:R1: % VR`: .V` .:J:J:H %:C;8J .1 H: V:10Ω `V 1 Q`1: % VR `Q` .VCQ:R8.V:0V`:$VH%``VJ ``QI .V]:`:CCVC 11 H.1J$:JRC1JV:`GCQH@ 1V`V IV: %`VR11 .R1$1 :CRI%C 1IV V` 8 0.9 Vdd=3V; Vo=1+1*sin(wt) 0.8 Vo=0.5+0.5*sin(wt) 0.7 0.6 measured theory Efficiency 0.5 measured 0.4 theory 0.3 0 50 100 150 200 switching regulator current (ma) 1$%`V 80V`:$VV``1H1VJH7011 H.1J$`V$%C: Q`H%``VJ HQJ `1G% 1QJ7 1JR IQR%C: 1QJ Supply Voltage= 2V; Signal=va+vaSin(wt) 1 0.9 isr=isr* 0.8 0.7 0.6 0.5 theory 0.4 theory Efficiency 0.3 isr=idc measured 0.2 measured 0.1 0 0 0.2 0.4 0.6 0.8 1 Normalized Voltage Amplitude (V) 1$%`V 80V`:$VV``1H1VJH70VJ0VCQ]VIQR%C: 1QJ:I]C1 %RV7 1J%Q1R:C IQR%C: 1QJ8 Optimum Operating Strategies for Hybrid Voltage Regulators 109 $1$%`V .Q1 :0V`:$VV``1H1VJH70V` % .VH%``VJ HQJ `1G% 1QJQ` .V 11 H.1J$ `V$%C: Q``Q`:I]C1 %RV Q` .V 1J% Q1R:CR1:0V`Q`I8.V`V %C :`VHQI]:`VR Q .V]`VR1H VRH%`0V``QI^ _`Q`: %]]C70QC :$VQ`8QHQI]:`V .VV``1H1VJH7`Q` .V1RV:C 1 %: 1QJ5 .V I G1: H%``VJ Q` .VC1JV:``V$%C: Q`^/ _1: JQ 1JHC%RVR1J .VH:CH%C: 1QJ8.V:0V`:$V0QC :$VRVC10V`VR Q .VCQ:R`Q` .V 1QH%`0V 1: I :JR 5 HQ``V ]QJR1J$ Q ]Q1V` CV0VC R1 :JR R1 GVCQ1 I:61I%I ]Q1V`8.``1H1VJH70V` % 11 H.1J$`V$%C: Q`H%``VJ 1 VVJ QGV1J$QQR:$`VVIVJ 11 . .VQ`78 $Q` .V 1J% Q1R:CR 1:0V`Q`I .Q1J5 .V ]V:@ V``1H1VJH7 1 :`Q%JR Q51.1H.1 QGVCQ1 .V1RV:CV``1H1VJH7: ]`VR1H VR1J^ _8 . &1I1C:`H%`0V 1V`VI:]]VRQ% `Q`:I]C1 %RV 0:`71J$GV 1VVJL .V %]]C7 0QC :$V:JR`:1CR QR`:1C 11J$8.V`V %C HQ``V ]QJR1J$ QQ] 1I%IG1: 1J$:`V .Q1J 1J $1$%`V `Q` .V 1J% Q1R:CR H: V8 .V IV: %`VR R: : :`V Q0V`C:1R 11 . .V .VQ`V 1H:C]`VR1H 1QJ ``QI:GCV8C Q .Q1J1J$1$%`V 1 :HQI]:`1 QJQ` .V = * = Q] 1I%I H: V 1.V`V iSR iSR 5 :JR .V `:R1 1QJ:C H: V 1.V`V iSR iDC 8 $Q` .1$. :I]C1 %RV 5 .V :$`VVIVJ GV 1VVJ .VQ`7 :JR IV: %`VIVJ 1 $QQR8 CQ1V` :I]C1 %RV 5IV: %`VRV``1H1VJH71 CV .:J]`VR1H VRR%V QV6 `:G1: ]Q1V`1J .V HC: R1Q% ]% :$V:JR QCV`:JHV1J V 1J$ .VG1: H%``VJ Q` .V 11 H.1J$`V$%C: Q`8 .VV``1H1VJH71.VJ .V 11 H.1J$`V$%C: Q` %]]C1V .V ]Q1V`I: H.V .VQ`711 . $QQR:$`VVIVJ :H`Q .V`:J$VQ`Q]V`: 1QJ8 Optimum Operating Strategies for Hybrid Voltage Regulators 110 Supply Voltage= 2V; Signal=2*va*abs(Sin(wt/2)) 1 0.9 isr=isr* 0.8 0.7 0.6 0.5 isr=isr* 0.4 isr=idc Efficiency isr=idc 0.3 isr=isr* 0.2 isr=idc 0.1 0 0 0.2 0.4 0.6 0.8 1 Normalized Voltage Amplitude (V) 1$%`V 8!1QR QJVIQR%C: 1QJ7HQI]:`1QJQ` .VQ`7 QIV:%`VIVJ 0.9 0.8 0.7 0.6 0.5 isr=isr* Efficiency CDMA 0.4 isr=idc isr=isr* 0.3 802.11a isr=idc 0.2 -5 0 5 10 15 20 25 Average Output Power (dBm) 1$%`V 8" R %& 5 8:,-IV:%`VRV``1H1VJH7 $1$%`V .Q1 IV: %`VR .VQ`V 1H:C R: : `Q` .V 1QR QJV IQR%C: VR 1$J:C : :J:C7 :$`VVIVJ 11 . .VQ`75:JRI: H.11 . 1I1C:`:HH%`:H7: .V 1J% Q1R:CRH: V8.V I:61I%IV``1H1VJH7`Q``%CCR H:CVIQR%C: 1QJ1 VVJ QGV 8 QHQI]:`VR Q 8Q: ]`VR1H VR1J:GCV8 Optimum Operating Strategies for Hybrid Voltage Regulators 111 $1$%`V .Q1 IV: %`VR`V %C `Q` :JR... 8: %]]C7IQR%C: 1QJ 1:0V`Q`I 8.V V1:0V`Q`I :`V$VJV`: VR11 . .V$1CVJ R0:JHVR V 1$J 7 VI ^ &_ Q` 1:`V:JRHQJ0V` VR Q:`Q`I: %1 :GCV`Q`R: :HQJ0V` 1QJ8.V1:0V`Q`I 1V`VRVC10V`VR Q .V.7G`1R`V$%C: Q`11 ./:G01V1:JR .V7 5: .Q1J1J $1$%`V 8.V6R:61 .Q1 :0V`:$V]Q1V`RVC10V`VR Q .VΩCQ:R8J .1 V Q` V6]V`1IVJ .VI:61I%I:0V`:$V]Q1V`RVC10V`VR1J .V 1:0V`Q`I 1: =% Q0V`R1I8.V 8:1:0V`Q`I 1V`V V Q`V`CVH :R: :`: VQ` 1L 5 %H. .: I:61I%I:0V`:$V]Q1V`1: R1I8.V.1$.V`]V:@R:0V`:$V]Q1V``: 1Q^;;?_ Q` .V 8: :JR:`R^;;?Y8 R1_1 .V]`1JH1]:C`V: QJ .: :0V`:$VV``1H1VJH71 CQ1V` .:J .V Q .V` 1:0V`Q`I 8 .V .1$.V` ;;? Q` 8: 1JR1H: V .: .V R7J:I1HQ% ]% 0QC :$VRV01: V %G :J 1:CC7``QI .V:0V`:$V0QC :$V8.1 `VR%HV .V :0V`:$V V``1H1VJH7 Q` .V C1JV:` `V$%C: Q`8 J .V H: V5 $1$%`V H:J GV HQI]:`VR Q .V 1I%C: VR`V %C .Q1J1J$1$%`V 8.V6R:61 ]Q1V` H:CV1 C1$. C7 R1``V`VJ 1J .V 1Q]CQ GVH:% V .V 1I%C: 1QJ1: `%J11 .:8 %]]C70QC :$V:JR :I:6Q% ]% ]Q1V`Q`8 Optimum Operating Strategies for Hybrid Voltage Regulators 112 2.5 2 1.5 isr*/idc 1 CDMA 0.5 WLAN SinAM 0 -5.00 0.00 5.00 10.00 15.00 20.00 25.00 Average Output Power (dBm) 1$%`V 8.] 1I%I11 H.1J$`V$%C: Q`H%``VJ ^JQ`I:C1 * Q% ]% ]Q1V` G7 ]CQ 1J$ .V `: 1Q Q` iSR / iDC `Q` V0V`:C VJ0VCQ]V 1$J:C 8 .1$. Q% ]% ]Q1V` .V&1J% Q1R:CR:JR Q] 1I%IH%``VJ 1 JV:`C7 .V :IV: .V H%``VJ 8 .V /7 Q] 1I%I H%``VJ 1 .1$.V` : I:61I%I ]Q1V` GVH:% V .V 1$J:C .: .1$.V`;;?8 J :CC H: V 5 .VQ] 1I%I H%``VJ 1JH`V: V : Q% ]% ]Q1V` * ⋅ RVH`V: V 8J .V 1JRH: V iSR :]]`Q:H.V 2 iDC : CQ1Q% ]% ]Q1V`5: 1J^ _8 * &QIVR1 H`V]:JH71 QG V`0VRR%V Q QCV`:JHV 1JIV: %`1J$:JR V 1J$ .V iSR :JR * iDC CV0VC 8 .1 1 VVJ 1J .: .V iSR / iDC `: 1Q `:CC C1$. C7 GVCQ1 %J1 7 : I:61I%I]Q1V`8?V:C1 1H:CC75 .1 1 H:% VRG7IV: %`VIVJ V``Q`:JRGVH:% V51J .V * iSR Q] 1I1<: 1QJ]`QHV 5V``1H1VJH70V` % iSR 1 `VC: 10VC7`C: : 1 ]V:@8.1 I:@V 1 R1``1H%C Q V .V V6:H ]V:@ V``1H1VJH7 G7 .:JR5 :JR CV:R Q C1$. RV01: 1QJ 1J Optimum Operating Strategies for Hybrid Voltage Regulators 113 * Q] 1I%I iSR 0:C%V ``QI .VQ`V 1H:C]`VR1H 1QJ 8$Q` %J: VC75GVH:% VQ` .V .:CCQ1 I1J1I%I1J]Q1V`R1 1]: 1QJ5 .1 1 11 .Q% I:=Q`HQJ V_%VJHV Q:0V`:$VV``1H1VJH78 I]Q` :J C75 $1$%`V R .Q1 .: 1$J1`1H:J ]Q1V` :01J$ :`V ]Q 1GCV 1` .V * 11 H.1J$`V$%C: Q` %]]C1V .VQ] 1I%IH%``VJ 5iSR 5`: .V` .:J .V H%``VJ Q .V CQ:R8 .V ]Q1V` :01J$ :`V IQ R`:I: 1H : CQ1 Q% ]% ]Q1V` CV0VC 5 1.VJ .V :0V`:$VQ% ]% 0QC :$V1 1$J1`1H:J C7CV .:J .V %]]C70QC :$V8 CQ1]Q1V`5 .V 11 H.1J$ `V$%C: Q` %]]C1V IQ`V .:J .V H%``VJ 8 .1 `VR%HV .V JV H%``VJ .: .VC1JV:``V$%C: Q`R`:1 ``QI .V %]]C78J .V 1I]CVH: V Q` 1J% Q1R:CR * :JR 1QR QJV IQR%C: 1QJ5 iSR H:J GV `Q%JR G7 .:JR H:CH%C: 1QJ 11 . `V: QJ:GCV * :HH%`:H78 8Q1V0V`5 .V GV V` QC% 1QJ I:7 GV Q :R:] 10VC7 VV@ iSR 11 . :J V6 `VI%IR VV@1J$:R:] 10VHQJ `QC:`H.1 VH %`V5 %H.: 1 ]`V VJ VR1J` a`Q`RV:RR 1IVQ] 1I1<: 1QJ8 RVIQJ `: VR1J$1$%`V R 5 .1 IV .QR]`QI1 V 1$J1`1H:J ]Q1V` :01J$ `Q` .V.7G`1R`V$%C: Q`:`H.1 VH %`V`Q`R7J:I1H %]]C7:]]C1H: 1QJ 8 8 :CH%C: 1QJ JHC%R1J$ Q:R 7J:I1H Figure 62. Hybrid regulator model including output capacitance Optimum Operating Strategies for Hybrid Voltage Regulators 114 ` .VCQ:R1I]VR:JHV1JHC%RV %G :J 1:C`V:H 10VR7J:I1H 5 .VQ] 1I%IQ]V`: 1J$ HQJR1 1QJ H.:J$V C1$. C78Figure 62 .Q1 :IQRVC`Q`:.7G`1R0QC :$V`V$%C: Q` .: 1JHC%RV Q% ]% H:]:H1 :JHV1J]:`:CCVC11 . .V`V 1 10VCQ:R8J .1 H: V5 QIVH%``VJ 1 %]]C1VR Q .V `V:H 10V ]:` Q` .V CQ:R 1I]VR:JHV 1.VJ .V Q% ]% 0QC :$V 1 R7J:I1H:CC7 :R=% VR8 1 V6]VH VR .: :RR1 1QJ:C ]Q1V` CQ 11CC QHH%` R%V Q VJV`$7CQ 1J .VH:]:H1 Q`8 %`J Q% `Q` .1 V6:I]CV5 .: .V]Q1V`CQ 1 `VC: VR Q .V 1IVHQJ :J 5τ = RC 5Q` .VQ% ]% JV 1Q`@`VC: 10V Q .V``V_%VJH7HQJ VJ Q` .V0QC :$V 1$J:C8 .V GV.:01Q` H:J GV QC0VR V6]C1H1 C7 `Q` .V 1J% Q1R:C :I]C1 %RVRIQR%C: 1QJ H: V5 :JR Q1J .1 VH 1QJ1V11CC% V .1 H: V Q.1$.C1$. .V$VJV`:CGV.:01Q`Q` .V.7G`1R `V$%C: Q`11 .CQ:RR7J:I1H 8 %I1J$ .: .VQ% ]% 0QC :$V `:=VH Q`7`QCCQ1 v (t) = v + v ⋅ cos(w t) 5 o DC a a ^ _ 1.V`V vDC 1 .V Q% ]% 0QC :$V5 va 1 .V:I]C1 %RVQ` .VIQR%C: 1QJ 1$J:C5:JR wa 1 .V``V_%VJH7Q` .V:I]C1 %RVIQR%C: 1QJ QJV8.VJ .VCQ:RH%``VJ 1JHC%R1J$ .V`V:H 10VR7J:I1H `QCCQ1 = []+ ⋅ ⋅ + 1 io (t) vDC va cos(wat) jwaC 5 R ^ _ 1 1.V`V jw C + is the admittance of the load network at the frequency of the AM tone. a R Optimum Operating Strategies for Hybrid Voltage Regulators 115 The current supplied to the load by the linear regulator, following the development of section 5.4 follows as = []+ ⋅ ⋅ + 1 − iLR (t) vDC va cos(wat) jwaC iSR (t) 5 R ^ _ %H. .: .VHQJR%H 1QJ:J$CVQ` .VC1JV:``V$%C: Q`1 i − i Φ = cos −1 SR DC + ⋅ 8 ia jwaC Va ^ _ VVJ1J^ _5 .VHQJR%H 1QJ:J$CV1 HQI]CV65G% :0V`:$V_%:J 1 1V H:J 1CCGV `Q%JR% 1J$ .VI:$J1 %RVQ` .1 _%:J 1 75 − i − i 1 Φ = cos 1 SR DC + 8 ia 1 jwa RC ^ _ .V:0V`:$VC1JV:``V$%C: Q`H%``VJ .VJ`QCCQ1 : Φ 1 i = ()i − i +V cos(φ) ⋅ jw C + /1 R dφ LR π ∫ DC SR a a 8 2 − Φ ^ _ ^ _1 .VJ QC0VR:JR 1I]C1`1VR Q ~ i i = a []sin Φ − Φ cos Φ . LR π 51.V`V ^ _ ~ = + ia ia 1 jwa RC 8 .1 `V %C 1JJV:`C7 .V :IV`Q`I`Q` .V]`V01Q% 1J% Q1R:CH: V5V6HV] .: ^ _ 1JHC%RV .V `1` Q`RV` R7J:I1H 8 1J$ .V :IV Q] 1I1<: 1QJ ]`QHVR%`V : 1J Optimum Operating Strategies for Hybrid Voltage Regulators 116 ]`V01Q% V6:I]CV 5 .V 7 VI1 QC0VR`Q` .VI1J1I%I]Q1V`CQ HQJR1 1QJ 5 %H. d η .: = 0 8.V`V %C 1J$Q] 1I%IHQJR1 1QJ `QCCQ1: diSR πV Φ* = DC 5 VDD ^ _ ~ i* = i + i cos Φ* SR DC a 5:JR ^ _ V i + a a VDC iDC ^ _ * 2 η = ~ 8 i V i +V a sin Φ* DC DC DD π 8V`V5 .V`Q`IQ`^ _R^ _1 1I1C:` Q^ _R^ _5G% 1JHC%RV .V`V:H 10VR7J:I1H Q` .VQ% ]% H:]:H1 :JHV8.V VV6]`V 1QJ HQJ0V`$V Q .VJQI1J:C`V 1 10VV_%: 1QJ 1.VJ .V ``V_%VJH7 Q` .V :I]C1 %RV IQR%C: 1QJ 1 1VCC GVCQ1 .V ``V_%VJH7 Q` .V ]QCV: .VQ% ]% 88Q1V0V`51` .V``V_%VJH7Q`:I]C1 %RVIQR%C: 1QJ:]]`Q:H.V Q` V6HVVR .VQ% ]% ]QCV5 %G :J 1:CCQ V I:7QHH%`GVH:% VQ` .VCQ:RH:]:H1 Q`8 1 0.9 0.8 0.7 0.6 0.5 0.4 Vo=0.5+0.5Cos(wt) --Calc Efficiency Efficiency 0.3 Vo=0.5+0.5Cos(wt) --Sim 0.2 Vo=0.25+0.25Cos(wt) --Calc 0.1 Vo=0.25+0.25Cos(wt) --Sim 0 0 0.1 0.2 0.3 0.4 0.5 Normalized time constant (wRC) Optimum Operating Strategies for Hybrid Voltage Regulators 117 Figure 63. Hybrid regulator with load capacitance: efficiency versus normalized time constant (simulation vs theory) Figure 63 .Q1 .VV``1H1VJH7Q` .V.7G`1R0QC :$V`V$%C: Q`R`101J$:`1` RQ`RV`? CQ:R5: 1JIQRVCVR1JFigure 628.V6R:61 1 JQ`I:C1 .V ``V_%VJH7 Q` .V :I]C1 %RV IQR%C: 1QJ 1$J:C 1 : ]V`HVJ :$V Q` .V Q% ]% ]QCV ``V_%VJH78 .V I:61I%I V``1H1VJH7 `QCCQ11J$ ^ _ 1 ]CQ VR % 1J$ .V QC1R C1JV 8 &1I%C: 1QJ `V %C :`V .Q1J 11 . R1 H`V V ]Q1J 8 8V`V5 1I%C: 1QJ I: H.V .V V6]`V 1QJ RV`10VR1J^ _R^ _11 .V6HVCCVJ :$`VVIVJ 8 Figure 63 .Q1 .: 1` .V``V_%VJH7HQJ VJ Q` .V:I]C1 %RVIQR%C: 1QJ 1$J:C1 . 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These topologies can provide fast dynamic regulation with low noise and high efficiency. If the operating conditions are carefully considered, power efficiency can be comparable to a pure switching regulator solution. The key is to consider the time-domain operation of the switching and linear regulator portions as many waveforms can have the same power spectrum. In many cases, the switching regulator should supply more than the average load current, with the linear regulator sinking more current to ground in a push-pull output stage. There are many conceivable circuit architectures that could optimize the bias conditions of the hybrid regulator through online sensing and slow adaptive feedback. A final practical consideration includes the dynamics of the load network. From an efficiency perspective, it is best to have any poles at the output be substantially higher frequency than the modulation signal to avoid reactive losses. This implies that the linear regulator may be best optimized with internal compensation rather than using a dominant pole at the output. 119 Chapter 6 Direct Digital Modulation: A New Approach to Polar Systems Figure 64. Conventional cellular phone block diagram: digital application processor, DSP, Audio, Power management; Radio is still largely analog Figure 65. 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Effect of polarity on amplitude quantization - ∆Σ process remains linear near zero .V].: VR`VVR`Q`1:`R `: V$7.: :R1``V`VJ V``VH QJ .V:I]C1 %RV]: .81 . .V]QC:`1 7G1 5 .V:I]C1 %RVH:JGV `V: VRJ%IV`1H:CC7: :G1R]QC:` 1$J:C8&.Q1J1J Figure 915 .V 1IVR :JR ``V_%VJH7RRQI:1J `V]`V VJ : 1QJ :`V J%IV`1H:CC7 R1``V`VJ 8 8Q1V0V`5 .1 1 QJC7 :J :` 1`:H Q` .V R1$1 :C `V]`V VJ : 1QJ8 ?V:C1 1H:CC75 .V :I]C1 %RV ]: . 11CC `V_%1`V .V :IV G:JR11R . : GV`Q`V Q H:``7 .V VJ0VCQ]V 1J`Q`I: 1QJ8.VGVJV`1 Q`]QC:`1 7VJHQR1J$1 1J .VC1JV:`1 7Q` .V∆ΣJQ1 VR .:]1J$ Direct Digital Modulation: A New Approach to Polar Systems 156 ]`QHV 81 .]QC:`1 75 .V∆Σ]`QHV RQV JQ : %`: V: .VJQ1 VR .:]1J$]`QHV `VI:1J C1JV:`JV:` GV JV$: 10V8 17 ]`V0VJ 1J$ :I]C1 %RV : %`: 1QJ : $VJV`: V JV:`R .:JRCV :JR:`R 1.V`V .V:I]C1 %RV$QV Q V``VH 10VC7 .:J11 .Q% ]QC:`1 71J`Q`I: 1QJ8 6.5.5 ∆∆∆Σ∆ΣΣΣ Noise-shaping process J .1 1Q`@5 .V ∆Σ IQR%C: Q` 1J V``:HV GV 1VVJ .V .1$.R`V QC% 1QJ G: VG:JR 1$J:C :JR .V ]%C VRRVJ 1 7 IQR%C: Q`8 .V _%:J 1 ]QC:`1 7 Q` .V RG1 `V]`V VJ : 1QJ8 ?C RVHQRV` I:] .V G1R]QC:` RCV0VC _%:J 1<: 1QJ Q RG1 11 . ]QC:`1 7 `Q` .V JV6 R :$V ; GCQH@8 1 . .V 7 VI HCQH@VR: .VG: VG:JR``V_%VJH7Q`8<5]V:@ 1J .VJQ1 V ]VH `%I:`VQ`` V ``QI .VH:``1V```V_%VJH7G7 8<8 A = I 2 + Q 2 Figure 93. Error-feedback digital ∆Σ modulator Direct Digital Modulation: A New Approach to Polar Systems 157 .V∆ΣIQR%C: Q`1 1I]CVIVJ VR11 .:R1$1 :CV``Q`R`VVRG:H@ `%H %`V5: .Q1J1J $1$%`V 8 R1 H% VR1J VH 1QJ 85 .VV``Q``VVRG:H@ `%H %`V .:]V _%:J 1<: 1QJ Y (z) JQ1 V11 . `:J `V``%JH 1QJ NTF(z) = = G(z) 51.V`V .VV``Q`R `:J`V`R`%JH 1QJ%1 E(z) G(z) −1` a8.1 ]`Q01RV `CV61G1C1 71J:`%CC7R1$1 :C 7 VI1.V`V1 1 `:1$. `Q`1:`R Q H.:J$V .V R1 H`V VR 1IV ^<_ $? `:J `V` `%JH 1QJ8 J Figure 935 `Q` V6:I]CV5 − 2 G(z) = (1− z 1 ) 5 %H. .: .V`V:`V 1Q -30 -50 -70 POWER (dBm) POWER -90 0 10 20 30 40 50 FREQUENCY (MHz) Figure 94. Example baseband 3rd order ∆Σ modulator spectrum with a notch at ±12MHz, − − − G(z) = −z 3 + 5.2 z 2 − 5.2 z 1 Direct Digital Modulation: A New Approach to Polar Systems 158 Figure 95. ∆Σ Modulator: 1st, 2nd, 3rd order comparison, all zeros at 2.4GHz $1$%`V :JR$1$%`V .1$.C1$. .V`CV61G1C1 7Q` .VV``Q`R`VVRG:H@ 7 VI8$1$%`V .Q1 .V 1I%C: VR`V ]QJ VQ`: .1`RRQ`RV``1C V`11 . 1QHQI]CV6 .V CQQ] `1C V` 1 ]C:HVR :]]`Q61I: VC7 8< ``QI .V H:``1V`8 7Q H.V 1J .V _%:J 1<: 1QJJQ1 V ]VH `%II:7GV% V`%C Q.VC]IVV ]VH `:CI: @`V_%1`VIVJ 1J QIV H1`H%I :JHV 8 J`Q` %J: VC75 .1$.V` Q`RV` IQR%C: Q` :C Q 1JH`V: V .V ]V:@ ± ^%J`1C V`VR_ _%:J 1<: 1QJ JQ1 V .: QHH%` JV:` f 0 f S 5 1.V`V f 0 1 .V H:``1V` ∆Σ ``V_%VJH7:JR f S 1 .V :I]C1J$``V_%VJH7Q` .V IQR%C: Q`8JI:J7H: V 5 .V ]V:@Q% RQ`RG:JRJQ1 V1 .VC1I1 1J$`:H Q`QJ ]VH `:CI: @HQI]C1:JHV8` Q5CQ1V` Q`RV`IQR%C: Q` H:J]`Q01RVCQ1V`]V:@JQ1 V: .V `:RVQ``Q`.1$.V`1JRG:JRJQ1 V8 Figure 95 .Q1 .V 1I%C: VR``V_%VJH7 `V ]QJ VQ` .V 7 VI 11 . 0:`1Q% CQQ] `1C V` `Q`: %]]`V VRH:``1V` 1$J:C8.V`RQ`RV` 7 VI.: .VCQ1V JQ1 V: Direct Digital Modulation: A New Approach to Polar Systems 159 .VHVJ V```V_%VJH75G% .1$.V ]V:@Q% RQ`RG:JRJQ1 V8.V`1` RQ`RV` 7 VI.: CQ1V`]V:@Q% RQ`RG:JRJQ1 V5G% I:7.:0V QJV 1J .VQ% ]% ]VH `%I`Q`HV` :1J 1J]% 1$J:C 8 VHQJRRQ`RV``1C V`:H.1V0V GQ .`:0Q`:GCVJQ1 VR .:]1J$:JR`VR%HVR ]Q 1G1C1 7 Q` QJV 1J .V Q% ]% ]VH `%I8 .V VHQJRRQ`RV` `1C V` 1: % VR 1J .V V6]V`1IVJ :C]`Q Q 7]V8 6.5.6 Class-D PA Figure 96. Complementary class D PA schematic &11 H.1J$ ]Q1V` :I]C1`1V` `:R1 1QJ:CC7 % V JRH.:JJVC ]Q1V` RV01HV GVH:% V Q` .1$.V`IQG1C1 78.1 CV:R Q I:CCV`RV01HV :JRCQ1V` 11 H.1J$CQ V 8 C: R.:JR HC: R$ Q` R 11 H.1J$ VH.J1_%V 1I]`Q0V V``1H1VJH7 %JRV` JQ`I:C H1`H%I :JHV G7 `VR%H1J$]Q1V`CQ Q`V:H 10V]:`: 1 1HHQI]QJVJ `a88Q1V0V`5 .V V:I]C1`1V` `VC7 QJ .V Q% ]% JV 1Q`@ Q .:]V .V 0QC :$V 1:0V`Q`I :H`Q .V :H 10V RV01HV8 .1 H:J`V %C 1J.1$.0QC :$V `V 8QRV`J C&]`QHV V .:0V`: :H 10VRV01HV .: :`VHQJ `:1JVRG7CQ1G`V:@RQ1J0QC :$V 8J .1 HVJ:`1Q5 .VHQI]CVIVJ :`7 HC: R Q% ]% :$V.: :R0:J :$V Q0V`IQ`V `:R1 1QJ:C Q]QCQ$1V 8 Direct Digital Modulation: A New Approach to Polar Systems 160 &.Q1J1JFigure 965G7% 1J$:HQI]CVIVJ :`7Q% ]% :$V11 .:H 10V;C&]%CCR%] `:J 1 Q` 5 .VR`:1J0QC :$V1 : _%:`V1:0V8I]Q` :J C75 .VQ% ]% :$V1 :C1:7 CQ1 1I]VR:JHV CQQ@1J$ G:H@ 1J Q .V 11 H.1J$ JQRV8 .1 VJ:GCV .1$. 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COMPARISON: FV-FI FIGURE OF MERIT FOR VARIOUS AMPLIFIER CLASSES (DATA FOR CLASS E, F-1, F2,3,4,5 FROM [34]) Amplifier Class FV FI E 3.56 1.54 F-1 3.14 1.41 E/F2,3,4,5 3.20 1.45 D 2.00 1.57 Table IV HQI]:`V .V HC: R Q]QCQ$7 Q Q .V` 11 H.1J$RHC: :I]C1`1V` 8 C61RV `V : :`%JH 1QJQ` %]]C70QC :$V1 CQ1V``Q`HC: R 5V ]VH1:CC7HQI]:`VR QHC: R.8 .1 :CCQ1 .V RV01HV Q RVC10V` .1$.V` :0V`:$V ]Q1V` Q .V CQ:R `Q` : $10VJ ]V:@ Q61RV `V 8&1JHVV:H. 11 H..: .:C`R1:0V 1J% Q1R:CR`:1JH%``VJ 5 1 HQI]:`:GCV Q .VQ .V` :I]C1`1V` Q]QCQ$1V 8 J 1I]Q` :J :R0:J :$V Q` .V HC: R :I]C1`1V` 1 .: .V Q% ]% :$V 1 :C1:7 CQ1 1I]VR:JHV8 :`1: 1QJ 1J .V 1I]VR:JHV Q` .V Q% ]% JV 1Q`@H:% VRG7CQ:R]%CC``QI .V:J VJJ:RQV JQ :``VH :JR`: 1Q 8 .1 I:@V .V HC: R Q% ]% :$V`QG% :$:1J 1I]VR:JHV 0:`1: 1QJ HQI]:`VR Q Q .V` 11 H.1J$:I]C1`1V` Q]QCQ$1V 8 .V `:R1 1QJ:CR1 :R0:J :$VQ` .VHQI]CVIVJ :`7HC: R Q]QCQ$71 .V% VQ`]R H.:JJVCRV01HV 11 .CQ1V`` .:J .VJRH.:JJVCRV01HV 8.1 1JH`V: V H:]:H1 :JHV5 `VR%H1J$V``1H1VJH7HQI]:`VR Q7C&RQJC7 Q]QCQ$1V 88Q1V0V`51JRVV]R %GI1H`QJ ]`QHV V 5]RH.:JJVCRV01HV I:7.:0V` 1JV6HV Q`K8<`a8 V01HV H:C1J$`%` .V` 1I]`Q0V Q]V`: 1QJ ``V_%VJH1V :JR `VR%HV 11 H.1J$ CQ V `a8 J .1 RV 1$J .V Direct Digital Modulation: A New Approach to Polar Systems 162 :R0:J :$V Q` % 1J$ : CQ1R1I]VR:JHV HQI]CVIVJ :`7 Q% ]% :$V Q% 1V1$. .1$.V` CQ V 1J .V]RH.:JJVCRV01HV8 C: R 1 :C QIQ`VC1JV:`11 .]%C VRRVJ 1 7IQR%C: 1QJ .:JQ .V`:I]C1`1V`HC: V 8 $Q` .V]%C VRRVJ 1 7IQR%C: 1QJ H.VIV5 .VHC: R Q% ]% :$V.: .V:R0:J :$V .: .VR`:1J0QC :$V1:0V`Q`I1 JQ :``VH VRG7]%C VR @1]]1J$8$Q`HC: R.Q`$5 .V :` %] 1IV Q :H.1V0V JQI1J:C V:R7 : V Q]V`: 1QJ H:J CV:R Q R1 Q` 1QJ8 .1 VHQJRRQ`RV` V``VH 1 H:% VR G7 `VC1:JHV QJ .V Q% ]% JV 1Q`@ Q .:]V .V R`:1J 0QC :$V1:0V`Q`I8QC :$VRIQRVHC: R :I]C1`1V` `Q`HV:JV:`C71RV:CR`:1J0QC :$V GVH:% V .V 11 H.1J$RJQRV1 :C1:7 CQ11I]VR:JHV8 C: R :I]C1`1V` :`VCV C1@VC7 Q JVVR ]`VR1 Q` 1QJ Q HQI]VJ : V R :JR R; R1 Q` 1QJ .:J HC: R. Q` HC: R$:I]C1`1V` R%V Q1J.V`VJ Q]VJRCQQ]C1JV:`1 71J; Q]V`: 1QJ8 6.5.7 CMOS Class D PA Implementation Figure 97. Schematic representation of class-D power amplifier with cascode output stage Direct Digital Modulation: A New Approach to Polar Systems 163 Figure 98. Current recycling scheme: excess current from PMOS drive stage used by digital processing source drain source drain current 5µm G C C G G C Figure 99. Class-D PA output stage NMOS layout: gate and cascode share diffusion region to reduce junction capacitance Figure 97 .Q1 .V H.VI: 1H Q` .V C& HC: R ;8 Q :H.1V0V .1$.V` Q% ]% ]Q1V`5 .VQ% ]% :$V% V H: HQRVRV01HV 5:CCQ11J$.1$.V`0QC :$VQ]V`: 1QJ8.V Q% ]% RV01HV :`V .1JRQ61RV `:J 1 Q` 11 ..1$.` 1.1H.H:J:H.1V0V.1$.V`V``1H1VJH7 Direct Digital Modulation: A New Approach to Polar Systems 164 .:J .1H@RQ61RVRV01HV `Q` .V :IV %]]C70QC :$V` a8.V;Q]V`: V 11 .:.1$. 0QC :$V`:1C5Y85:JR:HVJ V`0QC :$V`:1C5.:C`Y88.1 C1I1 .VI:61I%I Q61RV `V Q81JJQ`I:CQ]V`: 1QJ8 &.Q1J 1J Figure 985 .V .:C` JQRV 1 .:`VR G7 .V .1$.R 1RV :JR CQ1R 1RV R`10V` %H. .: H%``VJ ``QI R`101J$ .V ;C& Q% ]% RV01HV 1 `V% VR Q R`10V .V 7C& RV01HV8.V`V1 7]1H:CC7V6HV H%``VJ ``QI .V;C&R`10V` GVH:% V .V;C&1 11HV .V 1 ]`QHV 1J$ GCQH@5 ]`Q01RVR .: 0QC :$V `:J 1VJ :`V :RV_%: VC7 `1C V`VR8 .V .:C` JQRV ]Q VJ 1:C1 `V$%C: VR11 .:JQ``RH.1]]Q1V` %]]C78]$QJRH.1]G7]: H:]:H1 Q` %]]C1V .1$.R``V_%VJH7 H%``VJ ``QI .V JQRV8 &1I1C:` G7]: 1J$ 1 ]C:HVRQJ .V.:C`JQRV8 .VQ% ]% :$V1 1 11 .G:C:JHVR 11 H.1J$:JRHQJR%H 1QJCQ `Q`8K8<Q]V`: 1QJ8.VQ% ]% :$V1 .:`R 11 H.VR QI:1J :1J:HH%`: VHQJ `QCQ` .V]%C VRRVJ 1 7IQR%C: 1QJ1:0V`Q`I8 8:`R 11 H.1J$ 1 ]V``Q`IVR G7 1J0V` V` R`10V` 5 1.1H. :`V H:CVR 11 . :]]`Q61I: V `:JQ% Q` .`VV8 &.Q1J 1J Figure 995 V:H. H: HQRV RV01HV 1: G%1C Q .:`V .V R1``% 1QJ`V$1QJQ` .V 11 H.1J$RV01HV1JQ`RV` Q`VR%HV]:`: 1 1H=%JH 1QJH:]:H1 :JHV : .VH: HQRVJQRV8.V`1J$V`11R .`Q`GQ .H: HQRV:JR 11 H.1: -I QI1J1I1 $: V`V 1 :JHV8 Direct Digital Modulation: A New Approach to Polar Systems 165 Figure 100. Level shift and deadtime control .VCV0VC .1` GCQH@5 .Q1J1JFigure 10051 % VR Q1J V``:HV .VJQI1J:C8R1$1 :C ]`QHV 1J$GCQH@ Q .V;Q% ]% RV01HV 8.V:`H.1 VH %`V1 1I1C:` Q .: ]`Q]Q VR 1J` a8/: H.1J$ `%H %`V 1V`V% VR Q`V Q`V 1$J:C 11J$QJ1J V`IVR1: VJQRV 8 Q%]C1J$H:]:H1 Q` 1JH`V: V``V_%VJH7`V ]QJ VQ` .VR1$1 :C 1$J:C 8 V:R 1IVHQJ `QC 1 1I]CVIVJ VR11 .`16VRRVC:7Q` ] 1J .V.1$.R 1RV:JRCQ1R 1RV 1$J:C]: . 8.V RV:R 1IV H1`H%1 ]`V0VJ .QQ R .`Q%$. H%``VJ :JR 7JH.`QJ1 0QC :$V 1:0V`Q`I 8 .V ] RV:R 1IV Q] 1I1 `V: QJ:GCV G%``V` `Q` ]`QHV :JR VI]V`: %`V 0:`1: 1QJ8 J .V RV:R 1IV H1`H%1 5 H:]:H1 Q` :`V]C:HVRGV 1VVJ .V.1$.R 1RV:JRCQ1R 1RV 1$J:C Q: %`V]`Q]V` 1IVR :C1$JIVJ 8 Direct Digital Modulation: A New Approach to Polar Systems 166 6.5.8 System Implementation FPGA On-Board On-Chip ) A ( de u it pl m A Matlab Labview Figure 101. System-level implementation of Bluetooth transmitter Figure 102. Die Photo of CMOS class D PA and RF pulse-density modulator circuits .V 7 VI1 1I]CVIVJ VR11 . 1Q V H.1] 1J JI C&8`1` H.1]HQJ :1J .V HC: R ; :JR R`10V` ^:H 10V :`V: 8 II _8 VHQJR H.1] HQJ :1J .V ; `%H %`V5 7JH.`QJ1<: 1QJ5HCQH@`VHQ0V`7:JR?C^:H 10V:`V:8II _8R1V].Q Q1 .Q1J1JFigure 1028.VG: VG:JR:JR∆ΣIQR%C: Q`:`V1I]CVIVJ VR1J:J$;K8 Direct Digital Modulation: A New Approach to Polar Systems 167 .V 7 VI1 V VR11 .:/:G01V1; V %]11 .?$%]HQJ0V` V`:JRRQ1JHQJ0V` V`8 .VC:G01V1 7 VI:JR$;K% V: 7JH.`QJQ% HCQH@ Q]V``Q`I 1IVR:C1$JIVJ Q` .V :I]C1 %RV:JR].: V 1$J:C 8.VQ% ]% `1C V`1 1I]CVIVJ VRQ``RH.1]:JRHQJ 1 Q`: `:R1 1QJ:C /RI: H.1J$ JV 1Q`@ :JR :J :RR1 1QJ:C G:JR]: `1C V` HQI]QJVJ 8 .V G:JR]: `1C V` 1 : EQ.:J QJ 1; 1 HQI]QJVJ `Q` .V 8 K8< G:JR 11 . 8R1I:61I%I1J V` 1QJCQ 8 6.5.9 Experimental results 2 V RF Pulse- Density 1-bit PA Modulator (@ 2.4GHz) RFclk Class-D (φ) Figure 103. Block diagram of the experimental setup .V V6]V`1IVJ :C V %] 1 .Q1J 1J Figure 1038 .V :I]C1 %RV ]: . Q` .V R1$1 :C ]QC:` `:J I1 V` 1 HQJ `QCCVR G7 : 7C1J6 $;K8 .V ?$ HCQH@ HQJ :1J1J$ ].: V 1J`Q`I: 1QJ1 1I]CVIVJ VR1J/:G01V1:JR %]]C1VRR1`VH C7 Q .VH.1]8.V/:G01V1 %]HQJ0V` V` 1 7JH.`QJ1 Q%`HV1 :C Q% VR Q 7JH.`QJ1 .V ].: V Q` .V ?$ HCQH@ 1 :R=% VR %J 1C .V 7 VI `V:H.V I:61I%I . ]V``Q`I:JHV8 a.) PA output with 200MHz clock signal 1.0 0.75 0.50 0.25 0.0 -0.25 -0.50 -0.75 -1.0 0.0 25 50 75 100 125 150 175 200 225 250 Time (us) b.) Downconverted transmitter output with 2.4GHz clock, linear ramp signal programmed into amplitude path Figure 104. Time-domain waveforms at transmitter output Figure 104 .Q1 1IVRQI:1J1:0V`Q`I : .VQ% ]% Q` .V 7 VI8Figure 104R: .Q1 .V H`VVJH:] %`VQ`:JQ H1CCQ HQ]V1:0V`Q`I: .VQ% ]% Q` .V;R%`1J$ ; Q]V`: 1QJ8.V 7 VIHCQH@1 CQ1VR Q8< QVJ:GCV .VQ H1CCQ HQ]V Q Direct Digital Modulation: A New Approach to Polar Systems 169 H:] %`V .V ?$ 1:0V`Q`I8 .V ; Q% ]% 1 .Q1J Q @1] ]%C V Q H`V: V .V :I]C1 %RVRIQR%C: VRQ% ]% Q` .V 7 VI8 Figure 104RG .Q1 .V Q% ]% Q` .V ]QC:` `:J I1 V` :` V` .V /:G01V1 RQ1JHQJ0V` V`11 .8K8<H:``1V```V_%VJH78.V:I]C1 %RV 1$J:C1 ]`Q$`:IIVR Q GV:`%CCR H:CVC1JV:``:I] 1$J:C11 .]QC:`1 78` V` .VRQ1JHQJ0V` V`5 .VC1JV:``:I] I: H.V .VRV 1`VR]: V`J11 .Q% RV01: 1QJQ`JQ 1HV:GCVR1 Q` 1QJ8.V]QC:`1 7Q` .VVJ0VCQ]V 1$J:CH.:J$V : 45% 20 18 35% 16 14 Efficiency 25% 12 Output Power (dBm) Power Output 15% 10 1.4 1.6 1.8 2 2.2 2.4 Supply Voltage (V) Figure 105. Efficiency and output power vs supply voltage VHV=2.0V, Vhalf=1.0V, fo=2.4GHz, Tamb=27oC 3.0 40% 30% 2.0 20% 1.0 Efficiency Efficiency 10% (V) Amplitude 0% 0.0 0 1 2 3 4 5 6 7 8 9 Code (# pulses in 9 full RF-clock cycles) Figure 106. Efficiency and linearity0]%CVRRVJ1 7 Direct Digital Modulation: A New Approach to Polar Systems 170 Figure 105 .Q1 .V Q :CQ% ]% ]Q1V`:JRV``1H1VJH7Q` .VHC: R ;:H`Q %]]C7 0QC :$V11 .`%CCIQR%C: 1QJ^]V:@]Q1V`_88V`V5V``1H1VJH71JHC%RV ]Q1V`Q` .V; R`10V` :JR CQ 1J .V I: H.1J$ JV 1Q`@5 G% RQV JQ 1JHC%RV 1J V` 1QJ CQ Q` .V G:JR]: `1C V`8 .V ]V:@ Q% ]% ]Q1V` Q` R1I QHH%` `Q` .V I:61I%I %]]C7 0QC :$VQ`8^I:61I%IQ61RV `V Q`8_8.V]V:@V``1H1VJH7Q`8 QQHH%` `Q` : %]]C7 0QC :$V Q` 88 1 . .V G:JR]: `1C V` 1JHC%RVR5 ]V:@ V``1H1VJH7 1: IV: %`VR: 8 Q8Figure 106 .Q1 C1JV:`1 7:JRV``1H1VJH7: V:H.Q` .VRCV0VC Q` :I]C1 %RV _%:J 1<: 1QJ8 /1JV:`1 7 `Q` .V ; 1 .1$. 11 . ]%C VRRVJ 1 7 IQR%C: 1QJ8 I]Q` :J C75V``1H1VJH7 :7 .1$.V`: CQ1V`]Q1V`CV0VC .:J11 . 7]1H:CHC: L1 ]Q1V`:I]C1`1V` 8.``1H1VJH7Q` .V;51JHC%R1J$R`10V`]Q1V`5 :7 :GQ0V Q`Q`R1 ]Q1V`G:H@Q``8 12 10 8 6 4 Power (mW) (mW) Power 2 0 0 0.5 1 1.5 2 2.5 3 Carrier Frequency (GHz) without current recycle with current recycle Figure 107. Power of digital processing (pulse-density modulation, clock recovery, sampling and synchronization) with and without current recycling scheme. Measured as power drawn from Vhalf regulator Direct Digital Modulation: A New Approach to Polar Systems 171 .V :0V`:$V V``1H1VJH7 Q` .V 7 VI 1 `%` .V` 1I]`Q0VR 11 . : H%``VJ `VH7HC1J$ H.VIV8&.Q1J1JFigure 985 1JHV .V.:C`JQRV1J .V;Q]V`: V : 85 .1 JQRV H:JGV .:`VR11 . .V8JQRV8.1 :CCQ1 V6HV H%``VJ ``QIR`101J$ .V;C& ]Q1V`RV01HV1J .V;1 % VR Q]Q1V` .V`VI:1J1J$8H1`H%1 `78 8K8< .1 `VR%HV .VH%``VJ R`:1J``QI .V8 %]]C7``QI8 I Q8 I8.VH%``VJ `VH7HC1J$ H.VIV:CCQ1 .VVJ 1`V 7 VI QQ]V`: V11 .Q:0V`:$VV``1H1VJH7`Q` πL F;&G:JR ;&GIQR%C: VR 1$J:C 11 .:]]`Q61I: VC7R1;;?8 /Q1R1$1 :C]`QHV 1J$]Q1V`:JR.1$.:0V`:$VV``1H1VJH7I:@V .1 H.VIV:IVJ:GCV Q CQ1R]Q1V` ]Q` :GCV 11`VCV :JR:`R 5 %H. : 1C%V QQ .8 QI]:`:GCV 1Q`@ ]%GC1 .VR1J .VC1 V`: %`V:H.1V0V .1$.V` ]VH `:C`1RVC1 7: .V `:RVQ``Q` 1$J1`1H:J C7 .1$.V` ]Q1V` HQJ %I] 1QJ8 ?V`V`VJHV ` a RVIQJ `: V : 7 VI 11 . ∆Σ Q]V`: 1J$ : 8K8< .: IVV HVCC%C:` HQV61 VJHV `V_%1`VIVJ `Q` 8GL$ :JR 8 V8 1$1 :C ]`QHV 1J$ ]Q1V` 1 1J V6HV Q` I `Q` `I Q% ]% ]Q1V` Q` 8 R1I8 .V QC% 1QJ ]`V VJ VR .V`V `V_%1`V GV 1VVJ R I `Q` .V R1$1 :C ; GCQH@`Q`RR1I`I ]Q1V`CV0VC 8 Direct Digital Modulation: A New Approach to Polar Systems 172 a.) π/4DQPSK (2MBPS) b.) 8DPSK (3MBPS) Figure 108. Measured constellation diagrams Direct Digital Modulation: A New Approach to Polar Systems 173 Figure 109. Efficiency and output power vs supply voltage Figure 108 .Q1 .VIV: %`VRHQJ VCC: 1QJR1:$`:I`Q`πL F;&G:JR ;&G V 0VH Q` 8.V V V 1$J:C IVV .V`V_%1`VIVJ Q` .V1C%V QQ .8U. ? :JR:`R π = `Q` .V1;&:JR1;&R: :`: V ` a8V: %`VR.`Q` L F;&G1 EVM rms 8.1 % = = = :JR EVM peak 8.2 % 8$Q` ;&G5 EVM rms 1.2 % :JR EVM peak 9.2 % 8 VVJ`Q` .V ;&G R: :1JFigure 108RG5 .V `:J I1 V`1 H:]:GCVQ`$VJV`: 1J$HQJ VCC: 1QJ `:=VH Q`1V .: ]: .`Q%$. .VQ`1$1J^1J`1J1 V]V:@RI1J1I%I`: 1Q_8.V 7 VI`VI:1J C1JV:` JV:` .1` 11 . .VR1$1 :C]QC:`1 7G1 1J .V:I]C1 %RV]: .8.1 1$J1`1H:J C7`VR%HV .V G:JR11R . `V_%1`VIVJ Q` .V ].: V IQR%C: Q` :JR 1I]`Q0V ]V``Q`I:JHV `Q` .1$. ;;? 1$J:C 8 Quantization noise of the digital modulator is a limiting factor for spectral performance. Figure 109 a-d.) shows that the nearband spectral requirements for Bluetooth 2.1+EDR are satisfied for both π/4DQPSK and 8DPSK test signals. Average power levels at the spectrum analyzer are between 11-14dBm. The wideband