1. 1 AES AMSTERDAM 2008 Power Amplifier Workshop

2. 2 Power amplifier configurations The standard configuration Single differential input stage + push-pull VAS Double differential input stage + push-pull VAS Series balanced input stage + push-pull VAS Multiple differential pairs + push-pull VAS (Otala)

3. 3 Standard configuration

4. 4 Single differential input stage + push-pull VAS: 1

5. 5 Single differential input stage + push-pull VAS: 2

6. 6 Double differential input stage + push-pull VAS

7. 7 Double differential input stage + push-pull VAS VAS enhanced with Emitter-Follower

8. 8 Series balanced input

9. 9 The Standard Configuration: how it works. Open loop gain above dominant pole frequency is simply determined. VAS linearisation by C dom local feedback Feedback transferred from global to local around VAS as frequency increases Pole-splitting enhances stability. Can give excellent linearity.

10. 10 The Standard Configuration: equations LF gain is: LF gain= gm.β. Rc Eqn 1 HF gain is: HF gain= gm/( ω *Cdom) Eqn 2 Pole freq is: P1= 1/(Cdom*β*Rc) Eqn 3 gm is input stage transconductance. β is VAS current gain. Rc is VAS collector impedance ω= 2*π*freq The open-loop (O/L) gain has two regimes; flat below the lowest pole frequency P1, (LF) and falling at 6dB/octave above it. (HF)

11. 11 Possible distortion performance of standard configuration. Cambridge Audio 840W EF confign, 4 output device pairs. (Class XD switched off)

12. 12 Power amplifier distortion: std config D1: Input stage non-linearity D2: Voltage Amplifier Stage (VAS) non-linearity D3: Output stage non-linearity D4: Non-linear loading of VAS CONFIGURATION TOPOLOGY D5: Decoupling ground problems D6: Rail induction D7: Negative feedback takeoff point errors COMPONENTS D8: Capacitor distortion INTERFACING D9: Non-linear input currents

13. 13 Model amplifiers No complex output stage distortions. No non-linear loading on Voltage-Amplifier Stage. Much less chance of explosions. Power amplifier circuit with the output stage replaced with a small-signal Class-A stage that drives only the feedback network and the test equipment. Advantages:

14. 14 Model amplifier

15. 15 Distortions to not worry about ND1: Input-Stage Common-Mode Distortion ND2: Thermal Distortion over a cycle

16. 16 ND1: Input-Stage Common-Mode Distortion Standard configuration, output 10 Vrms Closed-loop gain CM voltage V rms 15 kHz THD meas 15 kHz THD calc 1.0010.00.0112%.00871% 1.228.20.00602%.00585% 1.476.81.00404% 2.005.00.00220%.00218% 230.43---------0.000017% Common-mode distortion is second-harmonic.

17. 17 ND2. Thermal distortion: or rather not. EF output stage Double output devices. 20W/8Ω 40W/4Ω 60W/3Ω

18. 18 D1: Input stage non-linearity How to optimise it. Ensure collector current balance Use emitter degeneration Use more sophisticated input stage

19. 19 D1: Input stage non-linearity The output current is related to the differential input voltage Vin by: Iout= I e.tanh(-Vin/2Vt) Vt is the "thermal voltage" of about 26mV at 25 degC I e is the tail current Transconductance is maximal when collector currents equal Transconductance is proportional to tail current Gray & Meyer "Analysis & Design of Analog Integrated Circuits." Wiley 1984, p194.

20. 20 D1: Input stage non-linearity a: Ic unbalancedb: Ic roughly balancedc: Ic closely balanced

21. 21 D1: Input stage non-linearity and Ic imbalance. 1: 0% 2: 0.5% 3: 2.2% 4: 3.6% 5: 5.4% 8: 10%

22. 22 D1: Complete amplifier; varying R2, input stage with mirror

23. 23 D1: Emitter degeneration to linearise input stage

24. 24 D1: Emitter degeneration to linearise input stage For a single BJT, the value of the internal re is approximated by: r e = 25/I c Ohms (I c in mA)

25. 25 D1: Constant-gm degeneration

26. 26 D1: Input stage enhancements

27. 27 D2: Voltage Amplifier (VAS) non-linearity VAS linearisation by Cdom local feedback. Feedback transferred from global to local as frequency increases. Not easy to model in SPICE as Early effect is only modelled linearly.

28. 28 D2: VAS non-linearity. Varying V- rail to input stage and VAS only. Model amplifier with Class-A output stage.

29. 29 D2: VAS enhancements StandardBootstrappedEmitter-follower added CascodedBufferedCascoded with buffer

30. 30 D2: VAS non-linearity. Model amplifier, 100R input degen.

31. 31 D3: Output stage non-linearity D3a: Crossover distortion D3b: Large-Signal Non-linearity (LSN) D3c: Switch-off distortion

32. 32 D3: Common types of output stages

33. 33 D3a: THD residual: underbiased

34. 34 D3a: THD residual: optimal bias

35. 35 D3a: THD residual: overbiased

36. 36 D3a: Reducing crossover distortion Lowest practical value of Re Multiple output devices Accurate Vbias Class AB? Gives higher THD at high levels Crossover displacement (Class-XD)

37. 37 D3a: Effect on crossover of Re value in EF stage

38. 38 D3a: Effect on crossover of Re value in CFP stage

39. 39 D3a: Reducing crossover distortion with six pairs of output transistors

40. 40 D3a: Class AB reduces crossover distortion, but...

41. 41 D3a: Reducing crossover distortion with Class-XD

42. 42 D3a: Reducing crossover distortion with Class-XD Resistive mode

43. 43 D3a: Reducing crossover distortion with Class-XD Constant-current mode

44. 44 D3a: Reducing crossover distortion with Class-XD Push-pull mode

45. 45 D3a: Reducing crossover distortion with Class-XD

46. 46 D3a: Reducing crossover distortion with Class-XD http://www.cambridgeaudio.com/assets/do cuments/840Awhitepaper8-2-06web.pdf Effective. Crossover distortion has been pushed away from the central point where the amplifier output spends most of its time. Push-pull displacement also reduces distortion when in Class-B operation. Simple. Only 5 extra transistors are used, of which 3 are small-signal and of very low cost. No extra presets or adjustments. Does not affect HF stability Versatile. Can act as a bolt-on distortion reducer which may be attached to almost any kind of Class-B amplifier.

47. 47 D3b: Large-Signal Non-linearity Mediocre output transistors

48. 48 D3b: Incremental gain: EF output stage

49. 49 D3b: Large-Signal Non-linearity: what is the mechanism? As Ic increases, output transistor beta falls Output transistor base draws more current from the driver emitter Increased current drawn reduces driver gain in current-dependant manner Output-device gain is NOT directly affected

50. 50 D3b: Large-Signal Non-linearity: Evidence for the mechanism? In SPICE simulation, driving the output bases directly from zero-impedance voltage-sources (not emitter-followers) abolishes the gain droop. SPICE Gummel-Poon model can be altered so output device beta does not drop with Ic; gain- droop does not occur, with drivers in use. Measured LSN levels correlate well with the degree of beta-falloff shown in manufacturer's data sheets.

51. 51 D3b: Reducing Large-Signal Non-linearity Sustained-beta output devices to minimise increase in base currents Multiple output devices to do the same Clever driver circuitry with very low output impedance? If an amplifier has the same distortion at 4 Ohm loading as at 8 Ohm loading, it can be called a Load-Invariant amplifier. How to approach that?

52. 52 D3b: Large-Signal Non-linearity Better output transistors

53. 53 D3b: Large-Signal Non-linearity Sustained-beta output transistors

54. 54 D3b: Large-Signal Non-linearity: beta

55. 55 D3b: Large-Signal Non-linearity Doubled sustained-beta output transistors

56. 56 D3b: Large-Signal Non-linearity Six pairs of sustained-beta output transistors

57. 57 D3c: Switching distortion

58. 58 D3c: Switching distortion Caused by delay in output devices switching off Can be improved by keeping resistors on output device bases as low as possible Driver emitter resistors in the EF output stage Driver collector resistors in the CFP output stage Use Type 2 EF output stage with a single driver emitter resistor

59. 59 D4: Non-linear loading of VAS The input impedance of the output stage is not linear VAS output impedance falls with frequency when the usual Miller dominant- pole compensation is used.

60. 60 D4: VAS collector impedance

61. 61 D4: Input impedance of the output stage

62. 62 D5: Decoupling ground problems How not to do it.

63. 63 D5: Decoupling ground problems: THD residual

64. 64 D5: Decoupling ground problems

65. 65 D5: Decoupling ground problems Correct method of grounding

66. 66 D6: Rail induction distortion Half-wave currents generate magnetic fields due to loops in output stage conductors. Magnetic fields crosstalk into sensitive parts of the circuit by induction. Cherry "A New Distortion Mechanism In Class-B amplifiers." JAES May 1981

67. 67 6: Rail induction distortion

68. 68 D6: Rail induction distortion: THD residual

69. 69 D7: NFB takeoff point errors

70. 70 D7: NFB takeoff point errors

71. 71 D8: Capacitor distortion D8a: Output capacitor distortion D8b: Compensation capacitor problems

72. 72 D8a: Output capacitor distortion: standard cap

73. 73 D8a: Output capacitor distortion: v large cap

74. 74 D8a: Output capacitor distortion: ‘audiophile’ cap

75. 75 D8: Compensation capacitor problems

76. 76 Complete amplifier: the story so far

77. 77 D9: Non-linear input currents: source resistance Rs

78. 78 D9: Non-linear input currents: vary R s

79. 79 D9: Non-linear input currents: High-beta input devices

80. 80 D9: Non-linear input currents: reduced Itail, Rs= 3K9

81. 81 D9: Non-linear input currents: cascoding the tail source

82. 82 D9: Non-linear input currents: cascoding the tail source

83. 83 D9: Non-linear input currents: conclusions Use high-beta input transistors Cascode the tail current-source Less of a problem than it used to be as balanced inputs becoming more common in hifi, so amplifier will be fed from low source resistance.

84. 84 New developments in power amplifier linearity. Crossover displacement (Class XD) Error-correction Wrapping Miller compensation around the output stage New method #1

85. 85 Seriously underbiased amplifier with and without new plan.

86. 86 Noise in power amplifiers Noise from input transistors Noise from feedback network resistance Noise from emitter degeneration resistors Noise from upstream circuitry

87. 87 Noise in power amplifiers: source resistance Rs

88. 88 Power amplifier internal noise sources NFB network Johnson noise = -132.6 dBu Degen resistors Johnson noise = -129.6 dBu Neglect input transistor noise for now Total noise referred to input = -127.8 dBu Gain is 30.6 dB Calculated output noise = -97.3 dBu Measured output noise = -92.0 dBu 5.3 dB difference is due to input transistors.

89. 89 Power amplifier external noise sources: 1 Series input resistor Rs (EMC filter etc) 820 Ohm Johnson noise = -123.5 dBu RMS sum is -120.0 dBu Noise degraded by 2.6 dBu already, with no active circuitry upstream. Measured noise output was -92.0 dBu referred to input = -122.6 dBu

90. 90 Power amplifier external noise sources: 2 NE5532 unity-gain buffer output noise = -119 dBu Noise degraded by 5 dB NE5532 balanced input amp 10K res = -105 dBu Noise degraded by 17 dB NE5532 balanced input amp 820R res = -112 dBu (Lowest that can be driven, buffered inputs) Noise degraded by 11 dB

91. 91 Power amplifier external noise sources: 3 840W balanced input required to be quieter than the unbalanced input. Using 5532s, final design of balanced input was quieter by 0.9 dB V2.0 with 5532s was quieter by 2.8 dB Using more expensive parts: 4.7 dB

92. 92 AES AMSTERDAM 2008 Power Amplifier Workshop drgself@dsl.pipex.com Class-XD: http://www.cambridgeaudio.com/assets/docu ments/840Awhitepaper8-2-06web.pdf