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The current source R + I Vref Thevenin Norton I= Vref R R 4kT R •Minimum noise equals: DC current through resistor gives an increase of 1/f noise (granular structure) •Accuracy of source also determined by the accuracy of R •Output impedance mostly too low Use active V I converter Reference Sources A. van Staveren and W.A. Serdijn 37 The Active Current Source Vref + - - + I R • Output impedance is ……… • What about the noise? Reference Sources A. van Staveren and W.A. Serdijn 38 1 Nullor implemented by one CE stage I Vref R • I = -(Vref - VBE)/R • Temperature behavior VBE found in I (how to solve?) • Output impedance: β f ro − R rout = r0 + R + R ⋅ rb + rπ + R • If R >> rπ and R >> rb rout = ( β f + 1)r0 Reference Sources A. van Staveren and W.A. Serdijn 39 Plot of the output impedance vs R rout ro 0.7(βf+1) (βf+1) 1 R rπ 2 VR = I ⋅ R = I ⋅ 2rπ = 2 β kT q β f = 100, kT = 25 mV q VR=5V • Lower βf reduces VR but also rout • Better nullor approximation helps (ro must be increased) Reference Sources A. van Staveren and W.A. Serdijn 40 2 Noise behavior of active current source 4kTrb 2qIC 2qIB rb 1 4kT( + 2 ) 2qIC 2qIB R R Sout = + r + (1+βfR )2 (1+ π )2 (1+rπ )2 rπ βfR βfR I R II I II III infinite Sout 4kT/R R III 0 2qIB 0 (4kT/R) Only base shot noise remains Reference Sources A. van Staveren and W.A. Serdijn 41 Plot of noise vs R Sout 2qIc 1 2/βf 1/βf 1 2 R rπ If contribution of 2qIC plus 4kT/R equals 2qIB, then 2β VR = 5 V and Sout = 4qIB R= gm f Lowering βf for reducing VR does not help also, as: Sout = 8kT I/VR = 2·2qIB The lower VR the higher the noise Reference Sources A. van Staveren and W.A. Serdijn 42 3 Current source demo 25 V 10kΩ Switch open: R2 Sout ≈ 4kT 2 + 4kTR2 + 2qI B R22 R1 10kΩ R1 Q1 βf = 200 1 mA 15kΩ vn ,out ≈ 22 nV / Hz = −33 dBµV + 10kΩ V analyzer R2 - Switch closed: S out ≈ 0 + 4kTR2 + 2qI C R22 vn ,out ≈ nV / Hz = Reference Sources A. van Staveren and W.A. Serdijn dBµV 43 Current sources in 1V circuits Output impedance: VR relatively small 1V rout • Reduction of the DC loop gain accuracy • Does not need to cost bandwidth as pole also shifts rπ Noise: VAF rout= I C 1V 2qIC • Noise of the active part approximately doubles 2qIC Reference Sources A. van Staveren and W.A. Serdijn 44 4 Saturating transistors IC IB VBC VCE VBE • Transistor saturates if IC/IB < βF • Collector-emitter voltage is the difference of VBE and VBC 1 1+ 1 + IC / I B βr kT VCE = ln I q 1− C PTAT IBβ f LM MM MN b g OP PP PQ • For IC/IB = βf denominator equals zero VCE not determined • VCE reduces for larger βr (saturation voltage reduces) • VCE reduces for larger IC/IB (deeper saturation) Reference Sources A. van Staveren and W.A. Serdijn 45 Influence of layout on Vsaturation (I) C B E I II • electron at I has a larger chance on recombination than electron at II Bad for βr Take care of a large βr C I B E II • Most of the electrons have a short way to go Less recombination βr increases General: Collector and emitter overlap should be as large as possible Reference Sources A. van Staveren and W.A. Serdijn 46 5 The current mirror Iin + - - + (n) Mirror used for: • biasing purposes • current-gain stages • buffering (cascode) Iout (m) Transfer : Iin Iout Again nullor can be implemented by wire = m n standard current mirror Reference Sources A. van Staveren and W.A. Serdijn 47 Signal-to-noise ratio and dynamic range of a current mirror • SNR is the ratio of smallest and largest signal that can be processed at the same time • DR is ratio of smallest and largest signal that can be processed, not necessarily at the same time • Noise power proportional to collector current (2qIC) • Signal power proportional to the square of IC (IC2) For IC=1 nA and B=10 kHz P,S Psignal SNR Snoise DR SNR = 52dB DR → ∞ I Reference Sources A. van Staveren and W.A. Serdijn 48 6 Peaking current source Derived from current mirror ln FG I IJ = lnFG I IJ − I R H I K H I K kT / q 2 1 S2 S1 1 I1 1 R2 I2 R1 dI C 2 =0 dI C1 for R ⋅ I C1 = kT q Q2 Q1 • Source I1 can be implemented by a resistor • R1 relatively low ohmic and accurate a broad resistor • R2 relatively high ohmic and not very accurate a small resistor • What about PSSR ? Reference Sources A. van Staveren and W.A. Serdijn VR1 = kT q 49 T = 300 K R1=50 Ω R1=100 Ω Reference Sources A. van Staveren and W.A. Serdijn 50 7 Peaking current source vs Current mirror 510µA R1 8.2 kΩ 200µA 200µA R2 21 kΩ 200µA 50 Ω Q1 Qp2 Q2 Qp1 • 50 must be accurate • 8k2 does not need to be accurate • 21k must be accurate Reference Sources A. van Staveren and W.A. Serdijn 51 R1, R2 : 70%, 100% 130% Current mirror Peaking current source Reference Sources A. van Staveren and W.A. Serdijn 52 8 Conclusion/Summary • Several configurations of voltage and current sources discussed • Current level is the performance determining quality, not a 1V constraint • Circuit design is hampered by 1V criterion Reference Sources A. van Staveren and W.A. Serdijn other topologies 53 9