Analog Integrated Circuits (Jieh Tsorng Wu)

jssc 1292 pp 18431853 gm c filters 22 44 analog ics

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Unformatted text preview: m-C Filters G m2 G m1 G m1 C Gm1 · Gm2 L2 = 22-17 G m2 V1 V2 C Gm1 · Gm2 Analog ICs; Jieh-Tsorng Wu Gm-C Simulated Gyrators Gyrator G m2 V1 Simulated Grounded Inductor G m1 V2 V1 G m2 G m1 C G m2 V1 G m1 V2 V1 G m2 G m1 C Simulated Floating Inductor V1 G m2 G m1 G m1 G m2 V2 G m1 G m2 V2 C V1 Gm-C Filters G m2 G m1 C 22-18 Analog ICs; Jieh-Tsorng Wu MOST Transconductors Io1 Io1 Io2 Io2 1/2 Vi1 Vi2 Vi1 Tuning 1/2 1 1 Tuning 0.15 I 0.85 I VSS Gm-C Filters Vi2 VSS 22-19 Analog ICs; Jieh-Tsorng Wu MOST Transconductors Bias Offset Linearization Adaptive Source Degeneration Io1 Io1 Io2 Vi1 Io2 Vi2 Vi1 VB Vi2 M1 M2 M3 VB M4 Tuning VSS Gmo/ Gm VSS 1 Let M1=M2=M3=M4, -1 Gm-C Filters 0 Gmo Vi / IBias 1 ID = k (VGS − VT )2 2 Io1 = Io2 = kVB (Vi 1 − Vi 2) 1 22-20 Analog ICs; Jieh-Tsorng Wu MOST Transconductors with Source Degeneration Io2 Io1 Io1 Vi1 Vi1 Io2 M1 Vi2 M2 M1 V CA V’i1 Ia MA M4 V’i2 V Vi2 M2 MA VC V’i1 M3 V’i2 CB MB V’i1 V’i2 Ib Ia VSS VSS Fully Balanced Type Double-MOST Type Gm-C Filters 22-21 Analog ICs; Jieh-Tsorng Wu MOST Transconductors with Source Degeneration Let Vi Vi Vi 2 = − + V0 Vi 1 = + + V0 2 2 For the fully balanced differential transconductor Ia = G × Vi − ge Vi + 2 − ge Vi − 2 G = k (VC − V0 − Vt ) − go Io1 − Io2 = 2Ia ≈ 2G × Vi − 2go + Vi 2 Vi + 2 − go Vi − 2 ≈ 2G × Vi For the double-MOSFET differential transconductor Vi Ia = GA × Vi − g + 2 Vi −g − 2 Vi Ib = GB × Vi − g + 2 Vi −g − 2 Io1 − Io2 = 2(Ia − Ib) = 2(GA − GB ) × Vi Gm-C Filters 22-22 Analog ICs; Jieh-Tsorng Wu BJT Transconductors Vi1 Io1 Io2 Io1 Q1 Vi2 Q2 Vi1 Io2 Q1 Q2 Vi2 R VEE VEE VEE gm Multi-tanh Doublet Total Io2 Io1 Q2-Q4 Q1-Q3 4x Vi1 1x Q1 1x Q2 Q3 4x Q4 Vi2 VOS VOS VOS VOS = VEE Gm-C Filters 22-23 kT q V i I ln IS 1 S2 Analog ICs; Jieh-Tsorng Wu Multi-Input Transconductors VDD Va G ma M4 Io M3 VB1 Vo Vb G mb M5 M6 Io G ma Io G mb Vo M7 Va VB2 Vb M8 M9 M10 Io = Gma · Va + Gmb · Vb VB3 Io VB4 VSS • Need only one output common-mode feedback. • Reference: Edited by Y.P. Tsividis and J.O. Voorman, “Integrated Continuous-Time Filters”, IEEE Press, 1993. Gm-C Filters 22-24 Analog ICs; Jieh-Tsorng Wu Transconductor’s Imperfections Nonideal Model Vi Io Vi Vo G m1 go Ci Io = Gm(s) × Vi Vo Vi C Gm(j ω) = Gm 1 + j ω/ω2 go Ci ≈ Gm e − j φ φ = tan−1 C ω ω2 For the Gm-C integrator Vo Gm Gm 1 = × = Vi sC + go sC 1 + ωo + g 1 + s2 1 + s/ω2 o ω ωω 2 Gm-C Filters 22-25 ωo = go C o2 Analog ICs; Jieh-Tsorng Wu The Effect of Non-Zero go on Gyrators Gm go Vi Vi Gm Vi L1 C Gm go Rs C go G m L= Gm-C Filters C Rs = 2 Gm 22-26 go 2 Gm Analog ICs; Jieh-Tsorng Wu The Effect of Phase Shift on Gyrators Vi Gm Vi Vi Gm C Gm Rp L1 C Gm If Gm(j ω) = Gme −j φ φ = tan −1 ω ≈ ω2 ω ω2 1 We have L= Gm-C Filters C 2 Gm 2 2 2Gm 2Gm 2 1 ·φ≈− =− ≈− Rp ωC ω2 C ω2L 22-27 Analog ICs; Jieh-Tsorng Wu Gm-C First-Order Filters 1 Vi Vi2 α1s + α0 1 sτ G m4 Vo Vi1 G m1 G m2 C Vi1 G m5 Vo G m3 G m1 = G m2 G m1 C Vi2 G m3 Vo G m3 = G m4 = G m5 sCGm4 Vi 2 + (Gm1 Gm3Vi 1 + Gm2Gm4Vi 2) Gm1Vi 1 1 H (s ) = − · G + Gm4Vi 2 · =− sC + Gm2 m3 Gm5 (sC + Gm2) · Gm5 • The output requires another buffer to prevent loading effects. • Use only grounded capacitors. Gm-C Filters 22-28 Analog ICs; Jieh-Tsorng Wu Gm-C Second-Order Filters 1 Vo3 1/Q G m4 G m5 Vi3 G m3 Vi K Vh 1 sτ Vb 1 sτ Vl Vi1 G m4 Vi1 Vb = Gm-C Filters G m1 Vb C1 G m2 G m2 C1 Vl Vi2 Vi2 = Vi3 = 0 G m3 = G m5 Vo2 C2 C2 sC2Gm1 s2 C1C2 G m1 Vo1 + sC2 Gm1 + Gm2Gm4 Vl = − 22-29 Gm1Gm2 s2C1 C2 + sC2 Gm1 + Gm2Gm4 Analog ICs; Jieh-Tsorng Wu Gm-C Second-Order Filters The transfer functions are Vo1 = [1/D (s)] · [sC2 Gm1(Gm5 Vi 1 − Gm4 Vi 3) + Gm1Gm2Gm4Vi 2] Vo2 = [1/D (s)] · [(sC1 Gm2Gm5 + Gm1Gm2Gm3)Vi 2Gm1Gm2(Gm4 Vi 3 − Gm5Vi 1)] Vo3 = [1/D (s)] · [s2 C1C2Gm4Vi 3 + s(C2 Gm1Gm3Vi 1 − C1Gm2Gm4Vi 2) + Gm1Gm2Gm4Vi 1] D (s) = C1C2Gm5 s2 + s 1 Gm1Gm3 Gm1Gm2Gm4 + C1 Gm5 C1C2Gm5 If Vi 1 = Vi 2 = 0, then Vo1 sC2 Gm1Gm4 = HBP(s) = − Vi 3 D (s) Vo2 Vi 3 Vo3 Vi 3 Gm-C Filters = HLP(s) = Gm1Gm2 Gm4 D (s) 2 = HHP(s) = s C1C2Gm4 22-30 D (s) Analog ICs; Jieh-Tsorng Wu Gm-C Second-Order Filters If Vi 1 = Vi 2 = Vi 3 = Vi , then Vo3 Vi 2 = s C1C2Gm4 + s(C2 Gm1Gm3 − C1Gm2Gm4) + Gm1Gm2Gm4 D (s) • If C2Gm1Gm3 = C1Gm2Gm4, it is a band-reject biquad. • If C1Gm2Gm4 = 2C2Gm1Gm3 and Gm4 = Gm5, it is an allpass biquad. • There is one parasitic pole in the biquad. Gm-C Filters 22-31 Analog ICs; Jieh-Tsorng Wu Gm-C First-Oder Filters Using Miller Integrators 1 Vi α1s + α0 1 sτ 2C X 2C A Vo Vi Vo G m1 CX G m2 Vi 2C X Vo G m1 2C A G m2 CA Gm-C Filters 22-32 Analog ICs; Jieh-Tsorng Wu Gm-C First-Oder Filters Using Miller Integrators Without the Miller Integrator α1s + α0 = = s + ωo Vi Vo Gm1 = α0(CA + CX ) CX CA + CX s s+ Gm2 = ωo(CA + CX ) G m1 CA + CX + G m2 CA + CX α1 CX = CA 1 − α1 where 0 ≤ α1 < 1 With the Miller Integrator Vo α1s + α0 = = s + ωo Vi s CX CA s+ + G m1 CA G m2 CA •...
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This note was uploaded on 03/26/2013 for the course EE 260 taught by Professor Choma during the Winter '09 term at USC.

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