Analog Integrated Circuits (Jieh Tsorng Wu)

Bjt 2 23 analog ics jieh tsorng wu common base

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Unformatted text preview: /UT 1, then IS V /U IE ≈ − e BE T − IS αF thus IS eVBE /UT = −αF IE − αF IS and 1 IC = −αF IE + − αF IS = −αF IE + ICO αR where ICO IS ≡ (1 − αF αR ) αR • ICO is the collector-base leakage current with the emitter open. • In practice, because of surface leakage effects, ICO is several orders of magnitude larger than the value predicted by the above definition. BJT 2-23 Analog ICs; Jieh-Tsorng Wu Common-Base Transistor Breakdown • Avalanche multiplication at the junctions of a BJT limits the voltage that can be sustained. • BVCBO is the breakdown voltage of C-B junction with IE = 0. BVE BO is much less than BVCBO . Neglecting leakage currents IC = −αF IE M BJT where 2-24 M= 1 1− n VCB BVCBO Analog ICs; Jieh-Tsorng Wu Common-Emitter Transistor Breakdown IC VCE IB BJT 2-25 Analog ICs; Jieh-Tsorng Wu Common-Emitter Transistor Breakdown In this configuration, holes generated in the avalanche process are swept into the base where they act as a supply of base current. The avalanche current is thus effectively amplified by βF . IB = −(IC + IE ) = −IC + IC ⇒ MαF IC = M αF 1 − MαF IB where M is as defined above for the common-base case. BVCE O is defined as the value of VCE for which IC → ∞; that is, for which MαF → 1. Assume VCB ≈ VCE , then Mα = αF 1− BVCE O n BVCBO =1 ⇒ BVCE O BVCBO = (1 − αF ) 1/n = 1 (βF + 1)1/n ≈ 1 1/n βF • Note: Here must use value of BVCBO for intrinsic transistor. Actual BVCBO is lower than this because of sidewall effects. BJT 2-26 Analog ICs; Jieh-Tsorng Wu Small-Signal Model of Forward-Biased BJT rµ Ic Cµ Ib VCC Vbe B C vπ rπ Cπ g m vπ ro E In the forward-active region IC = IS eVBE /UT 1 + VCE VA IB = IC βF Bias and small-signal variables are: Ib = IB + ib BJT Ic = IC + ic 2-27 Vbe = VBE + vbe Analog ICs; Jieh-Tsorng Wu Small-Signal Model of Forward-Biased BJT • If βF is constant, then βo = βF . gm βo gπ go = = = = ∂IC ∂VBE ∂IC ∂IB = qIC kT = UT IC ∂ ∂IC βF = • η≡ IC −1 ∂IB gm 1 1 ∂IC = = = ∂VBE rπ βo ∂VBE βo ∂IC ∂VCE = IC VA = ηgm gµ = ∂IBB ∂IBB ∂IC 1 = = ∂VCB ∂IC ∂VCB rµ Cπ = = • If IB = IBB go ∂IB ∂IC gµ ≈ = ∂IC ∂VCE βo or rµ = βoro • Typically, rµ > 10βoro. For lateral pnp, rµ is 2βoro ∼ 5βoro. Cb + Cj e = τF gm + Cj e Cµ UT . VA Cj c • Junction capacitances are Cj = Cj 0 V 1−Ψ n n = 0. 2 ∼ 0. 5 0 BJT 2-28 Analog ICs; Jieh-Tsorng Wu Charge Storage In the intrinsic transistor charge is stored in the junction capacitances, Cj e and Cj c, and as minority carriers in the base (Qe) and emitter (Qp). • Both Qe and Qp are proportional to eVBE /UT . • Qe Qp and typically the effect of Qp is taken into account simply by modifying Qe. An equivalent forward base transit time, τF , is defined as Qe τF ≡ IC 2 τF = WB 2Dn for uniform-base transistor The diffusion capacitance is ∂IC ∂Qe Cb = = τF = τ F gm ∂VBE ∂VBE BJT 2-29 Analog ICs; Jieh-Tsorng Wu Complete Small-Signal Model with Extrinsic Components rµ rb Cµ B’ rc B C vπ rπ Cπ g m vπ ro Ccs rex E BJT 2-30 Analog ICs; Jieh-Tsorng Wu Typical values of Extrinsic Components rb rc rex Ccs 50–500 Ω 20–500 Ω 1–8 Ω 0.2–3 pF The value of rb varies significantly with IC because of current crowding. BJT 2-31 Analog ICs; Jieh-Tsorng Wu MOS Field-Effect Transistors Jieh-Tsorng Wu ES A October 8, 2002 1896 National Chiao-Tung University Department of Electronics Engineering MOS Transistors D Drain nMOST Gate Body ID G VD VG V Source VS Source pMOST S S VS Gate Body VG G ID Drain D MOST B 3-2 V B VD Analog ICs; Jieh-Tsorng Wu MOS Transistors • Lel ectri cal = Lgate − 2LD . In SPICE, L = Lgate. • For nMOST, VD > VS > VB . • For pMOST, VD < VS < VB . • The I − V equations of nMOST are identical to those of pMOST. • For enhancement-mode device, Vtn > 0 and Vtp < 0. MOST 3-3 Analog ICs; Jieh-Tsorng Wu Strong Inversion VS VG n+ Depletion Region VD n+ V(y) y 0 L N SUB p- Substrate VB The threshold voltage of VGB for strong inversion is Vt (y ) = V (y ) + 2φf + γ NSUB kT ln 2φf = 2 q ni MOST γ= 3-4 V (y ) + 2φf + VF B 2q si NSUB Cox Cox = ox tox Analog ICs; Jieh-Tsorng Wu Channel Charge Transfer Characteristics The induced channel charge per unit area is QI (y ) = Cox VGB − Vt (y ) when VGB > Vt (y ) The current along the channel is ID = W · µQI (y ) · E (y ) = W · µQI (y ) · dV dy ⇒ ID d y = W µQI (y )d V Integration along the channel from 0 to L gives L ID d y = 0 W ID = µCox L MOST VDB W µCox VGB − Vt (y ) d V VSB 1 2 (VGB − 2φf − VF B )V (y ) − V 2(y ) − γ [V (y ) + 2φf ]3/2 2 3 3-5 VDB VSB Analog ICs; Jieh-Tsorng Wu Simplified Channel Charge Transfer Characteristics The threshold voltage of VGS for strong inversion is simplfied as Vt (y ) + VSB = V (y ) + VSB + Vt (SB) ⇒ Vt (y ) = V (y ) + Vt The channel charge becomes QI (y ) = Cox VGS − V (y ) − Vt And the drain current is W ID = µCox L (VGS − Vt )VDS 12 W − VDS = k 2 L (VGS − Vt )VDS 12 − VDS 2 • Vt is the threshold vol...
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