Unformatted text preview: /UT 1, then IS V /U
IE ≈ − e BE T − IS
IS eVBE /UT = −αF IE − αF IS
IC = −αF IE +
− αF IS = −αF IE + ICO
≡ (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
• 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
BVCBO Analog ICs; Jieh-Tsorng Wu Common-Emitter Transistor Breakdown IC
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
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
∂IB = qIC
kT = UT IC ∂
∂IC βF = • η≡ IC
∂VBE rπ βo ∂VBE
∂VCE = IC
VA = ηgm gµ = ∂IBB
∂IC ∂VCB rµ Cπ =
= • If IB = IBB
∂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
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
IC 2 τF = WB 2Dn for uniform-base transistor The diﬀusion capacitance is
= τ F gm
∂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
Ccs 50–500 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
nMOST Gate Body ID G VD
VG V Source VS Source
pMOST S S VS Gate Body VG G
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
2φf = 2
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 =
ID = µCox
MOST VDB W µCox VGB − Vt (y ) d V VSB 1
(VGB − 2φf − VF B )V (y ) − V 2(y ) − γ [V (y ) + 2φf ]3/2
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
ID = µCox
L (VGS − Vt )VDS 12
− VDS = k
L (VGS − Vt )VDS 12
2 • Vt is the threshold vol...
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