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Unformatted text preview: nment. Major functions are
• Analog-to-digital conversion.
• Digital-to-analog conversion.
• Power supply conditioning.
Introduction 1-3 Analog ICs; Jieh-Tsorng Wu Design for Analog Circuits
• Small (variational) signals related by linear transfer function in the frequency domain.
• Model with linearized small-signal equivalent circuit.
• Analyze using Laplace transforms.
• Establish operating conditions of devices in signal path.
• Concern with sensitivity to variations in temperature, supply voltage, and fabrication
• Analyze using large-signal device models.
Introduction 1-4 Analog ICs; Jieh-Tsorng Wu Performance Considerations
• Small-signal response: gain, bandwidth, noises, . . .
• Large-signal response: settling time, distortion, . . .
• Sensitivity to device variation, temperature variation, external noises, . . .
• Cost: power dissipation, chip area, yield. Introduction 1-5 Analog ICs; Jieh-Tsorng Wu Design Practices
• Make simplifying assumptions that allow hand analysis.
• Keep in mind potential consequences of the assumptions.
• Use simulations to verify the design.
• Good designs are robust; i.e., insensitive to approximations in the modeling as well
as variations in temperature and fabrication process. Introduction 1-6 Analog ICs; Jieh-Tsorng Wu PN Junctions and Bipolar Junction Transistors Jieh-Tsorng Wu ES A September 6, 2002 1896 National Chiao-Tung University
Department of Electronics Engineering PN Junctions
Built-in potential = Ψ0 = UT ln NAND
≈ 26 mV at 300 K
ni ≈ 1.5 × 1010 cm−3 at 300 K for Si
UT = Solving Poisson’s equation,
1/2 2 (Ψ0 + VR ) W1 = NA
qNA 1 + N
D 1/2 2 (Ψ0 + VR ) W2 = ND
qND 1 + N
A BJT 2-2 Analog ICs; Jieh-Tsorng Wu Small-Signal Junction Capacitance
Depletion layer charge is Qj = qNAW1A = qND W2A, where A is the cross-sectional area.
d Qj NAND
2Ψ0 NA + ND 1/2 · 1 = V 1 + ΨR 0 BJT 2-3 Cj 0
V 1 + ΨR 0 Analog ICs; Jieh-Tsorng Wu Small-Signal Junction Capacitance
• Cj can be expressed as
Cj = A · • In general
Cj = xd = W1 + W2 xd Cj 0
Ψ0 m 1
2 – m = 1/2 for abrupt junction.
– m = 1/3 for graded junction.
• In forward bias, diﬀusion capacitance dominates. BJT 2-4 Analog ICs; Jieh-Tsorng Wu Large-Signal Junction Capacitance
Depletion layer charge can be rewritten as
Cj 0 VR
· Ψ0 · 1 +
Ψ0 1−m Average capacitance is deﬁned as
Cj −av = Qj (V2) − Qj (V1)
V2 − V1 For an abrupt junction, m = 0.5,
V Cj −av = 2Cj 0Ψ0 · 1 + Ψ2 −
0 V 1 + Ψ1 0 V2 − V1 • If V1 = 0 V, V2 = 5 V, and Ψ0 = 0.9 V
Cj −av = 0.56 · Cj 0 ≈ Cj 0
BJT 2-5 Analog ICs; Jieh-Tsorng Wu PN Junction in Forward Bias
ID Small-Signal Model
rd VD ID = IS (eVD /UT − 1) ≈ IS eVD /UT
rd d VD UT
Cd = τT ·
UT IS ≈ A CT 1
NA ND CT = Cd + Cj
τT = Transit Time
Cj , rd CT ≈ τT . • For moderate forward-bias currents, Cd
• For Schottky diode, Cd = 0.
BJT 2-6 Analog ICs; Jieh-Tsorng Wu PN Junction Avalanche Breakdown
• The maximum electric ﬁeld in the depletion region of an abrupt junction is
|Emax | = qNAW1 = 2qNAND (Ψ0 + VR ) 1/2 (NA + ND ) |Emax | increases with both VR and doping density.
• As |Emax | → Ecri t , carriers crossing the depletion region acquire enough energy
to create new electron-hole pairs when colliding with silicon atoms. The result is
IRA = MIR M= 1
BV n BV is the breakdown voltage. And typically 3 ≤ n ≤ 6
5 6 • Ecri t is a function of doping density, which can vary from 3 × 10 V/cm to 10 V/cm as
NA (or ND ) varying from 10 atoms/cm to 10 atoms/cm .
BJT 2-7 Analog ICs; Jieh-Tsorng Wu PN Junction Breakdown
• In very heavily doped junctions where the electric ﬁeld becomes large enough to strip
electrons always from the valence bonds. This process is called tunneling.
• The Zener breakdown mechanism is important only for breakdown voltages below
about 6 V.
• A form of breakdown that occurs when the depletion regions of two neighboring
junctions meet. BJT 2-8 Analog ICs; Jieh-Tsorng Wu Bipolar Junction Transistor (BJT) BJT 2-9 Analog ICs; Jieh-Tsorng Wu Minority Carrier Current in the Base Region
There is a negligible ﬂow of holes between emitter and collector junctions because
neither can supply a signiﬁcant ﬂow of holes into the base. Thus, in the neutral base
Jp = qµppb(x )E (x ) − qDp d pb
dx =0 ⇒ Dp 1 d pb kT 1 d pb
E (x ) =
µp pb dx
q pb dx • Note that for uniformly doped region d pb/dx = 0 ⇒ E (x ) = 0
For electrons in the base, BJT = nb d pb
d nb qDn
= kT µn
qµnnb(x )E (x ) + qDn
dx = Jn d nb qDn d (nb pb)
dx 2-10 Analog ICs; Jieh-Tsorng Wu Minority Carrier Current in the Base Region
Assuming negligible recombination in the base, so that Jn is constant,
WB Jn pb(x )
qDn 0 dx = WB
0 d (nbpb)
dx dx = nb(0)pb (0) − nb(WB )pb(WB ) From the Boltzman approximation at the edges of the depletion layers,
nb(0)pb(0) = n2eVBE /UT
Jn = qn2
0 Dn nb(WB )pb(WB ) = n2eVBC /UT
i eVBE /UT − eVBC /UT = JS...
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