Analog Integrated Circuits (Jieh Tsorng Wu)

Major functions are amplication filtering analog to

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Unformatted text preview: nment. Major functions are • Amplification. • Filtering. • Analog-to-digital conversion. • Digital-to-analog conversion. • Power supply conditioning. Introduction 1-3 Analog ICs; Jieh-Tsorng Wu Design for Analog Circuits Signal path • Small (variational) signals related by linear transfer function in the frequency domain. • Model with linearized small-signal equivalent circuit. • Analyze using Laplace transforms. Biasing Circuit • Establish operating conditions of devices in signal path. • Concern with sensitivity to variations in temperature, supply voltage, and fabrication process. • 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 n2 i kT ◦ ≈ 26 mV at 300 K q ◦ 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. Depletion-region capacitance d Qj NAND q =A Cj = d VR 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 1+ VR Ψ0 m 1 1 ≤m≤ 3 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 + Qj = 1−m 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 1 Cj −av = 0.56 · Cj 0 ≈ Cj 0 2 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 d ID ID 1 = = rd d VD UT ID τT Cd = τT · = rd UT IS ≈ A CT 1 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 avalanche breakdown. IRA = MIR M= 1 1− VR 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 15 3 18 3 NA (or ND ) varying from 10 atoms/cm to 10 atoms/cm . BJT 2-7 Analog ICs; Jieh-Tsorng Wu PN Junction Breakdown Zener 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. Punch Through • 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 region, 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 d pb d nb nb = kT µn + qDn = + pb qµnnb(x )E (x ) + qDn pb dx pb dx dx dx dx = Jn d nb qDn d (nb pb) 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 i Thus Jn = qn2 i WB pb dx 0 Dn nb(WB )pb(WB ) = n2eVBC /UT i eVBE /UT − eVBC /UT = JS...
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