SIGNIFICANT EQUATIONS 1 Semiconductor Diodes W = QV, 1 eV = 1.6 * 10-19 J, ID = Is (eVD>nVT - 1), VT = kT>q, TK = TC + 273⬚, k = 1.2 V (GaAs), RD = VD>ID, rd = 26 mV>ID, rav = ⌬Vd >⌬Id 兩 pt. , PD = VD ID, TC = (⌬VZ >VZ)>(T1 - T0) * 100%>⬚C 2 Diode Applications Silicon: VK ⬵ 0.2 V; half-wave: Vdc = 0.318Vm; full-wave: Vdc = 0.636Vm 3 Bipolar Junction Transistors IE = IC + IB, IC = ICmajority + ICOminority, IC ⬵ IE, VBE = 0.7 V, adc = IC>IE, IC = aIE + ICBO, aac = ⌬IC >⌬IE, ICEO = ICBO >(1 - a), bdc = IC>IB, bac = ⌬IC >⌬IB, a = b>(b + 1), b = a>(1 - a), IC = bIB, IE = (b + 1)IB, PCmax = VCEIC 4 DC Biasing—BJTs In general: VBE = 0.7 V, IC ⬵ IE , IC = bIB; fixed-bias: IB = (VCC - VBE)>RB,VCE = VCC - ICRC, ICsat = VCC>RC; emitter-stabilized: IB = (VCC - VBE)>(RB + (b + 1)RE), Ri = (b + 1)RE , VCE = VCC - IC(RC + RE), ICsat = VCC >(RC + RE); voltage-divider: exact: RTh = R1 储 R2, ETh = R2VCC >(R1 + R2), IB = (ETh - VBE)>(RTh + (b + 1)RE), VCE = VCC - IC(RC + RE), approximate: bRE Ú 10R2, VB = R2VCC >(R1 + R2), VE = VB - VBE, IC ⬵ IE = VE >RE; voltage-feedback: IB = (VCC - VBE)>(RB + b(RC + RE)); common-base: IB = (VEE - VBE)>RE; switching transistors: ton = tr + td , toff = ts + tf ; stability: S(ICO) = ⌬IC >⌬ICO; fixed-bias: S(ICO) = b + 1; emitter-bias: S(ICO) = (b + 1)(1 + RB >RE)>(1 + b + RB >RE); voltage-divider: S(ICO) = (b + 1)(1 + RTh >RE)>(1 + b + RTh >RE); feedback-bias: S(ICO) = (b + 1)(1 + RB>RC)>(1 + b + RB>RC), S(VBE) = ⌬IC >⌬VBE; fixed-bias: S(VBE) = - b>RB; emitter-bias: S(VBE) = - b>(RB + (b + 1)RE); voltage-divider: S(VBE) = - b>(RTh + (b + 1)RE); feedback bias: S(VBE) = - b>(RB + (b + 1)RC), S(b) = ⌬IC >⌬b; fixed-bias: S(b) = IC1 >b1; emitter-bias: S(b) = IC1(1 + RB>RE)> (b1(1 + b2 + RB>RE)); voltage-divider: S(b) = IC1(1 + RTh >RE)>(b1(1 + b2 + RTh >RE)); feedback-bias: S(b) = IC1(1 + RB >RC)>(b1(1 + b2 + RB >RC)), ⌬IC = S(ICO) ⌬ICO + S(VBE) ⌬VBE + S(b) ⌬b 5 BJT AC Analysis re = 26 mV>IE; CE fixed-bias: Zi ⬵ bre, Zo ⬵ RC, Av = - RC>re; voltage-divider bias: Zi = R1 储 R2 储 bre, Zo ⬵ RC, Av = - RC>re; CE emitter-bias: Zi ⬵ RB 储 bRE, Zo ⬵ RC, Av ⬵ - RC>RE; emitter-follower: Zi ⬵ RB 储 bRE, Zo ⬵ re, Av ⬵ 1; common-base: Zi ⬵ RE 储 re, Zo ⬵ RC, Av ⬵ RC>re; collector feedback: Zi ⬵ re >(1>b + RC>RF), Zo ⬵ RC 储 RF, Av = - RC>re; collector dc feedback: Zi ⬵ RF1 储 bre, Zo ⬵ RC 储 RF2, Av = - (RF2 储 RC)>re; effect of load impedance: Av = RLAvNL >(RL + Ro), Ai = - Av Zi >RL; effect of source impedance: Vi = RiVs>(Ri + Rs), Avs = Ri AvNL >(Ri + Rs), Is = Vs>(Rs + Ri); combined effect of load and source impedance: Av = RLAv NL >(RL + Ro), Avs = (Ri >(Ri + Rs))(RL >(RL + Ro))AvNL, Ai = - Av Ri >RL, Ais = - Avs(Rs + Ri)>RL; cascode connection: Av = Av1Av2; Darlington connection: bD = b1b2; emitter-follower configuration: IB = (VCC - VBE)>(RB + bDRE), IC ⬵ IE ⬵ bDIB, Zi = RB 储 b1b2RE, Ai = bDRB >(RB + bDRE), Av ⬵ 1, Zo = re1>b2 + re2; basic amplifier configuration: Zi = R1 储 R2 储 Zi⬘, Zi⬘ = b1(re1 + b2re2), Ai = bD(R1 储 R2)>(R1 储 R2 + Zi⬘), Av = bDRC>Zi⬘, Zo = RC 储 ro2; feedback pair: IB1 = (VCC - VBE1)>(RB + b1b2RC), Zi = RB 储 Zi⬘, Zi⬘ = b1re1 + b1b2RC, Ai = - b1b2RB >(RB + b1b2RC) Av = b2RC >(re + b2RC) ⬵ 1, Zo ⬵ re1 >b2. 6 Field-Effect Transistors IG = 0 A, ID = IDSS(1 - VGS>VP)2, ID = IS , VGS = VP (1 - 2ID >IDSS), ID = IDSS >4 (if VGS = VP>2), ID = IDSS >2 (if VGS ⬵ 0.3 VP), PD = VDSID , rd = ro >(1 - VGS>VP)2; MOSFET: ID = k(VGS - VT)2, k = ID(on) >(VGS(on) - VT)2 7 FET Biasing Fixed-bias: VGS = - VGG, VDS = VDD - IDRD; self-bias: VGS = - IDRS, VDS = VDD - ID(RS + RD), VS = IDRS; voltage-divider: VG = R2VDD>(R1 + R2), VGS = VG - ID RS, VDS = VDD - ID(RD + RS); common-gate configuration: VGS = VSS - IDRS, VDS = VDD + VSS - ID(RD + RS); special case: VGSQ = 0 V: IIQ = IDSS, VDS = VDD - IDRD, VD = VDS, VS = 0 V. enhancement-type MOSFET: ID = k(VGS - VGS(Th))2, k = ID(on) >(VGS(on) - VGS(Th))2; feedback bias: VDS = VGS, VGS = VDD - IDRD; voltage-divider: VG = R2VDD >(R1 + R2), VGS = VG - IDRS; universal curve: m = 0 VP 0 >IDSSRS, M = m * VG > 0 VP 0 ,VG = R2VDD >(R1 + R2) 8 FET Amplifiers gm = yfs = ⌬ID>⌬VGS, gm0 = 2IDSS >兩VP 兩, gm = gm0(1 - VGS >VP), gm = gm0 1ID>IDSS, rd = 1>yos = ⌬VDS >⌬ID 0 VGS = constant; fixed-bias: Zi = RG, Zo ⬵ RD, Av = - gmRD; self-bias (bypassed Rs): Zi = RG, Zo ⬵ RD, Av = - gmRD; self-bias (unbypassed Rs): Zi = RG, Zo = RD, Av ⬵ - gmRD>(1 + gmRs); voltage-divider bias: Zi = R1 储 R2, Zo = RD, Av = - gmRD; source follower: Zi = RG, Zo = RS 储 1>gm , Av ⬵ gm RS >(1 + gm RS); common-gate: Zi = RS 储 1>gm, Zo ⬵ RD, Av = gm RD; enhancement-type MOSFETs: gm = 2k(VGSQ - VGS(Th)); drain-feedback configuration: Zi ⬵ RF >(1 + gmRD), Zo ⬵ RD, Av ⬵ - gmRD; voltage-divider bias: Zi = R1 储 R2, Zo ⬵ RD, Av ⬵ - gmRD.
9 BJT and JFET Frequency Response logea = 2.3 log10a, log101 = 0, log10 a>b = log10 a - log10 b, log101>b = - log10b, log10ab = log10 a + log10 b, GdB = 10 log10 P2 >P1, GdBm = 10 log10 P2 >1 mW兩 600 ⍀ , GdB = 20 log10 V2>V1, GdBT = GdB1 + GdB2 + g + GdBn PoHPF = 0.5Pomid , BW = f1 - f2; low frequency (BJT): fLS = 1>2p(Rs + Ri)Cs, fLC = 1>2p(Ro + RL)CC, fLE = 1>2pR eCE, Re = RE 储 (R⬘s >b + re), R⬘s = Rs 储 R1 储 R2, FET: fLG = 1>2p(Rsig + Ri)CG, fLC = 1>2p(Ro + RL)CC , fLS = 1>2pReqCS, Req = RS 储 1>gm(rd ⬵ ⬁ ⍀); Miller effect: CMi = (1 - Av)Cf , CMo = (1 - 1>Av)Cf ; high frequency (BJT): fHi = 1>2pRThi Ci, RThi = Rs 储 R1 储 R2 储 Ri, Ci = Cwi + Cbe + (1 - Av)Cbc, fHo = 1>2pRThoCo, RTho = RC 储 RL 储 ro, Co = CWo + Cce + CMo, fb ⬵ 1>2pbmidre(Cbe + Cbc), fT = bmid fb; FET: fHi = 1>2pRThiCi, RThi = Rsig 储 RG, Ci = CWi + Cgs + CMi, CMi = (1 - Av)Cgd fHo = 1>2pRThoCo, RTho = RD 储 RL 储 rd, Co = CWo + Cds + CMo; CMO = (1 - 1>Av)Cgd; multistage: f 1⬘ = f1 > 221>n - 1, f 2⬘ = ( 221>n - 1)f2; square-wave testing: fHi = 0.35>tr , % tilt = P% = ((V - V⬘)>V ) * 100%, fLo = (P>p)fs 10 Operational Amplifiers CMRR = Ad >Ac; CMRR(log) = 20 log10(Ad >Ac); constant-gain multiplier: Vo >V1 = - Rf >R1; noninverting amplifier: Vo >V1 = 1 + Rf >R1; unity follower: Vo = V1; summing amplifier: Vo = - [(Rf >R1)V1 + (Rf >R2)V2 + (Rf >R3)V3]; integrator: vo(t) = - (1>R1C1) 1v1dt 11 Op-Amp Applications Constant-gain multiplier: A = - Rf >R1; noninverting: A = 1 + Rf >R1: voltage summing: Vo = - [(Rf >R1)V1 + (Rf >R2)V2 + (Rf >R3)V3]; high-pass active filter: foL = 1>2pR1C1; low-pass active filter: foH = 1>2pR1C1 12 Power Amplifiers Power in: Pi = VCCICQ power out: Po = VCEIC = IC2RC = VCE 2 >RC rms = VCEIC >2 = (IC >2)RC = VCE 2 2 >(2RC) peak = VCEIC >8 = (IC >8)RC = VCE 2 2 >(8RC) peak@to@peak efficiency: %h = (Po >Pi) * 100%; maximum efficiency: Class A, series-fed ⫽ 25%; Class A, transformer-coupled ⫽ 50%; Class B, push-pull ⫽ 78.5%; transformer relations: V2 >V1 = N2 >N1 = I1 >I2, R2 = (N2 >N1)2R1; power output: Po = [(VCE max - VCE min ) (IC max - IC min )]>8; class B power amplifier: Pi = VCC 3 (2>p)Ipeak 4 ; Po = VL2(peak)>(2RL); %h = (p>4) 3 VL(peak)>VCC 4 * 100%; PQ = P2Q >2 = (Pi - Po)>2; maximum Po = VCC 2 >2RL; maximum Pi = 2VCC 2 >pRL; maximum P2Q = 2VCC 2 >p 2RL; % total harmonic distortion (% THD) = 2D2 + D3 + D4 + g * 100%; heat-sink: TJ = PDuJA + TA, uJA = 40⬚C/W (free air); 2 2 2 PD = (TJ - TA)>(uJC + uCS + uSA) 13 Linear-Digital ICs Ladder network: Vo = [(D0 * 20 + D1 * 21 + D2 * 22 + g + Dn * 2n)>2n ]Vref; 555 oscillator: f = 1.1RAC; VCO: fo = (2>R1C1)[(V + - VC)>V + ]; phase- locked loop (PLL): fo = 0.3>R1C1, fL = {8 fo >V, fC = {(1>2p) 22pfL >(3.6 * 103)C2 14 Feedback and Oscillator Circuits Af = A>(1 + bA); series feedback; Zif = Zi(1 + bA); shunt feedback: Zif = Zi >(1 + bA); voltage feedback: Zof = Zo>(1 + bA); current feedback; Zof = Zo(1 + bA); gain stability: dAf >Af = 1>(兩1 + bA兩)(dA>A); oscillator; bA = 1; phase shift: f = 1>2pRC 16, b = 1>29, A 7 29; FET phase shift: 兩A兩 = gm RL, RL = RDrd >(RD + rd); transistor phase shift: f = (1>2pRC)[1> 26 + 4(RC >R)], hfe 7 23 + 29(RC>R) + 4(R>RC); Wien bridge: R3 >R4 = R1 >R2 + C2 >C1, fo = 1>2p 1R1C1R2C2; tuned: fo = 1>2p 1LCeq, Ceq = C1C2 >(C1 + C2), Hartley: Leq = L1 + L2 + 2M, fo = 1>2p 1LeqC 15 Power Supplies (Voltage Regulators) Filters: r = Vr (rms)>Vdc * 100%, V.4Idc>C, Vdc = Vm - 4.4>RLC * 100%, Ipeak = T>T1 * Idc; RC filter: V⬘dc = RL Vdc > (R + RL), XC = 2.326>C (full@wave), V⬘r (rms) = (XC> 2R2 + X2C); regulators: IR = (INL - IFL)>IFL * 100%, VL = VZ (1 + R1 >R2), Vo = Vref (1 + R2 >R1) + IadjR2 16 Other Two-Terminal Devices Varactor diode: CT = C(0)>(1 + 兩Vr >VT 兩)n, TCC = (⌬C>Co(T1 - T0)) * 100%; photodiode: W = hf, l = v>f, 1 lm = 1.496 * 10-10 W, 1 Å = 10-10 m, 1 fc = 1 lm>ft2 = 1.609 * 10-9 W>m2 17 pnpn and Other Devices Diac: VBR1 = VBR2 { 0.