Basic BJT Small-Signal Model VC VE VB VC VE rp + V - gmV ro VB VB VE VC rp= b UT / IC gm = IC / UT ro = VA / IC Key Terms: gm rp= b ; gm ro = VA / UT Current Gain Voltage Gain

Computing Small-Signal Models Forward-Active Model: (Exponential Form) VBE/UT VCE/VA IC = IC0 e e dIC VBE/UT VCE/UT gm = = IC0 e e (1 / UT) = IC / UT dVBE dIC VBE/UT VCE/VA 1/ ro = = IC0 e e (1 / VA) = IC / VA dVCE

Basic BJT Small-Signal Model Current Gain Voltage Gain Iout Vdd GND ro Iref Iin Vin Vout GND Vout + V - GND Vin rp Iout gmV + V - rp Iin GND GND gmV GND GND GND AV = gm ro = VA / UT AI = gm rp= b

Basic Frequency Effects Cje = base-emitter depletion capacitance (forward biased) Cjbc = base-collector depletion capacitance (reversed biased) Cb = Base-Charging Capacitance of the Small Signal BJT Model Modifying Charge from the Base when changing Base voltage: Cb = tF gm Cp = Cje + Cb; Cm = Cjbc

BJT Small-Signal Model Cm VB VC + V - ro Cp rp gmV VE Basic measures of Frequency Characteristics: fT

Frequency Dependence of a BJT

Current Gain versus Frequency 2 10 1 b0 10 Collector current / Base current 10 fT 3 4 5 6 7 8 9 10 10 10 10 10 10 10 Frequency (Hz)

Frequency Dependence of a BJT

Complete Small-Signal Model

Additional Effects Series Resistance (rb, rc, re) ---- Finite conductivity of doped regions Collector-Base Resistance of the Small Signal BJT Model (rµ) In general, rµ ³ 10 boro for the npn BJT and about 2-5 boro for the lateral pnp BJT

Complete Circuit Element Model