1. Basic BJT Small-Signal ModelVC 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

2. 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

3. 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

4. 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

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

6. Frequency Dependence of a BJT

7. Current Gain versus Frequency2 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)

8. Frequency Dependence of a BJT

9. Complete Small-Signal Model

10. 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

11. Complete Circuit Element Model