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ENGI 242/ELEC 222 January 2004 BJT Small Signal Model 1 Transistor Modeling ENGI 242 ELEC 222 January 2004 ENGI 242/ELEC 222 2
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 1
Transistor Modeling
ENGI 242ELEC 222
January 2004 ENGI 242/ELEC 222 2
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 2
January 2004 ENGI 242/ELEC 222 3
Hybrid Equivalent Circuit for BJT
1 11 12 1
2 21 22 2
V h h I =
I h h V
January 2004 ENGI 242/ELEC 222 4
h-parameter Model for Common Emitter
Parameters from the spec sheet (x = lead based on circuit configuration):h11 = hix
h12 = hrx
h21 = hfx
h22 = hox
hrx and hfx are dimensionless ratioshix is an impedance <Ω>hox is an admittance <S>
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 3
January 2004 ENGI 242/ELEC 222 5
Short Circuit Input Impedance
January 2004 ENGI 242/ELEC 222 6
Open Circuit Reverse Transfer Ratio
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 4
January 2004 ENGI 242/ELEC 222 7
Short Circuit Forward Transfer Ratio
January 2004 ENGI 242/ELEC 222 8
Open Circuit Output Admittance
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 5
Transistor ModelingHybrid Model Pi
ENGI 242ELEC 222
January 2004 ENGI 242/ELEC 222 10
HYBRID MODEL PI
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 6
January 2004 ENGI 242/ELEC 222 11
HYBRID MODEL PI PARAMETERS• Parasitic Resistances• rb = rb’b = ohmic resistance – voltage drop in base region
caused by transverse flow of majority carriers, 50 ≤ rb ≤ 500
• rc = rce = collector emitter resistance – change in Ic due to change in Vc, 20 ≤ rc ≤ 500
• rex = emitter lead resistance – important if IC very large, 1 ≤ rex ≤ 3
January 2004 ENGI 242/ELEC 222 12
HYBRID MODEL PI PARAMETERS• Parasitic Capacitances• Cje0 = Base-emitter junction (depletion layer) capacitance,
0.1pF ≤ Cje0 ≤ 1pF• Cµ0 = Base-collector junction capacitance, 0.2pF ≤ Cµ0 ≤
1pF• Ccs0 = Collector-substrate capacitance, 1pF ≤ Ccs0 ≤ 3pF• Cje = 2Cje0 (typical)• ψ0 =.55V (typical)• τF = Forward transit time of minority carriers, average of
lifetime of holes and electrons, 0ps ≤ τF ≤ 530ps
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 7
January 2004 ENGI 242/ELEC 222 13
HYBRID MODEL PI PARAMETERS• rπ = rb’e = dynamic emitter resistance – magnitude varies to
give correct low frequency value of Vb’e for Ib
• rµ = rb’c = collector base resistance – accounts for change in recombination component of Ib due to change in Vc which causes a change in base storage
• cπ = Cb’e = dynamic emitter capacitance – due to Vb’e
stored charge• cµ = Cb’c = collector base transistion capacitance (CTC)
plus Diffusion capacitance (Cd) due to base width modulation
• gmVπ = gmVb’e = Ic – equivalent current generator
January 2004 ENGI 242/ELEC 222 14
Hybrid Pi Relationships
Cm
T
T
Cm
C B
I g = V k T V = = 26mV @ 300 K
q I g =
26mV (26mV) ( ) 26mV r = =
I Iπ
°
β
β = gm rππ
c m ππ
β v i = = g vr
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 8
January 2004 ENGI 242/ELEC 222 15
Hybrid Pi Relationships
January 2004 ENGI 242/ELEC 222 16
HYBRID MODEL PI MID BAND
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 9
January 2004 ENGI 242/ELEC 222 17
HYBRID MODEL PI HIGH FREQ.
January 2004 ENGI 242/ELEC 222 18
Common Emitter Amplifier
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 10
January 2004 ENGI 242/ELEC 222 19
Common Emitter Amplifier – DC Bias Model
January 2004 ENGI 242/ELEC 222 20
Common Emitter Amplifier - Complete Hybrid PI
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 11
January 2004 ENGI 242/ELEC 222 21
Mid Band Hybrid PI Common Emitter
January 2004 ENGI 242/ELEC 222 22
Equivalent Circuit to find ZO
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 12
January 2004 ENGI 242/ELEC 222 23
High Frequency Hybrid PI CE Amp
January 2004 ENGI 242/ELEC 222 24
Common Emitter Amplifier
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 13
January 2004 ENGI 242/ELEC 222 25
CE Amplifer Example output
January 2004 ENGI 242/ELEC 222 26
Common Emitter Amplifier
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 14
January 2004 ENGI 242/ELEC 222 27
CE Amplifer Example output
January 2004 ENGI 242/ELEC 222 28
Emitter Follower
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 15
January 2004 ENGI 242/ELEC 222 29
Emitter Follower
January 2004 ENGI 242/ELEC 222 30
Emitter Follower
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 16
January 2004 ENGI 242/ELEC 222 31
Emitter Follower
January 2004 ENGI 242/ELEC 222 32
Emitter Follower
ENGI 242/ELEC 222 January 2004
BJT Small Signal Model 17
January 2004 ENGI 242/ELEC 222 33
Common Base
January 2004 ENGI 242/ELEC 222 34
Common Base
