Transistor Modeling

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Hybrid Equivalent Circuit for BJT

1 11 12 1

2 21 22 2

V h h I =

I h h V

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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 <>hox is an admittance <S>

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Short Circuit Input Impedance

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Open Circuit Reverse Transfer Ratio

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Short Circuit Forward Transfer Ratio

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Open Circuit Output Admittance

Transistor ModelingHybrid Model Pi

ENGI 242ELEC 222

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HYBRID MODEL PI

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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

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HYBRID MODEL PI PARAMETERS

• Parasitic Capacitances• Cje0 = Base-emitter junction (depletion layer) capacitance,

0.1pF ≤ Cje0 ≤ 1pF• C0 = Base-collector junction capacitance, 0.2pF ≤ C0 ≤

1pF• Ccs0 = Collector-substrate capacitance, 1pF ≤ Ccs0 ≤ 3pF• Cje = 2Cje0 (typical) 0 =.55V (typical) F = Forward transit time of minority carriers, average

of lifetime of holes and electrons, 0ps ≤ F ≤ 530ps

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HYBRID MODEL PI PARAMETERS

• r = rb’e = dynamic emitter resistance – magnitude varies to give correct low frequency value of Vb’e for Ib

• r = 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

• c = Cb’e = dynamic emitter capacitance – due to Vb’e stored charge

• c = Cb’c = collector base transistion capacitance (CTC) plus Diffusion capacitance (Cd) due to base width modulation

• gmV = gmVb’e = Ic – equivalent current generator

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Hybrid Pi Relationships

Cm

T

T

Cm

C B

I g =

V k T

V = = 26mV @ 300 Kq

I g =

26mV (26mV) ( ) 26mV

r = = I I

= gm r

πc m π

π

β v i = = g v

r

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Hybrid Pi Relationships

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HYBRID MODEL PI MID BAND

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HYBRID MODEL PI HIGH FREQ.

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Common Emitter Amplifier

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Common Emitter Amplifier – DC Bias Model

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Common Emitter Amplifier - Complete Hybrid PI

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Mid Band Hybrid PI Common Emitter

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Equivalent Circuit to find ZO

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High Frequency Hybrid PI CE Amp

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Common Emitter Amplifier

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CE Amplifer Example output

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Common Emitter Amplifier

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CE Amplifer Example output

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Emitter Follower

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Emitter Follower

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Emitter Follower

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Emitter Follower

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Emitter Follower

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Common Base

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Common Base