Transcript Multistage BJT Amplifier - Brookdale Community College

Two Stage Amplifier Design
ENGI 242
ELEC 222
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
• C0 = Base-collector junction capacitance, 0.2pF ≤ C0 ≤
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
gm =
VT =
gm =
r =
IC
VT
kT
= 26mV @ 300K
q
IC
26mV
(26mV) ()
26mV
=
IC
IB
 = gm r 
ic =
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β vπ
= gm vπ
rπ
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Hybrid Pi Relationships
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Design of a Two Stage Amplifier
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Two Stage Amplifier Design Specifications
Design a two stage common emitter amplifier with partial
emitter bypass for the following specifications:
VCC = 20V
RE1A = .25RE1
RE2A = .4RE2
R2 = .1RE1
fCL1 = 16Hz
fCL4 = 67Hz
VE = .1VCC
VC1 = .6VCC
VC2 = .55VCC
R4 = .1RE2
fCL2 = 13Hz
fCL5 = 8Hz
IC1 = 2mA
IC2 = 2.5mA
RL = 10k
fCL3 = 12Hz
For both stages:
 = 140
C  8pF
CB = 150ps
fT = 150MHz
VA = 100V
rb = 19
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Hybrid Pi Model
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Low Critical Frequencies
• There is one low critical frequency for each coupling and
bypass capacitor
• We start by determining the (Thevenin) impedance seen by
each capacitor
• Then we construct a RC high pass filter (output across Z)
• We may then calculate the critical frequency by letting
|XC| = Z and solving for either fCL or C
1
fCL =
2πZC
1
C=
2 π fCL Z
and fCL = fCL1 + fCL2 + fCL3 + fCL4 + fCL5
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Hybrid Pi Model Input First Stage
ZIN1 = R1//R2// rb1 + rπ1 + (β + 1)RE1A 
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Hybrid Pi Model Output First Stage
ZO1 = RC1// rO1 + RE1A 
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Hybrid Pi Model Input Second Stage
ZIN2 = R3//R4// rb2 + rπ2 + (β + 1)RE2A
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Hybrid Pi Model Output Second Stage
ZO2 = RC2// rO2 + RE2A 
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Hybrid Pi Model Emitter Bypass First Stage
  R1//R2  + rb1 + rπ1 

ZTH_IN1 = 
 + RE1A  // RE1B
+1



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Hybrid Pi Model Emitter Bypass Second Stage
  R3//R4//RC1//(ro1 + RE1A) + rb2 + rπ2 

ZTH_IN2 = 
 + RE2A  // RE2B
+1



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fCL1
1
fCL1 =
2  ZIN1 C1
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fCL2
Determine the Thevenin Impedance seen by C2
1
fCL2 =
2   ZO1 + ZIN2  C2
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fCL3
Determine the Thevenin Impedance seen by C3
1
fCL3 =
2   ZO2 + RL  C3
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fCL4
Determine the Thevenin Impedance seen by CE1
fCL4 =
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1
2   ZTH_IN1  C4
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fCL5
Determine the Thevenin Impedance seen by CE2
fCL5 =
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1
2   ZTH_IN2  C5
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Schematic of Design
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Simulation Profile
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Probe Plot – Y Axis Settings
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Probe Plot – X Axis X Grid Settings
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Frequency Response
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Frequency Response
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