10 Multistage
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Two Stage Amplifier Design
ENGI 242ELEC 222
January 2004 ENGI 242/ELEC 222 2
HYBRID MODEL PI
January 2004 ENGI 242/ELEC 222 3
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 4
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
January 2004 ENGI 242/ELEC 222 5
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
January 2004 ENGI 242/ELEC 222 6
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
January 2004 ENGI 242/ELEC 222 7
Hybrid Pi Relationships
January 2004 ENGI 242/ELEC 222 8
Design of a Two Stage Amplifier
January 2004 ENGI 242/ELEC 222 9
Two Stage Amplifier Design Specifications
Design a two stage common emitter amplifier with partial emitter bypass for the following specifications:
VCC = 20V VE = .1VCC
RE1A = .25RE1 VC1 = .6VCC IC1 = 2mARE2A = .4RE2 VC2 = .55VCC IC2 = 2.5mAR2 = .1RE1 R4 = .1RE2 RL = 10kfCL1 = 16Hz fCL2 = 13Hz fCL3 = 12HzfCL4 = 67Hz fCL5 = 8Hz
For both stages: = 140 CB = 150ps VA = 100VC 8pF fT = 150MHz rb = 19
January 2004 ENGI 242/ELEC 222 10
Hybrid Pi Model
January 2004 ENGI 242/ELEC 222 11
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
and fCL = fCL1 + fCL2 + fCL3 + fCL4 + fCL5
CL
CL
1 f =
2 π Z C 1
C = 2 π f Z
January 2004 ENGI 242/ELEC 222 12
Hybrid Pi Model Input First Stage
IN1 1 2 b1 π1 E1AZ = R //R // r + r + (β + 1)R
January 2004 ENGI 242/ELEC 222 13
Hybrid Pi Model Output First Stage
O1 C1 O1 E1AZ = R // r + R
January 2004 ENGI 242/ELEC 222 14
Hybrid Pi Model Input Second Stage
IN2 3 4 b2 π2 E2AZ = R //R // r + r + (β + 1)R
January 2004 ENGI 242/ELEC 222 15
Hybrid Pi Model Output Second Stage
O2 C2 O2 E2AZ = R // r + R
January 2004 ENGI 242/ELEC 222 16
Hybrid Pi Model Emitter Bypass First Stage
1 2 b1 π1 TH_IN1 + E1A E1B
R //R + r + rZ = R // R
+ 1
January 2004 ENGI 242/ELEC 222 17
Hybrid Pi Model Emitter Bypass Second Stage
3 4 C1 o1 E1A b2 π2 TH_IN2 + E2A E2B
R //R //R //(r + R ) + r + rZ = R // R
+ 1
January 2004 ENGI 242/ELEC 222 18
fCL1
CL1
IN1 1
1 f =
2 Z C
January 2004 ENGI 242/ELEC 222 19
fCL2
CL2
O1 IN2 2
1 f =
2 Z + Z C
Determine the Thevenin Impedance seen by C2
January 2004 ENGI 242/ELEC 222 20
fCL3
CL3
O2 L 3
1 f =
2 Z + R C
Determine the Thevenin Impedance seen by C3
January 2004 ENGI 242/ELEC 222 21
fCL4
Determine the Thevenin Impedance seen by CE1
CL4
TH_IN1 4
1 f =
2 Z C
January 2004 ENGI 242/ELEC 222 22
fCL5
Determine the Thevenin Impedance seen by CE2
CL5
TH_IN2 5
1 f =
2 Z C
January 2004 ENGI 242/ELEC 222 23
Schematic of Design
January 2004 ENGI 242/ELEC 222 24
Simulation Profile
January 2004 ENGI 242/ELEC 222 25
Probe Plot – Y Axis Settings
January 2004 ENGI 242/ELEC 222 26
Probe Plot – X Axis X Grid Settings
January 2004 ENGI 242/ELEC 222 27
Frequency Response
January 2004 ENGI 242/ELEC 222 28
Frequency Response