# Ch-10 : Multistage Amplifiers¶

## Page No. 316 Example 10.1.¶

In :
hie=1600.
hfe=60.
hre=5*10**-4
hoe=25*10**-6
hic=1600.
hfc=-61.
hrc=1.
hoc=25*10**-6
print "For the second stage ZL = RE2 and the current gain of the second stage is"
RE2=4000.
AI2=-hfc/(1+(hoc*RE2))
print "                 AI2 = -Ie2 / Ib2 = -hfc / (hoc*RE2) =%0.2f"%AI2
print "For the second stage,"
Ri2 = hic + (hrc*AI2*RE2)
Ri22=Ri2*10**-3
print "          Ri2 = hic + (hrc*AI2*RE2) =%0.2f kohm"%Ri22
Re2=4000.
AV2=(AI2*Re2)/Ri2
print "                 AV2 = Vo/V2 = (AI2*Re2) / Ri2 = %0.2f "%AV2
print "The First Stage :"
RC1=4000.
RL1=(RC1*Ri2)/(RC1+Ri2)
RL11=RL1*10**-3
print "              RL1= RC1 || Ri2 =%0.2f kohm"%RL11
print "Current gain,"
AI1= -hfe/(1+(hoe*RL1))
print "                 AI1 = -IC1/Ib1 = -hfe/(1+(hoe*RL1)) =%0.2f"%AI1
print "The input impedance of the first stage, which is also the input impedance of the cascaded amplifier is"
Ri1=hie +(hre*AI1*RL1)  # answer in textbook is wrong
Ri11=Ri1*10**-3
print "         Ri1 = hie + hre*AI1*RL1 =%0.2f kohm"%Ri11
print "The voltage gain of the first stage is"
AV1=(AI1*RL1)/Ri1  # answer in textbook is wrong
print "                 AV1 = V2/V1 = (AI1*RL1) / Ri1 =%0.2f"%AV1
print "The output admittance of the first transistor Q1"
RS=600.
Yo1=hoe-((hfe*hre)/(hie+RS))
Yo0=Yo1*10**6
print "           Yo1(uA/V) = hoe - ((hfe*hre) / (hie+RS)) =%0.2f"%Yo0
print "The output impedance of the first stage"
Ro1=1./Yo1
Ro0=Ro1*10**-3
print "          Ro1 = 1 / Yo1 =%0.2f kohm"%Ro0
print "The output impedance taking RC1 into account is"
Rot1=(Ro1*RC1)/(Ro1+RC1)
Rott=Rot1*10**-3
print "        Rot1(k-ohm) = Ro1 || RC1 =%0.2f kohm"%Rott
print "The output admittance of the second stage"
Yo2=hoc-((hfc*hrc)/(hic+Rot1))
print "            Yo2 = hoc-((hfc*hrc) / (hic+Rot1)) =%0.2f A/V"%Yo2
print "Output impedance,"
RO2=1/(11.525*10**-3)
print "            RO2 = 1 / Yo2 =%0.2f ohm"%RO2
Ro2=(87.*4000.)/(87+4000)
print "Hence,      Ro2(ohm) = (RO2*RE2) / (RO2+RE2) =%0.2f ohm"%Ro2
Rc1=4000.
x=(-Rc1)/ (Rc1+Ri2)
print "         Ib2/Ic1 = -Rc1/ Rc1+Ri2 =%0.2f"%x
AI=-AI2*x*AI1
print "             AI = -AI2*AI1*(Rc1 / Ri2+Rc1) =%0.2f"%AI
AV=AV2*AV1
print "            AV = AV2*AV1 =%0.2f"%AV  # answer in textbook is wrong
print "The overall voltage gain taking the source impedance into account,"
AVs=AV*(Ri1/(Ri1+RS))
print "          AVs = Vo/Vs = Av(Ri1 / Ri1+Rs) =%0.2f"%AVs # answer in textbook is wrong

For the second stage ZL = RE2 and the current gain of the second stage is
AI2 = -Ie2 / Ib2 = -hfc / (hoc*RE2) =55.45
For the second stage,
Ri2 = hic + (hrc*AI2*RE2) =223.42 kohm
AV2 = Vo/V2 = (AI2*Re2) / Ri2 = 0.99
The First Stage :
RL1= RC1 || Ri2 =3.93 kohm
Current gain,
AI1 = -IC1/Ib1 = -hfe/(1+(hoe*RL1)) =-54.63
The input impedance of the first stage, which is also the input impedance of the cascaded amplifier is
Ri1 = hie + hre*AI1*RL1 =1.49 kohm
The voltage gain of the first stage is
AV1 = V2/V1 = (AI1*RL1) / Ri1 =-143.83
The output admittance of the first transistor Q1
Yo1(uA/V) = hoe - ((hfe*hre) / (hie+RS)) =11.36
The output impedance of the first stage
Ro1 = 1 / Yo1 =88.00 kohm
The output impedance taking RC1 into account is
Rot1(k-ohm) = Ro1 || RC1 =3.83 kohm
The output admittance of the second stage
Yo2 = hoc-((hfc*hrc) / (hic+Rot1)) =0.01 A/V
Output impedance,
RO2 = 1 / Yo2 =86.77 ohm
Hence,      Ro2(ohm) = (RO2*RE2) / (RO2+RE2) =85.15 ohm
Ib2/Ic1 = -Rc1/ Rc1+Ri2 =-0.02
AI = -AI2*AI1*(Rc1 / Ri2+Rc1) =-53.29
AV = AV2*AV1 =-142.80
The overall voltage gain taking the source impedance into account,
AVs = Vo/Vs = Av(Ri1 / Ri1+Rs) =-101.86


## Page No. 325 Example 10.2.¶

In :
from math import pi
hfe=50.
hie=1200.
hoe=30*10**-6
hre=2.5*10**-4
RC=5*10**3
C=160*10**-12
CC=6*10**-6
R1=100*10**3
R2=10*10**3
gm=50*10**-3
Ro=1./hoe
x1=(Ro*10**-3)
print "Ro = 1/hoe =%0.2f kohm"%x1
RB=(R1*R2)/(R1+R2)
x2=RB*10**-3
print "RB = R1 || R2 =%0.2f kohm"%x2
Ri=hie
x3=Ri*10**-3
print "Ri = hie =%0.2f kohm"%x3
R_C=(RC*Ro)/(RC+Ro)
x4=R_C*10**-3
print "RC'' = RC || Ro =%0.2f kohm"%x4
R_i=(RB*Ri)/(RB+Ri)
x6=R_i*10**-3
print "Ri'' = RB || Ri =%0.2f kohm"%x6
R_ci=(R_C*R_i)/(R_C+R_i)
x7=R_ci*10**-3
print "Rci'' = Rc'' || Ri'' =%0.2f kohm"%x7
rbe=hfe/gm
print "rbe = hfe / gm =%0.2f ohm"%rbe
print "(a) Mid-band current gain,"
AIm=(-50*4.35*10**3)/((4.35*10**3)+(1.1*10**3))
print "AIm = (-hfe*R''C) / (RC''+Ri'') =%0.2f"%AIm
print "(b) Mid-band voltage gain,"
AVm=(-50)*((0.87*10**3)/(1.2*10**3))
print "AVm = (-hfe) * (Rcid/hie) =%0.2f"%AVm
print "(c) Lower 3dB frequency,"
fL=1./(2*pi*6*10**-6*(5.45*10**3))
print "fL = 1 / (2*pi*CC*(R_C+R_i)) =%0.2f Hz"%fL
print "Higher 3dB frequency,"
fH=1/(2*pi*C*rbe)
x8=fH*10**-3
print "fH = 1 / (2*pi*C*rbe) =%0.2f kHz"%x8  # answer in textbook is wrong
print "(d) Voltage gain x bandwidth"
y=abs(AVm*fH)
x9=(y*10**-6)
print "|AVmfH| =%0.2f"%x9

Ro = 1/hoe =33.33 kohm
RB = R1 || R2 =9.09 kohm
Ri = hie =1.20 kohm
RC'' = RC || Ro =4.35 kohm
Ri'' = RB || Ri =1.06 kohm
Rci'' = Rc'' || Ri'' =0.85 kohm
rbe = hfe / gm =1000.00 ohm
(a) Mid-band current gain,
AIm = (-hfe*R''C) / (RC''+Ri'') =-39.91
(b) Mid-band voltage gain,
AVm = (-hfe) * (Rcid/hie) =-36.25
(c) Lower 3dB frequency,
fL = 1 / (2*pi*CC*(R_C+R_i)) =4.87 Hz
Higher 3dB frequency,
fH = 1 / (2*pi*C*rbe) =994.72 kHz
(d) Voltage gain x bandwidth
|AVmfH| =36.06