Ch-14 : Feedback Amplifiers¶

Page No. 452 Example 14.1.¶

In [1]:
A=1000.
beta=0.04
dA=10.
print "The percentage change in gain of the amplifier with feedback is"
dAf=dA*(1/(1+(A*beta)))
print "    dAf/Af = dA/A * 1/(1+A*beta) = %0.2f %%"%dAf

The percentage change in gain of the amplifier with feedback is
dAf/Af = dA/A * 1/(1+A*beta) = 0.24 %


Page No. 452 Example 14.2.¶

In [1]:
Af=100.
dAf=0.02
dA=0.2
Ab=dA/dAf
print "(1 + A*beta) =%0.2f"%Ab
print "Also, the gain with feedback is"
print "      Af = A / (1+A*beta)"
A=Af*Ab
print "Therefore,      A =%0.2f"%A
print "       1 + A*beta = 10# i.e. A*beta = 9"
beta=9./A
print "Therefore,      beta =%0.2f"%beta

(1 + A*beta) =10.00
Also, the gain with feedback is
Af = A / (1+A*beta)
Therefore,      A =1000.00
1 + A*beta = 10# i.e. A*beta = 9
Therefore,      beta =0.01


Page No. 455 Example 14.3.¶

In [3]:
A=125.
BW=250*10**3
beta=0.04
print "(a) We have BWf = (1 + A*beta) * BW"
BWf = (1 + (A*beta))*BW
x1=BWf*10**-6
print "    BWf  =%0.2f MHz"%x1
Af=A/(1+(A*beta))
print "Gain with feedback,  Af = A / (1+ A*beta) =%0.2f"%Af
print "(b) BWf = (1 + A*beta'') * BW"
print "1*10**6 = (1 + 125*beta'')*250*10**3"
Bd=3./125
print "Therefore,     beta =%0.2f"%Bd
Bd1=Bd*100
print "i.e.   beta (in %%) =%0.2f"%Bd1

(a) We have BWf = (1 + A*beta) * BW
BWf  =1.50 MHz
Gain with feedback,  Af = A / (1+ A*beta) =20.83
(b) BWf = (1 + A*beta'') * BW
1*10**6 = (1 + 125*beta'')*250*10**3
Therefore,     beta =0.02
i.e.   beta (in %) =2.40


Page No. 456 Example 14.4.¶

In [5]:
A=400.
f1=50.
f2=200*10**3
D=10.
beta=0.01
print "The voltage gain with feedback"
Af=A/(1+(A*beta))
print "  Af = A / (1 + A*beta) =%0.2f"%Af
print "New lower 3dB frequency,"
f1f=f1/(1+(A*beta))
print "  f_1f = f1 / 1+A*beta =%0.2f Hz"%f1f
print "New upper 3dB frequency,"
f2f=(1+(A*beta))*f2
x2=f2f*10**-6
print "  f2f = (1+A*beta)*f2 =%0.2f MHz"%x2
print "Distortion with feedback,"
Df=D/(1+(A*beta))
print "  Df = D / 1+A*beta =%0.2f %%"%Df

The voltage gain with feedback
Af = A / (1 + A*beta) =80.00
New lower 3dB frequency,
f_1f = f1 / 1+A*beta =10.00 Hz
New upper 3dB frequency,
f2f = (1+A*beta)*f2 =1.00 MHz
Distortion with feedback,
Df = D / 1+A*beta =2.00 %


Page No. 458 Example 14.5¶

In [7]:
A=500.
Ri=3*10**3
Ro=20*10**3
beta=0.01
Af=A/(1+(A*beta))
print "Voltage gain,      Af = A / (1+A*beta) =%0.2f"%Af
Rif=(1+(A*beta))*Ri
x1=Rif*10**-3
print "Input resistance,  Rif = (1+(A*beta))*Ri =%0.2f kohm"%x1
Rof=Ro/(1+(A*beta))
x2=Rof*10**-3
print "Output resistance, Rof = Ro / (1+A*beta) =%0.2f kohm"%x2

Voltage gain,      Af = A / (1+A*beta) =83.33
Input resistance,  Rif = (1+(A*beta))*Ri =18.00 kohm
Output resistance, Rof = Ro / (1+A*beta) =3.33 kohm


Page No. 460 Example 14.6.¶

In [8]:
Ai=1+80
print "  Ai = 1 + hfe =%0.2f"%Ai
Ri=(5*10**3)+((1+80)*(2*10**3))  #in ohm
x1=Ri*10**-3 #in k-ohm
print "  Ri = hie + (1+hfe)*RL =%0.2f kohm"%x1
Av=(81*2*10**3)/(167*10**3)
print "  Av = Ai*RL / Ri =%0.2f"%Av
Ro=(5000.+600)/(1.+80) # in ohm
print "  Ro = hie+Rs / 1+hfe =%0.2f ohm"%Ro
Rof=(69.13*2000)/(2069.13)  #in ohm
print "  Rof = Ro || RL =%0.2f ohm"%Rof

  Ai = 1 + hfe =81.00
Ri = hie + (1+hfe)*RL =167.00 kohm
Av = Ai*RL / Ri =0.00
Ro = hie+Rs / 1+hfe =69.14 ohm
Rof = Ro || RL =66.82 ohm


Page No. 461 Example 14.7.¶

In [9]:
RL=((40*2)/42)*10**3 #in ohm
print "  R''L = RB || RL =%0.2f ohm"%RL
Av=(-80*1905.)/5000.
print "  Av = -hfe*R''L / hie =%0.2f"%Av
x1=(40000.)/(1+30.48)
Rif=(x1*5000.)/(x1+5000) #in ohm
print "  Rif = hie || (RB / 1-Av) =%0.2f ohm"%Rif
Avf=(-30.48*1013.172)/(600+1013.172)
print "  Avf = Vo/Vs = Av*Rif / RS+Rif =%0.2f"%Avf
Rof=(40000/600.)*(5600./80) #in ohm
x2=Rof*10**-3 #in k-ohm
print "  Rof = (RB / RS) * (RS+hie / hfe) =%0.2f kohm"%x2
Roff=(4.666*2)/(6.666) #in k-ohm
print "  R''of = Rof || RL =%0.2f kohm"%Roff,

  R''L = RB || RL =1000.00 ohm
Av = -hfe*R''L / hie =-30.48
Rif = hie || (RB / 1-Av) =1013.17 ohm
Avf = Vo/Vs = Av*Rif / RS+Rif =-19.14
Rof = (RB / RS) * (RS+hie / hfe) =4.67 kohm
R''of = Rof || RL =1.40 kohm


Page No. 462 Example 14.8.¶

In [10]:
from math import log10
R1=20.*10**3
R2=20.*10**3
hie=2.*10**3
RL=1.0*10**3
Re=100.
hfe=80.
A=(-hfe*RL)/hie
print "(a)  A = -hfe*RL / hie =%0.2f"%A
print "     Ri = hie = 2 k-ohm"
beta=Re/RL
print "(b)  beta = Re / RL =%0.2f"%beta
Rif=hie+((1+hfe)*Re)
x1=Rif*10**-3
print "(c)  Rif = hie + (1+hfe)*Re =%0.2f kohm"%x1
Af=(-hfe*RL)/Rif
print "(d)  Af = -hfe*RL / Rif =%0.2f"%Af
lg=20.*log10(4)
print "(e)  Loop gain, beta = -40*0.1 = -4 i.e. 20log4 =%0.2f dB"%lg

(a)  A = -hfe*RL / hie =-40.00
Ri = hie = 2 k-ohm
(b)  beta = Re / RL =0.10
(c)  Rif = hie + (1+hfe)*Re =10.10 kohm
(d)  Af = -hfe*RL / Rif =-7.92
(e)  Loop gain, beta = -40*0.1 = -4 i.e. 20log4 =12.04 dB