# Chapter 6: Feedback Amplifiers And Oscillators¶

## Example 6.1,Page number 331¶

In :
#Variable declaration
Vo=12.            #output voltage(V)
f=1.5*10**3       #frequency(Hz)
h=0.25            #second harmonic content(%)
ho=2.5            #reduced harmonic content of output(%)
A=100             #power amplifier gain

#Calculations
Vd=Vo*h              #second harmonic content in output(V)
Vd1=Vo*ho            #reduced value of second harmonic content(V)
beta=((Vd1/Vd)-1)/A  #feedback gain from formula Vd1=Vd/(1+beta*A)
Vs=Vo*(1+beta*A)/A   #signal voltage(V) from formula (A/(1+Beta*A))*Vs
V=Vo/A               #signal input needed without feedback
s=Vs/V               #additional signal amplification needed before feedback amplifier

#Results
print"feedback gain is",beta
print"signal input to the overall system is",s

feedback gain is 0.09
signal input to the overall system is 10.0


## Example 6.2,Page number 332¶

In :
#Variable declaration
Ao=1000.              #high frquency response

#Calculations
beta=((w2new/w2)-1)/Ao #feedback factor
Anew=Ao/(1+beta*Ao)   #overall gain of amplifier from formula w2new=w2(1+beta*Ao)
p=w2*Ao               #gain bandwidth product without feedback from formula Anew=Ao/1+beta*Ao
pnew=Anew*w2new       #gain bandwidth product with feedback

#Results
print"beta is",beta
print"overall gain is",Anew
print"gain-bandwidth products with and without feedback are",p,"and",pnew,"resp."

beta is 0.009
overall gain is 100.0
gain-bandwidth products with and without feedback are 10000000.0 and 10000000.0 resp.


## Example 6.3,Page number 333¶

In :
#Variable declaration
A=100.                               #high frquency response
Af=100                               #gain
A1=A**2                              #forward gain
A1new=50                             #gain reduces to 50%

#Calculations
beta=((A1/Af)-1)/A1                  #feedback factor
Afnew=A1new**2/(1+beta*A1new**2)     #new value of A
g=Af-Afnew                           #reduction in overall gain

#Results
print"% change in gain of feedback unit is",round(g,2)

% change in gain of feedback unit is 2.91


## Example 6.4,Page number 337¶

In :
#Variable declaration
beta=0.008                   #positive gain

#Calculations
Ao=-(8/beta)**(1/3)          #A=Ao/2,so beta(A^3)=-1

#Results
print"% change in gain of feedback unit is",round(Ao/1E-1)

% change in gain of feedback unit is -10.0


## Example 6.5Page number 337¶

In :
import cmath
from math import pi,degrees

#Variable declarations
A = complex(0,60)                  #amplifier
B = complex(0,30)                  #amplifier
AB = A*B
C = (1+A)/AB                       #condition for oscillation
phi = cmath.phase(C)               #phase

#Result
print "C =",round(abs(C),4),"with phase =",round(degrees(phi),2)

C = 0.0333 with phase = -90.95


## Example 6.7,Page number 347¶

In :
#Variable declaration
Rbb=8*10**3                  #base resistance(k ohms)
eta=0.7                     #efficiency
R1=0.2                      #R1(k ohms)
Rt=40*10**3                 #Rt(ohms)
Ct=0.12*10**-6              #capacitance(F)
Vv=2                        #capacitor is charged to voltage(V)
Iv=10*10**-3                #current to capacitor(A)
Ip=10*10**-3                 #peak current(A)
Vd=0.7                      #diode voltage(V)
V=12.                        #voltage(V)

#Calculations
#Part a
Rb1=eta*Rbb    #base resistance(ohms)
Rb2=Rbb-Rb1             #base resistance(ohms)

#Part b
Vp=Vd+((Rb1+R1)*V/(Rbb+R1))    #peak voltage(V)

#Part c
Rtmin=(V-Vv)/Iv          #Rt minimum(k ohms)
Rtmax=(V-Vp)/Ip          #Rt minimum(k ohms)

#Part d
Rb11=.12                #resistance during discharge(ohms)
t1=Rt*Ct*1.27           #charging time(mS)
t2=(Rb11+R1)*Ct*1.52    #discharging time(uS)
T=t1+t2                 #cycle time
foscE=1/T               #oscillations frequency(Hz)
foscA=1/(Rt*Ct*1.2)     #oscillations frequency(Hz)

#Part e
vR1=(R1*V)/(R1+Rbb)             #vR1 at discharging period
vR1d=(R1*(Vp-Vd))/(R1+Rb11)      #vR1 at discharging period

#Results
print"Rb1 and Rb2 are",round((Rb1/1E+3),1),"k ohms and",round((Rb2/1E+3),1),"k ohms resp."
print"Vp is",round(Vp,1),"V"
print"Rtmin is",round(Rtmin/1E+3),",k ohms and Rtmax is",round(Rtmax/1E+1),"k ohms,hence Rt is in the range"
print"foscE is",round(foscE),"Hz and foscA is",round(foscA),"Hz"
print"vR1 is",round((vR1/1E-3),3),"and vRd1 is",round(vR1d,2),"V (range of Rt is wrong in the book)"

Rb1 and Rb2 are 5.6 k ohms and 2.4 k ohms resp.
Vp is 9.1 V
Rtmin is 1.0 ,k ohms and Rtmax is 29.0 k ohms,hence Rt is in the range
foscE is 164.0 Hz and foscA is 174.0 Hz
vR1 is 0.3 and vRd1 is 5.25 V (range of Rt is wrong in the book)


## Example 6.8,Page number 350¶

In :
#Variable declaration
A=1500                         #voltage gain
beta=1/25.                     #current gain

#Calculations
#Part a
Af=A/(1+A*beta)                 #voltage gain with feedback

#Part b
g=0.1                        #amplifier gain changes by 10%=0.1
gf=g/(1+A*beta)              #% by which its gain in feedback mode changes dAf/Af

#Results
print"Amplifier gain with feedback is",round(Af,1)
print"% by which gain in feedback changes is",round((gf/1E-2),3),"%"

Amplifier gain with feedback is 24.6
% by which gain in feedback changes is 0.164 %


## Example 6.9,Page number 351¶

In :
#Variable declaration
A=500                      #voltage gain
beta=1/20.                 #current gain
Ro=50*10**3                #output resistance(ohms)
Ri=1.5*10**3               #input resistance(ohms)

#Calculations
#Part a
Af=A/(1+A*beta)            #voltage gain with feedback

#Part b
Rif=Ri*(1+(A*beta))         #input resistance(k ohms)
Rof=Ro/(1+A*beta)           #output resistance(k ohms)

#Results
print"Amplifier gain is",round(Af,2)
print"input resistance is",round(Rif/1E+3),"K ohms and output resistance is",round((Rof/1E+2),2),"Kohms"

Amplifier gain is 19.23
input resistance is 39.0 K ohms and output resistance is 19.23 Kohms


## Example 6.10,Page number 351¶

In :
#Variable declaration
Ro=50*10**3                 #output resistance(ohms)
Rd=10*10**3                 #drain resistance(ohms)
R1=800*10**3                #resistance(ohms)
R2=200*10**3                #resistance(ohms)
gm=5500*10**-6              #transconduuctance(us)

#Calculations
r=(Rd*Ro)/(Rd+Ro)            #Rd||Ro
R=R1+R2                      #combined resistance of R1 and R2
A=-gm*Rl                     #voltage gain without feedback
beta=R2/(R1+R2)              #current gain
Af=A/(1+A*beta)              #voltage gain with feedback

#Results
print"Amplifier gain with feedback is",round((Af/1E+1),1),"and without feedback is",A

Amplifier gain with feedback is -4.5 and without feedback is -45.452


## Example 6.11,Page number 352¶

In :
#Variable declaration
Re=1.25*10**3              #emitter resistance(ohms)
Rc=4.8*10**3                #collector resistance(ohms)
Rb=800*10**3               #base resistance(ohms)
rpi=900                    #dynamic resistance(ohms)
Vcc=16                     #supply voltage(V)
beta=100.                  #current gain

#Calculations
A=-(beta/rpi)             #amplifier voltage gain
B=-Re
V=(A*Rc)/(1+B*A)          #V=Vo/Vs

#Results
print"Amplifier voltage gain is",round(V,1)

Amplifier voltage gain is -3.8


## Example 6.12,Page number 352¶

In :
 import math

#Variable declaration
C1=800*10**-9                   #capacitance(F)
C2=2400*10**-9                  #capacitance(F)
L=50*10**-6                     #inductance(H)

#Calculations
Ceq=(C1*C2)/(C1+C2)                #equivalent capacitance(F)
fo=1/(2*math.pi*math.sqrt(L*Ceq))  #output frequency(Hz)

#Results
print"the oscillation frequency is",round((fo/1E+3),2),"KHz"

the oscillation frequency is 29.06 KHz


## Example 6.13,Page number 353¶

In :
import math

#Variable declaration
C=200*10**-9               #capacitance(F)
Lrcf=0.5*10**-3            #shunt across L2
L1=800*10**-6              #inductance(H)
L2=800*10**-6              #inductance(H)
M=200*10**-6

#Calculations
L21=(L2*Lrcf)/(L2+Lrcf)                  #effective value of L2(uH)
Leq=L1+L21+2*M                           #equivalent inductance(H)
fo=1/(2*math.pi*math.sqrt(Leq*C))        #output frequency(Hz)

#Results
print"the oscillation frequency is",round((fo/1E+3),2),"KHz"

the oscillation frequency is 9.17 KHz