# CHAPTER 11 : MULTISTAGE TRANSISTOR AMPLIFIERS¶

## Example 11.1 : Page number 285¶

In :
from math import log10
#Variable declaration
#(i)
A_v=30;                 #Voltage gain

#(ii)
A_p=100;                #Power gain

#Calculations
#(i)
A_v_dB=20*log10(A_v);          #Voltage gain, dB
A_p_dB=10*log10(A_p);          #Power gain, dB

#Results
print("(i) Voltage gain in dB=%.2fdB"%A_v_dB);
print("(ii) Power gain in dB=%ddB"%A_p_dB);

(i) Voltage gain in dB=29.54dB
(ii) Power gain in dB=20dB


## Example 11.2 : Page number 285-286¶

In :
#(i)
A_p_dB=40.0;                #Power gain in dB
A_p_b=A_p_dB/10;            #Power gain in bel
A_p=10**A_p_b;              #Power gain in number

#Result
print("(i) Power gain in number=%d"%A_p);

#(ii)
A_p_dB=43.0;                #Power gain in dB
A_p_b=A_p_dB/10;            #Power gain in bel
A_p=round(10**A_p_b,-4);              #Power gain in number

#Result
print("(ii) Power gain in number=%d"%A_p);

(i) Power gain in number=10000
(ii) Power gain in number=20000


## Example 11.3 : Page number 286¶

In :
from math import log10

#Variable declaration
Av_1=100.0;                     #Voltage gain of stage 1
Av_2=200.0;                     #Voltage gain of stage 2
Av_3=400.0;                     #Voltage gain of stage 3

#Calculations
Av_1_dB=20*log10(Av_1);                     #Voltage gain of stage 1, dB
Av_2_dB=20*log10(Av_2);                     #Voltage gain of stage 2, dB
Av_3_dB=20*log10(Av_3);                     #Voltage gain of stage 3, dB

Av_T=Av_1_dB+Av_2_dB+Av_3_dB;            #Total voltage gain

#Result
print("The total voltage gain=%ddB"%Av_T);

The total voltage gain=138dB


## Example 11.4 : Page number 286¶

In :
from math import log10

#Variable declaration
A_p_absolute=30.0;                          #Absolute gain of each stage
number_of_stages=5.0;                       #number of stages
negative_feedback=10.0;                     #negative feedback, dB

#Calculations
#(i)
A_p_dB=round(10*log10(A_p_absolute),2);              #Power gain of one stage. dB
A_p_T=number_of_stages * A_p_dB;            #Total power gain, dB

#(ii)
A_p_resultant=A_p_T-negative_feedback;      #Resultant power gain with negative feedback, dB

#Results
print("The total power gain = %.2fdB."%A_p_T);
print("The resultant power gain with negative feedback = %.2fdB."%A_p_resultant);

The total power gain = 73.85dB.
The resultant power gain with negative feedback = 63.85dB.


## Example 11.5 : Page number 286¶

In :
from math import log10

#Variable declaration
P_out_2kHz=1.5;                 #Output power at 2 kHz, W
P_out_20kHz=0.3;                #Output power at 20 kHz, W
P_in=10.0;                      #Input power, mW

#Calculations
A_p_dB_2kHz=10*log10(P_out_2kHz*1000/P_in);         #dB power gain at 2 kHz
A_p_dB_20kHz=10*log10(P_out_20kHz*1000/P_in);       #dB power gain at 20 kHz
Fall_in_gain=A_p_dB_2kHz-A_p_dB_20kHz;              #Fall in gain from 2kHz to 20kHz

#Results
print("The fall in gain from 2kHz to 20kHz=%.2fdB"%Fall_in_gain);

The fall in gain from 2kHz to 20kHz=6.99dB


## Example 11.6 : Page number 287¶

In :
from math import log10

#Variable declaration
A_v=15.0;                   #Voltage gain, dB
V_1=0.8;                    #Input signal voltage, V

#Calculations
#Since, Av(in decibel)=20*log10(V_2/V_1),
V_2=V_1*(10**(A_v/20));                 #Output voltage, V

#Results
print("The output voltage= %.1fV."%V_2);

The output voltage= 4.5V.


## Example 11.7 : Page number 287¶

In :
#Variable declaration
A_0_dB=70.0;                   #Open circuit voltage gain, dB
A_v_dB=67.0;                   #Voltage gain, dB
R_out=1.5;                     #Output resistance, kilo ohm

#Calculations
#Since, A_0_dB-A_v_dB=20*log10(A_0/A_v)
ratio_A0_Av=round(10**((A_0_dB-A_v_dB)/20),2);                  #Ratio of open-circuit voltage gain to normal voltage gain

#Since, A_v/A_0 = RL/(R_out+RL)

#Results

#Note: The value of load resistor is calculated to be 3.6585 kilo ohm and approximated to 3.66. But, in the text it has been approximated to 3.65.

The load resistance=3.66 kilo ohm.


## Example 11.8 : Page number 287¶

In :
#Variable declaration
A_v=40.0;               #Voltage gain, dB
V_in=10.0;              #Input signal voltage, mV

#Calcultaions
#(i)
#Since, A_v=20*log10(V_out/V_in)
V_out=V_in*(10**(A_v/20))/1000;              #Output voltage, V

#(ii)

#Results
print("(i)The output voltage is %dV."%V_out);

(i)The output voltage is 1V.


## Example 11.9 : Page number 287-288¶

In :
from math import log10

#Variable declaration
P_2=40.0;                     #Output power, W
R=10.0;                        #Resistance of speaker, ohm

#Calculations
#(i)
A_p_dB=25.0;                                   #Power gain, dB
#Since, A_p_dB=10*log10(P_2/P_1)
P_1=(P_2/10**(A_p_dB/10))*1000;                #Input power, mW

#(ii)
A_v_dB=40.0;                                    #Voltage gain, dB

#Since, P=(V**2)/R,
V_2=(P_2*R)**0.5;                               #Output voltage, V

#Since, A_v_dB=20*log10(V_2/V_1)
V_1=(V_2/10**(A_v_dB/20))*1000;                #Input voltage, mV

#Results

print("(i)The input power=%.1fmW."%P_1);
print("(ii)The input voltage=%dmV."%V_1);

(i)The input power=126.5mW.
(ii)The input voltage=200mV.


## Example 11.10 : Page number 288¶

In :
#Variable declaration
A_v_max=2000.0;                 #Maximum voltage gain
f_max=2.0;                      #Frequency at which maximum voltage gain occurs,kHz
A_v=1414.0;                     #Voltage gain at 50 Hz and 10kHz
f1=50;                          #Lower frequency at which gain is 1414, Hz
f2=10;                          #Upper frequency at which gain is 1414, kHz

#Calculation
#Since, bandwidth is the range of frequency  over which gain is greater than or equal to 70.7% of maximum gain
if((A_v/A_v_max)*100 ==70.7):
print("(i)The bandwidth is from %dHz to %dkHz."%(f1,f2));
print("(ii)The lower cut-off frequency=%dHz."%f1);
print("(iii)The upper cut-off frequency=%dkHz."%f2);

(i)The bandwidth is from 50Hz to 10kHz.
(ii)The lower cut-off frequency=50Hz.
(iii)The upper cut-off frequency=10kHz.


## Example 11.11 : Page number 291¶

In :
#Variable declaration
A_v=60.0;               #Voltage gain of single stage amplifier
R_in=1.0;               #Input impedance, kilo ohm

#Calculation
#Since, there is no loading , second stage gain remains at A_v
#But, due to loading effect of input impedance of second stage, gain of first stage decreases
A_v_2=A_v;                                                    #Voltage gain of second stage
R_AC=round((R_C*R_in*1000)/(R_C+R_in*1000),0);              #Effective load of first stage, ohm
A_v_1=A_v*R_AC/R_C;                                         #Gain of first stage
A_v_T=A_v_1*A_v_2;                                            #Total gain

#Results
print("The total gain=%d."%A_v_T);

The total gain=2397.


## Example 11.12 : Page number 291-292¶

In :
#Variable declaration
Rin=1.0;                        #Input resistance, kilo ohm
beta=100.0;                     #base current amplification factor

#Calculation
#(i)
R_AC=(RC*Rin)/(RC+Rin);               #Effective load on first stage, kilo ohm
A_v_1=round(beta*(R_AC/Rin),0);                #Voltage gain of first stage

#(ii)
A_v_2=round(beta*RC/Rin,0);                      #Voltage gain of second stage

#(iii)
A_v_T=A_v_1*A_v_2;                      #Total voltage gain

#Results
print("(i)The voltage gain of first stage =%d."%A_v_1);
print("(ii)The voltage gain of second stage =%d."%A_v_2);
print("(iii)The total voltage gain =%d."%A_v_T);

#Note: The approximation inthe text for A_v_1=66.66 is taken as 66 but here it has been taken 67 and therefore the total voltage is 13400 instead of 13200.

(i)The voltage gain of first stage =67.
(ii)The voltage gain of second stage =200.
(iii)The total voltage gain =13400.


## Example 11.13 : Page number 292¶

In :
#Variable declaration
RC=10.0;                    #Collector load of single stage amplifier, kilo ohm
Rin=1.0;                    #Input resistance, kilo ohm
beta=100.0;                 #base current amplification factor

#Calculations
A_v=beta*R_AC/(Rin*1000);                              #Voltage gain

#Results
print("The voltage gain=%d."%A_v);

The voltage gain=10.


## Example 11.14 : Page number 292-293¶

In :
#Variable declaration
VCC=20.0;                       #Collector suppply voltage, V
R1=10.0;                        #resistor R1, kilo ohm
R2=2.2;                         #resistor R2, kilo ohm
R3=10.0;                        #resistor R3, kilo ohm
R4=2.2;                         #resistor R4, kilo ohm
RC_1=3.6;                         #Collector resistor of first stage, kilo ohm
RC_2=4.0;                         #Collector resistor of second stage, kilo ohm
RE_1=900.0;                     #Emitter resistor of first stage, ohm
RE_2=1.0;                       #Emitter resistor of second stage, kilo ohm

#Calculations
#Biasing potential for the second stage is the voltage across R4 resistor,
#so, by voltage divider rule:
VB=VCC*R4/(R3+R4);                #Biasing potential for second stage,(Voltage across R4), V

print("The biasing voltage for the second stage=%.1fV."%VB);

#If coupling capacitor C_c is replaced by a wire, RC_1 and R3 become parallel
Req=round((RC_1*R3)/(RC_1+R3),2);        #Equivalent resistance of R3 parallel with RC_1, kilo ohm
VB=VCC*R4/(Req+R4);             #Biasing voltage if coupling capacitor is replaced by a wire, V

print("The biasing voltage after replacing coupling capacitor by wire=%.2fV."%VB);

The biasing voltage for the second stage=3.6V.
The biasing voltage after replacing coupling capacitor by wire=9.07V.


## Example 11.15 : Page number 293-294¶

In :
#Function for calculating parallel resistance
def pr(r1,r2):
return (r1*r2)/(r1+r2);

#Variable declaration
VCC=15.0;                           #Collector supply voltage, V
R1=22.0;                            #Resistor R1, kilo ohm
R2=3.3;                            #Resistor R2, kilo ohm
R3=5.0;                            #Resistor R3, kilo ohm
R4=1.0;                            #Resistor R4, kilo ohm
R5=15.0;                            #Resistor R5, kilo ohm
R6=2.5;                            #Resistor R6, kilo ohm
R7=5.0;                            #Resistor R7, kilo ohm
R8=1.0;                            #Resistor R8, kilo ohm
beta=200;                           #Base current amplification factor
V_BE=0.7;                           #Base-emitter voltage, V

#Calculations
#for 2nd stage
V_R6=round(VCC*R6/(R5+R6),2);                #Voltage across R6, V (voltage divider rule)
V_R8=round(V_R6-V_BE,2);                     #Voltage across R8, V
IE_2=round(V_R8/R8,2);                         #Emitter current through R8, mA (OHM's LAW)
re_2nd_stage=round(25/IE_2,1);                 #a.c emitter resistance for 2nd stage, ohm

#For 1st stage
V_R2=round(VCC*R2/(R1+R2),2);                     #Voltage across R2, V (voltage divider rule)
V_R4=round(V_R2-V_BE,2);                          #Voltage across R4, V
IE_1=round(V_R4/R4,2);                            #Emitter current through R4, mA (OHM's LAW)
re_1st_stage=round(25/IE_1,1);                    #a.c emitter resistance for 1st stage, ohm

#(i)
Zin_base_2nd_stage=round((beta*re_2nd_stage)/1000,2);               #input resistance of transistor base of 2nd stage, kilo ohm
Zin=round(pr(pr(R5,R6),Zin_base_2nd_stage),2);                      #Input impedance of the 2nd stage, kilo ohm
R_AC_1st_stage=round(pr(R3,Zin),2);                                          #Effective collector load for 1st stage, kilo ohm
A_v_1=round(R_AC_1st_stage*1000/re_1st_stage,0);                                  #voltage gain of 1st stage

#(ii)
R_AC_2nd_stage=round(pr(R7,RL),2);                          #Effective collector load for 2nd stage, kilo ohm
A_v_2=round(R_AC_2nd_stage*1000/re_2nd_stage,1);                  #voltage gain of 2nd stage

#(iii)
A_v_overall=A_v_1*A_v_2;                            #overall voltage gain

#results
print("(i)The voltage gain of 1st stage=%.0f."%A_v_1);
print("(i)The voltage gain of 2nd stage=%.1f."%A_v_2);
print("(i)The overall voltage gain =%d."%A_v_overall);

(i)The voltage gain of 1st stage=53.
(i)The voltage gain of 2nd stage=191.4.
(i)The overall voltage gain =10144.


## Example 11.16 : Page number 297¶

In :
#Variable declaration
Primary_impedance=1000.0;                       #Primary impedance, ohm

#Calculation
#since,for maximum power transfer primary impedance should be equal to output impedance
#and, impedance of secondary should be equal to load impedance
#therfore, primary_impedance/load_impedance=square of(primary to secondary turn ratio)
n=(Primary_impedance/Load_impedance)**0.5;           #Primary to secondary turn ratio

#Result
print('The primary to secondary turn ratio for maximum power transfer=%d.'%n);

The primary to secondary turn ratio for maximum power transfer=10.


## Example 11.17 : Page number 297¶

In :
#Variable declaration
R_p=10.0;                   #Output impedance of primary, kilo ohm
Vp=10.0;                    #Terminal voltage of the source, V

#Calculation
#Since, for maximum power transfer, the impedance of the primary should be equal to output impedance of the source
n=(R_p*1000/RL)**0.5;                        #Primary to secondary turns ratio

#Since, power in a transformer remains constant,
#ratio of primary to secondary voltageis equal to primary to secondary turns ratio
Vs=Vp/n;                                #Voltage across the external load, V

#Result
print("The primary to secondary turns ratio=%d."%n);
print("The voltage across the external load=%.1fV."%Vs);

The primary to secondary turns ratio=25.
The voltage across the external load=0.4V.


## Example 11.18 : Page number 297-298¶

In :
#Variable declaration
Rp=300.0;                   #D.C resistance of primary, ohm
R_out=3.0;                  #Ouput resistance of the transistor, kilo ohm

#Calculation
#when no signal is applied, only Rp is seen to be the load.
#But, when a.c signal is applied, RL in secondary reflects as RL*(squre of turns ratio).
#Therefore, load is seen to be Rp in series with the reflected RL in primary.
#i.e, R_out=Rp+(n**2 * RL), where n is the turns ratio
n=((R_out*1000-Rp)/RL)**0.5;                     #turns ratio

#Result
print("Turns ratio for maximum power transfer=%d."%n);

Turns ratio for maximum power transfer=30.


## Example 11.19 : Page number 298¶

In :
from math import pi

#Variable declaration
f=200.0;                        #Frequency, Hz
Z_out=10.0;                     #Output impedance of the transistor, kilo ohm
Z_in=2.5;                       #Input impedance of the next stage, kilo ohm

#Calculation
#For perfect impedance matching,
#Z_out should be equal to primary impedance
#Z_out=2*pi*f*(primary inductance)
Lp=(Z_out*1000)/(2*pi*f);                   #Primary inductance, H

#for the secondary side,
#Z_in should be equal to impedance of secondary
Ls=(Z_in*1000)/(2*pi*f);                    #Secondary inductance, H

#result
print("The primary inductance=%.0fH."%Lp);
print("The secondary inductance=%.0fH."%Ls);

The primary inductance=8H.
The secondary inductance=2H.


## Example 11.20 : Page number 299¶

In :
#Variable declaration
Lp=8.0;                     #Primary inductance, H
Ls=2.0;                     #Secondary inductance, H
K=10**-5;                   #Inductance to turns ratio, constant

#Calculations
Np=(Lp/K)**0.5;                  #Primary turns
Ns=(Ls/K)**0.5;                  #Secondary turns

#Result
print("The primary turns=%.0f."%Np);
print("The secondary turns=%.0f."%Ns);

The primary turns=894.
The secondary turns=447.


## Example 11.21 : Page number 300-301¶

In :
#Variable declaration
VCC=12.0;                   #Collector supply voltage, V
R1=100.0;                   #Resistor R1, kilo ohm
R2=22.0;                    #Resistor R2, kilo ohm
R3=22.0;                    #Resistor R3, kilo ohm
R4=4.7;                     #Resistor R4, kilo ohm
R5=10.0;                    #Resistor R5, kilo ohm
R6=10.0;                    #Resistor R6, kilo ohm
beta=125;                   #Base current amplification factor
V_BE=0.7;                   #Base-emitter voltage, V

#Calculation
#(i) D.C voltages
#For 1st stage:
V_B1=VCC*R2/(R1+R2);                    #Voltage at the base of 1st transistor, V (Voltage across R2, using voltage divider rule)
V_E1=V_B1-V_BE;                         #Emitter voltage of the 1st transistor, V
I_E1=round(V_E1/R4,2);                           #Emitter current of 1st transistor, mA (OHM's LAW)
I_C1=I_E1;                              #Collector current of 1st transistor, mA(approximately equals to emitter current)
V_C1=VCC-I_C1*R3;                       #Collector voltage of 1st transistor, V

#For 2nd stage:
V_B2=V_C1;                              #Voltage at the base of 2nd transistor, V (equals to collector voltage of 1st transistor)
V_E2=V_C1-V_BE;                         #Emitter voltage of the 2nd transistor, V
I_E2=V_E2/R6;                           #Emitter current of 2nd transistor, mA (OHM's LAW)
I_C2=I_E2;                              #Collector current 2nd transistor, mA(approximately equals to emitter current)
V_C2=VCC-I_C2*R5;                       #Collector voltage of 2nd transistor, V

print("(i) D.C voltages");
print("First stage: VB1=%.2fV , VE1=%.2fV and VC1=%.2fV"%(V_B1,V_E1,V_C1));
print("First stage: VB2=%.2fV , VE2=%.2fV and VC2=%.2fV"%(V_B2,V_E2,V_C2));

#(ii)Voltage gain
#First stage
re_1=25/I_E1;                                   #a.c emitter resistance of 1st transistor, ohm
re_2=25/I_E2;                                   #a.c emitter resistance of 2nd transistor, ohm
Zin_2nd_stage=beta*re_2/1000;                   #Input impedance of 2nd stage, kilo ohm
R_AC=R3*Zin_2nd_stage/(R3+Zin_2nd_stage);       #Total a.c collector load, kilo ohm
A_v1=round(R_AC*1000/re_1,0);                                 #Voltage gain of first stage

print("The voltage gain of first stage=%d."%A_v1);

#Second stage
R_AC=R5;                                        #Total a.c collector load for 2nd stage, kilo ohm(Due to no loading effect, equal to R5)
A_v2=round(R5*1000/re_2,0);                                   #Voltage gain of 2nd stage

print("The voltage gain of second stage=%d."%A_v2);

A_vT=A_v1*A_v2;                                 #Overall voltage gain

print("Overall voltage gain=%d."%A_vT);

(i) D.C voltages
First stage: VB1=2.16V , VE1=1.46V and VC1=5.18V
First stage: VB2=5.18V , VE2=4.48V and VC2=7.52V
The voltage gain of first stage=66.
The voltage gain of second stage=179.
Overall voltage gain=11814.

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