CHAPTER 24 : HYBRID PARAMETERS

Example 24.1 : Page number 644-645

In [2]:
#Variable declaration
R1=10.0;                          #1st resistor, Ω
R2=5.0;                           #2nd resistor, Ω


#Calculation
print("To find h11 and h21, output terminals are shorted.");
h11=R1;                 #Input impedance with output shorted,  Ω

print("h11=%dΩ."%h11);

print("Output current flowing into the box= input current flowing out of the box.");
print("i2=-i1");                        #Output current flowing into the box= input current flowing out of the box.
print("h21=i2/i1 = -i1/i1= -1.");       #Current gain with output shorted.


print("For finding h22 and h12, voltage source is connected at the output");
#As, there will be no current through 10kΩ resistor due to open circuited input,
print("v1=v2");                         #Output voltage is equal to input voltage(equal to voltage drop across 5kΩ resistor)
print("h12=v1/v2 = v2/v2 = 1");         #Voltage feedback ratio with input terminals open

h22=1/R2;                               #Output admittance, mho
print("h22=%.1f mho"%h22);

To find h11 and h21, output terminals are shorted.
h11=10Ω.
Output current flowing into the box= input current flowing out of the box.
i2=-i1
h21=i2/i1 = -i1/i1= -1.
For finding h22 and h12, voltage source is connected at the output
v1=v2
h12=v1/v2 = v2/v2 = 1
h22=0.2 mho

Example 24.2 : Page number 645-646

In [4]:
#Variable declaration
R1=4.0;                          #1st resistor(at the input side), Ω
R2=4.0;                          #2nd resistor(at the middle), Ω
R3=4.0;                          #3rd resistor(at the output side), Ω

#Calculation
print("To find h11 and h21, output terminals are shorted.");
h11=R1 + (R2*R3/(R2+R3));                 #Input impedance with output shorted,  Ω
print("h11=%dΩ."%h11);

#As the input current gets divided in half due to R2=R3.
print("Output current flowing into the box=negative of half of input current flowing out of the box.");
print("i2=-i1/2 = -0.5i1");                        
print("h21=i2/i1 = -0.5i1/i1= -0.5.");       #Current gain with output shorted.

print("For finding h22 and h12, voltage source is connected at the output");
#As, there will be no current through the 1st 4kΩ resistor due to open circuited input,
#Voltage gets equally divided across R2 and R3 resistor
print("v1=v2/2 = 0.5v2");                    #Input voltage is equal to half of input voltage
print("h12=v1/v2 = 0.5v2/v2 = 0.5");         #Voltage feedback ratio with input terminals open

h22=1/(R2+R3);                               #Output admittance, mho
print("h22=%.3f mho"%h22);

To find h11 and h21, output terminals are shorted.
h11=6Ω.
Output current flowing into the box=negative of half of input current flowing out of the box.
i2=-i1/2 = -0.5i1
h21=i2/i1 = -0.5i1/i1= -0.5.
For finding h22 and h12, voltage source is connected at the output
v1=v2/2 = 0.5v2
h12=v1/v2 = 0.5v2/v2 = 0.5
h22=0.125 mho

Example 24.3 ; Page number 649-650

In [5]:
#Variable declaration
R1=10.0;                  #Resistor at the input side, Ω
R2=5.0;                   #Resistor at the middle, Ω
rL=5.0;                   #Load resistor, Ω

#h-parameter values from 24.1
h11=10.0;                     #Input impedance with output shorted,  Ω
h21=-1.0;                     #Current gain with output shorted
h12=1.0;                      #Voltage feedback ratio with input terminal open
h22=0.2;                    #Output admittance, mho

#Calculation
#(i)
Zin=h11-(h12*h21/(h22+(1/rL)));                 #Input impedance, Ω

#(ii)
Av=-h21/(Zin*(h22+(1/rL)));                     #voltage gain,

#Result
print("(i)  The input impedance=%.1fΩ."%Zin );
print("(ii) The voltage gain=1/%d."%(1/Av));

(i)  The input impedance=12.5Ω.
(ii) The voltage gain=1/5.

Example 24.4 : Page number 652-653

In [9]:
#Variable declaration
VCE=10.0;                 #Collector-emitter voltage, V
IC=1.0;                   #Collector current, mA
rL=600.0;                 #a.c load seen by the transistor,Ω

#h-parameters
hie=2000.0;               #Input impedance with output shorted, Ω
hoe=10**-4;             #Output impedance, mho
hre=10**-3;             #Voltage feedback ratio with input terminal open
hfe=50.0;                 #Current gain with output shorted


#Calculation
#(i)
Zin=hie - (hre*hfe/(hoe+(1/rL)));                  #Input impedance, Ω
print("Input impedance=%.0f Ω. \n As second term in the expression of Zin is small compared to first, Zin~hie=%dΩ."%(Zin,hie));

#(ii)
Ai=hfe/(1+hoe*rL);                      #Current gain
print("Current gain=%d"%Ai);
print("if hoe*rL<<1, then Ai~hfe=%d."%hfe);

#(iii)
Av=-hfe/(Zin*(hoe+(1/rL)));                   #Voltage gain
print("Voltage gain=%.1f"%Av);

Input impedance=1972 Ω. 
 As second term in the expression of Zin is small compared to first, Zin~hie=2000Ω.
Current gain=47
if hoe*rL<<1, then Ai~hfe=50.
Voltage gain=-14.4

Example 24.5 : Page number 653

In [11]:
from math import ceil

#Variable declaration
VCE=5.0;                 #Collector-emitter voltage, V
IC=1.0;                   #Collector current, mA
rL=2.0;                 #a.c load seen by the transistor,Ω


#h-parameters
hie=1700.0;               #Input impedance with output shorted, Ω
hoe=6*10**-6;           #Output impedance, mho
hre=1.3*10**-4;         #Voltage feedback ratio with input terminal open
hfe=38.0;                 #Current gain with output shorted

#Calculation
#(i)
Zin=hie - (hre*hfe/(hoe+(1/(rL*1000))));                  #Input impedance, Ω
print("Input impedance=%.0f Ω."%Zin);

#(ii)
Ai=ceil((hfe/round((1+hoe*rL*1000),3))*10)/10;            #Current gain
print("Current gain=%.1f"%Ai);

#(iii)
Av=-hfe/(Zin*(hoe+(1/(rL*1000))));                   #Voltage gain
print("Voltage gain=%.1f"%abs(Av));

Input impedance=1690 Ω.
Current gain=37.6
Voltage gain=44.4

Example 24.6 : Page number 653-654

In [12]:
#Function for calculating parallel resistance
def pr(r1,r2):
    return r1*r2/(r1+r2);


#Variable declaration
RC=10.0;                  #Collector resistance, kΩ
RL=30.0;                  #Load resistance, kΩ
R1=80.0;                  #Resistor R1, kΩ
R2=40.0;                  #Resistor R2, kΩ

#h-parameters
hie=1500.0;               #Input impedance with output shorted, Ω
hoe=5*10**-5;           #Output impedance, mho
hre=4*10**-4;           #Voltage feedback ratio with input terminal open
hfe=50.0;                 #Current gain with output shorted


#Calculation
rL=((RC*RL)/(RC+RL))*1000;             #a.c load as seen by resistance, Ω

#(i)
Zin=round(hie - (hre*hfe/(hoe+(1/rL))),-1);                  #Input impedance, Ω
print("Input impedance=%.0f Ω."%Zin);

#Input impedance of stage=input impedance || bias resistors
Zin_stage=round(pr(pr(R1,R2)*1000,Zin),-1);        #Ω
print("Input impedance of the stage=%.0f Ω."%Zin_stage);

#(ii)
Av=-hfe/(Zin*(hoe+(1/rL)));                   #Voltage gain
print("Voltage gain=%d"%Av);
print("The negative sign represents phase reversal.");


#(iii)
Zout=(1/(hoe-(hfe*hre/hie)))/1000;                     #Output impedance of transistor, kΩ
Zout_stage=pr(Zout,pr(RL,RC));                    #Output impedance of the stage, kΩ
print("Output impedance=%.2f kΩ."%Zout);
print("Output impedance of the stage=%.2f kΩ."%Zout_stage);

Input impedance=1390 Ω.
Input impedance of the stage=1320 Ω.
Voltage gain=-196
The negative sign represents phase reversal.
Output impedance=27.27 kΩ.
Output impedance of the stage=5.88 kΩ.

Example 24.7 : Page number 654

In [14]:
#Function for calculating parallel resistance
def pr(r1,r2):
    return r1*r2/(r1+r2);

#Variable declaration
RC=4.7;                  #Collector resistance, kΩ
RL=10.0;                   #Load resistance, kΩ
R1=33.0;                   #Resistor R1, kΩ
R2=10.0;                   #Resistor R2, kΩ

#h-parameters
hie=1;                  #Input impedance with output shorted, kΩ
hoe=25;                 #Output impedance, μS
hre=2.5*10**-4;         #Voltage feedback ratio with input terminal open
hfe=50;                 #Current gain with output shorted


#Calculation
rL=(RC*RL)/(RC+RL);             #a.c load as seen by resistance, kΩ

Ai=hfe/(1+hoe*10**-6*rL*1000);            #Current gain
print("Current gain=%.1f"%Ai);

Current gain=46.3

Example 24.8 : Page number 654-655

In [16]:
#Variable declaration
R_S=100.0;                    #Series resistance, Ω 

#h-parameters
hie=1.0;                  #Input impedance with output shorted, kΩ
hoe=25.0;                 #Output impedance, μS
hre=2.5*10**-4;         #Voltage feedback ratio with input terminal open
hfe=50.0;                 #Current gain with output shorted


#Calculation
Zout=(1/(hoe*10**-6-(hfe*hre/(hie*1000+R_S))))/1000;                #Output impedance of transistor, kΩ
print("Output impedance=%.1f kΩ."%Zout);

Output impedance=73.3 kΩ.

Example 24.9 : Page number 656

In [17]:
from math import floor

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

#Variable declaration
RC=12.0;                  #Collector resistance, kΩ
RL=15.0;                  #Load resistance, kΩ
R1=50.0;                  #Resistor R1, kΩ
R2=5.0;                   #Resistor R2, kΩ
hie=1.94;               #Input impedance with output shorted, kΩ
hfe=71.0;                 #Current gain with output shorted



#Calculation
rL=(RC*RL)/(RC+RL);             #a.c load as seen by resistance, Ω

#(i)
Zin_base=hie;                                           #Transistor input impedance, kΩ
Zin_circuit=floor(pr(Zin_base,pr(R1,R2))*100)/100;      #Circuit input impedance, kΩ
print("Circuit input impedance=%.2fkΩ"%Zin_circuit);


#(ii)
Av=hfe*rL/hie;                   #Voltage gain
print("Voltage gain=%.0f"%Av);

Circuit input impedance=1.35kΩ
Voltage gain=244

Example 24.10 : Page number 656

In [18]:
from math import sqrt

#Variable declaration
hie_min=600;            #Minimum input impedance with output shorted, Ω
hfe_min=110;            #Minimum current gain with output shorted
hie_max=800;            #Maximum input impedance with output shorted, Ω
hfe_max=140;            #Maximum current gain with output shorted
rL=460;                 #a.c collector load, Ω

#Calculation
hie=round(sqrt(hie_min*hie_max));          #Input impedance with output shorted, Ω
hfe=round(sqrt(hfe_min*hfe_max));          #Current gain with output shorted
Av=hfe*rL/hie;                      #Voltage gain

#Result
print("Voltage gain=%.1f"%Av);

Voltage gain=82.3

Example 24.11 : Page number 658-659

In [20]:
#(a)Variable declaration
Ib=10;              #Base current, μA
Ic=1;               #Collector current, mA
Vbe=10;             #Base-emitter voltage, mV

#Calculation
hie=Vbe*10**-3/(Ib*10**-6);           #Input impedance with output shorted, Ω
hfe=Ic*10**-3/(Ib*10**-6);            #Current gain with output shorted

#(b) Variable declaration
Vbe=0.65;             #Base-emitter voltage, mV
Ic=60;                #Collector current, μA
Vce=1;                #Collector-emitter voltage, V

#Calculation
hre=Vbe*10**-3/Vce;           #Voltage feedback ratio with input terminal open
hoe=Ic/Vce;                   #Output impedance, μmho


#Result
print("hie=%dΩ"%hie);
print("hfe=%d"%hfe);
print("hre=%.2fe–03"%(hre*1000));
print("hoe=%dμmho"%hoe);

hie=1000Ω
hfe=100
hre=0.65e–03
hoe=60μmho