# Chapter 25 , Hybrid Parameters¶

## Example 25.1 , Page Number 626¶

In [1]:
import math

#Variables

R1 = 6.0                     #Resistance (in ohm)
R2 = 4.0                     #Resistance (in ohm)
R3 = 4.0                     #Resistance (in ohm)

#Calculation
#Let i1 = 10 A and v2 = 10 V.
i1 = 10.0                    #Assumed current (in Ampere)
v2 = 10.0                    #Assumed voltage (in volts)
#Parameters h11 and h21

h11 = R1 + R2 * R3/(R2 + R3) #Input resistance looking from the input terminals (in ohm)
i2 = -i1 / 2                 #Current2 (in Ampere)
h21 = i2/i1                  #h21

#Parameters h12 and h22

v1 = v2/2                    #Voltage1 (in volts)
h12 = v1 / v2                #h12
rnet = R2 + R3               #Output resistance (in ohm)
h22 = 1/rnet                 #h22 (in mhos)

#Result

print "h11 : ",h11,"\nh21 : ",h21,"\nh12 : ",h12,"\nh22 : ",h22

h11 :  8.0
h21 :  -0.5
h12 :  0.5
h22 :  0.125


## Example 25.2 , Page Number 635¶

In [2]:
import math

#Variables

hie = 1.0 * 10**3                      #hie (in ohm)
hre = 1.0 * 10**-4                     #hre
hoe = 100.0 * 10**-6                   #hoe (in mho)
RC = 1.0 * 10**3                       #Collector resistance (in ohm)
RS = 1000.0                            #Source resistance (in ohm)
hfe = beta = 50.0                      #Common emitter current gain

#Calculation

rL = RC                                #a.c. load resistance (in ohm)
Ai = -hfe /(1 + hoe * rL)              #Current gain of a transistor
Ri = hie + hre * Ai * rL               #Input resistance looking directly into the base (in ohm)
Ris = Ri                               #Iput resistance of the amplified stage (in ohm)
dh = hie * hoe - hre * hfe             #Change in h
Ro = (RS + hie)/(RS * hoe + dh)        #Output resistance looking directly into collector (in ohm)
Ros = Ro * rL /(Ro + rL)               #Output resistance of the amplified stage (in ohm)
Ais = Ai * RS / (RS + Ris)             #Current gain of amplified stage
Av = Ai * rL / Ri                      #Voltage gain of transistor
Avs = Av * Ris / (RS + Ris)            #Voltage gain of amplified stage

#Result

print "Input resistance of the amplifier stage is ",round(Ris)," ohm.\nOutput resistance of amplifier stage is ",round(Ros)," ohm.\nCurrent gain of amplified stage is ",round(Ais,1),"\nVoltage gain of amplifier stage is ",round(Avs,1),"."

Input resistance of the amplifier stage is  995.0  ohm.
Output resistance of amplifier stage is  911.0  ohm.
Current gain of amplified stage is  -22.8
Voltage gain of amplifier stage is  -22.8 .


## Example 25.3 , Page Number 637¶

In [3]:
import math

#Variables

hie = 1.1 * 10**3                      #hie (in ohm)
hre = 2.5 * 10**-4                     #hre
hoe = 25.0 * 10**-6                    #hoe (in mho)
RS = 1000.0                            #Source resistance (in ohm)
hfe = beta = 50.0                      #Common emitter current gain
rL = 1000.0                            #ac.c load resistance (in ohm)

#Calculation

Ai = hfe /(1 + hoe * rL)               #Current gain of a transistor
Ri = hie + hre * Ai * rL               #Input impedance (in ohm)
Av = Ai * rL / Ri                      #Voltage gain

#Result

print "Current gain is ",round(Ai,2),"\nInput impedance is ",round(Ri,1),"\nVoltage gain is ",round(Av,2)

Current gain is  48.78
Input impedance is  1112.2
Voltage gain is  43.86


## Example 25.4 , Page Number 639¶

In [4]:
import math

#Variables

RC = 4.0 * 10**3              #Collector resistance (in ohm)
RB = 40.0 * 10**3             #Base resistance (in ohm)
RS = 10.0 * 10**3             #Source resistance (in ohm)
hie = 1100.0                  #hie (in ohm)
hfe = 50.0                    #hfe
hre = hoe = dh = 0            #hre and hoe

#Calculation

RB2 = RB                      #Resistance (in kilo-ohm)
rL = RC * RB2 /(RC +RB2)      #a.c. load resistance (in ohm)
Ai = -hfe                     #Current gain
Ri = hie                      #Input resistance of the amplifier looking into the base (in ohm)
Av = Ai * rL / Ri             #Voltage gain
RB1 = RB/(1 - Av)             #Resistance (in ohm)
Ris = Ri * RB1 / (Ri + RB1)   #Input resistance  looking from source terminals (in ohm)
Ro = "infinite"               #Output resistance (in ohm)
Ros = rL                      #Output resistance of the stage (in ohm)
Avs = Av * Ris / (RS + Ris)   #Voltage gain of the stage

#Result

print "Voltage gain is ",round(Avs,1),".\nInput resistance is ",round(Ris)," ohm.\nOutput resistance is ",round(Ros)," ohm."

#Slight variation due to higher precision.

Voltage gain is  -3.2 .
Input resistance is  197.0  ohm.
Output resistance is  3636.0  ohm.


## Example 25.5 , Page Number 640¶

In [1]:
import math

#Variables

hie = 1.1 * 10**3                       #hie (in ohm)
hre = 2.5 * 10**-4                      #hre
hoe = 25.0 * 10**-6                     #hoe (in mho)
RS = 10000.0                            #Source resistance (in ohm)
hfe = beta = 50.0                       #Common emitter current gain
rL = 1000.0                             #ac.c load resistance (in ohm)
RB = 200.0 * 10**3                      #Feedback resistor (in ohm)
RC = 5.0 * 10**3                        #Collector resistance (in ohm)

#Calculation

rL = RC * RB / (RC + RB)                #a.c. load resistance (in ohm)
Ai = hfe /(1 + hoe * rL)                #Current gain
Ri = hie + hre * Ai * rL                #Input resistance of the amplifier looking into the base (in ohm)
Av = Ai * rL / Ri                       #Voltage gain
RB1 = RB/(1 - (-17.4))                    #Resistance (in ohm)
Ris = Ri * RB1 / (Ri + RB1)             #Input resistance  looking from source terminals (in ohm)
Avs = Av * Ris / (RS + Ris)             #Voltage gain of the stage

#Result

print "Ai is ",round(Ai,2),"\nAv is ",round(Av,2),"\nAvs is ",round(Avs,1),"\nRi is ",round(Ri*10**-3,3)," kilo-ohm."

Ai is  44.57
Av is  188.32
Avs is  17.8
Ri is  1.154  kilo-ohm.


## Example 25.6 , Page Number 643¶

In [6]:
import math

#Variables

hib = 28.0                   #hib (in ohm)
hfb = -0.98                  #hfb
hrb = 5.0 * 10**-4           #hrb
hob = 0.34 * 10**-6          #hoh (in Siemen)
rL = 1.2 * 10**3             #a.c. load resistance (in ohm)
RS = 0.0                     #Source resistance (in ohm)

#Calculation

Ai = -(hfb/(1 + hob * rL))   #Current gain
Ri = hib + hrb * Ai * rL     #Input resistance (in ohm)
dh = hib * hob - hrb * hfb   #change in h
Ro = (RS + hib)/(RS*hib + dh)#Output resistance (in ohm)
Av = Ai * rL / Ri            #Voltage gain

#Result

print "The value of input resistance is ",round(Ri,1)," ohm.\nThe value of output resistance is ",round(Ro * 10**-3)," kilo-ohm.\nThe value of current gain is ",round(Ai,2)," .\nThe value of voltage gain is ",round(Av)," ."

The value of input resistance is  28.6  ohm.
The value of output resistance is  56.0  kilo-ohm.
The value of current gain is  0.98  .
The value of voltage gain is  41.0  .


## Example 25.7 , Page Number 644¶

In [7]:
import math

#Variables

hic = 2.0 * 10**3                           #hic (in ohm)
hfc = -51.0                                 #hfe
hrc = 1.0                                   #hrc
hoc = 25.0 * 10**-6                         #hoc (in mho)
rL = RE = 5.0 * 10**3                       #a.c. load resistance (in ohm)
RS = 1.0 * 10**3                            #Source resistance (in ohm)
R1 = R2 = 10.0 * 10**3                      #Resistance (in ohm)

#Calculation

Ai = -hfc / (1 + hoc * rL)                  #Current gain
Ri = hic + hrc * Ai * rL                    #Input resistance (in ohm)
Ris = (R1*R2*Ri)/(Ri*R1 + Ri*R2 + R1*R2)    #Input resistance of the amplified stage (in ohm)
Ro = -(RS + hic)/hfc                        #Output resistance (in ohm)
Ros = Ro * RE / (Ro + RE)                   #Input resistance of the amplified stage (in ohm)
Ais = Ai * RS / (RS + Ris)                  #Current gain of amplified stage
Av = Ai * rL / Ri                           #Voltage gain
Avs = Av * Ris / (RS + Ris)                 #Voltage gain of amplified stage

#Result

print "The value of input resistance of amplified stage is ",round(Ris)," ohm.\nThe value of output resistance of amplified stage is ",round(abs(Ros),1)," kilo-ohm.\nThe value of current gain of amplified stage is ",round(Ais,1)," .\nThe value of voltage gain of amplified stage is ",round(Avs,3)," ."

#Slight variation due to higher precision.

The value of input resistance of amplified stage is  4893.0  ohm.
The value of output resistance of amplified stage is  58.1  kilo-ohm.
The value of current gain of amplified stage is  7.7  .
The value of voltage gain of amplified stage is  0.823  .


## Example 25.8 , Page Number 646¶

In [8]:
import math

#Variables

hie = 1500.0                                #hie (in ohm)
hfe = 50.0                                  #hfe
hre = 50.0 * 10**-4                         #hre
hoe = 20.0 * 10**-6                         #hoe
R1 = 20.0 * 10**3                           #Resistance (in ohm)
R2 = 10.0 * 10**3                           #Resistance (in ohm)
RC = 5.0 * 10**3                            #Collector resistance (in ohm)
RE = 1.0 * 10**3                            #Emitter resistance (in ohm)
RL = 10.0 * 10**3                           #Load resistance (in ohm)
RS = 0                                      #Source resistance (in ohm)

#Calculation

Ai = -hfe
rL = RC * RL /(RC + RL)                     #a.c. load resistance (in ohm)
Ri = hie                                    #Input resistance (in ohm)
Ris = (R1*R2*Ri)/(Ri*R1 + Ri*R2 + R1*R2)    #Input resistance of the amplified stage (in ohm)
Ro = 1 / hoe                                #Output resistance (in ohm)
Ros = Ro * rL /(Ro + rL)                    #Output resistance of the stage (in ohm)
Av = Ai * rL / Ri                           #Voltage gain
Avs = Av * Ris / (RS + Ris)                 #Voltage gain of the stage
Ais = Ai                                    #Current gain of the stage

#Result

print "Input resistance of the stage is ",round(Ris * 10**-3,2)," kilo-ohm.\nOutput resistance of the stage is ",round(Ros * 10**-3,1)," kilo-ohm.\nVoltage gain of the stage is ",round(Avs)," .\nCurrent gain of the stage is ",Ai," ."

#Slight variation due to higher precision.

Input resistance of the stage is  1.22  kilo-ohm.
Output resistance of the stage is  3.1  kilo-ohm.
Voltage gain of the stage is  -111.0  .
Current gain of the stage is  -50.0  .


## Example 25.9 , Page Number 647¶

In [9]:
import math

#Variables

RC = 12.0 * 10**3                       #Collector resistance (in ohm)
RL = 4.7 * 10**3                        #Load resistance (in ohm)
R1 = 33.0 * 10**3                       #Resistance (in ohm)
R2 = 4.7 * 10**3                        #Resistance (in ohm)
IC = 1.0 * 10**-3                       #Collector current (in Ampere)
hiemin = 1.0 * 10**3                    #hie minimum (in ohm)
hiemax = 5.0 * 10**3                    #hie maximum (in ohm)
hfemin = 70.0                           #Current gain minimum
hfemax = 350.0                          #Current gain maximum

#Calculation

hie = (hiemin * hiemax)**0.5            #hie (in ohm)
hfe = (hfemin * hfemax)**0.5            #current gain
Ri = hie                                #input resistance (in ohm)
Ris = (R1*R2*Ri)/(Ri*R1+Ri*R2+R1*R2)    #Input resistance of the amplified stage (in ohm)
Ai = hfe                                #Current gain of transistor
rL = RC * RL / (RC + RL)                #a.c. load resistance (in ohm)
Avs = Av = Ai*rL / Ri                   #overall voltage gain

#Result

print "Input impedance is ",round(Ris * 10**-3,2)," kilo-ohm.\nOverall voltage gain is ",round(Avs,1),"."

#Calculation error in book for hfe.

Input impedance is  1.45  kilo-ohm.
Overall voltage gain is  236.4 .


## Example 25.10 , Page Number 648¶

In [10]:
import math

#Variables

RB = 330.0 * 10**3                    #Base resistance (in ohm)
RC = 2.7 * 10**3                      #Collector resistance (in ohm)
hfe = 120.0                           #current gain
hie = 1.175 * 10**3                   #hie (in ohm)
hoe = 20 * 10**-6                     #hoe (in Ampere per volt)

#Calculation

Ri = hie                              #Input resistance of transistor (in ohm)
Ris = hie * RB /(hie + RB)            #Input resistance of the circuit (in ohm)
Ro = 1 / hoe                          #Output resistance of transistor (in ohm)
Ros = Ro * RC / (Ro + RC)             #Output resistance of the circuit (in ohm)
Ai = hfe                              #Current gain of the circuit
Avs = Ai * RC / Ri                    #Overall voltage gain

#Result

print "Input resistance of the circuit is ",round(Ris * 10**-3,2)," kilo-ohm.\nOutput resistance of the circuit is ",round(Ros * 10**-3,2)," kilo-ohm.\nCurrent gain of the circuit is ",Ai,".\nVoltage gain of the circuit is ",round(Avs,1),"."

Input resistance of the circuit is  1.17  kilo-ohm.
Output resistance of the circuit is  2.56  kilo-ohm.
Current gain of the circuit is  120.0 .
Voltage gain of the circuit is  275.7 .


## Example 25.11 , Page Number 649¶

In [11]:
import math

#Variables

hfe = 50.0                  #Current gain

#Calculation

hfb = -hfe / (1 + hfe)      #hfb
hfc = -(1 + hfe)            #hfc

#Result

print "Value of hfb = ",round(hfb,2),".\nValue of hfc = ",hfc,"."

Value of hfb =  -0.98 .
Value of hfc =  -51.0 .


## Example 25.12 , Page Number 649¶

In [12]:
import math

#Variables

hie = 1100.0                          #hie (in ohm)
hre = 2.5 * 10**-4                    #hre
hfe = 50.0                            #Current gain
hoe = 24.0 * 10**-6                   #hoe (in Ampere per volt)
rL = RL = 10.0 * 10**3                #Load resistance (in ohm)
RS = 1.0 * 10**3                      #Source resistance (in ohm)

#Calculation

hic = hie                             #hic (in ohm)
hrc = (1 - hre)                       #hrc
hfc = -(1 + hfe)                      #hfc
Ai = -(hfc/(1 + hoe * rL))            #Current gain
Ri = hic + hrc * Ai * rL              #Input resistance (in ohm)
Av = Ai * rL / Ri                     #Voltage gain

#Result

print "Current gain is ",round(Ai,1),".\nInput resistance is ",round(Ri * 10**-3,1)," kilo-ohm.\nVoltage gain is ",round(Av,3),"."

#Slight variation due to higher precision.

Current gain is  41.1 .
Input resistance is  412.3  kilo-ohm.
Voltage gain is  0.998 .