chapter09:Solid State Microwave devices¶

Example 9.1, Page number 411¶

In [1]:
#Calculate Frequncy of IMPATT diode
#Variable declaration
L = 2*10**-6          #drift length(m)
Vd = 10**7*10**-2      #dfrift velocit(m/s)

#Calculations
f = Vd/(2*L)

#Results
print "Frequncy of IMPATT diode is",round((f/1E+9),2),"GHz"

Frequncy of IMPATT diode is 25.0 GHz


Example 9.2, Page number 411¶

In [2]:
#Calculate threshold electric field
#Variable declaration
f = 10*10**9         #operating frequency(Hz)
L = 75*10**-6        #device length(m)
V = 25.              #voltage pulse amplified(V)

#Calculations
Eth = V/(L)

#Result
print "The threshold electric field is",round((Eth/1E+5),2),"KV/cm"

The threshold electric field is 3.33 KV/cm


Example 9.3, Page number 411¶

In [3]:
#Calculate Power gain,Power gain as USB converter
#chapter-9 page 411 example 9.3
import math
fs=2.*10.**9.;#Signal Frequency in Hz
fp=12.*10.**9.#Pump Frequency in Hz
Ri=16.;#O/P resistance of signal generator in ohms
Rs=1000.;#On types resistance of signal generator in ohms

#CALCULATION
P=10*math.log10((fp-fs)/fs);#Power gain in dB
Pusb=10*math.log10((fp+fs)/fs);#Power gain as USB converter in dB

#OUTPUT
print '%s %.2f %s %s %.2f %s' %('Power gain is P=',P,'dB','\nPower gain as USB converter is Pusb=',Pusb,'dB')

#Note: Answer given in textbook is wrong Check it once..
#Correct answers are Power gain is P=6.99 dB
#Power gain as USB converter is Pusb=8.45 dB

Power gain is P= 6.99 dB
Power gain as USB converter is Pusb= 8.45 dB


Example 9.4, Page number 411¶

In [4]:
#Calculate Critical voltage ,Breakdown voltage,Breakdown electric field
#Variable declaration
Es = 12.5             #relative dielectric constant
N = 3.2*10**22        #donor concentration(/m**3)
L = 8*10**-6          #length(m)
Eo = 8.854*10**-12    #dielectric constant
q = 1.6*10**-19

#Calculations
#Part a
Vc = (q*N*L**2)/(2*Eo*Es)

#Part b
Vbd = 2*Vc

#Part c
Ebd = Vbd/L

#Results
print "Critical voltage =",round((Vc/1E+3),2),"kV"
print "Breakdown voltage =",round((Vbd/1E+3),2),"kV"
print "Breakdown electric field =",round((Ebd/1E+8),2),"*10**8 V/cm"

Critical voltage = 1.48 kV
Breakdown voltage = 2.96 kV
Breakdown electric field = 3.7 *10**8 V/cm


Example 9.5, Page number 412¶

In [5]:
#Calculate avalanche zone velocity
#Variable declaration
Na = 2.5*10**16       #doping concentration(/cm**3)
J = 33*10**3          #current density(A/cm**2)
q = 1.6*10**-19

#Calculations
Vz = J/(q*Na)

#Results
print "The avalanche zone velocity is",round((Vz/1E+6),2),"*10**6 cm/s"

The avalanche zone velocity is 8.25 *10**6 cm/s


Example 9.6, Page number 412¶

In [6]:
#Calculate power gain
#Variable declaration
Rd = -25      #negative resistance(Ohms)

#Calculations
G = ((Rd-Rl)/(Rd+Rl))**2

#Results
print "Power gain =",G

Power gain = 9


Example 9.7, Page number 412¶

In [8]:
#Calculate minimum voltage required
#chapter-9 page 412 example 9.7
#For a Gunn Diode
L=5.*10.**(-4.);#Drift Length in cm
Vg=3300.;#Voltage gradient in V/cm [Vg>3.3 kV/cm]

#CALCULATION
Vmin=Vg*L;#Minimum Voltage needed to initiate Gunn effect in volts

#OUTPUT
print '%s %.2f %s' %('\nMinimum Voltage needed to initiate Gunn effect is Vmin=',Vmin,'volts');

Minimum Voltage needed to initiate Gunn effect is Vmin= 1.65 volts


Example 9.8, Page number 412¶

In [9]:
#calculate Natural(Rational) Frequency,Critical Voltage of the diode
#chapter-9 page 412 example 9.8
#For a Gunn Diode
L=20.*10.**(-4.);#Active Length in cm
Vd=2.*10.**7.;#Drift Velocity of Electrons in cm/sec
Ec=3.3*10.**3.;#Criticl Field for GaAs in V/cm

#CALCULATION
fn=(Vd/L)/10.**9.;#Natural(Rational) Frequency in GHz
Vc=L*Ec;#Critical Voltage of the diode in volts

#OUTPUT
print '%s %.f %s %s %.1f %s ' %('\nNatural(Rational) Frequency is fn=',fn,'GHz','\nCritical Voltage of the diode is Vc=',Vc,'volts');

Natural(Rational) Frequency is fn= 10 GHz
Critical Voltage of the diode is Vc= 6.6 volts


Example 9.9, Page number 412¶

In [10]:
#Calculate the resonant frequency,Efficiency
from math import pi,sqrt

#Variable declaration
Cj = 0.5*10**-12       #capacitance of IMPATT diode(F)
Lp = 0.5*10**-9        #Inductance of IMPATT diode(H)
Vbd = 100              #breakdown voltage(V)
Ib = 100*10**-3        #dc bias current(A)
Ip = 0.8               #peak current(A)

#Calculations
f = 1/(2*pi*sqrt(Lp*Cj))
Pl = ((Ip**2)*Rl)/2
Pdc = Vbd*Ib
N = (Pl/Pdc)*100

#Results
print "The resonant frequency is",round((f/1E+9)),"GHz"
print "Efficiency is",round(N,2),"%"

The resonant frequency is 10.0 GHz
Efficiency is 6.4 %


Example 9.10, Page number 413¶

In [11]:
#Calculate Drift time of the carrier,Operating frequency of diode

#Variable declaration
Vd = 10**5     #carrier dirft velocity(cm/s)
L = 2*10**-6   #drift length(m)

#Calculations
#Part a
tou = L/Vd

#Part b
f = 1/(2*tou)

#Results
print "Drift time of the carrier is",round((tou/1E-11),2),"*10**-11 sec"
print "Operating frequency of diode is",(f/1E+9),"GHz"

Drift time of the carrier is 2.0 *10**-11 sec
Operating frequency of diode is 25.0 GHz


Example 9.11, Page number 413¶

In [12]:
#Calculate Breakdown voltage,Breakdown electric field

#Variable declaration
Er = 11.8          #relative dielectric constant
N = 3*10**21       #donor concentration(m^-3)
L = 6.2*10**-6     #Si length(m)
q = 1.6*10**-19    #charge of an electron(C)
Eo = 8.854*10**-12 #dielctric constant

#Calculations
#Part a
Vbd = (q*N*L**2)/(Eo*Er)

#Part b
Ebd = Vbd/L

#Results
print "Breakdown voltage =",round(Vbd,1),"V"
print "Breakdown electric field =",round((Ebd/1E+7),2),"*10**7 V/m"

Breakdown voltage = 176.6 V
Breakdown electric field = 2.85 *10**7 V/m


Example 9.12, Page number 413¶

In [13]:
#Calculate Maximum power gain,Noise figure,Bandwidth

import math

#Variable declaration
rQ = 8.        #figure of merit
fo_fs = 8.     #ratio of o/p to i/p frequency
Td = 300.      #diode temperatur(K)
To = 300.      #ambient temperature(K)
r = 0.2

#Calculations
#Part a
X = rQ**2/fo_fs
G = (X/((1+math.sqrt(1+X))**2))*fo_fs
g = 10*math.log10(G)

#Part b
F = 1+((2*Td)/To)*((1/rQ)+(1/rQ**2))
f = 10*math.log10(F)

#Part c
BW = 2*r*math.sqrt(fo_fs)

#Results
print "Maximum power gain =",round(g,2),"dB"
print "Noise figure =",round(f,2),"dB"
print "Bandwidth =",round(BW,2)

Maximum power gain = 6.02 dB
Noise figure = 1.08 dB
Bandwidth = 1.13


Example 9.13, Page number 414¶

In [14]:
#Calculate Equivalent noise resistance,Gain,Noise figure,Bandwidth
#Variable declaration
import math
fs = 2*10**9       #signal frequency(Hz)
fp = 12*10**9      #amplifier frquency(Hz)
fi = 10*10**9      #input frequency(Hz)
fd = 5*10**9       #diode frequency(Hz)
Ri = 1*10**3       #input resistance(Ohms)
Rg = 1*10**3       #gate resistance(Ohms)
RTs = 1*10**3      #resistance(Ohms)
RTi = 1*10**3      #resistance(Ohms)
r = 0.35           #resistane(Ohms)
rQ = 10.            #figure of merit
rd = 300           #diode temperature(K)
C = 0.01*10**-12   #capacitance(F)
Td = 300
To = 300

#Calculations
#Part a
ws = 2*math.pi*fs
wi = 2*math.pi*fi
R = (r**2)/(ws*wi*C**2*RTi)
a = R/RTs

#Part b
G = (4*fi*Rg*Ri*a)/(fs*RTs*RTi*(1-a)**2)
g = 10*math.log10(G)

#Part c
F = 1+((2*Td)/To)*((1/rQ)+(1/rQ**2))
f = 10*math.log10(F)

#Part d
BW = (r/2)*math.sqrt(fd/(fs*G))

#Results
print "Equivalent noise resistance =",round(a,2),"Ohms"
print "Gain =",round(g,1),"dB"
print "Noise figure =",round(f,2),"dB"
print "Bandwidth =",round(BW,3),"(Calculation error in the textbook)"

Equivalent noise resistance = 1.55 Ohms
Gain = 20.1 dB
Noise figure = 0.86 dB
Bandwidth = 0.027 (Calculation error in the textbook)