In [1]:

```
import math
#Variables
fo = 22.0 * 10**3 #Frequency (in Hertz)
C = 2.0 * 10**-9 #Capacitance (in Farad)
#Calculation
L = (0.159/fo)**2/C #Inductance (in Henry)
#Result
print "Inductance is ",round(L,3)," H."
```

In [2]:

```
import math
#Variables
fo = 2.2 * 10**6 #Frequency (in Hertz)
#Calculation
f1o = fo * 2**0.5 #New frequency (in Hertz)
#Result
print "It will work at frequency of ",round(f1o * 10**-6,2)," MHz when capacitance is reduced by 50%."
```

In [3]:

```
import math
#Variables
C = 100.0 * 10**-12 #Capacitance (in Farad)
L1 = 30.0 * 10**-6 #Inductance1 (in Henry)
L2 = 1.0 * 10**-8 #Inductance2 (in Henry)
#Calculation
L = L1 + L2 #Net inductance (in Henry)
fo = 1/(2*math.pi*(L * C)**0.5) #Frequency of oscillations (in Hertz)
#Result
print "Frequency of oscillations is ",round(fo * 10**-6,1)," MHz,"
```

In [4]:

```
import math
#Variables
L1 = 1000.0 * 10**-6 #Inductance1 (in Henry)
L2 = 100.0 * 10**-6 #Inductance2 (in Henry)
M = 20.0 * 10**-6 #Mutual Inductance (in Henry)
C = 20.0 * 10**-12 #Capacitance (in Farad)
#Calculation
L = L1 + L2 + 2 * M #Net inductance (in Henry)
fo = 1/(2*math.pi*(L * C)**0.5) #Frequency of oscillations (in Hertz)
#Result
print "Frequency of oscillations is ",round(fo * 10**-6,3)," MHz,"
#Slight variation due to higher precision.
```

In [5]:

```
import math
#Variables
C = 1.0 * 10**-9 #Capacitance (in Farad)
L1 = 4.7 * 10**-3 #Inductance1 (in Henry)
L2 = 47.0 * 10**-6 #Inductance2 (in Henry)
#Calculation
L = L1 + L2 #Net inductance (in Henry)
fo = 1/(2*math.pi*(L * C)**0.5) #Frequency of oscillations (in Hertz)
#Result
print "Frequency of oscillations is ",round(fo * 10**-3,2)," kHz,"
#Slight variation due to higher precision.
```

In [6]:

```
import math
#Variables
L1 = 2.0 * 10**-3 #Inductance1 (in Henry)
L2 = 20.0 * 10**-6 #Inductance2 (in Henry)
fomin = 950.0 * 10**3 #Frequency minimum (in Hertz)
fomax = 2050.0 * 10**3 #Frequency maximum (in Hertz)
#Calculation
L = L1 + L2 #Net inductance (in Henry)
C1 = 1.0/(4 * math.pi**2*(L*fomin**2)) #Capacitance1 (in Farad)
C2 = 1.0/(4 * math.pi**2*(L*fomax**2)) #Capacitance2 (in Farad)
#Result
print "Range of capacitance required is ",round(C2 * 10**12,2)," pF and ",round(C1 * 10**12,1)," pF."
```

In [7]:

```
import math
#Variables
L1 = 0.1 * 10**-3 #Inductance1 (in Henry)
L2 = 10.0 * 10**-6 #Inductance2 (in Henry)
M = 20.0 * 10**-6 #Mutual Inductance (in Hnery)
fo = 4110.0 * 10**3 #Frequency (in Hertz)
#Calculation
L = L1 + L2 + 2*M #Net inductance (in Henry)
C = 1.0/(4 * math.pi**2 * L*fo**2) #Capacitance (in Farad)
beta = L2 / L1 #Feedback ratio
Av = 1/beta #Voltage gain
#Result
print "Capacitance required is ",round(C * 10**12,4)," pF.\nVoltage gain for sustained condition is ",Av,"."
#Calculation error in the value of M used in formula , therefore incorrect value of C.
```

In [8]:

```
import math
#Variables
C1 = 0.001 * 10**-6 #Capacitance (in Farad)
C2 = 0.01 * 10**-6 #Capacitance (in Farad)
L = 5.0 * 10**-6 #Inductance (in Henry)
#Calculation
Av = C2 / C1 #Voltage gain
C = C1 * C2 / (C1 + C2) #Net capacitance (in Farad)
fo = 1 /(2*math.pi*(L * C)**0.5) #Frequency (in Hertz)
#Result
print "Required voltage gain is ",Av,".\nFrequency of oscillation is ",round(fo * 10**-6,2)," Mhz."
#Slight variation due to higher precision.
```

In [9]:

```
import math
#Variables
C1 = 0.1 * 10**-6 #Capacitance (in Farad)
C2 = 1.0 * 10**-6 #Capacitance (in Farad)
L = 470.0 * 10**-6 #Inductance (in Henry)
#Calculation
C = C1 * C2/ (C1 + C2) #Net capacitance (in Farad)
fo = 1 /(2*math.pi*(L * C)**0.5) #Frequency (in Hertz)
#Result
print "Frequency of oscillation is ",round(fo * 10**-3,2)," kHz."
#Slight variation due to higher precision
```

In [10]:

```
import math
#Variables
C1 = 100.0 * 10**-12 #Capacitance (in Farad)
C2 = 7500.0 * 10**-12 #Capacitance (in Farad)
fomin = 950.0 * 10**3 #Frequency minimum (in Hertz)
fomax = 2050.0 * 10**3 #Frequency maximum (in Hertz)
#Calculation
C = C1 * C2/ (C1 + C2) #Net capacitance (in Farad)
L1 = 1.0/(4 * math.pi**2*(C*fomin**2)) #Inductance1 (in Henry)
L2 = 1.0/(4 * math.pi**2*(C*fomax**2)) #Inductance2 (in Henry)
#Result
print "The range of inductance required is from ",round(L2 * 10**6)," micro-Henry to ",round(L1 * 10**6)," micro-Henry."
```

In [8]:

```
import math
#Variables
fo = 450.0 * 10**3 #Frequency(in Hertz)
#Let us assume
C1 = C2 = C = 10.0 * 10**-6 #Capacitance (in Farad)
C21 = 2 * C2 #Capacitance (in Farad)
#Calculation
fo1 = fo * (3.0/4.0)**0.5 #New Frequency (in Hertz)
#Result
print "The oscillation frequency if C2 is doubled is ",round(fo1 * 10**-3,1)," kHz."
```

In [12]:

```
import math
#Variables
C1 = 0.1 * 10**-6 #Capacitance (in Farad)
C2 = 1.0 * 10**-6 #Capacitance (in Farad)
C3 = 100.0 * 10**-12 #Capacitance (in Farad)
L = 470.0 * 10**-6 #Inductance (in Henry)
#Calculation
C = (1.0/C1 + 1.0/C2 +1.0/C3)**-1 #Capacitance (in Farad)
fo = 1/(2*math.pi *(L*C)**0.5) #Frequency (in Hertz)
#Result
print "Frequency of oscillation is ",round(fo * 10**-3,1)," kHz."
```

In [13]:

```
import math
#Variables
L = 0.33 #Inductance (in Henry)
C1 = 0.065 * 10**-12 #Capacitance (in Farad)
C2 = 1.0 * 10**-12 #Capacitance (in Farad)
R = 5.5 * 10**3 #Resistance (in ohm)
#Calculation
fs = 1/(2*math.pi*(L*C1)**0.5) #Series Resonant frequency (in Hertz)
Qfactor = 2*math.pi*fs*L/R #Q-factor
#Result
print "Series resonant frequency is ",round(fs * 10**-6,2)," MHz.\nQ-factor of the crystal is ",round(Qfactor,1),"."
#Slight variation due to higher precision
```

In [14]:

```
import math
#Variables
gm = 5000.0 * 10**-6 #Transconductance (in mho)
rd = 40.0 * 10**3 #Resistance (in ohm)
R = 10.0 * 10**3 #Resistance (in ohm)
fo = 1.0 * 10**3 #Frequency (in Hertz)
Av = 40.0 #Voltage gain
#Calculation
C = 1/(2*math.pi*(R)*6**0.5*fo) #Capacitance (in Farad)
rL = Av / gm #a.c. load resistance (in ohm)
RD = (rL * rd)/(rd-rL) #Drain resistance (in ohm)
#Result
print "Value of capacitor is ",round(C* 10**6,5)," micro-Farad."
print "Value of drain resistance is ",RD * 10**-3," kilo-ohm."
```

In [15]:

```
import math
#Variables
fo = 2.0 * 10**3 #Frequency (in Hertz)
mu = 50.0 #Amplification factor
rd = 5.0 * 10**3 #Resistance (in ohm)
Av = 40.0 #Voltage gain
R = 10.0 * 10**3 #Resistance (in ohm)
#Calculation
gm = mu / rd #Transconductance (in mho)
rL = Av/ gm #a.c. load resistance (in ohm)
RD = (rL * rd)/(rd-rL) #Drain resistance (in ohm)
RC = 0.065/(fo) #RC product (in second)
C = RC / R #Capacitance (in Farad)
#Result
print "Maximum value of RD is ",RD * 10**-3," kilo-ohm.\nValue of the RC product is ",RC," s.\nValue of R is ",R * 10**-3," kilo-ohm.\nValue of C is ",C * 10**9," nF."
```

In [16]:

```
import math
#Variables
fo = 2.0 * 10**3 #Frequency (in Hertz)
hie = 2.0 * 10**3 #hie (in ohm)
R1 = 20.0 * 10**3 #Resistance (in ohm)
R2 = 80.0 * 10**3 #Resistance (in ohm)
RC = 10.0 * 10**3 #Collector Resistance (in ohm)
R = 8.0 * 10**3 #Resistance (in ohm)
#Calculation
C = 1/(2*math.pi*R)*(1/(6 + 4*RC/R)**0.5)/fo #Capacitance (in Farad)
hfe = 23 + 29 * R/RC + 4* RC /R #Current gain
Ri = (1/R1 + 1/R2 + 1/hie)**-1 #Input resistance (in ohm)
R3 = R - Ri #Feedback resitor (in ohm)
#Result
print "Value of capacaitor C is ",round(C * 10**6,3)," micro-Farad.\nValue of transistor gain is hfe >= ",hfe,".\nValue of feedback resistor R3 is ",round(R3 * 10**-3,1)," kilo-ohm."
```

In [17]:

```
import math
#Variables
fo = 10.0 * 10**3 #Frequency (in Hertz)
R = 100.0 * 10**3 #Resistance (in ohm)
#Calculation
C = 1/(2*math.pi*R*fo) #Capacitance (in Farad)
#Result
print "Value of the capacitor C is ",round(C * 10**12)," pico-Farad."
```