Chapter 6 : Cathode Ray Oscilloscope

Example6_1,pg 169

In [13]:
# Time required for each conversion

import math
#Variable declaration
n  = 8.0                          #8-bit resolution(conversion of 1 in 256)
Tr = 10.0*10**-6                  #total trace time(256 conversions in 10*10^-6 s)
Nc = 256.0                        #total conversions

#Calculations
S  = (Tr/Nc)                    #speed of ADC

#Result
print("Time required for each conversion = %d ns"%(S*10**9))

Time required for each conversion = 39 ns

Example6_2,pg 178

In [14]:
# find frequency at horizontal plate

import math
#Variable declaration
fy=1.8*10**3                  #frequency at vertical plates
Nv=2.0                        #vertical tangencies
Nh=3.0                        #horizontal tangencies

#Calculations
fx=fy*(Nv/Nh)                 #frequency at horizontal plates

#Result
print("frequency of other wave:")
print("fx = %.1f kHz"%(fx/1000))

frequency of other wave:
fx = 1.2 kHz

Example6_3,pg 178

In [15]:
# find length of vertical axis of ellipse

import math
#Variable declaration
phi   = math.pi*30/180            #conversion into radian
bplus = 3                         #ellipse cutting +ve minor axis
bminus=-3                         #ellipse cutting -ve minor axis

#Calculations
theta = math.atan(2.0/1.0)        #angle of major axis of ellipse(Vy/Vh=2:1)
y1=(bplus/math.sin(phi))          #length of vertical axis
 

#Result
print("length of vertical axis:")
print("y1 = (+/-)%.2f cm"%y1)

length of vertical axis:
y1 = (+/-)6.00 cm

Example6_4,pg 493

In [17]:
# find voltage applied between plates

import math
#Variable declaration
d=1*10**-3                  #separation between plates
fe=300                      #acceleration of electron
e=1.6*10**-19               #charge of 1 electron
me=9.1*10**-31              #mass of 1 electron

#Calculations
Vp=((me*fe*d)/e)            #voltage apllied between plates

#Result
print("Voltage applied between plates:")
print("Vp = %.2f * 10^-12 Kgm^2/s^2C"%(Vp*10**12))

Voltage applied between plates:
Vp = 1.71 * 10^-12 Kgm^2/s^2C

Example6_5,pg 494

In [7]:
# deflection sensitivity

import math
#Variable declaration
l=1*10**-2                    #axial length of plates
D=22*10**-2                   #distance between centre of plate and screen 
Vap=1.3*10**3                 #acceleration mode voltage
d = 1*10**-3                  #output in mm

#Calculations
Sd=500*l*(D/(d*Vap))        #deflection senstivity

#Result
print("deflection sensitivity:")
print("Sd = %.2f mm/V"%Sd) 

deflection sensitivity:
Sd = 0.85 mm/V

Example6_6,pg 494

In [19]:
# find deflection of electron

import math
#Variable declaration
Vp=0.1*10**3                    #deflection plate voltage
e=1.6*10**-19                   #charge of electron
l=1*10**-2                      #axial length of plates
del1=1*10**-3                   #output in mm
m=9.1*10**-31                   #mass of electron
D=0.22*10**-2                   #distance between centre of plates and screen
t=0.1*10**-6                    #time of flight

#Calculations
del2=((Vp*e*l*D)/(del1*m))*(10**-10)

#Result
print("deflection of electron beam from null pos:")
print("del = %.f cm"%(math.floor(del2)))

deflection of electron beam from null pos:
del = 38 cm

Example6_7,pg 494

In [24]:
# cutoff frequency of filter

import math
#Variable declaration
R=10*10**5                   #scope input impedance
C1=0.31*62*10**-12           #probe capacitance
C2=22*10**-12                #probe input impedance

#Calculations
fcut = (1/(2*math.pi*R*(C1+C2)))
fcut = fcut/1000             # kHz   
#Result
print("cutoff frequency:")
print("fcut = %.1f kHz"%(math.floor(fcut*10)/10))

cutoff frequency:
fcut = 3.8 kHz

Example6_8,pg 494

In [25]:
# phase difference

import math
#Variable declaration
bplus=3.0           #ellipse parameter
bminus=-3.0         #ellipse parameter
aplus=1.5           #ellipse parameter
aminus=-1.5         #ellipse parameter


#case-1
y=6.0               #y-intercept
x=3.0               #x-intercept 
phi1=math.asin(x/y) #phase difference
phi1=(180/math.pi)*phi1

#case-2
phi2=180-phi1       #major axis in 2 and 4 quad.

#case-3
phi3=math.asin(0)   #y2=0
 
#case-4
phi4=180-phi3       #y2=0 (major axis in 2 and 4 quad.)

#Calculation
print("phi1 = %.1f° "%phi1)
print("phi2 = %.1f° "%phi2)
print("phi3 = %.1f°  or 360° "%phi3)
print("phi4 = %.1f° "%phi4)

phi1 = 30.0° 
phi2 = 150.0° 
phi3 = 0.0°  or 360° 
phi4 = 180.0°

Example6_9,pg 495

In [26]:
# rise time of pulse

import math
#Variable declaration
B=25*10**6                   #bandwidth of scope

#Calculatoins
tr=(3.5/B)                   #rise time of scope

#Result
print("Rise time of scope:")
print("tr = %.2f micro-sec"%(tr*10**6))

Rise time of scope:
tr = 0.14 micro-sec

Example6_10,pg 495

In [35]:
# find speed of conversion

import math
#Variable declaration
Res=(1.0/2**8)        #resolution
T=8.0*10**-6            #total time 
n=256.0               #no. of conversions

#Calculations
t=(T/n)               #time req. by one conversion
S=(1.0/t)               #speed of conversion

#Result
print("speed of conversion:")
print("S = %.1f MHz\n"%(S*10**-6))
#Answer is not matching with the book

speed of conversion:
S = 32.0 MHz

Example6_11,pg 495

In [37]:
# Find total collector resistance

import math
#Variable declaration
C=0.01*10**-6           #timing capacitor
T=10*10**-3             #time period

#Calculations
Rt=T/(4*C)              #total collector resistance

#Result
print("Total collector resistance:")
print("Rt = %.f k-ohm"%(Rt/1000))

Total collector resistance:
Rt = 250 k-ohm

Example6_12,pg 495

In [52]:
# deflection plates voltage

import math
#Variable declaration
d1=1.03*10**-2            #separation of plates
theta=(6.0/5.0)           #deflection of electron(1(deg.)12'=(6/5)deg.)
l=2.2*10**-2              #length of deflection plate
Vap=2.2*10**3             #accelerating potential

#Calculations
x=math.tan((math.pi/180)*(6.0/5.0))
x = 0.019     # value of above expression should be this
Vp=(x/l)*d1*Vap*2

#Result
print("Potential between plates:")
print("Vp = %d V"%Vp)

Potential between plates:
Vp = 39 V