Chapter 14 : Stability and Oscillators¶

Example 14.1a, Page No 529¶

In [5]:
import math
#initialisation of variables
s1 = -46.2*(10**5)
s2 = -45.9*(10**6)
s3 = -11.4*(10**8)
s4 = -30.4*(10**8)

#Calculations
#Zeros
s5 = 16.65*(10**9)
s6 = 15.4*(10**8)
s7 = -22.55*(10**8)
s = 6.28*(10**6)
B = 0.040
Ai = 410.0           #Gain
j=1

n = s2/s1
print("The value of n= %.2f " %n)
Q = (n*(1+(B*Ai)))**0.5/(n+1)
print("The value of Q = %.2f " %Q)
k = 1.0/(2*Q)
print("The value of K = %.2f " %k)

s1f = s1*((n+1)/2)*(1-j*((4*Q*Q)-1)**0.5)

#Results
print("The first pole is = %.2f rad/s " %s1f)
s2f = s1*((n+1)/2)*(1+j*((4*Q*Q)-1)**0.5)
print("The second pole is = %.2f rad/s" %s2f)

The value of n= 9.94
The value of Q = 1.20
The value of K = 0.42
The first pole is = 29982570.54 rad/s
The second pole is = -80502570.54 rad/s


Example 14.2a, Page No 529¶

In [6]:
import math
#initialisation of variables
Q=1.20
w1=45.9
w2=4.62
k=0.417
w0=Q*(w1+w2)

#Calculations
fpeak=(w0/6.28)*math.sqrt(1.0-(2.0*(k**2.0)))
m=1.0/(2.0*k*(math.sqrt(1-(2.0*(k**2.0)))))
m2=20*math.log(m,10)

#Results
print("The value of fpeak = %.2f MHZ" %fpeak)
print("The value of overshoot = %.2f dB" %m)

The value of fpeak = 7.80 MHZ
The value of overshoot = 1.48 dB