Wien Bridge Oscillator¶

A Wien bridge oscillator is a type of electronic oscillator that generates sine waves. See https://en.wikipedia.org/wiki/Wien_bridge_oscillator.

Design calculations for Wien Bridge Oscillator. See page 21-1 of Handbook of Operational Amplifier Circuit Design, by David F. Stout and edited by Milton Kaufman. Reference designators match figure 21.1.

The Opamp used in the implementation is a LM324, from the TI datasheet:

Input bias current: 20nA
output offset voltage: 1.4 volts due to 20nA input bias current.  1.4 volts in the test condition measured under open loop conditions. 
unity gain frequency: 1.2 MHz

Notes:

The output offset voltage in the datasheet didn't seem to make sense when looking at the reference design, which used 0.1 volts as the output offset voltage.
The design equations suggest a value for R6 of 100 times R2. The reference design has this part as a pot. A value of 4.5 times R2 makes the spice simulation work better.

from math import *

# opamp parameters
Ib1 = 20.0e-9 #input bias current of A1
dVo_max = 0.1   #output offset due to bias current of A1
fu2 = 1.2e6  #unity gain cross over freuqncy of A1

#frequency of oscillation
fo = 1.0  #design frequency at mid band

# step 1: compute a value for R1_max
R1_max = dVo_max/Ib1
print('R1_max = {:.2f}'.format(R1_max))

R1_max = 5000000.00

#step 2: determine other resistor values
R2 = sqrt(R1_max)
R4 = R2
R5 = R2
R6 = R2
R3 = 1.1*R2
R6 = 4.5*R3    # 100.0*R3
# display resistor values
#print('R1 = {:.2f}'.format(R1))
print('R2 = {:.2f}'.format(R2))
print('R3 = {:.2f}'.format(R3))
print('R4 = {:.2f}'.format(R4))
print('R5 = {:.2f}'.format(R5))
print('R6 = {:.2f}'.format(R6))

R2 = 2236.07
R3 = 2459.67
R4 = 2236.07
R5 = 2236.07
R6 = 11068.54

#step 3: determine nominal values for C1 and C2
C1 = 1.0/(2.0*pi*fo*R2)
C2 = C1
#display capacitor values
print('C1 = {:.3e}'.format(C1))
print('C2 = {:.3e}'.format(C2))

C1 = 7.118e-05
C2 = 7.118e-05

#step 4: compute fixed portion of R1
R1_min = (R4**2.0/(4.0*pi**2.0*R2*C1*C2*fu2**2.0))**0.3333
print('R1_min = {:.2f}'.format(R1_min))

R1_min = 0.20

#step 5: compute frequency limits
fo_max = (fu2/(4.0*pi**2.0*R2*R4*C1*C2))**0.333
fo_min = (1/(2.0*pi))*(Ib1/(R2*C1*C2*dVo_max))**0.5
print('fo_min = {:f}'.format(fo_min))
print('fo_max = {:f}'.format(fo_max))

fo_min = 0.021147
fo_max = 105.771181

#step 6, oscillator frequency is recalculated
fo_min = 1/((2*pi)*(R1_max*R2*C1*C2)**0.5)
print('fo_min = {:f}'.format(fo_min))
R1_nom = R2
fo_nom = 1/((2*pi)*(R1_nom*R2*C1*C2)**0.5)
print('fo_nom = {:f}'.format(fo_nom))
R1_mid = (R1_min+R1_max)/2.0  #set R1 to be the mid point between min and max values of R1
fo_mid = 1/((2*pi)*(R1_mid*R2*C1*C2)**0.5)
print('fo_mid = {:f}'.format(fo_mid))
fo_max = 1/((2*pi)*(R1_min*R2*C1*C2)**0.5)
print('fo_max = {:f}'.format(fo_max))

fo_min = 0.021147
fo_nom = 1.000000
fo_mid = 0.029907
fo_max = 106.257253