Wein Bridge Oscillators

Additional Notes

MathCAD Application File

f20 j

w j

f10 j

w j

f1 j

w j

Sensitivity of the Loop Gain versus frequency for different Amplifier Gains

fi j

1Ra

i

Rb

R2 C1 jj wj

jj wj

2 R1 R2 C1 C2 jj wj

R1 C1 R2 C1 R2 C2( ) 1

Considering the transfer function of the circuit:

wo 1 104

jj 1

wo1

C1 R1Rb 250

Ra10

500Rai

xi

C2 0.01106R2 10000

C1 0.01106R1 10000

wj

5000 500 jxi

450 i 5

j 1 20i 1 20

Wienbridge Oscillator - Transfer Function - Frequency Analysis - P. F. Ribeiro

s 1 jj 999 A 3

Given

R2 C2 s A s2

R12 C1

2 s 3 R1 C1 1

ss Find s( ) ss 3.222 105 i 10

4

t 0 0.0001 0.01

y t( ) A eRe ss( ) t sin Im ss( ) t( ) [Try R1=11395, R2=10005]

y t( )

tFrequency of Oscilation

1

R1 R2 C1 C2

1 104

Gain

Avi

1Ra

i

Rb

Gain

Avi

1Ra

i

Rb

Av i

i

Sensitivity of the Loop Gain versus Amplifier Gain for different frequencies

f i 1

Rai

f i 10

Rai

3-D of the Magnitude of the Transfer Function

f

f

MathCAD Application File

An Investigation of the Wien-Bridge Oscillator Troy Cok and P.F. Ribeiro

The Wien-bridge oscillator, shown below in Figure 1, is a circuit that provides a sinusiodal output voltage using no voltage source. The RC circuit uses the initial charge on one of the capacitors to provide voltage to the rest of the circuit.

Figure 1: Wien-Bridge Oscillator Circuit

The gain of this circuit can be examined in terms of the individual component values. The noninverting amplifier gain is determined by the resistors R1 and R2, according to:

G 1R2

R1

The loop gain (or transfer function) of the Wien-bridge oscillator is determined by the noninverting gain and the remaining circuit elements.

T j R C G j

1 2

R2 C

2 3 j R C

C 0.1FC

1

R oo

1

R CR 10ko 1kHz

For a resonance frequency of 1 kHz, the resistor and capacitor values can be:

R2 2 104 R2 G 1( ) R1

G 3R1 10k

G 1R2

R1 solve R2 G 1( ) R1

To investigate the circuit in more detail, we can use a PSPICE simulation. To begin, we will try to get a unity gain. The individual component values are determined according to the transfer function. Using standard resistor values, R1 will be set to 10 k.

So, if the noniverting gain is 3, the loop gain will be 1.

T j G

3At resonance, the transfer function reduces to

o1

R C

For stability, the phase shift is preferred to be zero. In order to accomplish this, the real part of the denominator of the transfer function must be zero. The real part of the denominator will be zero if the operating frequency is at resonance. The resonant frequency is:

T j R C G j

1 2

R2 C

2 3 j R C

Varying the frequency of the transfer function can be examine for the calculated component values. Both the theoretical and computer simulated data are plotted using radians.

j i T R C G j

1 2

R2 C

2 3 j R C 10 20 100000

B 20log T

spice unity 6 2 Tspice unity 7

10 100 1 103

1 104

1 105

40

20

0

Frequency Response

Frequency (rad)

Gai

n (d

B) B ( )

Tspice

spice

The peak gain of the frequency analysis occurs at the resonance frequency for each circuit model. The two traces exhibit nearly identical Bode plots.

A better design would cause the circuit to exhibit a constant (not decaying) oscillation . We can attempt to update the circuit using a form of amplitude stabilization. There are a couple of available design methods, but one of the better schemes involves the introduction diodes into the circuit. Along with the diodes, two additional resistors are added to form an amplitude control network. The schematic for this circuit is shown below.

The new resistors are determined according to the following equation. This ensures that the noninverting gain of the circuit will be slightly more than 3 when the diodes are off and slightly less that 3 when one is active.

R2 R3

R12 So, if R1 is now 15 k, R2 and R3 can be 15 k and 16 k respectively.

R1 15k R2 15k R3 18k

R2 R3

R12.2

Here, the parallel combination of R3 and R4 must be slightly less than R2. Since R3 is a bit greater than R2, a mid-range resistor value of R4 will suffice.

R2R3 R4

R3 R4

R12

R4 33k

R2R3 R4

R3 R4

R11.776

R2R3 R4

R3 R4

R11.776

The updated circuit can again be examined using PSPICE. The resulting transient waveforms are shown below. With the modification, the circuit appears to operate with a steady oscillation as time passes.

tspice unity 0 Uspice unity 1

0 0.02 0.0410

0

10Wien-bridge with Amplitude Stabilization

Time (s)

Vol

tage

(V

)

Uspice

tspice0 0.5 1 1.5 2

10

0

10Steady Oscillation over Time

Time (s)

Vol

tage

(V

)Uspice

tspice

Wien-Bridge Oscillator DesignApplication Notes 1

Wien-Bridge Oscillator DesignApplication Notes 2