Wien bridge oscillator circuit and operation

Positive feedback: feedback in which a part of the output signal is fed back to the input in phase with the input signal, so that it adds to it. It increases the gain and is used in oscillators and Schmitt triggers.

Wien bridge oscillator

It is an RC oscillator that produces a sine wave at audio frequencies. It uses an op-amp amplifier with a Wien bridge network (a series RC branch and a parallel RC branch) as the frequency-selective feedback network.

           +------[ Rf ]-------+
           |                   |
 GND--[R1]-+        |\         |
           +--------|- \       |
                    |   >------+----o Vo
           +--------|+ /       |
           |        |/         |
           |                   |
           +--[ R ]--||--------+
           |         C     (Z1: series R and C)
         +-+-+
         |   |
        [R] === C   (Z2: R parallel C)
         |   |
         +-+-+
           |
          GND

Connections:

• The op-amp works in non-inverting mode with gain Av = 1 + Rf/R1.
• Positive feedback network: a series R-C branch (Z1) from the output to the non-inverting input, and a parallel R-C branch (Z2) from the non-inverting input to ground.
• Negative feedback network: the resistors R1 and Rf set the gain.

Principle of operation

• The Wien network gives a phase shift of 0° at only one frequency, f0, and at that frequency it passes 1/3 of the output (attenuation 1/3).
• With equal resistors R and equal capacitors C in the two branches:

f0 = 1/(2πRC)

• At f0, the feedback is in phase with the input (the non-inverting amplifier also gives 0°), so the loop phase shift is 0°. This satisfies the phase condition of the Barkhausen criterion.
• The loop gain must be at least 1: Av × (1/3) ≥ 1, so Av ≥ 3, that is Rf ≥ 2R1 (Rf = 2R1 for steady oscillations).
• Oscillations start from noise. At first the gain is slightly more than 3, so the amplitude grows. The amplitude is then stabilised by a non-linear element, such as a lamp or diodes in the Rf path, which reduces the gain to 3.
• At other frequencies the phase shift is not zero, so only f0 is sustained.

Example: R = 10 kΩ, C = 0.01 µF gives f0 = 1/(2π × 10⁴ × 10⁻⁸) = 1.59 kHz.

The output is a clean sine wave. It is used in audio signal generators.