Wien bridge RC oscillator, Barkhausen criteria

Wien bridge RC oscillator

It is a sine wave oscillator for audio frequencies. It uses a non-inverting op-amp amplifier with a Wien (lead-lag) RC network as positive feedback.

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

Parts

• The series R-C and parallel R-C arms (with the same R and C) give the positive feedback to the non-inverting input.
• Rf and R1 give negative feedback that sets the amplifier gain A = 1 + Rf/R1.

Operation

1. At low frequencies, the series C acts almost as an open circuit, so the feedback is small and leads in phase. At high frequencies, the parallel C almost shorts the non-inverting input to ground, so the feedback is small and lags in phase.
2. At only one frequency, f₀ = 1/(2πRC), the phase shift of the network is exactly 0° and the feedback factor is at its maximum, β = 1/3.
3. The amplifier is non-inverting (0° phase shift), so at f₀ the total loop phase shift is 0°.
4. With gain A = 3 (Rf = 2R1), the loop gain Aβ = 1 and a stable sine wave at f₀ is produced. Initially, noise starts the oscillation, with A slightly more than 3.
5. The amplitude is stabilised by using a lamp or a diode-resistor network in the Rf path, so that the gain falls when the output grows.

Frequency: f₀ = 1/(2πRC)

Barkhausen criteria

1. |Aβ| = 1 (loop gain unity).
2. Phase shift around the loop = 0° or 360°.