page_title: Wien bridge oscillator
section_title: Oscillators without automatic gain control
hierarchical_section_title: Wien bridge oscillator / Background / Oscillators without automatic gain control
caption_attribution_description: English: A Wien bridge oscillator that uses diodes to limit the output. The design yield total harmonic distortion of 1% to 5% depending on how carefully it is adjusted.
context_page_description: A Wien bridge oscillator is a type of electronic oscillator that generates sine waves. It can generate a large range of frequencies. The oscillator is based on a bridge circuit originally developed by Max Wien in 1891 for the measurement of impedances.
  The bridge comprises four resistors and two capacitors. The oscillator can also be viewed as a positive gain amplifier combined with a bandpass filter that provides positive feedback. Automatic gain control, intentional non-linearity and incidental non-linearity limit the output amplitude in various implementations of the oscillator.
  The circuit shown to the right depicts a once-common implementation of the oscillator, with automatic gain control using an incandescent lamp. Under the condition that R₁=R₂=R and C₁=C₂=C, the frequency of oscillation is given by:
  and the condition of stable oscillation is given by
context_section_description: The conventional oscillator circuit is designed so that it will start oscillating ("start up") and that its amplitude will be controlled.
  The oscillator at the right uses diodes to add a controlled compression to the amplifier output.  It can produce total harmonic distortion in the range of 1-5%, depending on how carefully it is trimmed.
  For a linear circuit to oscillate, it must meet the Barkhausen conditions: its loop gain must be one and the phase around the loop must be an integer multiple of 360 degrees. The linear oscillator theory doesn't address how the oscillator starts up or how the amplitude is determined. The linear oscillator can support any amplitude.
  In practice, the loop gain is initially larger than unity. Random noise is present in all circuits, and some of that noise will be near the desired frequency. A loop gain greater than one allows the amplitude of frequency to increase exponentially each time around the loop. With a loop gain greater than one, the oscillator will start.
  Ideally, the loop gain needs to be just a little bigger than one, but in practice, it is often significantly greater than one. A larger loop gain makes the oscillator start quickly. A large loop gain also compensates for gain variations with temperature and the desired frequency of a tunable oscillator. For the oscillator to start, the loop gain must be greater than one under all possible conditions.
  A loop gain greater than one has a down side. In theory, the oscillator amplitude will increase without limit. In practice, the amplitude will increase until the output runs into some limiting factor such as the power supply voltage (the amplifier output runs into the supply rails) or the amplifier output current limits. The limiting reduces the effective gain of the amplifier (the effect is called gain compression). In a stable oscillator, the average loop gain will be one.
  Although the limiting action stabilizes the output voltage, it has two significant effects: it introduces harmonic distortion and it affects the frequency stability of the oscillator.
  The amount of distortion is related to the extra loop gain used for startup. If there's a lot of extra loop gain at small amplitudes, then the gain must decrease more at higher instantaneous amplitudes. That means more distortion.
  The amount of distortion is also related to final amplitude of the oscillation. Although an amplifier's gain is ideally linear, in practice it is nonlinear. The nonlinear transfer function can be expressed as a Taylor series. For small amplitudes, the higher order terms have little effect. For larger amplitudes, the nonlinearity is pronounced. Consequently, for low distortion, the oscillator's output amplitude should be a small fraction of the amplifier's dynamic range.
caption: Schematic of a Wien bridge oscillator that uses diodes to control amplitude.  This circuit typically produces total harmonic distortion in the range of 1-5% depending on how carefully it is trimmed.
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