According to chapter 21 of Electronic Principles(8th edition), the Wien bridge oscillator uses the Johnson-Nyquist noise from one of the resistors as the startup voltage. It selects for a desired harmonic and amplifies it. Some schematics show a Wien bridge oscillator using a tungsten lamp as a source of resistor noise. Now is this also true for the phase shift oscillator? This seems quite different from other oscillators which use the rising voltage on a capacitor connected to the DC power supply to build up oscillations. Part of this question is based on the fact that neither the Wien bridge oscillator nor the phase shift oscillator have inductors.
Electronic – Is the Wien Bridge oscillator essentially a resonant filter
analogoscillatorphase shiftwien-bridge
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If the gain of a system at every particular delay is constant, the system will produce oscillations with those periods which have a gain of one. At periods where the gain exceeds one, the strength of the oscillations will grow unless or until something causes the gain falls to below one. If there were one frequency where the gain stabilized at exactly one, and it were less than one at all other frequencies, the circuit would produce a sine wave at the frequency in question. The wave would be a sine wave because any other type of wave would have content at frequencies where the gain is less than one.
Note that in practice, many types of oscillating circuits have gains which vary widely during the course of each "cycle". Such variations make it very difficult to predict analytically the frequency content of their output. Because there is a very fine line between having oscillations die down to nothing, and having oscillations grow without bound, even circuits which are intended to produce sine waves generally end up having a gain which is sometimes greater than 1 and sometimes less than one, though ideally there's a gain control mechanism that will try to settle on the right value.
Incidentally, some circuits use incandescent light bulbs for that purpose, since their resistance varies with temperature. If the power fed to a light bulb is proportional to the strength of an oscillator's signal, and if an increase in resistance will cause a reduction in gain, then the light bulb's temperature will tend to reach an equilibrium where the gain is 1. If the frequency in question is fast enough, the light bulb will only heat up or cool down a little bit during each cycle, allowing reasonably-clean sine waves to be generated.
Addendum
Rather than using the term "constant gain", it may be more helpful to use the term "linear circuit". To borrow an analogy from a magazine I read some years back, comparing "linear circuits" to "non-linear circuits" is like comparing "kangaroo biology" to "non-kangaroo biology"; linear circuits are a particular subcategory of circuits, and non-linear circuits are everything else.
A one-input one-output linear black box is one which takes an input signal and produces an output signal, with the characteristic that if F(x) represents the signal produced by the box when it is fed signal x, and if A and B are two input signals, then F(A+B) will equal F(A)+F(B). There are many kinds of things a linear black box can do to a signal, but all must obey the above criterion. The output produced by a linear black box when given a combination of many different frequency signals will be the sum of the outputs that would be produced for each frequency in isolation.
The behavior of many practical circuits is close to that of a one-input one-output linear black box. Since any wave other than a sine wave is a combination of sine waves at multiple frequencies, for a circuit to oscillate with anything other than a sine wave, there must be multiple frequencies which, if fed in individually, would cause the output to precisely match the input in phase and amplitude. While it is certainly possible to construct such circuits, most practical circuits will only have one frequency where such behavior will occur.
The gain you measure depends on the amplitude of the signal in this circuit. This is the function of the diodes.
For example, if the output signal amplitude is small (say less than 0.6 V), then neither of the diodes across the resistor (R6 ? -- it's hidden) will conduct, and your gain will be 4x (with the 10k resistors). When the amplitude exceeds about 2.4 V peak, then at the extremes of the sinusoidal output, the diodes will conduct, and effectively limit the voltage across R6 to about 0.6 V. This reduces the gain beyond this amplitude to 3x (the other resistors control it).
If you were to draw a graph, the gain (slope of VOUT vs. VIN) would be 4x until the peaks reached 2.4 V, then would reduce to 3x for the portion of signal beyond that. Because gain changes with signal amplitude, you would get distortion.
This is the exact purpose of the diodes in this circuit -- they allow the gain to change, and if you get the resistors (and other components) right, for small signal amplitudes the overall lop gain will be just greater than 1, and oscillations will build up. However, when the amplitude reaches about 2.4 V, the gain will fall, and the amplitude will stabilize around where the 'average' gain is 1.0
Best Answer
Before Johnson noise ever kicks a Wien bridge into action, the sheer monstrous transient of applying power does the job.
It may look like that but almost certainly (as certain as I can be without the schematic you saw) the lamp is there to provide non linear gain so that the peak to peak amplitude doesn’t crash into the power rails.
You seem to be describing a Schmitt trigger single RC oscillator. It doesn’t use phase shift at all. It uses thresholds and the charging time of the capacitor to dictate oscillation frequency. Go look up relaxation oscillators.
These type of oscillators rely on the changing phase shift of a network of resistors and capacitors to produce a phase shift of 180 degrees at one particular frequency. At different frequencies, the phase shift is not 180 degrees and hence, when wrapped around an inverting op-amp, won’t oscillate.
In fact oscillators like the Colpitts (that use an inductor) hardly ever oscillate at resonance because the phase change at perfect amplitude resonance just isn’t right for sustained stable oscillation. Taking this further, hardly any (if any at all) oscillators use perfect amplitude resonance. Try googling Barkhausen stability criterion for oscillators.
Whether the oscillator is Wien bridge or phase shift or, "so-called" resonant oscillators like the Colpitts, Hartley or Pierce, the guiding principal is that of providing the right phase shift to produce a stable oscillation.