# Why the Wien Oscillator output is a sine?

I don't understand why the output signal of the Wien oscillator is a sinusoidal waveform.

I can easily understand how a sine waveform can be generated by an oscillator which contains an LC circuit (such as the Colpitts oscillator) or by a square waveform generator with a low-pass filter.

But for the Wien Bridge (like the following scheme) I don't understand the physical mechanism of generation of the sine. The only thing that I think when I see this circuit is that it seems quite similar to the astable multivibrator with an Op-Amp (except for the capacitor in the positive feedback and the resistor R between the + input and GND), which generates a square waveform. Does this capacitor in the positive feedback make the difference? • whats the conceptual difference between using RC and LC filters? Mar 7 '19 at 18:24
• *spell checked :D Mar 7 '19 at 21:53

Here is the Wien Bridge Oscillator with a 100 Ohm trimpot slider on the LEFT side so you can INCREASE the loop gain to stabilize the output. THus the Wien bridge resembles an LC tank circuit with high Q but at unity gain so that the output does not saturate. It accomplishes this by phase gain cancellation from Feedback RC to Shunt RC. The result resembles an LC parallel tank circuit. If you explore the two Simulations above and add scope traces as you wish to any component or add a wire and scope that. Adjust the Pot and see how it works. The scope trace is like a fast chart recorder but in slow motion.

This may be more instructive than my words.
HINT: Slide POT to the LEFT to reduce Rshunt and increase Gain.

============================================ Here is another sine wave Oscillator. " The Phase SHift RC Sine OSC. It has the same properties but is less sensitive than the Wein to gain stability and component matching.

That uses 3 Low pass Filters to obtain 60 degrees each x3 =180 degrees with negative overall feedback to achieve 0 degrees at the unity gain breakpoint and thus have a condition for oscillation.

Here is a javascript simulation of the frequency response. Due to simulator's hard limiting a full swing sine can be produced. But in reality, if the loop gain is 1.001 at 180 deg phase shift, the amplitude will grow slowly and the output may clip, a condition where the OP Amp gain drops to or near zero. So soft limiting diodes are often used back to back with a high series R to not distort the sine wave yet prevent output saturation.

Other trivia

Low Pass filters in negative feedback become high pass filters. Notch Filters with negative feedback can become BandPass filters and Negative Impedance Converters can convert capacitance current to simulate an inductor current ( within limits) using the same applied voltage. • @Sunnyskyguuy_I dont hink we can say that the Wien bridge "resembles an LC tank circuit with high Q". The Wien bandpass has a quality factor Q=1/3 only. More than that...you have shown a circuit that is NOT a WIEN oscillator but a two-intergator oscillator, which realizes another oscillator concept than the Wien oscillator.
– LvW
Mar 7 '19 at 20:11
• oops TY @LvW.... But actually the phase shift from the negative feedback capacitor in the loop does behave like an Inductor.\ Mar 7 '19 at 20:12
• I dont think so. Lets take as an example the well-known MILLER integrator. The capacitor in the feedback loop behaves like a magnified capacitor (multiplied by the open-loop gain of the opamp). Here we exploit the classical MILLER effect.
– LvW
Mar 7 '19 at 20:29
• May I add something (perhaps not too important): Barkhausen has never formulated a "stability criterion". In this respect, wikipedia is not correct! Instead, Barkhausen has formulated an oscillation criterion, which - however - is a necessary condition only! This oscillation criterion cannot be used as a "stability criterion" (which was given by Nyquist).
– LvW
Mar 7 '19 at 20:40
• @Ale..chenski Did you notice the 100 Ohm pot you can control to increase the Gain >=1 then RESET > Try again with the Pot to the left. I guess the semantics is that Barkhausens oscillation criteria also defines the boundary of an unstable 2nd order system as shown in the Bode Plot as a high Q filter that rings until it oscillates. on its own. I agree the Nyquist Stability condition is a better criteria than Bode plots Phase margin when it comes to higher orders Mar 7 '19 at 21:34

Because (at least in steady-state) it is a system that behaves according to linear, time-invariant, ordinary differential equations. Such systems only have modes that involve exponentials, exponentially growing (or shrinking) sine waves, and either of the previous two multiplied by time (i.e., $$\t e^{-at}\$$).

There's a whole science around how and why I needed to put that "in steady-state" qualifier in there (and how the circuit you show doesn't quite meet it -- your circuit either won't start oscillating or it'll clip, at least mildly). But that wasn't your question.

• TimWescott_your contribution reminds me on the nice sentence: With the aim to behave as linear as possible, any "linear" harmonic oscillator must contain a certain amount of non-linearity.
– LvW
Mar 7 '19 at 20:44
• @LvW see my new simulations and revised answer. Is that more acceptable? Mar 7 '19 at 21:00
• Sunnyskyguy...Sorry, but there are still errors in your explanation.
– LvW
Mar 8 '19 at 9:32
• @LvW there are also errors in your comments. The Q is variable by the amount of negative feedback loop gain near -2 and loop gain of -1 with a Pot that has a ~10% range (100R/1k). As you vary the pot, the Q maximizes at the point for stable Sine gain, here at 180 Hz. WIth a Large SigGen source R it becomes a current source with V output so it is a Vector Impedance Analysis. THis demonstrates the LC equivalent circuit here tinyurl.com/yyyvmhjm Tim , you can comment too, as your answer doesn't say much into how it works Mar 8 '19 at 16:00
• @SunnyskyguyEE75 The only clear question was "why is it sinusoidal" -- so I limited myself to answering that. Mar 8 '19 at 16:31

Kinka-Byo, for realizing an oscillator fulfilling Barkhausens oscillation condition, you need a frequency-selective feedback which - together with an amplifier - gives a total loop gain (gain around the complete loop) of LG=1 for one single frequency only (this means: unity magnitude and zero phase shift). For this purpose, there are several genaral realization concepts (this a very short introduction in oscillator circuits):

• RC bandpass in the feedback loop: WIEN-bandpass, which at the resonant frequency (phase shift zero) has a damping of 0.333; hence, we need a positive amplifier with a gain of +3 (0.3333x3=1)

• LC bandpass in the feedback loop: This band pass must have a series resistor Rs and a parallel resistor Rp, hence the damping at f=fo is Rp/(Rs+Rp) and we need an amplifier with a gain of (1+Rs/Rp) in order to realize a loop gain of LG=1.

• There are other concepts based on a third-order lowpass or highpass circuits in the feedback loop. In these cases, we realize a phase shift of -180 deg at f=fo - and we need an inverting amplifier that provides the additional 180 deg phase shift.

*Final remark: Due to tolerance effects it is never possible to exactly realize LG=1. Therefore, we design all oscillator ciruits for LG>1 (with the result of oscillation with rising amplitudes) - and we introduce an additional nonlinearity which automatically brings the gain back to LG=1 for rising amplitudes. But that$$$$s another problem. Without such an amplitude regulation, the rising sinus signal is limited (clipped) at the supply rail and we need additional filtering.

• LvW THere a trick I learned long ago to optimize the tradeoff harmonic distortion, startup time and stable sine wave. So no filtering is needed unless you want more than 40 dB SNR. It comes down to the ratio of the R ratios and the dynamic range of the diode.. Mar 7 '19 at 21:46
• Sunnyskyguy.. as I have mentioned, additional filtering is often necessary WITHOUT amplitude regulation (diodes, OTA,...). However, there are two-opamp oscillator topologies with automatic (inherent) filtering.
– LvW
Mar 8 '19 at 9:31