Wein Bridge Oscillators, how do they work?

In summary, the conversation discusses a question about the phase change in a Wein Bridge oscillator circuit and how to mathematically prove the oscillatory frequency at which the phase change is zero. The conversation concludes with an explanation of the correct calculation for the total impedance at resonance, showing that the imaginary component is indeed zero and therefore the phase change is also zero.
  • #1
Azelketh
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Homework Statement



Hi, I am revising for an exam, so this isn't really a homework question, but not sure which sub-forum it really fits on so its here.

Anyway, I am trying to understand how a simple wein brige oscillator circuit works, as shown in the diagram
http://www.electronics-tutorials.ws/oscillator/osc27.gifWhat I am finding difficult is the phase change of the circuit, apparently at resonance there is no phase change over the whole circuit, so the imaginary component of the impedances of the capacitors has to be 0 in total, but how do you mathmatically prove that for this circuit the oscillatory frequecny that this happens at is

[tex]\omega = \frac{1}{CR} [/tex]
?

Homework Equations


The Attempt at a Solution



I've tried adding the impedance of the capacitor and resistor in series with that of the capacitor and resistor in parallel.
resistance of capacitor and resistor in series = [tex] z_u [/tex]
resistance of capacitor and resistor in parallel = [tex] z_L [/tex]

[tex] z_u = R - \frac{\imath}{ C \omega} [/tex]

[tex] \frac{1}{z_L} = \frac{1}{R} + \imath C \omega [/tex]
thus
[tex] z_L = \frac{R}{1 + \imath C \omega R} [/tex]

multiplying by the complex conjugate of the denominator to get an easier to work with number

[tex] z_L = \frac{R - \imath \omega C R^2}{1 + \omega^2 C^2 R^2 } [/tex]

total impedance= [tex] z_T= z_u + z_L [/tex]

[tex] z_T = \frac{R - \imath \omega C R^2}{1 + \omega^2 C^2 R^2 } + R - \frac{\imath}{ C \omega}[/tex]

rearranging into real and imaginary sections
[tex] z_T = \frac{R}{1+ \omega^2 C^2 R^2} + R -\imath (\frac{\omega C R^2}{1+ \omega^2 C^2 R^2} + \frac{1}{\omega C}) [/tex]

then as the imaginary component has to be 0 for no overall phase change of the output, only considering the imaginary part;

[tex] 0 = \frac{\omega C R^2}{1+ \omega^2 C^2 R^2} + \frac{1}{\omega C}[/tex]

which if [tex]\omega = \frac{1}{CR} [/tex] gives

[tex]\frac{1}{2} = -1 [/tex]
which is impossible, so i don't understand how the resonant frequency can be that.

Can anyone help point out where I've gone wrong? Or explain how the phase change at resonant frequency is 0?
Thanks for your time if you've read this.
 
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  • #2


Hi there,

First of all, great job on your attempt at solving this problem! I can see that you have a good understanding of complex impedance and how to calculate it for different components in a circuit.

To answer your question, let's take a closer look at the Wein Bridge oscillator circuit. At resonance, the output voltage is in phase with the input voltage, meaning there is no phase difference between them. This can be seen by the fact that the output voltage is taken from the midpoint of the two capacitors, and this voltage is the same as the input voltage.

Now, let's consider the impedance of the two capacitors in the circuit. At resonance, the two capacitors are in parallel, and their combined impedance is given by:

Z = (1/jωC) || (1/jωC) = (1/jωC)/2 = -j/(ωC)

This means that at resonance, the capacitors have an equivalent impedance of -j/(ωC), which is purely imaginary. This is where your calculation went wrong - you assumed that the imaginary component of the capacitor impedance is zero, when in fact it is purely imaginary at resonance.

Now, let's substitute this value for the capacitive impedance into your equation for the total impedance:

ZT = R + (-j/(ωC))

= R - j/(ωC)

= R(1 - j/(ωCR))

= R(1 - j/1)

= R(1 - j)

= R - jR

As you can see, the imaginary component of the total impedance is indeed zero at resonance, as the output voltage is in phase with the input voltage. This also means that the phase change over the whole circuit is zero, as you correctly mentioned in your post.

I hope this helps to clarify things for you. Good luck with your exam!
 

FAQ: Wein Bridge Oscillators, how do they work?

1. What is a Wein Bridge Oscillator?

A Wein Bridge Oscillator is an electronic circuit that is used to generate a sinusoidal waveform at a desired frequency. It was first invented by Max Wien in 1891 and has been widely used in various applications such as audio signal generation and frequency stabilization.

2. How does a Wein Bridge Oscillator work?

A Wein Bridge Oscillator consists of a bridge circuit with two resistors and two capacitors, with an operational amplifier acting as the feedback element. The circuit is designed to produce a feedback signal that is in phase with the input signal, resulting in a positive feedback loop that generates a continuous oscillation at the desired frequency.

3. What are the advantages of using a Wein Bridge Oscillator?

There are several advantages to using a Wein Bridge Oscillator, including its simplicity, low cost, and stability. It also has the ability to generate a wide range of frequencies and can be easily tuned by adjusting the values of the resistors and capacitors in the circuit.

4. What are the limitations of a Wein Bridge Oscillator?

One of the main limitations of a Wein Bridge Oscillator is its sensitivity to external noise and variations in the circuit components. This can affect the accuracy and stability of the output frequency. Additionally, the circuit may require frequent adjustments to maintain the desired frequency.

5. How is a Wein Bridge Oscillator different from other types of oscillators?

Compared to other types of oscillators, such as the RC phase shift oscillator or the LC oscillator, the Wein Bridge Oscillator has a simpler circuit design and is less prone to distortion. It also has a higher output impedance, making it suitable for driving low-impedance loads. However, it may not be as efficient as other types of oscillators in terms of power consumption.

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