# Wien bridge oscillator question

Discussion in 'General Electronics Chat' started by Piggins, May 6, 2014.

1. ### Piggins Thread Starter New Member

May 5, 2014
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http://www.electronics-tutorials.ws/oscillator/wien_bridge.html.

It states that the wien bridge is essentially a band pass filter for that desired frequency fr. But then it states that at that resonant frequency fr, the reactance equals its resistance. Doesnt that mean that there is reactance and therefore phase shift?

and where does that equation for fr = 1/(2piRC) come from? Does it have something to do with the equation for Xc?

Also, I cant understand where that dampening of the signal to third from the original comes from.

2. ### Wendy Moderator

Mar 24, 2008
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It comes from reactance. When the reactance of the caps = the resistance of the resistance, this is where the frequency trade offs occur.

Work the math.

3. ### Piggins Thread Starter New Member

May 5, 2014
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I tried doing the maths but it gave me no right answer. I can understand that if there is both inductive and capacitive reactance in the circuit then they can cancel eachother out. But with this wien bridge it just seems to me that there is only capacitive reactance.

Also, do you mean the reactance of a single capacitor is the resistance of a single resistor? That is how I tried to calculate it.

So if we have, for example a lowpass and high pass filter cascaded with the resistance of the resistors in both of the filters being 10kohm.

Does that mean that basically what we have is 2 resistors of 10kohm in series and 2 resistors of 10 kohm in paraller? So 5kohm / 20kohm = 0.25 dampening

4. ### AnalogKid AAC Fanatic!

Aug 1, 2013
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Not the right perspective. What you have is a simple two-element attenuator like a resistive voltage divider, except the series resistor is a series RC network and the shunt resistor is a parallel RC network. The center point between the two networks is the "output" of the divider. Make the two resistors equal and the two capacitors equal.

If you drive this network with a signal generator, steadily increase the frequency, and measure the voltage at the output, you will see that as the frequency increases the output voltage increases, then peaks, then starts to decrease. The peak value happens when the compound impedances of the series and shunt legs are equal. This happens at 1/2piRC for each network.

To see this in numbers, start with the values for something easy, like a 1 KHz circuit (R=1.59K, C=0.1uF). For a 1 V input, calculate the output voltage. Now calculate it at 800 Hz and 1200 Hz.

Yes, there is phase shift in each RC network, and the two phase shifts combine to meet the requirement for oscillation.

ak

5. ### Piggins Thread Starter New Member

May 5, 2014
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So they produce that 180degree shift? Or do the capacitances cancel eachother?

6. ### alfacliff Well-Known Member

Dec 13, 2013
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rc circuits like these produce a 90 degree phase shift at a specific frequency. two in series give you 180 degrees for oscilation.

7. ### Wendy Moderator

Mar 24, 2008
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Uhh, no. There is 0° phase shift at resonance in a Wien bridge. This is why it uses the non-inverting input to the op amp for feedback.

Besides the phase shift you have a high pass filter followed by a low pass filter. There will be one frequency that get through both with minimum attenuation, which is to say both attenuate that frequency a bit, but together not as much.

Resonance is probably not the right term to use here, but it gets the point across.

8. ### AnalogKid AAC Fanatic!

Aug 1, 2013
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True about resonance. I see that my last sentence left the door open for a mis-conclusion.

Unlike LC and crystal oscillators, there is no electrical or mechanical resonance in a Wein oscillator. The Wein network is a low-rent bandpass filter with no phase shift (actually, offsetting phase shifts that cancel each other out) and a little attenuation. The Barkhausen stability requirements are 0 degrees phase shift or multiples like 360, 720, etc, and exactly unity gain. The Wein network is connected to the non-inverting input for 0 degrees shift, and the negative feedback loop tunes the circuit for just enough gain to offset the attenuation through the Wein network.

An alternative is the Phase Shift Oscillator (nice name). In the usual case there are three successive RC networks between the output and the inverting input. At the freq of oscillation, each network contributes 60 degrees shift, and the opamp makes up the remaining 180 degrees with inversion. Each network also attenuates the feedback signal, so the opamp has to make up about 26 dB of gain (working from memory here).

ak

Last edited: May 7, 2014
9. ### studiot AAC Fanatic!

Nov 9, 2007
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The Barkhausen criterion requires the product of the feedback fraction and the open loop gain to be exactly one.

The attenuation of the Wein network is 1:3 so the gain of an amp for a Wein network is 3.

For a phase shift oscillator the network attenuation is 1:29 (say 30) so the gain requirement is 30.

10. ### Piggins Thread Starter New Member

May 5, 2014
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Thank you all for commenting. I have done some more reading on the maths about the reactances of the filters that combined form the wien bridge. So here goes my second attemp at it, maybe I got it right this time.

So if we have:
Resistors 10kohm each
Capacitors 10nF each,
the resonant frequency fr = 1/2piRC = 1591.5Hz
At that frequency the capacitive reactance for the caps is 10kohm (Xc= 1/2pifC = 10kohm) That makes the impedance for the series connected capacitor and resistor 14142ohms at the angle -45degrees.

The impedance for the paraller connected capacitor and resistor is 1/( 1/10000 + 1/-j10000) = 5000 -j5000 = 7071 ohms at -45degrees.

Now, if what we have is like a voltage divider formed of two impedances of 14,142kohm and 7,071kohm then the voltage over the the one formed by the paraller resistor and capacitor should be 7,071kohm at -45degrees / (14.142+7,071)kohm at -45degrees. That gives 0.3333 so thats 1/3Vin at 0 degrees so no phase shift either.

Am I on the right track now?

11. ### AnalogKid AAC Fanatic!

Aug 1, 2013
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Looks good to me.

ak