What is the Wien bridge frequency proof and how do you solve it?

In summary, the conversation discusses solving for the frequency in a Wien bridge circuit when the bridge is balanced. The general solution for AC bridges is used and the attempt at solving for impedances is shared. With the help of equating real parts, the solution is found to be R2R4C2C4*w^2 + 1 = 0.
  • #1
birdgirl
6
0
[SOLVED] Wien Bridge Frequency Proof

Homework Statement



The ac bridge circuit shown is called a Wien bridge (also Wein bridge).
Wien Bridge.png


Show that when the bridge is balanced, frequency is found by the Eqn attached.
Eqn.png

Homework Equations



w=2*pi*f

Using the number from each branch as a guide, the general solution to AC bridges is Z4 = (Z3/Z1)*Z2

The Attempt at a Solution



I keep trying to solve for impedences to plug into the second equation provided, but my j values do not cancel and the equation left is rather messy (R2R4C2C4*w^2 +jw(RzR4C2 -R2C2 -R4C4) +1 = 0.

For my impedence values I have been using
Z1 = R1
Z2 = R2 -j/wC2
Z3 = R3
Z4 = (R4/jwC4)/(R4 +jwC4)

Any help with this would be greatly appreciated.
 
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  • #2
I think [tex] Z_4 = \frac {-jR_4} {\omega C_4 (R_4 - \frac{j}{\omega C_4})} [/tex]


Both the real and the imaginary parts of Z4 = (Z3/Z1)*Z2 must be 0
 
  • #3
Actually, I think our Z4 values are the same, since -j = 1/j. But thank you! I managed to figure it out after you got me thinking about real and imaginary parts.

It's fairly simple, actually: I just had to equate the real parts from my equation so that R2R4C2C4*w^2 + 1 = 0 (and then I took absolute value).
 

What is a Wien Bridge Frequency Proof?

A Wien Bridge Frequency Proof is a method used to test the frequency response of a circuit, specifically a bridge circuit, to determine its resonance frequency.

How does a Wien Bridge Frequency Proof work?

A Wien Bridge Frequency Proof works by comparing the output voltage of a circuit at different frequencies to the input voltage. When the output voltage is equal to the input voltage, the circuit is at its resonance frequency.

What is the purpose of a Wien Bridge Frequency Proof?

The purpose of a Wien Bridge Frequency Proof is to accurately determine the resonance frequency of a circuit, which is important in designing and troubleshooting electronic circuits.

What are the components of a Wien Bridge Frequency Proof circuit?

A Wien Bridge Frequency Proof circuit typically includes a variable frequency oscillator, an amplifier, a bridge circuit, and a voltmeter.

What are the advantages of using a Wien Bridge Frequency Proof?

Using a Wien Bridge Frequency Proof allows for a precise measurement of a circuit's resonance frequency, which can help in optimizing circuit design and detecting any issues or malfunctions in the circuit.

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