# Wien Bridge Oscelator

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The Wien Bridge Oscilator uses two interconnected RC networks to produce a sinusoidal output.

In RC Oscillator training, we found that a series of resistances and capacitors can be connected by an inverter amplifier to create an oscillating circuit.

One of the simplest sinus wave oscillators using an RC network instead of a conventional LC-tuned tank circuit to produce a sinusoidal output waveform is called a wien bridge oscillator.

The Wien bridge oscilator is referred to by this name because it is based on a frequency selective form of the circuit wheatstone bridge circuit. The Wien bridge oscillator is a two-stage RC coupling amplifier circuit with good stability, low distortion and very easy to adjust at resonance frequency, making it a popular circuit as a sound frequency oscillator, but the phase shift of the output signal is quite large. differs from the previous phase shift RC oscilator at this point.

The Wien bridge oscilator uses a feedback circuit consisting of a series of RC circuits connected by a parallel RC with the same component values that produce a phase delay or phase progression circuit depending on the frequency. Phase shift at resonance frequency εr is 0^{o.}

The above RC circuit consists of a series of RC circuits connected to a parallel RC and basically creates a High Pass Filter connected to a Low Pass Filter at the selected frequency, which produces a Band Pass Filter connected to a very selective circumstial frequency with a high Q factor. .

At low frequencies, the reactance of the serial capacitor (C1) is very high, so it acts a bit like an open circuit, blocks any input signal on vin and has almost no output signal, Vout. Similarly, at high frequencies, the recess of the parallel capacitor (C2) is very low, so the parallel connected capacitor acts as a little short circuit along the output, so again there is no output signal.

Therefore, between these two ends, where C1 is an open circuit and C2 shorts out, there should be a frequency point where the output voltage reaches the maximum value of VOUT. The frequency value of the input waveform in which this occurs is called the Resonance Frequency of oscillators( εr).

At this resonance frequency, it equals the reassurance of the circuits, that is: X_{c} = R and the phase difference between input and output is equal to zero degrees. The size of the output voltage is therefore maximum and equals one-third (1/3) of the input voltage, as shown.

## Oscilator Output Gain and Phase Shift

At very low frequencies, the phase angle between the input and output signals can be seen as "Positive" (Advanced Phase) and at very high frequencies the phase angle is "Negative" (Phase Delay). In the middle of these two points, the circuit is at its own resonance frequency, (εr) and the two signals are "in the same phase" or 0^{o.} Therefore, we can define this resonance frequency point with the following statement.

## Wien Bridge Osciplator Frequency

Where:

εr is Resonance Frequency in Hertz

R, Resistance in Ohm is

C, Capacitance in Farad

Previously, we said that the size of the output voltage from the RC network is the maximum value of the Vout and equals one-third (1/3) of the input voltage to allow oscillations to occur. To understand why the output from the above RC circuit should be one-third, that is, 0.333xVin, we must take into account the complex impedance (Z = R ± jX) of the two connected RC circuits.

We know from our AC Theory courses that the real part of complex impedance is resistance, R, and the imaginary part is reassurance, X. When dealing with capacitors here, the reassurance part will be capacitive reassurance, Xc.

### RC Network

If we redraw the RC network above as shown, we can clearly see that it consists of two RC circuits connected by the output from their connections. Resistance R_{1} and capacitor C_{1} form the upper series network, while resistance R_{2} and capacitor C_{2} form the lower parallel network.

Therefore, the total DC impedance of the serial combination (R_{1}C_{1),}the total impedance of the parallel combination (R_{2}C_{2),}which we can call Z_{P.} _{} Since Z_{S} and Z_{P}are effectively connected serially via V_{IN} input, they form a voltage dividing network from output Z_{P}as shown.

So let's say that the component values of R_{1} and R_{2}are the same at 12kΩ, the C_{1} and C_{2} capacitors are the same at 3.9nF, and the feed frequency is ε 3.4kHz.

#### Serial Circuit

The total impedance of the series combination with resistance R1 and capacitor C1 is simply:

We now know that with a feed frequency of 3.4 kHz, the reactance of the capacitor is the same as its resistance in resistance of 12 kΩ. This then gives us the 17kΩ upper series impedance, the Z_{S.}

For the lower parallel impedance ZP, since the two components are parallel, since the impedance of the parallel circuit is affected by this parallel combination, we must handle it differently.

#### Parallel Circuit

The total impedance of the lower parallel combination with resistance R2 and capacitor C2 is given as follows:

At a feed frequency of 3.4kHz, the combined DC impedance of the RC parallel circuit is 6kΩ (R|| Xc) and the vector sum of this parallel impedance is calculated as follows:

Now our value for the vector sum of serial impedance is: 17kΩ, (ZS = 17kΩ) and for parallel impedance: 8.5kΩ, (ZP = 8.5kΩ). Therefore, at the given frequency, the total output impedance of the voltage dividing network, Zout:

Then at the oscillation frequency, the size of the output voltage will be equal to Zout x Vin, which, as shown, equals one-third (1/3) of the input voltage, Vin and this frequency selective RC network that forms the basis of the Wien Bridge Oscillator circuit.

Now if we place this RC network in an inverted riser with a gain of 1+R1/R2, the following basic Wien bridge oscillator circuit is produced.

The output of the transactional amplifier feeds back into both inputs of the riser. Part of the feedback signal is connected to the inverter input terminal (negative or degenerative feedback) through the resistance divider network of R1 and R2, which allows the voltage gain of the riser to be adjusted within narrow limits.

The other part, which forms serial and parallel combinations of R and C, forms the feedback network and feeds back to the inverted input terminal (positive or regenerative feedback) through the RC Wien Bridge network, which is this positive feedback combination, which causes its release.

The RC network is connected to the positive feedback pathway of the amplifier and has zero phase shift at just one frequency. Then, at the selected resonance frequency, the voltages applied to the inverter and non-inverter inputs will be equal and "intra-phase", so that positive feedback will cancel the negative feedback signal that causes the circuit to be released.

The voltage gain of the amplifier circuit for the onset of oscillations must be much or greater than three, since, as we see above, the input is 1/3 of the output. This value is set by the feedback resistance network R1 and R2 (Av ≥ 3), and for an inverted amplifier, this is given as a ratio of 1+(R1/R2).

In addition, frequencies above 1 MHz cannot be reached without the use of special high frequency op-amps due to the open loop gain limitations of transactional amplifiers.

### Wien Bridge Osciplator Question Example 1

Calculate the maximum and minimum oscillation frequency of a Wien Bridge Oscillator circuit with resistance ranging from 10kΩ and capacitor value from 1nF to 1000nF.

To calculate the frequency of oscillations for the Wien Bridge Oscillator, we use the following equation:

#### Lowest Frequency

#### Highest Frequency

### Wien Bridge Oscitor Question Example 2

Wien Bridge Oscillator circuit is required to create a 5,200 Hertz (5.2kHz) sinusoidal waveform. Calculate the values of frequency determination resistors R_{1} and R_{2} and two capacitors C_{1} and C_{2}to produce the required frequency.

Also, if the oscillator circuit is based on a non-inverted transactional amplifier configuration, set the minimum values of gain resistances to produce the required oscillations. Finally draw the resulting oscillator circuit.

The frequency of oscillations for the Wien Bridge Oscillator was given as 5200 Hertz. If the resistors are R_{1} = R_{2} and the capacitors are C_{1} = C_{2} and we accept a value of 3.0nF for the feedback capacitors, the corresponding value of the feedback resistors is calculated as follows:

For sinusoidal oscillations to begin, the voltage gain of the Wien bridge circuit must be equal to or greater than 3 (Hunting ≥ 3). For an inverted op-amp configuration, this value is set by the feedback resistance network of R3 and R4 and given as follows:

If we choose a value of 100kΩ for resistance R3, the value of resistance R4 is calculated as follows:

Although the minimum value required to ensure oscillations is a gain of 3, in reality a slightly higher value is usually required. If we accept a gain value of 3.1, the R4 resistance is recalculated to give the value of 47kΩ. This gives the last Wien Bridge Oscillator circuit as follows:

## Summarize

The following conditions must apply for oscillations to occur in the Wien Bridge Oscillator circuit.

- A Wien Bridge Oscillator without an input signal produces continuous output oscillations.
- The Wien Bridge Osciplator can produce a wide frequency range.
- The voltage gain of the amplifier should be greater than 3.
- The RC network can be used with an amplifier that does not invert.
- The input resistance of the amplifier should be high compared to R so that the RC network does not overload and change the necessary conditions.
- The output resistance of the amplifier should be low to minimize the effect of external loading.
- Some methods should be provided to stabilize the amplitude of oscillations. If the voltage gain of the amplifier is too small, the desired oscillation will deteriorate and stop. If it is too large, the output will be saturated and spoiled to the value of the feeding rails.
- With amplitude stabilization in the form of feedback diodes, oscillations from the Wien Bridge oscillator can continue indefinitely.