Here it is explained how does a Wien-Bridge oscillator work, how to design and construct Wien-Bridge oscillator. Wein-Bridge oscillator is one of the earliest discovered sine wave oscillator. Any oscillator has two main components-(1) an amplifier and (2) feedback circuit. The amplifier component of Wien-Bridge oscillator can be either BJT transistor amplifier, JFET transistor amplifier or Operational Amplifier(Op-Amp). The feedback circuit used in Wien-Bridge oscillator is the lead lag RC networks. Here the working principle of LM358N IC(Integrated Circuit) op-amp based wien bridge oscillator is explained.
Wien-bridge oscillator circuit diagram
The following shows Op-Amp based Wien bridge oscillator circuit diagram.
The above Op-Amp Oscillator is also know as RC Wien Bridge oscillator
with op-amp. It is a single supply Wien bridge oscillator where L358N
op-amp is used as the amplifier and the RC network, R1,C1, R2 and C2
forms the feedback circuit. These the series and parallel RC networks is
called lead lag circuit in Wien bridge oscillator. The R1,C1
forms the lead and R2,C2 forms the lag RC network which causes the
circuit to oscillate. This back and forth oscillation generates the
Wein-Bridge oscilator sine wave at the output.
The values of R1 and R2 are the same and the values of C1 and C2 are the same. These resistor and capacitor values sets frequency of Wien Bridge oscillator.
Frequency of Wien Bridge oscillator
The Wien-Bridge oscillator frequency formula is as follow.
\(F_{r}= \frac{1}{2\pi RC}\) ------------->(1)
where, R=R1=R2 and C=C1=C2 in the above wien bridge oscillator schematic diagram.
Feedback Fraction or Beta(\(\beta\)) of Wein-Bridge Oscillator
The amount of voltage feedback back to the non-inverting input is called feedback. That is, if \(V_o\) is the output signal of the oscillator and the \(V_i\) is the input signal at the non-inverting input coming from the lead lag RC circuit, then feedback fraction denoted by \(\beta\) is,
\(\beta=\frac{V_o}{V_i}\) ----------------->(2)
We can solve the above equation to relate the resistor value R=R1=R2 and the capacitive reactance Xc which results into:
\(\beta=\frac{1}{\sqrt{9-(X_{c}/R-R/X_{c})^2}}\) ---------------->(3)
Gain(A) of Wein-Bridge Oscillator
The resistors R3 and RF in the above Wein-Bridge circuit schematic sets the gain(A) of the amplifier. Here a potentiometer RF is used for the feedback resistor in the Wien bridge oscillator. The Wien-Bridge oscillator gain is same as gain for an non-inverting amplifier and is given by,
\(A=1+\frac{R_3}{R_F}\) ---------------->(4)
For oscillation, the condition for oscillation in Wien bridge oscillator is provided by the Barkhausen criteria which is,
\(A \beta = 1\) ---------------->(5)
where A is the gain of the amplifier and \(\beta\) is the feedback fraction.
While the resistor and capacitor values in the lead lag feedback circuit, R=R1=R2 and C=C1=C2 can be determined by using the Wien bridge oscillator frequency formula given in equation(1) above, the value for the feedback resistor RF and the resistor R1 can be determined by solving the Wien-Bridge oscillator gain equation(4) and the equation(5) which is the condition for oscillation in Wien bridge oscillator.
Gain Control and Stablity
Solving equation(4) and (5) for feedback resistor(\(R_F\)) we have,
\(R_F=\frac{(1-\beta)R_3}{\beta}\)
or in terms of gain A,
\(R_F= (1-A)R_3\)
These
resistors values, \(R_F\) and \(R_3\), controls the gain of the
oscillator and hence the Wien-Bridge oscillator stability because of the
relation between gain and feeback fraction \(\beta\). Note that the
feedback \(\beta\) is related to the lead lag RC network. Also these
resistors sets the Wien bridge oscillator amplitude of the output sine
wave.
Wein-Bridge Oscillator Design Example
Here we will explain the wien bridge oscillator design with example calculation. First we need to set desired sine wave frequency of the oscillator. Let say the frequency of the oscillator is 160Hz. The frequency of oscillation of a wien bridge oscillator is given by,
\(F_{r}= \frac{1}{2\pi RC}\)
We abitarily select value of capacitor equal to C=0.1uF then solving for R in the above equaion, we get,
R = 10KOhm
Next we first calculate the feedback fraction, beta(\(beta\)) for the RC lead, lag circuit. We have,
\(\beta=\frac{1}{\sqrt{9-(X_{c}/R-R/X_{c})^2}}\)
R=10KOhm and Xc=2*3.14*f= 2*3.14*160Hz=1004Ohm and therefore feedback is \(\beta\)=33.33.
Then we need to calculate the gain resistor values. If we set R3=2KOhm then using the above wien bridge oscillator equation derived above,
\(R_F=\frac{(1-\beta)R_3}{\beta}\)
We get,
\(R_F=\frac{(1-0.33)\times 4K\Omega}{0.33}=4K\Omega\)
We can set this feedback resistor value using the potentiomter.
So in this way we can calculate the component values for Wein-Bridge RC oscillator. You can also use the wien bridge oscillator calculator for calculating the component values.
Video of Wein Bridge Oscillator Simulation in Proteus
The following Wien-Bridge oscillator proteus simulation shows how the Wein-Bride oscillator works.
In the video we can see that by changing the feedback potentiometer resistor value the wien bridge oscillator output waveform changes in amplitude as explained in the wien bridge oscillator analysis above. It also shows wien bridge oscillator sine wave at the output.
Futhermore
The
circuit of wien bridge oscillator that was explained above is the basic
Wein-Bridge oscillator. A more practical Wein-Bridge oscillator circuit
uses diode and JFET transistor for automatic amplitude control by
controlling the feedback resistor which controls the gain and hence
relates to feedback beta value which in turn is related to the RC lead,
lag networks.The next tutorial Practical Wien-Bridge Ocillator with Automatic Amplitude Control explains how to build a practical Wein-bridge oscillator.
