# RC Phase Shift Oscillator Tutorial

**RC PHASE SHIFT OSCILLATOR**

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In this tutorial, we’ll discuss how RC phase-shift oscillators work and how to implement two versions of this circuit using Op-Amp and BJT. How to set the oscillation frequency to your desired value. And finally, test everything out and now let’s get right into it!

Tutorial Contents

** Circuit Diagram **

The general form for the RC phase shift oscillator is shown in the diagram below.

As you may have noticed, the circuit consists of 2 main parts

**I-** 3rd-Order Cascaded RC Filters

And you can pick the value for **R** and **C** to set your desired output frequency as we’ll discuss later.

**II-** Negative-Gain Amplifier

It can be realized using an op-amp or a BJT transistor. The value of the gain **K** should be carefully set for sustained oscillation. This will also be discussed in the next section.

** Principles of Operation **

The basic structure of the RC phase shift oscillator consist of 3rd-order cascaded RC filters and a negative-gain amplifier (-K). Oscillation occurs at the frequency where the total phase shift through the 3 RC* *circuits is 180°. The negative gain of the amplifier stage (-K) will add another 180° phase-shift. Resulting in a total phase-shift of 360° or 0° which is the required condition for oscillation.

For sustained oscillation, there is a required condition that must be met. It’s called “Greater Than 1 Total Loop-Gain”. The attenuation B of the 3rd-order RC feedback loop network is

Therefore, to meet the >1 total loop gain condition, the closed-loop gain of the amplifier **K** must be set to be slightly higher than **29**. This will guarantee a sustained oscillation at the frequency **F _{r}** which can be calculated using the below formula.

** Important Formulas **

**Fundamental Heuristic**

To maintain a sustained oscillation, the condition below must always be met

**Design Equations**

To set the desired output frequency, use the following formula

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Please be advised that the above equations are not general for all RC phase shift oscillators. They only hold true for 3rd-order RC network based oscillators. But for higher orders, the frequency at which oscillation occurs will change and you can use the below formula, where |

** Circuit Implementation **

There are a couple of ways to implement the RC phase shift oscillator. Each of which deploys a different element for creating the “Negative-Gain Amplifier”. The first one uses an Op-Amp, and the other one uses a BJT transistor as an amplifier.

Let’s assume we’re using resistors of **R** = 5000Ω, and capacitors of **C** = 1nF, then the output frequency **F _{r}** should be as follows

** 1. The Op-Amp RC Phase Shift Oscillator**

**Design**

The ration Rf/R3 determines the closed-loop gain that should be >29. Which means we can pick Rf > R3*29

Rf > 145KΩ .. I’ve chosen 160KΩ

**Simulation**

Let’s Hook an oscilloscope’s probe to the output rail and see how it looks like in simulation!

The resulting output frequency F_{r} is, therefore,

Obviously, it’s not perfect but it’s close enough to the theoretically calculated value of 13KHz.

Here is an animation showing how the signal builds-up to the point where it becomes sustainably oscillating.

** 2. The BJT RC Phase Shift Oscillator**

**Design**

Another way to implement the RC phase shift oscillator is to use a BJT transistor as an amplifier instead of the Op-Amp showed above.

Let’s assume that it’s desired to get a sinusoidal output waveform oscillating @ a frequency F_{r} = **6.5KHz**. We’ve got some capacitors of **C** = 1nF, therefore, we’ve got to calculate the value of the resistance **R** in order to get our circuit to oscillate @ 6.5KHz. We’ll also use the same equation for the output frequency

Substituting by the given values

By solving for R, we’ll find that

Now, we’ve got everything we need in order to implement & build our new design. The schematic diagram for the circuit will look like the figure below.

**Simulation**

Let’s Now hook an oscilloscope’s probe to the output rail and see how it looks like in simulation!

As you can see, the resulting output frequency **F _{r }=**

**6.25KHz**which is very close to the theoretically calculated desirable frequency of

**6.5KHz**. That’s cool, you can now vary

**R**resistors and

**C**capacitors to set the output frequency to whatever value you need.

Here is an animation showing how the signal builds-up to the point where it becomes sustainably oscillating.

That’s it for this tutorial. I hope you find this helpful. if so, you can share it with your network!

if you’ve any questions, you can post them right below. I’ll be glad to help ^^

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So simple explanation

That’s a good thing or bad? XD

I’ve deliberately skipped a few pieces of information to make things more clear & easy to understand. I can do it in more detail for future tutorials.

Regards,

Khaled M.