### What is Phase Coherence, Anyway?

Great question! Phase coherence can be an ambiguous topic, yet one that’s important for RF, electrical, and design engineers to understand. In this post, you will learn some basic definitions of phase coherence. We will then break down these definitions into a simple way of fully understanding this topic. Finally, you will learn if and why phase coherence is affecting your various designs and applications. There’s lots to learn…let’s get to it!

### Two Definitions of Phase Coherence (Out of Many)

Turns out the internet is flooded with several different, and sometimes confusing, definitions. We saved you the time (and suffering) and found two of our favorite definitions:

- In many ways, the term “phase-coherent” is not strictly defined. Often, it is interpreted as signals/systems operating at the same frequency with a consistent phase relationship.
- In physics, two wave sources are perfectly coherent if they have a constant phase difference and the same frequency.

These are both great definitions, although I have a feeling you may be thinking to yourself:

“Ok...Got it! However, I’m still confused. What do these definitions *really* mean?”

Don’t worry! I hate definitions, too. Let’s get into the *good* stuff…

### These Two Questions Will Lead to Many Answers!

A better way to look at the problem of phase coherence might be to ask yourself two simple questions:

- How stable is the phase between the two waves (electrical, light, etc.)?
- Does it change quickly with time?

Keep these questions in mind as we break them down and find the answers you’re looking for!

With two perfect sine waves of the same frequency, the relative phase never changes. When the two waves are always shifted by the same amount *(Fig. 1)*, they’re said to be *coherent*. However, no real wave is perfectly sinusoidal. Also, the two frequencies aren’t always exactly the same. Instead think of a signal that looks sinusoidal in any small piece, but the phase is slowly drifting *(Fig. 2)*.

1. The two sine waves depicted are coherent.

2. The two sine waves depicted are not coherent.

Figure 1 is coherent. The relative difference between any two matching points is exactly the same. Figure 2 is not coherent. The relative difference is always fluctuating.

The figures above represent the ideal and the worst case. As with everything, real life is somewhere in the middle. Something like *Fig. 3* below would be more common to see. In the broad spectrum of the graph, the signals aren’t coherent. But if you look at a small time segment (a few cycles), they are close to being coherent.

3. Within a small time segment, the signals depicted are close to being coherent.

Looking at it this way, the signals are said to have a “coherence time.” If the phase difference of the two waves is the same, they are coherent. More generally, if the phase difference of two waves remains the same during this "coherence time,” they are coherent during that time. In reality, the waves do not remain coherent for an infinite interval, and after the coherence time the phase difference drifts.

### How Does Phase Coherence Affect You?

This phase difference can impact a lot of different fields. Phase is a property of sinusoidal signals (which is pretty much all electronic signals, thanks to Fourier series analysis). So, for example, things like lasers, semiconductor devices, radar, radio receivers, and power grids all can have situations where “electronic phase coherence” is a potential problem. That’s already a pretty broad list, and there are dozens more.

The biggest worry regarding this difference is interference, which *isn’t always* a bad thing. Interference is nothing more than the addition, in the mathematical sense, of wave functions. When interfering, two waves can add together to create a wave of greater amplitude than either one (constructive interference), as in Fig. 4 (left). Alternately, they can subtract from each other to create a wave of lesser amplitude than either one (destructive interference), as in *Fig. 4 (right)*, depending on their relative phase.

4. When interfering, two waves can either add together to create a wave of greater amplitude (left), or subtract from each other to create a wave of lesser amplitude (right).

Either “interference” can be useful depending on the application.

**The bottom line:** Think of signals as waves or vectors. If they are coherent, they add up constructively; if they are non-coherent, they may cancel each other or fading occurs.

Consider learning more about a crystal oscillator’s wave and signal outputs.

### How to Keep Your Future Free of Phase Coherence Problems

One way many industries avoid coherence problems is by using a phase-locked loop (PLL). A PLL is a fundamental concept widely used for different purposes in various fields of electrical engineering (e.g., communications, instrumentation, control system, and multimedia). The main idea of phase-locking is the ability to generate a sinusoidal signal whose phase is coherently following that of the main component of the input signal.

### Phase Coherence vs. Phase Noise

Now that you understand phase coherence, you’re ready to learn more phase noise. Bliley’s comprehensive five-step guide is a great place to start.