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Understanding ultra-low phase noise oscillators

Posted: 29 Jun 2015 ?? ?Print Version ?Bookmark and Share

Keywords:electrical noise? oscillator? jitter? Gaussian? Gaussian?

To an electrical engineer, in an ideal word there would be absence of noise. But what is noise? What is electrical noise? Or more to the point of this paper: What is phase noise? As engineers, we know intuitively that low noise in a system is better than high noise. However, we must somehow quantify this noise in units and terms that we can all be in agreement with C and we will. We will also examine the difference in phase noise performance of commodity vs. low-cost, high-performance crystal oscillators. Understanding the cost performance trade-offs between oscillators is important to a system design. Many times we see two competitive systems separated widely in performance, but NOT in price. The oscillator phase noise characteristics will dominate the entire system performance and spending a few more dollars on the oscillator can turn a mediocre system into a superb system.

However, an engineer can easily over-specify the oscillator, and hence the key is to understand exactly how the oscillator phase noise (or jitter) limits the system performance. To help with this understanding, a tutorial on phase noise and jitter is in order.

Phase noise and jitter in oscillators: A tutorial
In an oscillator, phase noise is the rapid random fluctuations in the phase component of the output signal. The equation of this signal is:

Where:
A0 = nominal peak voltage
f0 = nominal fundamental frequency
t = time
?(t) = random deviation of phase from nominal C "phase noise"

Above, ?(t) is the phase noise, but A0 will establish the signal-to-noise ratio. Figure 1 illustrates this.

Figure 1: The signal to noise ratio is a function of A0.

The noise floor
Noise signals are stochastic and, in a broad sense, noise can be characterized as any undesired signal that interferes with the main signal to be processed or generated. It can disturb any physical parameter such as voltage, current, phase, frequency (or time), etc. Therefore the idea is to maximise the signal and minimise the noise for a high signal-to-noise(S/N) ratio.

Noise power is quantified as

Where
K is the Boltzmann's contant = 1,38 x 10-23 (J/K)
T is the absolute temperature inK
And f= B is the bandwidth in which the measurement is made, in hertz

In the absence of any signal, there is thermal noise floor. This floor level can be specified in a variety of units: Watts, V2/Hz, V/ Hz , dBm/Hz to name a few. For oscillators, it is convenient to use dBm/Hz to define noise density.

Before defining dBm/Hz we need to first define dBm. dBm refers to decibels above 1 milliwatt in a 50? system and is given by

Thus from above equation, 1 milliWatt is equal to 0 dBm.

Equation 2 gives us the magnitude of thermal noise and substituting for K and T we get:

Where B is the bandwidth of interest, for which we will use 1Hz to normalise the result. Using the equation of dBm (Equation 3) , and using the result from above we have:

Setting the bandwidth B to 1Hz will give us the final result in dBm/Hz, and since the log(1) is zero, we have:


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