# Perfect timing: performing clock division with jitter and phase noise measurements

As clock speeds and communication channels run at ever higher frequencies, accurate jitter and phase noise measurements become more important, even as they become more difficult and expensive to manage. While measuring ultra low-jitter devices and equipment, the engineer is continually required to ask whether the measurement values are the result of the device under test (DUT) or if they are due to the equipment being used.

The engineer is also constantly looking for methods of expanding the reach of the equipment at hand. Here are some practical pointers and observations to assist in situations where clock signals have been divided down from higher frequency voltage-controlled oscillators (VCOs).**Time vs. frequency domain**

Most modern equipment that measures jitter can be placed into one of two broad categories: time domain and frequency domain. Time domain equipment typically comes in the form of a high-speed digital oscilloscope with high single-shot sampling bandwidth. Frequency domain equipment usually comes in the form of a spectrum analyzer, a spectrum analyzer with phase noise measurement capability or a phase noise analyzer. Each of these two categories of equipment has its own set of advantages and disadvantages. However, it should be remembered that they are measuring the same phenomena, albeit with a different approach. Let’s take a closer look at the key differentiating characteristics of these two approaches to measuring jitter.

As shown in figure 1, peak cycle-to-cycle jitter is the maximum difference between consecutive, adjacent clock periods measured over a fixed number of cycles, typically 1ku or 10ku. It is used whenever there is a need to limit the size of a sudden jump in frequency. For example, when driving a PLL it can be desirable to limit the size of an instantaneous change in frequency to ensure that downstream PLLs remain in lock.

Fig 1: Cycle-to-cycle jitter

Fig 1: Cycle-to-cycle jitter

As shown in figure 2, peak-to-peak period jitter is the difference between the largest clock period and the smallest clock period for all of individual clock periods within an observation window (typically 1ku or 10ku cycles). It is a very useful specification for guaranteeing the setup and hold time of flip flops in digital systems. The term peak-to-peak is defined to be the difference between the smallest and the largest period value sampled during a measurement.

Fig 2: Period jitter

Fig 2: Period jitter

As shown in figure 3, time interval error (TIE) jitter is also known as accumulated jitter and phase jitter. It is the actual deviation from the ideal clock period over all clock periods. It includes jitter at all jitter modulation frequencies and is commonly used in wide area network timing applications, such as SONET, synchronous Ethernet and optical transport networking (OTN).

*Fig 3: TIE jitter*

Note that different statistics can be taken for all types of jitter. That is, root means squared (RMS), peak-to-peak and other statistical values exist for cycle-to-cycle, period and TIE jitter, although some are in more common use than others. Whenever peak-to-peak statistics are used, the number of samples taken needs to be large enough to have confidence in the measurement. Typically, such sample sizes range from 1,000 to 10,000.

Time domain equipment has the virtue of being able to directly measure peak-to-peak, cycle-to-cycle, period and TIE jitter. This measurement approach permits the measurement of jitter for very low frequency clock (or carrier) signals. By post-processing the data with techniques such as FFTs and digital filters, it is possible to integrate the phase noise value over a specific band of frequencies to generate RMS phase jitter values. Another key point is that time domain equipment is much better at measuring data-dependent jitter, which makes it very useful for high-speed serial links that use serializer/deserializer (SERDES) technology.

Frequency domain equipment cannot directly measure peak-to-peak, cycle-to-cycle or period jitter, as its native capability is to measure the RMS power of signal in a given frequency band. Frequency domain equipment is also awkward for measuring data dependent jitter. However, the best frequency domain instruments have a lower noise floor than the best time domain instruments. This fact makes frequency domain equipment the instruments of choice for ultra-low phase noise clock signal measurements that are free of data-dependent jitter. Table 1 summarizes the differences between time and frequency domain instruments.

*Table 1: Time vs. frequency domain instrument differences*

Because we are focusing on the measurement of low-jitter clock signals, there is no need to further discuss time domain equipment other than to say that various mathematical estimation and translation approaches can be used to go from one type of jitter measurement to another. For example, it is possible to use a crest factor and a desired bit error rate (BER) to go back and forth between peak-to-peak and RMS jitter.

Another example is using a Fast Fourier Transform (FFT) of time domain data to provide frequency domain information and filtering. However, it should be remembered that most of these techniques rely on mathematical models that, though they may be good approximations in most situations, have their limitations and should only be utilized with care and thought.