Hello, and welcome to the TI Precision Lab discussing the PLL phase noise figures of merit. In this video, we'll discuss the phase noise performance metrics and shaping by the loop filtered transfer functions as well as how it applies to an actual design. And understanding of these key performance parameters will go a long way in helping achieve a clean and smooth PLL design implementation. If you would like more background on PLL basic building blocks or key parameters, we have additional Precision Labs training modules that cover these topics. 

Before we go into discussing noise characteristics, let's do a very quick PLL review. The purpose of the PLL is to phase-align the signal from the R divider and the feedback signal from the N divider. Most of the phase noise transfer functions are related to the N divider, VCO, phase detector, and loop filter. 

As discussed in the previous training, the PLL loop bandwidth is not set by the low-pass filter alone. Changing any of these parameters-- K VCO, K PD, and N also influences the closed loop bandwidth. For the basic PLL structure, we can define some fundamental transfer functions and notation to help with understanding phase noise. 

PLL transfer functions can be derived by classical control loop theory. G sub s is sometimes called open loop gain or open loop transfer function and is defined as the gain from the input of the phase detector to the output of the PLL where s is a complex frequency. The open loop gain is comprised of the phase detector charged from gain constant, K PD; the loop filter transfer function, Z sub s; and the V CO input voltage to phase relationship K VCO over s. Although the frequency path is simply 1 over N, we refer to it now as H to align with standard control theory notation for feedback. 

To derive the transfer function, one puts a summation block at each point of interest and solves for the ratio of the output noise to the input noise in a closed loop condition. You may notice that all blocks except for the V CO are multiplied by the low pass function, G over 1 plus GH. The V CO was multiplied by the high-pass transfer function, 1 over 1 plus GH. 

Let's take a closer look at these transfer functions because they will come up again in other training modules as critical factors in topics such as loop filter design, lock time, and spurious noise. 

For the reference oscillator, note the factor of 1 over R, implying a higher R divider is better. However, if the same Fosc frequency is used, the N divider increases proportionately with R. So there is theoretically no change in gain. 

On the other hand, if the Fosc frequency is increased and divided down to the same phase detector frequency, then there often is an improvement. This is because a higher Fosc frequency typically has better noise when scaled to frequency. 

The PLL N- divides the V CO frequency and phase by a factor of N. This means the phase noise from the V CO is reduced by a factor N before it shows up to the phase detector. Due to the properties of the closed loop system, the PLL in bad noise will be effectively multiplied by 20 log N. 

For example, an N-counter value of 100 translates to 40 dB gain of in-band noise. In other words, if you reduce N by a factor of 2, there is a theoretical 60 dB improvement. This principle can also be applied to the R-counter as well. For both the N and the R-counter, this rule holds provided that the phase detector rate does not change. For dividers which are outside the loop, such as the output dividers, higher divide values reduce the noise at the output as well. 

For the phase detector, note the factor of 1 over K PD. This implies a W charge pump current can theoretically yield a 6 dB improvement. However, this does not account for the fact that the charge pump noise itself increases as the gain is increased. In practice, there can often be a benefit, but not the full 6 dB. 

Depending upon the specific PLL device characteristics, there can be a point of diminishing returns, where increasing the charge pump current provides less phase noise improvement. For example, when increasing the charge pump current from 1,600 to 3,200 microamps, you may not always get the same relative benefit as an increase in gain from 100 microamps to 200 microamps. 

As noted previously, the V CO has a different transfer function. This can be approximated as unity gain for frequencies well outside the loop bandwidth and N over the open loop gain for frequencies well inside the loop bandwidth. For the normalized PLL in-band noise analysis, we can assume the V CO noise is not a major contributor. 

When all these noise sources are added up, we've got the PLL in-band noise. Here we see an example of the closed loop noise contributions. Note that both the flat noise and the 1/f noise of the PLL add together. At lower offsets below about 2 kilohertz, the flat noise did not contribute. But there was additional impact from the input reference noise. Around 10 kilohertz is the point where both the flat noise and 1/f noise contribute equally to the total phase noise. Above 1 megahertz, the noise largely follows that of the V CO. 

To simplify characterisation, one can lump all the PLL in-band noise contributions together, excluding the V CO. The normalized flat noise figure of merit and 1/f noise provide a convenient way to predict noise within the loop bandwidth of a PLL. These normalized values account for the charge pump, input path, N divider, and R divider. 

The figure of merit and 1/f noise can be used to predict phase noise and compare two different PLLs for phase noise under two different conditions. Note the figure of merit assumes the V CO noise did not dominate. And some adjustments may be needed for a fractional part since this is does account for phase noise advantage of having lower fractional N-counter. 

Inside the loop, at medium offsets, the major noise sources are the PLL noise floor, the so-called figure of merit. You may also recall this flat noise because you can see this plot-- the frequency response is flat line. The definition is shown where N is the N-counter value, f PD is the phase detector frequency in hertz, and PN is the phase noise. 

For offset frequencies close to the carrier, the PLL noise characteristic is the flicker noise sometimes called 1/f noise because its noise power is inversely proportional to the frequency. Therefore, one can normalize out the offset and output frequencies to get this normalized 1/f noise index. 

In this case, f out is the output frequency, delta f is the 1/f offset frequency from the carrier, and PN is the phase noise. When using the TI PLL phase noise software PLLatinum sim, these parameters are used for detecting PLL phase noise with good correlation to measure phase noise data. Source data for these two noise sources are usually found in the data sheet. Typically 1/f noise and figure of merit are better than minus 120 dBc per hertz and minus 230 dBc per hertz respectively. 

This table provides some guidance on design choices in PLL V CO design that can be manipulated to improve phase noise performance. In general, an architecture enabling higher phase detector frequencies will provide better phase noise profile. Keep in mind that no amount of clever design or optimization can overcome the use of components with high intrinsic noise. Selecting the best reference clock input while meeting application cost targets is always a sound design decision. If close-in phase noise is important for a particular application, then choose components that give the desired close-in performance and acceptable performance at higher offsets. 

That concludes this video. Thank you for watching. Please test your knowledge of the material with a simple four-question quiz to wrap it up. If you need more information or technical resources on TI clocks and timing products, please visit TI.com and type in backslash clocks.