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In part two of PLL Loop Filter Design, we'll pick up where we left off in part one, designing and optimizing loop filters. After that, we'll showcase how easy the process of designing the loop filter can be with the right simulation tool. How can we use the loop filter to attenuate different types of spurs?

Spurs can be divided into two broad categories based on the mechanisms of the PLL that help provide attenuation. These two categories are inband spurs and outband spurs.

Inband spurs are those spurs that go through the loop filter and are low pass filtered by the loop filter. The spur gain for inband spurs is defined as a gain of the closed-loop transfer function at the frequency offset of the spur. The level of inband spurs is directly related to the spur gain. If the spur gain decreases by 3 db after it changes to the loop filter, then you can also expect the spur magnitude to decrease by 3 db.

Outband spurs are high pass filtered coupled directly to the VCO and follow the VCO transfer function. VCO spur gain is the value of the VCO transfer function at the spur frequency of interest. A higher VCO spur gain will increase the magnitude of the spurs while a lower VCO spur gain will reduce the magnitude of the spurs. Recall that the VCO transfer function is a low pass filter.

In the previous Precision Labs video, we've covered the basics of spurs. Here, we get into more of the details. The table lists different types of spurs and whether they can be classified as inband or outband spurs. Spurs at the frequency offset of the input frequency or the phase detector frequency are usually outband spurs. While the crosstalk spurs can be either inband or outband.

The percentage symbol denotes the module operator. Equation, A module B is equal to the remainder of A when divided by B. Two common takeaways from this table are number one, many of the PLL spurs can be improved with a channel divider or a VCO divider in the output path. And number two, using a low amplitude and high slew rate reference clock can help mitigate several different kinds of spurs. To isolate and identify spurs correctly, you may need to vary some of the PLL settings to change the offsets of fpd, fosc, fvco, and change of PLL fraction.

For example, the fout module fosc can only be distinguished from fvco, modular fosc, when using the channel divider that is not equal to 1. When we say that the phase detector spur is impacted by the phase detector frequency, it means that using trial and error and shifting to spur, it is possible to find its patterns in how the spur changes with changing the phase detector frequency.

In some clocking devices, the spur level may decrease with increasing the frequency while in others, the spur level may decrease with decreasing the frequency. The graph illustrates how the gain of an open-loop transfer function changes with a loop filter order. The blue line denotes the gain of the second-order filter. The purple line corresponds to a third-order loop filter. And the red line denotes the gain of a fourth-order loop filter.

As the order of the loop filter increases, the number of poles increase. A fourth-order loop filter transfer function provides more attenuation at high-frequency offsets than a third-order transfer function. This is a beneficial feature to attenuate the magnitude of the spurs.

If you are designing a PLL with an imager end divider, you are likely not to see too many spurs at higher frequency offsets. In this case, you may want to start with a second-order loop filter and evaluate what benefits you can get from a third-order loop filter for the design.

Let's say you were designing a fractional PLL and start with a third only loop filter, if you see a lot of crosstalk spurs and offsets greater than approximately 20 times loop bandwidth, upgrading to a fourth loop filter may provide some extra attenuation to meet your system requirements.

Second-order filters do not provide the best attenuation of spurs as they only have one pole, T1, and can only provide a roll-off of 40 db per decade. With each additional pole, you can get an additional roll-off of 20 db per decade. Third and fourth-order loop filters are better for attenuating spurs. The higher pole ratio, the greater the attenuation. And with a fourth-order filter, you can get roll-off of up to 80 db per decade.

When the pole ratio is zero, there is no extra attenuation. When the pole ratio is one, you get maximum attenuation. , However, this isn't possible with a passive loop filter in reality as the resistors become infinitely large and capacitors tend towards zero. To get close to the best attenuation, a pole ratio of 68% is targeted. With this pole ratio, you can get an attenuation within 1 db of the maximum attainable benefit.

For second loop filter, there are three components and, therefore, three constraints that are needed to find them. The first two constraints come from choosing the loop bandwidth and phase margin, but a third constraint is still needed. The third constraint, gamma, comes from imposing the restriction that the phase margin at the loop bandwidth frequency is maximized.

For the second-order loop filter, this corresponds to choosing gamma equal to one and is a reasonable theoretical starting point. However, based on phase margin, it may be actually better to choose gamma different than one for optimal lock time or spur attenuation. The 3D graph illustrates how lock time varies with gamma and phase margin. The lock time was simulated based on a second-order loop filter with a 10-kilohertz loop bandwidth and a frequency jump from 800 to 900-megahertz.

Gamma is dependent on the ratio of the zero to the sum of the poles in the transfer function. In the equation, omega C denotes loop bandwidth in radians. Kappa is the sum of the poles in the loop filter. In the case of a third-order loop filter, T4 will be zero. And in the case of a second-order loop filter, both T3 and T4 will be zero.

So what is gamma used for? Once the loop bandwidth and phase margin are chosen, gamma can be used as a fine adjustment for spurs and lock time. Also, when the loop filter is partially integrated, tweaking gamma allows one to work around restrictions imposed by restricting component values.

The valley or the magenta-colored portion of the graph represents the best combinations of gamma and phase margin. When gamma is too low or too high, the lock time starts to increase. The recommendations for gamma and phase margin can be generalized as shown in this table. Whatever combination of phase margin and gamma is optimal for one loop bandwidth will be also optimal for another.

Passive loop filters are generally preferred due to reasons of lower cost and lower noise. In some cases, where the charge pump cannot supply the full tuning voltage of the VCO, an active filter may be preferred. Typically, these are devices without an integrated VCO.

On the left are two common types of active loop filters. Choosing an op-amp for an active filter requires paying attention to multiple parameters. Here are some of them. The input rails, particularly the negative input rail, is important to pay attention to as it is likely to have the least headroom. The op-amp must accept the voltage that the charge pump requires to be biased to.

The output from the op-amp must be compatible with the tuning voltage of the VCO. The general rule of thumb is to pick an op-amp, which is usually gain stable, to avoid the desirable voltage noise from multiplying and adding to the phase noise. If the gain is required that the op-amp selected should ideally have very low voltage noise. Other considerations include bias currents, slew rate, and bandwidth.

Let's step to an example loop filter design. A great way to make designing PLLs easier would be by using a software tool, such as TI's PLLATINUMSIM. Instead of going through iterations of extensive calculations, you can use this tool to optimize performance quickly for your clocking needs. At the end of this video, there'll be a link to download PLLATINUMSIM from TI.com.

Go to the Filter Designer tab of the PLLATINUMSIM software GUI to modify the loop filter. Changing the feature level gives you access to specify additional parameters and specific details about your desired loop filter. Select the Advance Feature level.

The order of the loop filter can be modified here. Set the loop filter order to third order. All the loop filter parameters we discussed in the PLL Loop Filter Design training videos, loop bandwidth, phase margin, gamma, and pole ratio can be specified here. Currently, T3 over T1 is the only pole ratio available. If we switch to a fourth-order loop filter, T4 over T3 pole ratio will also be available.

Let's design a loop filter to have a loop bandwidth of 400 kilohertz and a phase margin of 60 degrees, optimizing for jitter. First, we enter our design targets. To access the phase margin target text box, we need to uncheck the auto checkbox next to it. Once we have a design target entered, click on Calculate Loop Filter button to optimize the loop filter for the best jitter.

In the training video on PLL Transit Response, we discussed how to simulate lock time. If your lock time is also important to you, continue onto Simulate Lock Time, make changes to the loop filters needed, and try to achieve the best combination of phase noise, lock time, and spur attenuation for your system.

Thanks for watching this video on PLL loop filter design. Please take a few minutes to test your understanding of the concepts presented in this video by taking the short quiz. In case you haven't, consider watching the previous video in the series, PLL Loop Filter Design, Part One to learn about designing bandwidths for a frequency range and transfer functions of loop filters. If you need more information on clocks and timing products, visit TI.com/clocks.