**Sine Tracking Filters**

Isolate the pure sine tone generated by the drive output.

**The Problem**

When running a sine test, the main interest is the amplitude of the output frequency—the pure tone. We want to make sure we are really testing the product with the specified amplitude at the specified frequency. However, due to the inherent noise of a shaker system, a controller will pick up contributions from noise and harmonics in addition to the pure tone, which alters the reading of the pure tone's amplitude.

**Theoretical Example**

Let's run a sine sweep from 5 Hz to 100 Hz with a 1 G amplitude. As the sweep advances, let's look at one moment in time when we are at 10 Hz. At that very moment in time when we are at 10 Hz, the drive is outputting 1 G, but the input is acquiring noise from all the other frequencies (5 Hz, 20 Hz, 50 Hz, 100 Hz, etc). Perhaps there is a harmonics at 100 Hz which is contributing 0.5 G. And perhaps there is system noise at 50 Hz, which is contributing 0.3 G. The controller will then conclude that at 10 Hz, there is already 0.8 G. It adjusts the drive output to account for this G reading at 10 Hz and will now only output the remaining 0.2 G required to total 1 G at 10 Hz. It now measures a total of 1 G at 10 Hz, but it is not actually outputing 1 G at 10 Hz. It is only outputting 0.2 G at 10 Hz. This is a significant difference. The amplitude of the output frequency has been adjusted. Since the main interest in a sine test is the amplitude of the output frequency, the test is not truly producing the desired results.

**The Solution**

A sine tracking filter is used to isolate the pure sine tone so that the controller can obtain an accurate reading of the pure tone's amplitude and accurately control the pure tone. It is called a "tracking" filter because it tracks along with the test as it moves through different frequencies, filtering out noise at frequencies of non-interest, keeping the bandwitdth narrow, and thereby isolating the pure sine tone at each frequency.

In our example above, amplitude readings at frequencies other than 10 Hz were affecting our test. Applying the sine tracking filters to our test, we can now filter out the noise that was read at 100 Hz (0.5 G) and 50 Hz (0.3 G). At that one moment in time when the sine sweep is at 10 Hz, the controller now measures 0 G at 10 Hz (instead of 0.8 G), and adjusts the drive to output a full 1 G at 10 Hz. The test is now producing the desired results.

**Tracking Filters Experiment**

The above was a simple explanation to demonstrate how frequencies of non-interest affect control readings. In reality, the controller controls based on the average RMS that it sees of the defined bandwidth. The below experiment will probe this matter in more depth.

**Setup:**

VR9500 controller running a sine sweep from 300 - 4,000 Hz at 1 G. The output is looped to the input. A 1,000 Hz wave at 1 G is generated by a function generator and is fed into input channel 2.

**Without Tracking Filters:**

Without a tracking filter, the controller is reading 1 G over the entire bandwidth during the entire sweep. And therefore, the controller plots 1 G at every frequency. Even though there is 0 G being output at all frequencies other than 1,000 Hz, the display still shows a 1 G reading for all these other frequencies. Why? Because as it moves through every frequency, its sights are set on the entire bandwidth and not just the frequency of interest. The entire bandwidth has a 1 G acceleration at all times, but the individual frequencies (except at 1,000 Hz) are not contributing any acceleration to the bandwidth. Without a tracking filter the controller would read acceleration from all frequencies and control based on the average acceleration, even though the acceleration (from noise and harmonics) doesn't belong to the frequency of interest—all unfiltered contributions are averaged into the control.

**Applying Tracking Filters**

The user defines the bandwidth of the tracking filter in VibrationVIEW's Sine parameters. The tracking filter bandwidth is defined as both fractional bandwidth and maximum bandwidth.

** Fractional bandwidth** sets the bandwidth of the tracking filter as a percentage of the output frequency (not a percentage of the total bandwidth). For example, suppose we have a 20% fractional bandwidth. When the sine sweep (output frequency) is at 10 Hz, the tracking filter bandwidth is now 20% of 10 Hz which equals 2 Hz. With a 2 Hz tracking filter bandwidth, at a 10 Hz output frequency the control is averaging the accelerations from 9 Hz to 11 Hz, and filtering out all the other frequencies.

**sets the maximum allowable bandwidth of the tracking filter.**

*Maximum bandwidth*The fractional bandwidth is not allowed to exceed the maximum bandwidth. The smaller of the two bandwidths is always used. As the output frequency increases, the fractional bandwidth grows larger as we move into the higher frequencies. For example, at 10 Hz, the 20% fractional bandwidth is only 2 Hz. However, at 2,000 Hz the fractional bandwidth is 400 Hz - a very large tracking filter. Now noise from anywhere between 1,800 Hz and 2,200 Hz could be contributing to the reading.

Assuming the sweep starts with low frequencies, as it moves through the sweep, the fractional bandwidth grows larger and larger until it equals the maximum bandwidth. This point is considered the crossover frequency. After this point, tracking filter bandwidth is governed by the maximum bandwidth.

In our experiment, we set various fractional bandwidths for our tracking filter and observed the tracking filter's behaviour at 1,000 Hz.

The higher the fractional bandwidth percentage, the wider the tracking filter is. The wider the tracking filter is, the earlier the acceleration will rise. As the filter sweeps, a wider tracking filter will encouter the 1,000 Hz input signal sooner than a narrower tracking filter (lower bandwidth percentage) would. When viewing the figure above, this is why we see the acceleration rise sooner with the highest (20%) fractional bandwidth percentage. The acceleration rise happens much closer to 1,000 Hz when using the narrowest fractional bandwidth percentage (1%).

**Final Comments**

- Smaller value tracking filters (narrower bandwidths) provide increased filtering, which provides greater stability
- Stability can improve performance when sweeping through sharp resonances
- Reduced filtering (larger bandwidths) will improve performance at extreme low frequencies
- Increased filtering comes at the cost of increased response times (requires more measurement time)
- Tracking filter response time and bandwidth are inversely proportional. Although one can set a response time and a tracking filter bandwidth, performance is limited by this inverse relationship. 1/TFBW = minimum RT in seconds and 1/RT = narrowest TFBW