Modulation Domain Analysis

A New Measurement Technology

by
Garth Gelster
Product Marketing Engineer
Hewlett-Packard Company Test and Measurement Group, Santa Clara Division
[Ghost written by Mark Haas]

Every day, designers of a wide range of electronic and electro-mechanical systems confront the opposing demands for increased system performance and lower system cost. Communications channels must carry more information more quickly, laser printers need greater resolution and speed, computer systems need to process more data faster. But as error budgets for these designs shrink, the need for stability increases.

Jitter and other unintentional modulations can severely limit the performance of sophisticated, high-speed systems, but these effects can be difficult to study, and their sources virtually impossible to identify. Many of today's measurement techniques using traditional instruments like the oscilloscope and spectrum analyzer are no longer sufficient to provide adequate information to make demanding design decisions. Those that do are often cumbersome, difficult to use or very expensive. A new way of seeing data is needed to design and test the growing number of systems that either incorporate complex modulation techniques or are troubled with unintentional modulation or jitter.

The modulation domain analyzer is beginning to gain wide acceptance as an instrument capable of revealing information that has previously been expensive and difficult (and sometimes impossible) to obtain. As a complement to more traditional instruments, the modulation domain analyzer offers designers an easy, low-cost way to directly view the precise behavior of servo and stepper motors, laser printers, flow meters, tape drives and anti-lock braking systems. By directly measuring frequency, phase or time interval versus time, it reduces the complexity and time involved to measure the transient response of voltage-controlled oscillators (VCOs) and phase-locked loops -- common yet essential circuits in many electronic and electro-mechanical applications -- when compared to conventional measurement techniques. The analyzer's statistical functions provide insight into the operation of a variety of spread spectrum applications, from wireless local-area networks and cordless telephones, to advanced military communications, radar systems, and next-generation cellular telephones. And the modulation domain analyzer is essential to understanding potential sources of jitter and other undesired forms of modulation in integrated circuits, video and compact disk players, and digital communications systems.

Entering the Modulation Domain

Intentional modulation puts information on a carrier signal. Familiar examples are FM radio, CD players and motor control. Unintentional modulation, however, can hide or completely block the information being transmitted. Unintentional modulation is known by many names, including jitter, cogging, wobble, residual FM, phase noise and many more. The modulation domain can reveal both types of modulation.

Most engineers already are familiar with the time and frequency domains. The time domain is a view of voltage versus time, most commonly viewed on an oscilloscope, while the frequency domain is a view of voltage versus frequency, most commonly viewed on a spectrum analyzer. The modulation domain is the third way to look at signals -- frequency versus time. The modulation domain analyzer provides this missing view.

A frequency modulated signal offers a simple example to contrast these three views. Figure 1a shows a frequency modulated carrier in the time domain. It's very difficult to determine, however, exactly what is happening in this FM signal. The peak-to-peak deviation, modulation rate and the modulating wave shape are all hidden in the time domain view.

The frequency domain view, shown in Figure 1b, is a distinct improvement. The center frequency is easily determined, and some information about the peak-to-peak deviation and rate can be obtained. The modulating wave shape, however, is still unknown.

Frequency modulation on a carrier is easily viewed directly and analyzed in the modulation domain, as seen in Figure 1c. Precise center frequency, peak-to-peak deviation and rate information is displayed on screen, and the modulating wave shape is apparent.

In essence, the modulation domain analyzer does for frequency what the oscilloscope does for voltage. The digitizing oscilloscope, now a familiar test instrument on virtually every workbench, adds the time dimension to voltmeter readings, providing a picture of the voltage variations over time. Changes in voltage are easily captured and analyzed. Measurements like Vp-p, overshoot and rise time are simplified because continuous voltage measurements can be displayed as a function of time.

The modulation domain analyzer provides this same simplicity for frequency measurements. It adds the time dimension to frequency counter results, providing a picture of frequency variations over time. As a result, it becomes simple to study the step response and post-tuning drift of a voltage-controlled oscillator (Figure 2), or view acceleration and deceleration plots to characterize motor performance (Figure 3).

The modulation domain analyzer does more than just plot individual frequency measurements over time, however. It makes frequency measurements continuously without giving up precision, avoiding the dead times between measurements traditionally found in frequency counters or time-interval analyzers, as shown in Figure 4. These measurements are made by counting zero crossings of the input signal and "tagging" these with time stamps. Event and time registers continuously accumulate data, and a latch removes the data synchronously with the input signal without having to stop the counting or reset the registers. Then, by knowing the timing and event counts, frequency, as well as phase and time interval information, can be obtained either in real-time or using post-measurement processing.

This measurement technique not only maintains the relationship between measurements, but also ensures no measurement information is lost between samples. All this can be done with a single capture, thus eliminating the need for cumbersome, time-consuming profiling methods common with today's frequency counters, and ensuring the device is tested in the same way it is used.

In contrast, a conventional frequency counter accumulates events and time data only during a user-specified gate time or sampling interval. After a measurement is made, registers must be read, a frequency calculation done and the counter's internal circuitry must be reset. All this causes dead time between successive frequency measurements, resulting in missing information and the loss of timing correlation.

Sampling in the modulation domain is different from time domain sampling, as shown in Figure 5. A digitizing oscilloscope samples at a rate set by the internal time base, and the data gathered is the input voltage's amplitude. A modulation domain analyzer's sample rate is determined by the input signal, and the data acquired is the timing of the input event. For frequency and time interval measurements, modulation domain sampling is much more efficient, as only one sample per cycle is required, and sampling occurs only when the input signal is present. Further, modulation domain sampling is immune to variations in signal amplitude.

Precise, Single-Shot Signal Characterizations

Modulation domain analysis holds many advantages over traditional measurement techniques for characterizing complex signals. Perhaps one of the most widespread applications of modulation domain analysis is in characterizing the operation of voltage-controlled oscillators (VCOs).

VCOs are at the heart of many electronic systems, including phase-locked loops (PLLs), radars and communication systems. The overall performance of these systems is often limited by the VCO's performance. Therefore, a complete understanding of the VCO's characteristics is required to optimize system performance.

VCOs can exhibit various kinds of modulation, both intentional and unintentional, and both are of concern to the VCO designer and user. The VCO may be intentionally modulated in order to measure its sine wave bandwidth and tuning range. The unintentional modulations that can severely limit VCO performance include overshoot, settling, tuning nonlinearities, unstable frequency setting (repeatability) and post-tuning drift.

To properly characterize a VCO requires it to be tested in the same manner in which it will be used. Most applications require the VCO to operate at one frequency and then switch rapidly to another frequency where it will stay for some time. Conventional test techniques, however, either require repetitive signals or lack sufficient measurement resolution in single-shot modes, and are cumbersome and temperature sensitive. As will be seen, modulation domain analysis has distinct advantages over traditional methods.

VCO step response and post-tuning drift are two critical measurements required to determine VCO performance, and clearly demonstrate the advantages of modulation domain analysis over traditional measurement techniques. Step response is usually defined as the time required for the VCO to move from one frequency to another, plus the time required for the VCO to settle at the new frequency. This measurement is typically made using a very high sampling rate. Post-tuning drift looks at how stable the VCO is after it steps. It picks up where step response leaves off, beginning after the VCO has settled at the new frequency, is sampled at a much lower rate, and lasts up to many hundreds of seconds. Both are shown in Figure 6.

Two methods are currently used to measure VCO step response and post-tuning drift. One method uses a frequency counter and delay generator, while the other method employs a frequency discriminator and digitizing oscilloscope. Figure 7 represents a typical setup for the method that profiles the frequency step with a counter using an external gate. The gate is moved through the step sequentially as the step is repeated. In this way, a series of frequency snapshots of successive points in the step response is obtained, each offset from the input voltage step by an incremental time. Because this method requires the VCO to be stepped repeatedly, it assumes that the VCO steps the same each time and that heating and hysteresis effects are negligible. It also requires custom software for the computer to control the delay generator, read in the measurement from the counter and generate a frequency versus time plot.

Single-shot measurements are possible using a frequency discriminator followed by a digital oscilloscope and a computer, as shown in Figure 8. Because discriminators often have a narrower bandwidth than the VCO under test, it's not uncommon to need a different one each time a new frequency range is encountered. The discriminator is also sensitive to both ambient temperature and the amplitude of its input signal. Together, these factors suggest that full discriminator characterization is mandatory before it can be used in this setup. Furthermore, this type of test system needs frequent calibration if it is to be used with any confidence.

A low-cost solution can be achieved by using a variable persistence display in place of one with a conventional phosphor. This analog implementation not only has writing rate limitations, but it also adds noise, amplitude error and more calibration problems. Replacing the analog display with a waveform digitizer as in Figure 8 requires a computer and special software to be effective. This system gives single-shot performance and offers the potential for system automation. But, discriminator characterization and custom software remains a challenge to the designer.

The test setup shown in Figure 9 demonstrates how much simpler it is to make step response and post-tuning drift measurements with a modulation domain analyzer. The resulting display, Figure 10, shows VCO frequency directly as a function of time, and is from a single-shot measurement that duplicates typical VCO operation. The vertical dashed markers can be moved to provide numerical readouts of both overshoot and settling or transition time. The frequency triggering capability of some modulation domain analyzers eliminates the need for a separate sync signal to trigger the instrument.

Pulse Width Modulation and Jitter

Many of today's information storage devices, such as compact discs and tape drives, encode data using a form of pulse width modulation. Many other products like anti-lock braking systems, switching power supplies and servo control of motors use pulse width modulation to maintain control. The modulation domain analyzer is a valuable tool for characterizing these systems.

The important characteristics of pulse width modulation are the width of each pulse and the timing relationship between pulses. Although both the oscilloscope and the modulation domain analyzer can display a signal with pulse width modulation, it is difficult for the oscilloscope to actually measure it. The number of consecutive pulses that can be measured by a digitizing oscilloscope is limited to the depth of its memory, and it cannot automatically provide results of more than one pulse width at a time.

The modulation domain analyzer can make literally millions of pulse width measurements in seconds. The results are precise measurements of the pulse widths, as well as the relative timing of each pulse. The analyzer can arrange these measurements in value order to display a histogram showing how often a given pulse width value occurred, as shown in Figure 11. This not only yields pulse width distribution, but also gives an indication of each pulse width's timing stability in terms of standard deviation, mean, peak-to-peak deviation and probability of occurrence.

Jitter, a form of undesired modulation, can limit system performance in a wide range of applications, including telecommunications systems, digital storage devices like hard disk drives, electro-mechanical systems, laser printers and more. Modulation domain analyzers can measure and characterize jitter by plotting time interval measurements versus time, and analyzing the plot for the extent of the jitter and any periodic components. By performing a fast Fourier transform (FFT) on the data, the modulation domain analyzer can display the spectral content of the jitter, revealing otherwise hidden sources of jitter.

In the time domain, the oscilloscope will show that there is jitter on a signal, but has trouble characterizing it. The oscilloscope is incapable of collecting enough information to reveal repetitive patterns in the jitter. Without a large number of samples, statistical calculations cannot be meaningful.

The modulation domain analyzer measures jitter directly by measuring time intervals and displaying those measurements versus the time over which they were collected, revealing any variations. A large sample size can be collected at high rates, producing valid statistical calculations of key jitter measurement parameters such as minimum, maximum, standard deviation and mean. By viewing over time, periodic components can be identified, and peak-to-peak and periodic rate can be ascertained. The data can be displayed versus time (Figure 12a), presented as a distribution in a histogram or as a jitter spectrum plot (Figure 12b). Any periodic components are made apparent by this technique, an invaluable aid in tracing down the sources of the problem.

A New Measurement for Technology

Critical for the development of new products and systems is the availability of instrumentation to properly and efficiently test them from the design and prototype phase through manufacturing. Without such instruments, manufacturers can neither debug system problems, fine tune product performance nor ensure that products meet specifications.

The modulation domain analyzer offers designers an easy, low-cost way to directly view the precise behavior of servo and stepper motors, laser printers, flow meters, tape drives, anti-lock braking systems, and next-generation cellular telephones. It significantly reduces the complexity and time involved in studying the transient response of voltage-controlled oscillators (VCOs) and phase-locked loops as compared with conventional techniques. Statistical functions provide insight into the operation of a variety of spread spectrum applications, from wireless local-area networks and cordless telephones, to advanced military communications and radar systems. And the modulation domain analyzer is essential to understanding potential sources of jitter and other undesired forms of modulation in integrated circuits, video and compact disk players, and digital communications systems. The modulation domain analyzer can reveal information that has previously been expensive, difficult and even impossible to obtain, and will take its place beside the oscilloscope and spectrum analyzer found on every test bench.

Sidebar 1 -- Direct Display of Velocity Profiles

Motors, used in a wide range of applications from consumer products to industrial robotics, can operate under servo control or open loop. In either case, the motor's performance is often critical to the performance of the product or system. Consequently, an easy method is needed to characterize a motor's performance. The modulation domain analyzer can display trapezoidal and other velocity profiles without the need for an external controller.

Characterizing a motor's performance usually requires the use of indirect measurement methods. Tachometers can change the dymanics of a system enough to invalidate the measurements, and often don't work well at low speeds. Many systems today incorporate optical encoders for positioning information, and this is a useful source of measurement information. Still, this requires a controller and custom electronics to count and analyze pulses from the encoder for graphical display.

Viewing a shaft encoder or tachometer output on an oscilloscope shows the speed is changing, but it does not show anything about how it is changing, such as the linearity, overshoot or other quantitative details.

The modulation domain analyzer makes it easy to capture and view motor spin-up directly by measuring shaft encoder output frequency (motor speed) and displaying it as a function of time:

Sidebar 2 -- Characterizing Polygon Mirrors

Multi-faced polygon mirrors are a critical element in the operation of laser printers, phototypesetters, night vision goggles and a number of other hi-tech devices. Any imperfections in the alignment or surface of the mirror faces, any rotational wobbling (jitter) of the mirror assembly or any motor speed fluctuations will result in lowered system performance. Correct characterization of the polygon mirror/motor assembly, therefore, is essential.

In a laser printer, for example, a rapidly switched laser beam directed at the rotating mirror surfaces is swept across a metallic drum causing points or pixels on the drum to become charged (write black) or uncharged (write white). The resulting charge on the drum is then transferred to a sheet of paper which is then sprayed with toner that sticks to the charged areas, causing an image to be printed. Poor mirror assembly performance would adversely affect the print quality by causing misalignments of the pixels.

When the laser beam is scanned across the surface of the drum assembly (using the printer example), the scanning time from start of scan (SOS) to end of scan (EOS) can be measured continuously over time using a modulation domain analyzer in a setup similar to the one shown in Figure SB-2a. As the mirror assembly rotates, the laser beam directed at the mirror is swept past first one photodetector and then another, producing two pulse trains as shown in Figure SB-2b.

Ideally, the the time intervals between SOS and EOS from surface to surface, as well as for each surface individually, should be identical over any length of time. In the real world, however, variations will exist. The resulting timing variations represent motor speed fluctuations (rotational jitter) as well as imperfections in the geometry of the mirrors. Measuring "one-face" jitter can isolate the two sources of timing variations.

The maximum time interval deviation for any one mirror face is indicative of the motion control performance of the assembly. To measure one-face jitter, time interval measurements are made on only a single mirror face. Thus, on a hexagonal mirror, every sixth time interval is measured. This is accomplished easily with the sampling capabilities built into a modulation domain analyzer.

The modulation domain analyzer can display the results as a histogram to yield a direct measurement of rotational jitter. From the histogram, the minimum and maximum time intervals can be obtained, as well as the mean. The peak-to-peak jitter can then be calculated as (Tmax - Tmin) /Tavg.

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