Numeric Precision vs. DDS Calculations

Using the full frequency resolution of a direct digital synthesizer chip outstrips the capabilities of floating point numbers. Ed takes a look at what’s needed for high-resolution frequency calibration and measurements.

By Ed Nisley

As you saw in my July article, the filter bandwidths and frequency resolution required to characterize low-frequency quartz resonators far exceeded the capabilities of my bench instruments. I decided to take a look at building a special-purpose resonator tester around a cheap direct digital synthesizer sine-wave source, because DDS generators have

PHOTO 1
A knockoff Arduino Nano controls a generic AD9850 direct digital synthesizer circuit, both plugged into standard 0.1 inch headers, with hand-wiring connections below the proto board. The SMA connector provides a mechanically rugged output from the board; the DDS frequencies don’t require its RF properties.

advantages over traditional analog oscillators and frequency counters in computer-controlled measurement systems.

Of course, nothing is ever so simple as it seems. In this article, I’ll explain how numeric precision affects Direct Digital Synthesis (DDS) output frequency calculations, work through the effects of floating-point and fixed-point arithmetic, and show how a carefully tweaked DDS oscillator frequency varies with temperature.

DDS Calculations

You can think of a direct digital synthesizer as a lookup table holding the digitized values of an analog waveform, a counter addressing the table entries in ascending order, and a DAC converting the numbers to analog voltages. The Analog Devices AD8950 DDS chip in Photo 1 has the equivalent of a table with 232 10-bit entries defining a sine wave, a counter clocked at 125 MHz, and a differential output current-mode DAC. The PCB, complete with the DDS and a 125 MHz quartz oscillator, costs under \$20 on eBay or Amazon. …

Read the full article in the September 326 issue of Circuit Cellar

Not a Subscriber yet? Become one today:

Or purchase the September 2017 issue at the  CC-Webshop

Temperature-Compensated Crystal Oscillators

The IQXT-210 series of temperature-compensated crystal oscillators (TCXOs) offers frequency stabilities down to ±0.14 ppm over a –40°C-to-85°C full industrial temperature range. The small-footprint oscillators are encased in miniature eight-pad 5-mm × 3.2-mm package.

Powered from a 3.3-V supply, the IQXT-210 has a typical 12-A current draw depending on the frequency, which can be specified at 10 to 50 MHz. The TCXOs initially offer 11 standard frequencies, including 12.8, 19.2, and 26 MHz.

The IQXT-210s’ output can include various pulling range options, which enables the frequency to be adjusted by a fixed amount for various applications. This also provides remote usage capabilities. The TCXOs are primarily designed for low-power consumption applications (e.g., femtocells, smart wireless devices, fiber-optic networking, microwave satellite communications, LTE/4G base stations, backhaul infrastructure, packet transport network, computer networking, RF modules, Wi-Fi, and test and measurement equipment).

Contact IQD Frequency Products for pricing.

IQD Frequency Products, Ltd.
www.iqdfrequencyproducts.com

Measuring Jitter (EE Tip #132)

Jitter is one of the parameters you should consider when designing a project, especially when it involves planning a high-speed digital system. Moreover, jitter investigation—performed either manually or with the help of proper measurement tools—can provide you with a thorough analysis of your product.

There are at least two ways to measure jitter: cycle-to-cycle and time interval error (TIE).

WHAT IS JITTER?
The following is the generic definition offered by The International Telecommunication Union (ITU) in its G.810 recommendation. “Jitter (timing): The short-term variations of the significant instants of a timing signal from their ideal positions in time (where short-term implies that these variations are of frequency greater than or equal to 10 Hz).”

First, jitter refers to timing signals (e.g., a clock or a digital control signal that must be time-correlated to a given clock). Then you only consider “significant instants” of these signals (i.e., signal-useful transitions from one logical state to the other). These events are supposed to happen at a specific time. Jitter is the difference between this expected time and the actual time when the event occurs (see Figure 1).

Figure 1—Jitter includes all phenomena that result in an unwanted shift in timing of some digital signal transitions in comparison to a supposedly “perfect” signal.

Last, jitter concerns only short-term variations, meaning fast variations as compared to the signal frequency (in contrast, very slow variations, lower than 10 Hz, are called “wander”).

Clock jitter, for example, is a big concern for A/D conversions. Read my article on fast ADCs (“Playing with High-Speed ADCs,” Circuit Cellar 259, 2012) and you will discover that jitter could quickly jeopardize your expensive, high-end ADC’s signal-to-noise ratio.

CYCLE-TO-CYCLE JITTER
Assume you have a digital signal with transitions that should stay within preset time limits (which are usually calculated based on the receiver’s signal period and timing diagrams, such as setup duration and so forth). You are wondering if it is suffering from any excessive jitter. How do you measure the jitter? First, think about what you actually want to measure: Do you have a single signal (e.g., a clock) that could have jitter in its timing transitions as compared to absolute time? Or, do you have a digital signal that must be time-correlated to an accessible clock that is supposed to be perfect? The measurement methods will be different. For simplicity, I will assume the first scenario: You have a clock signal with rising edges that are supposed to be perfectly stable, and you want to double check it.

My first suggestion is to connect this clock to your best oscilloscope’s input, trigger the oscilloscope on the clock’s rising edge, adjust the time base to get a full period on the screen, and measure the clock edge’s time dispersion of the transition just following the trigger. This method will provide a measurement of the so-called cycle-to-cycle jitter (see Figure 2).

Figure 2—Cycle-to-cycle is the easiest way to measure jitter. You can simply trigger your oscilloscope on a signal transition and measure the dispersion of the following transition’s time.

If you have a dual time base or a digital oscilloscope with zoom features, you could enlarge the time zone around the clock edge you are interested in for more accurate measurements. I used an old Philips PM5786B pulse generator from my lab to perform the test. I configured the pulse generator to generate a 6.6-MHz square signal and connected it to my Teledyne LeCroy WaveRunner 610Zi oscilloscope. I admit this is high-end equipment (1-GHz bandwidth, 20-GSPS sampling rate and an impressive 32-M word memory when using only two of its four channels), but it enabled me to demonstrate some other interesting things about jitter. I could have used an analog oscilloscope to perform the same measurement, as long as the oscilloscope provided enough bandwidth and a dual time base (e.g., an old Tektronix 7904 oscilloscope or something similar). Nevertheless, the result is shown in Figure 3.

Figure 3—This is the result of a cycle-to-cycle jitter measurement of the PM5786A pulse generator. The bottom curve is a zoom of the rising front just following the trigger. The cycle-to-cycle jitter is the horizontal span of this transition over time, here measured at about 620 ps.

This signal generator’s cycle-to-cycle jitter is clearly visible. I measured it around 620 ps. That’s not much, but it can’t be ignored as compared to the signal’s period, which is 151 ns (i.e., 1/6.6 MHz). In fact, 620 ps is ±0.2% of the clock period. Caution: When you are performing this type of measurement, double check the oscilloscope’s intrinsic jitter as you are measuring the sum of the jitter of the clock and the jitter of the oscilloscope. Here, the latter is far smaller.

TIME INTERVAL ERROR
Cycle-to-cycle is not the only way to measure jitter. In fact, this method is not the one stated by the definition of jitter I presented earlier. Cycle-to-cycle jitter is a measurement of the timing variation from one signal cycle to the next one, not between the signal and its “ideal” version. The jitter measurement closest to that definition is called time interval error (TIE). As its name suggests, this is a measure of a signal’s transitions actual time, as compared to its expected time (see Figure 4).

Figure 4—Time interval error (TIE) is another way to measure jitter. Here, the actual transitions are compared to a reference clock, which is supposed to be “perfect,” providing the TIE. This reference can be either another physical signal or it can be generated using a PLL. The measured signal’s accumulated plot, triggered by the reference clock, also provides the so-called eye diagram.

It’s difficult to know these expected times. If you are lucky, you could have a reference clock elsewhere on your circuit, which would supposedly be “perfect.” In that case, you could use this reference as a trigger source, connect the signal to be measured on the oscilloscope’s input channel, and measure its variation from trigger event to trigger event. This would give you a TIE measurement.

But how do you proceed if you don’t have anything other than your signal to be measured? With my previous example, I wanted to measure the jitter of a lab signal generator’s output, which isn’t correlated to any accessible reference clock. In that case, you could still measure a TIE, but first you would have to generate a “perfect” clock. How can this be accomplished? Generating an “ideal” clock, synchronized with a signal, is a perfect job for a phase-locked loop (PLL). The technique is explained my article, “Are You Locked? A PLL Primer” (Circuit Cellar 209, 2007.) You could design a PLL to lock on your signal frequency and it could be as stable as you want (provided you are willing to pay the expense).

Moreover, this PLL’s bandwidth (which is the bandwidth of its feedback filter) would give you an easy way to zoom in on your jitter of interest. For example, if the PLL bandwidth is 100 Hz, the PLL loop will capture any phase variation slower than 100 Hz. Therefore, you can measure the jitter components faster than this limit. This PLL (often called a carrier recovery circuit) can be either an actual hardware circuit or a software-based implementation.

So, there are at least two ways to measure jitter: Cycle-to-cycle and TIE. (As you may have anticipated, many other measurements exist, but I will limit myself to these two for simplicity.) Are these measurement methods related? Yes, of course, but the relationship is not immediate. If the TIE is not null but remains constant, the cycle-to-cycle jitter is null.  Similarly, if the cycle-to-cycle jitter is constant but not null, the TIE will increase over time. In fact, the TIE is closely linked to the mathematical integral over time of the cycle-to-cycle jitter, but this is a little more complex, as the jitter’s frequency range must be limited.

Editor’s Note: This is an excerpt from an article written by Robert Lacoste, “Analyzing a Case of the Jitters: Tips for Preventing Digital Design Issues,” Circuit Cellar 273, 2013.

PWM Controller Uses BJTs to Reduce Costs

Dialog iW1679 Digital PWM Controller

The iW1679 digital PWM controller drives 10-W power bipolar junction transistor (BJT) switches to reduce  costs in 5-V/2-A smartphone adapters and chargers. The controller enables designers to replace field-effect transistors (FETs) with lower-cost BJTs to provide lower standby power and higher light-load and active average efficiency in consumer electronic products.

The iW1679 uses Dialog’s adaptive multimode PWM/PFM control to dynamically change the BJT switching frequency. This helps the system improve light-load efficiency, power consumption, and electromagnetic interference (EMI). The iW1679 provides high, 83% active average efficiency; maintains high efficiency at loads as light as 10%. It achieves less than 30-mW no-load standby power with fast standby recovery time. The controller meets stringent global energy efficiency standards, including: US Department of Energy, European Certificate of Conformity (CoC) version 5, and Energy Star External Power Supplies (EPS) 2.0.

The iW1679 offers a user-configurable, four-level cable drop compensation option. It comes in a standard, low-cost, eight-lead SOIC package and provides protection from fault conditions including output short-circuit, output overvoltage, output overcurrent, and overtemperature.

The iW1679 costs \$0.29 each in 1,000-unit quantities.

Dialog Semiconductor
www.iwatt.com

Client Profile: Pico Technology

Pico Technology
320 North Glenwood Boulevard
Tyler, TX 75702

Contact: sales@picotech.com

Embedded Products/Services: Pico Technology’s PicoScope 5000 series uses reconfigurable ADC technology to offer a choice of resolutions from 8 to 16 bits. For more information, visit www.picotech.com/picoscope5000.html.

Product information: The new PicoScope 5000 series oscilloscopes have a significantly different architecture. High-resolution ADCs can be applied to the input channels in different series and parallel combinations to boost the sampling rate or the resolution.

In Series mode, the ADCs are interleaved to provide 1 GB/s at 8 bits. In Parallel mode, multiple ADCs are sampled in phase on each channel to increase the resolution and dynamic performance (up to 16 bits).

In addition to their flexible resolution, the oscilloscopes have ultra-deep memory buffers of up to 512 MB to enable long captures at high sampling rates. They also feature standard, advanced software, including serial decoding, mask limit testing, and segmented memory.

The PicoScope 5000 series oscilloscopes are currently available at www.picotech.com.

The two-channel, 60-MHz model with built-function generator costs \$1,153. The four-channel, 200-MHz model with built-in arbitrary waveform generator (AWG) costs \$2,803. The pricing includes a set of matched probes, all necessary software, and a five-year warranty.

ISM Basics (EE Tip #100)

The industrial, scientific, and medical (ISM) bands are radio frequency ranges freely available for industrial, scientific and medical applications, although there are also many devices aimed at private users that operate in these bands. ISM devices require only general type approval and no individual testing.

Source: Wolfgang Rudolph & Burkhard Kainka’s article, “ATM18 on the Air,” 080852, Elektor, 1/2009.

The radio communication sector of the International Telecommunication Union (ITUR) defines the ISM bands at an international level. Wi-Fi and Bluetooth operate in ISM bands, as do many radio headphones and remote cameras, although these are not usually described as ISM devices. These devices are responsible for considerable radio communications interference (especially at 433 MHz and at 2.4 GHz).

ITU-R defines the following bands, not all of which are available in every country:

• 6.765 to 6.795 MHz
• 13.553 to 13.567 MHz
• 26.957 to 27.283 MHz
• 40.66 to 40.70 MHz
• 433.05 to 434.79 MHz
• 902 to 928 MHz
• 2.400 to 2.500 GHz
• 5.725 to 5.875 GHz
• 24 to 24.25 GHz

Some countries allocate further ISM bands in addition to those above. ISM applications have the lowest priority within any given band. Many bands available for ISM are shared with other spectrum users: for example the 433 MHz ISM band is shared with 70 cm amateur radio communications.

ISM users must not interfere with other users, but must be able to tolerate the interference to their own communications caused by higher-priority users in the same band. The band from 868 MHz to 870 MHz is often mistakenly characterized as an ISM band. It is nevertheless available to short-range radio devices, such as RFID tags, remote switches, remote alarm systems, and radio modules.

For more information, refer to Wolfgang Rudolph & Burkhard Kainka’s article, “ATM18 on the Air,” 080852, Elektor, 1/2009.

Dual-Display Digital Multimeter

The DM3058E digital multimeter (DMM) is designed with 5.5-digit resolution and dual display. The DMM can enable system integration and is suitable for high-precision, multifunction, and automatic measurement applications.

The DM3058E is capable of measuring up to 123 readings per second. It can quickly save or recall up to 10 preset configurations, including built-in cold terminal compensation for thermocouples.

The DMM provides a convenient and flexible platform with an easy-to-use design and a built-in help system for information acquisition. In addition, it supports 10 different measurement types including DC voltage (200 mV to approximately 1,000 V), AC voltage (200 mV to approximately 750 V), DC current (200 µA to approximately
10 A), AC current (20 mA to approximately 10 A), frequency measurement (20 Hz to approximately 1 MHz), 2-Wire and 4-Wire resistance (200 O to approximately 100 MO), and diode, continuity, and capacitance.

The DM3058 is ideal for research and development labs and educational applications, as well as low-end detection, maintenance, and quality tests where automation combined with capability and value are needed.

The DM3058E digital multimeter costs \$449.

Rigol Technologies, Inc.
www.rigolna.com

Accurate Measurement Power Analyzer

The PA4000 power analyzer provides accurate power measurements. It offers one to four input modules, built-in test modes, and standard PC interfaces.

The analyzer features innovative Spiral Shunt technology that enables you to lock onto complex signals. The Spiral Shunt design ensures stable, linear response over a range of input current levels, ambient temperatures, crest factors, and other variables. The spiral construction minimizes stray inductance (for optimum high-frequency performance) and provides high overload capability and improved thermal stability.

The PA4000’s additional features include 0.04% basic voltage and current accuracy, dual internal current shunts for optimal resolution, frequency detection algorithms for noisy waveform tracking, application-specific test modes to simplify setup. The analyzer  easily exports data to a USB flash drive or PC software. Harmonic analysis and communications ports are included as standard features.

Contact Tektronix for pricing.

Tektronix, Inc.
www.tek.com