Archive Article

# 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. …

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