RTC Magazine

Wireless technology has invaded nearly every aspect of consumer, business, commercial and government electronic markets. Ranging from Bluetooth headsets for cell phones to military radios in battlefield information networks, strong growth in product demand has spawned a wealth of low-cost devices delivering sophisticated RF performance. Niche markets for embedded computing benefit by adapting these kinds of new technologies to system solutions.

One such niche market is control systems for industrial, automotive, commercial and military systems. First offering purely mechanical solutions, control system vendors have continuously injected new technology to meet increasingly tough challenges for a tremendous variety of equipment from wall thermostats to interplanetary spacecraft.

Transducers and sensors for some advanced control systems are now being equipped with wireless RF transmitters that replace traditional hard-wired harnesses. This strategy saves cable weight, minimizes the complexity of connectors, eliminates troublesome slip ring contacts in rotating equipment, enhances maintainability and simplifies installation and upgrades. During system tests, the transducer signals can be monitored remotely with a wireless receiver that replaces a custom test connector and cable assembly.

In some cases, the analog output signal from the transducer modulates the amplitude, phase or frequency of the RF carrier directly. In other systems, a digitized representation of the transducer signal drives one of many different digital modulation schemes. The modulated RF signal itself usually occupies a relatively narrow frequency band with other sensor signals allocated to adjacent frequency channels.

At the receiving end for the control computer or test system, the RF band containing the transducer channels must first be picked up using a suitable antenna. The signal is then filtered and amplified using bandpass amplifiers to enhance the desired band and reject out-of-band signals. A frequency translation stage mixes the RF band down to a lower intermediate frequency (IF) band where demodulation occurs.

Newer receiver systems now implement software defined radio solutions for the demodulation instead of older analog technology. This accommodates new complex digital modulation schemes, improves channel selectivity and eliminates component tolerance, drift, aging and calibration headaches.

In these software radio systems, the IF signal band is sampled with an A/D converter. All further processing is done using digital signal processing hardware. This IF sampling process must be implemented carefully to ensure that subsequent signal processing will be successful.

Sampling Basics

One of the most important fundamentals for correctly sampling analog signals is the concept of aliasing. The famous Nyquist criterion states that we must digitize a signal at a sampling rate of at least twice the bandwidth of the signal. For “baseband” signals with frequency components starting at DC and extending up to some maximum frequency, this means the sampling rate must be at least twice this maximum frequency. In this case, the bandwidth and the maximum frequency are the same.

But for “bandpass” signals such as the IF output signal from an RF downconverter with a 70 MHz center frequency and a 10 MHz bandwidth, the Nyquist criterion imposes constraints on bandwidth, rather than on absolute frequency. There is a major difference between sampling an IF signal at a rate twice the 10 MHz bandwidth versus twice the 75 MHz upper edge of the IF band.

By taking advantage of this subtle but profound distinction in just the right way, system designers can simplify system design and save costs. This is the basic objective of a technique known as “undersampling”, which can best be appreciated only after a basic discussion of the effects of the sampling process itself.

Modeling the Sampling Process

One tried and true technique to visualize exactly what happens when sampling occurs is the “fan-fold” paper method. Start by imagining a small stack of semitransparent fan-fold computer printer paper. Holding the paper with the folds in the vertical direction, plot the frequency axis from left to right along the bottom edge with the inward creases at multiples of the A/D sampling frequency, Fs and the outward creases at odd multiples of Fs/2, as shown in Figure 1.

The vertical axis is used to plot the spectral amplitude of the signal to be sampled, such as the wideband signal shown with energy that extends across all of the sheets. In order to see what happens after sampling, simply collapse the stack of fanfold paper, hold it up to a light and look through the stack. As shown in Figure 2, signals on all of the sheets above Fs/2 are effectively “folded” down into sheet 1 between 0 Hz and Fs/2.