Case Studies
RF Testing and Calibration via CS8500 Subsampling
This application note will introduce subsampling and discuss the application of subsampling to testing and calibration of consumer-level remote RF transmitters.
INTRODUCTION
Traditional A/D sampling requires that one must adhere to the Nyquist theorem, which states that one must sample an analog signal at a rate of at least twice that of the highest frequency component of that signal. In fact, many applications require that you sample tens or hundreds of times faster than the fastest input frequency in order to reconstruct the input wave shape faithfully.
However, new techniques brought on by engineers working in digital (software) radio show that it is possible to recover signal information by purposely undersampling the input signal. This is also known as subsampling, digital down-conversion, bandpass sampling and direct IF down-conversion.
Subsampling Background
The theory behind subsampling is quite simple. The Nyquist theorem needs to be met with respect to the bandwidth of the input signal only, not the actual input frequency itself. In this case, a 200 kHz FM signal with a CW (carrier wave) frequency of 150 MHz need only be sampled at 400 kHz (twice the rate of the FM width). This results in the band of interest being aliased down to a frequency band close to DC.
A very important note is that the A/D card must also have an input analog bandwidth that will pass the entire signal. In the above case it must have a bandwidth of 150.400 MHz.
It is quite easy to predict where the new frequency will centered be in the FFT display. There are actually many multiples of this image that are present, analogous to the way multiple bandwidth images will be present when looking at the output of the mixer stage in a superhetrodyne receiver.
The bandwidth image is reflected across an imaginary line at the position of fs/2, where fs is the sample rate of the A/D converter. There are also other images which reflect about the point of DC into the complex domain of the FFT (imaginary numbers in the frequency domain which are less than DC). To keep this explanation simple, we will discuss the main reflected image which we will be able to view in the FFT window.
A simple equation which can express the new center frequency is as follows:
fi= fin mod(fs/2)
More simply said, a value fs/2 is repeatedly divided into fin. The dividend is tossed out and the remainder of the operation is the new image frequency.
If a sample rate of 125 MHz is chosen and the carrier was 150 MHz, we can expect to see the image carrier at 25MHz (fs/2=62.5 MHz; 65.2 MHz divides into 150 MHz twice with a remainder of 25 MHz).
 |
Test signal created with
Marconi 2018A test set as
seen directly on a Polarad
spectrum analyzer. Center
frequency 150 MHz 50 kHz/div.
Resolution BW 1 kHz. |
 |
Test signal captured with
CompuScope 8500 data acquisition
card using subsampling technique.
Signal has been digitally downconverted
to a CW center of 25 MHz. |
APPLICATION DETAILS
The above concepts can be applied to manufacturer testing of consumer-level remote transmitters such as door openers, remote alarms and those used in the automotive industry. They must be tested for range, carrier frequency and spectral leakage to make sure they meet federal communications standards.
Outfitting a manufacturing plant with standalone spectrum analyzers can be very expensive-test devices can cost upwards of $60,000 dollars and require a high level of technical expertise to operate them. The type of testing required is fairly simple and only a very small percent of the analyzer's capability is actually used. Secondly, spectrum analyzers use valuable shop floor space and electricity. By using a CompuScope product in the existing manufacture test PC, space, money and power are saved, and the user interface can be programmed as simply as possible for the floor technician.
The remote controls typically operate around a carrier frequency of 315 MHz, with sidebands as wide as +/-3.15 MHz . The CS8500 has an upper bandwidth of around 350 MHz, which gives it an adequate passband for this type of testing. In fact, the CS8500 can be modified to have an upper passband limit in excess of 600 MHz.
This application can be easily demonstrated using GageScope for Windows software with the FFT Analysis Plug-in. This first thing to do is to choose an appropriate sample rate in which to do the undersampling. A sample rate of 100 MHz is one of the standard CS8500 on-board sample rates. Selecting this rate would mean that we could expect to see our image band 315 MHz mod (100 MHz/2), or 15 MHz.
To demonstrate this, we used our Marconi test-set to output a 315 MHz CW with 3.15 MHz FM sidebands, modulated with a 1 kHz AF. The capture was made with GageScope for Windows and displayed using the FFT module.
As seen above, the band is translated down as expected. Bandwidth and amplitude are easily measured.
Below is an actual subsampled capture of the CW from a miniature transmitter.
In this case we are translating the band with a center of 305 MHz down to 5 MHz. (A subsample rate of 50 MS/s was used.) Knowing that, the actual CW frequency can be measured. In this case, it is 304.4 MHz.
Care must be taken to filter out frequencies outside the passband of interest, otherwise unwanted frequencies will be aliased down into the passband being measured.
This application clearly demonstrates that CompuScope products using subsampling techniques can bring lower costs to RF testing applications.
This application note is provided "as is" without any warranties of any kind, either expressed or implied, including but not limited to the implied warranties of merchantability or fitness for a particular purpose. Gage Applied Technologies further does not warrant the accuracy and completeness of the material contained herein. Gage Applied Technologies may make changes to this material, or to the products described in it, at any time without notice.
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