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Doppler Tracking Chuck McConaghy, WA6SYE 212 Garnet Dr, Livermore, CA 94550; [email protected] Doppler Tracking The author combines some simple electronics with a physics principle to measure speed and height of his model rocket launches. The “Doppler effect” is responsible for So, is the 23 cm band high enough in fre- frequency shifts of the received signal just by quency to make some measurements? We virtue of movement of the reflecting or trans- shall see. mitting source.1 It almost seems like you get something for nothing. By this I mean Theory that no complex electronics are required to The Doppler shifted frequency is given by produce the frequency shift, and those that this formula: are required are familiar to the typical ham f = f (1+v/c) [Eq 1] operator. The system that I will discuss uses rec where: some of my ham equipment. f is the transmitted frequency Most applications of the Doppler fre- f is the frequency of the wave arriving at quency shift have one thing in common: rec the receiver the object being measured is moving. These v is the velocity of the transmitter relative to applications include radar to track incoming the receiver in meters per second. storms or fast moving motorists, medical (v is positive when the transmitter and applications to measure blood flow in arter- receiver move towards one another and ies and veins, and astronomy applications to negative when they move away from each measure the speed of stars moving toward other) or away from Earth. Although the frequen- c is the speed of the wave (3×108 m/s for cies used, be they audio, RF, or optical, may electromagnetic waves traveling in air or a differ for each application, the effect is the vacuum) same. f is the Doppler frequency shift. But what can Joe Ham do with the ∆ This equation assumes that we are using Doppler effect? My own interest in using radio frequencies that propagate at the speed the Doppler effect comes from a second- use many kilowatts of power. I was more of light, and that the relative velocities of the ary hobby, model and high power rocketry. interested in milliwatts. I did not consider transmitter and receiver are a small percent- Do you think you have too many hobbies? a transponder because I thought it too com- age of the speed of light. These are good While attending rocket launches at the plex. I was after simplicity. There was some assumptions for the applications I had in Black Rock desert in Nevada, I all too often previous work on transponder systems done mind. observed rockets that would make great by Steve Bragg, KA9MVA. Steve referred What kind of frequency shift can we ascents but have ballistic descents caused to his experimental work as the “Digital 2 expect for 23 cm signals? For a velocity v = by parachute deployment problems. The Amateur Rocket Tracking System.” I also 25 m/s — which is about 56 mph — a fre- result was a destroyed rocket and, electron- wanted to make use of ham radio equip- quency shift of 108 Hz should result. Is this ics embedded in the desert floor. The thought ment I already owned or could easily build. enough shift? Do we need higher speeds? occurred to me that if these rockets had I decided early on to make use of the 23 cm Do we need higher frequencies? Frequency some sort of inexpensive and sacrificial RF band, and this decision was primarily based stability ultimately determines the frequency system, in case of a crash, maybe we could on owning an older ICOM IC-1271, which resolution and thus velocity resolution of the learn something about the speed and altitude is a multi-mode 23 cm. transceiver. The SSB measurement. It turns out 100 Hz is enough of these imperfect flights. mode was very important to make these shift for short-term — 1 minute or less I didn’t want the project to be so sophis- measurements, as this mode produces a tone — measurements. At 1200 MHz, 100 Hz ticated that it required extremely high RF from a CW signal. I was already familiar corresponds to a stability of 0.08 parts per power levels or specialized tracking anten- with the 23 cm band since I had worked million (ppm). Modern transceivers, particu- nas. For example, Doppler weather radars ATV and FM repeaters on that band. It helps with Doppler to use as high a frequency as larly those designed for SSB and CW, have possible, since the Doppler frequency shift stability specifications of at least 3 ppm. For 1Notes appear on page 37. is proportional to the operating frequency. example, my older IC-1271 has a stability 30 QEX – March/April 2010 of 3 ppm, and a newer transceiver like the The transmitter was custom built, but only Doppler data is a computer program that can IC-9500 has 0.05 ppm stability. I have found because I had some specialized requirements. measure frequency versus time. This is called the short-term stability, particularly when The transmitter needs only to generate a CW a spectrogram. I used a shareware computer the temperature is constant, is much better carrier of reasonable spectral purity and low program, in fact, called Spectrogram to both than the specified values. The specified val- drift. This is fairly easy to accomplish with record as well as analyze the data.4 This pro- ues assume long-term measurements over a modern phase-locked-loop circuits and crys- gram runs on either a PC laptop or desktop 50°C temperature range. tal oscillators. The transmitter consists of a and makes use of the sound card for audio crystal reference oscillator, a PLL chip with input. The program allows for adjustments of the time window and maximum and mini- Hardware and Software self contained EEPROM, and a power ampli- mum frequencies of the spectrogram. The Figure 1 shows a simple experiment. The fier chip. Size (23 mm × 100 mm) and power data displayed on the screen can simultane- transmitter and receiver are close enough so supplied <10 mW are low and allow use of ously be stored to a file by selection with a the receiver can hear the transmitter at the small, lightweight batteries. Figure 2 shows pull-down menu and a mouse driven record low desired power levels. The car can be a picture of the transmitter as well as the on-off feature. Spectrogram also allows driven away from the receiver for one test schematic. Cost, in case the transmitter is lost replaying or analysis of the previously and toward the receiver for another test. We or destroyed, is low (about $35). The total recorded files. There are probably other pro- need a receiver with SSB capability because transmitter weight is 1 oz, including batteries. grams that can perform this task but I found we are basically tracking the tone produced If the transmitter platform is larger, such as an Spectrogram met all my needs. in the receiver as it hears the unmodulated automobile for example, a larger and heavier carrier from the transmitter. This is the same transmitter can be tolerated. tone you hear when you listen to someone I was concerned about transmitter sta- Procedure for Taking and Analyzing tune their transmitter. The bandwidth of bility under acceleration, particularly the Data most SSB receivers can handle the expected G forces on the 32 MHz crystal oscillator The hardware and software setup for all velocities and corresponding Doppler fre- that is the reference for the PLL transmitter. the applications is as follows: quency shifts. For example a 2.4 kHz band- The data from the actual launches, however, 1) Turn on the transmitter. width, typical for an SSB receiver, would looked very similar to predicted velocity 2) Turn on the receiver. profiles from computer programs such as allow velocities as great as 581 m/s at 23 cm. 3 3) Tune the receiver VFO until the trans- Incidentally, Mach 1 (the speed of sound) RockSim. My conclusion was that G forces mitter is making a pleasant tone somewhere is 340 m/s at 15°C. I used the previously and short term temperature effects were not between 800 and 1500 Hz. The frequency of mentioned IC-1271 for the receiver, but any enough of an issue to use more sophisticated this tone is arbitrary. This is just like tuning in modern day 23 cm multimode receiver or reference schemes. your favorite CW signal. transceiver would suffice. A key requirement for analyzing the ƒrec= ƒ (1-v/c) Mobile Stationary Computer 23 cm Transmitter 23 cm Receiver ƒrec= ƒ (1+v/c) Mobile Stationary Computer 23 cm Transmitter 23 cm Receiver QX1003-McConaghy01 Figure 1 — Drawing showing mobile transmitter moving away from (top) or toward (bottom) a fixed receiver. QEX – March/April 2010 31 Figure 2 — Part A shows the transmitter circuit board, and Part B is a schematic diagram of the transmitter. Part C shows a model rocket, with an expanded photo showing the location of the transmitter board (A) (B) (C) 32 QEX – March/April 2010 23 cm Transmitter QX1003-McConaghy03 23 cm Receiver Computer Figure 3 — This drawing shows a transmitter spinning on the end of a lasso. Figure 4 — This spectrogram shows the data for the example of Figure 3. You can measure the rotation period of 0.81 s over most of the waveform, with a peak to peak Doppler shift near 100 Hz. This corresponds to a velocity of 11 m/s. QEX – March/April 2010 33 4) Start the Spectrogram software and involved putting the transmitter at the end of achieved with the transmitter at a fixed loca- you will see it displaying a horizontal line at a 5 foot long string and swinging the trans- tion and swinging the antenna.
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