How About an Intro to Radar?

Back last week, while talking about Rocket Lab launching a Synthetic Aperture Radar for the Japanese, I wrote, 

I used to design radars among other things, and when I thought of the questions being asked, my reaction was, "should I devote some time to things like the basics of what Synthetic Aperture Radars are and how they work?" Comments? 

Comments were in favor of doing that, so I decided to get started. It was starting to look like a long piece, so I started by putting together first a general introduction to radar, primarily to ensure everyone has a common language. 

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RADAR 101

To me, it’s always stretching myself to take something as involved as radar can be – the word is applied to many different kinds of systems – and write a generally understood text on it.  At root, radar isn’t new; it was known before WWII. The name itself comes from radio detection and ranging. As the name implies, radars use radio waves to determine the distance and velocity (motion) of the targets they hit. 

Radio is ultra low frequency light – and since wavelength is inversely related to frequency, radio waves are much longer than light waves. There are aspects of the frequency chosen and the intended use for the radar, and those are “beyond the scope” of this. That means a radio frequency (RF) source needs to generate the radio waves to use. How are they detected? With a radio receiver, tuned to the frequency of the source. That’s intentionally vague because the bandwidth required for the receiver depends on what the radar is being used for. 

Finally, how is ranging detected? The easiest thing to envision is radar sending a single pulse on a single frequency, and in this case the range is determined by measuring the time between the pulse being sent and the pulse caused by its reflection off the target arriving back at the receiver. That time difference between being sent and received is divided by two to get the time distance to the target. Divided by two because the pulse has gone from the transmitter to the target and back to the receiver and each trip to or from takes the same amount of time. 

All radio and light waves travel at the same velocity, the speed of light, usually referred to as c in physics books. The speed of light is 300 million meters per second (formally 299,792,458 m/sec, but 3*10⁸ or 300*10⁶ m/sec is close enough for now). Which is the same as 300 meters in one microsecond (millionth of a second). If you’re more comfortable in miles, that’s 186,282 miles per second – or 0.186282 miles per microsecond (millionth of a second) which turns to be 983.664 ft/msec.  

Just bear in mind that if you get your return pulse in 1 msec, it’s not 300 meters or 984 feet away. It’s half that because the pulse had to go twice that distance – half a msec out and half a msec back.

You can probably see from this how timing became very important in radar systems, but you may not see how timing became important in the antenna design. You see, every antenna that’s directional requires phasing differences between the elements of the antenna to establish patterns, whether it’s a simple yagi antenna with “a few” elements or a phased array antenna with dozens of elements, phasing is a mechanical way of establishing a timing difference. 

An easy Rule Of Thumb to remember is the more antenna elements you have the smaller and more concentrated your beamwidth will be. It’s why a yagi with seven elements will perform better than one with five or three. That is, the five element yagi will outperform the three, and the three will outperform a single dipole. Such an antenna will deliver a greater percentage of your transmitter’s output power onto a target and simultaneously deliver less power outside its beamwidth. Since part of the first sentence includes saying the smaller and more concentrated your beamwidth can be, that means the uncertainty in the direction the radar’s antenna is pointing goes down as the number of elements goes up. 

If this is new or puzzling, I've written a lot on this. See my post on, “A Ham Radio Series 31 – Phased Arrays, or A Dish Without A Dish” or “A Ham Radio Series 31 – Very Directional, Very High Gain Antennas”

How do these arrays of small antennas operate and produce patterns of gain that produce more signal in the desired direction? The phase differences between all the antennas combine to produce more gain in some directions and less in other directions. When antenna gain is measured and talked about, the antenna isn’t amplifying the signal; that requires active devices and electrical power. Antenna gain is measured in comparison to a defined antenna, usually a dipole or something more omnidirectional (transmits the same power in all directions). What the antenna is doing is combining the output of all the smaller antennas it's made of into one much higher power in one small angular width.

In optics, a telescope like the (78 year old) Hale telescope on Mount Palomar, the aperture of the single primary mirror, 200 inches, is the telescope’s aperture. In multiple mirror telescopes like the James Webb Space Telescope, combining the image data from several smaller optical instruments to generate an image as it would appear to a much larger mirror is referred to as the size of the combined image generating mirrors. In the case of the Webb (JWST) that aperture is a 6.5-meter-diameter (21 ft) mirror. Aperture for a radio telescope is the width of the antenna beam at a defined distance from the antenna. It's practically never talked about, but sometimes is mentioned in radar systems talk.

Because these high gain radio antennas approach having all of their gain in one direction with no signal transmitted or received from other directions, we’ve achieved the definition of radar.

Remember radar =  radio detection and ranging? The reflected radio pulse tells us something was detected, the time between the transmission and reception of the pulse tells the range, with the bonus of not just knowing “something’s out there” but the position of the antenna tells us the direction of that thing. If that radar is on something that’s moving, ship, car, airplane, or whatever, the motion of the vehicle and its position is constantly changing so that has to be incorporated in the calculations, too.  

Searching with Duck Duck Go for "Boeing 787 Weather Radar" because I've seen those. I found this and wanted to point out that the circular thing behind the nose with straight lines near the edges is the radar antenna array. Each of those small dark lines on the flat surface is an antenna, and the position of each one, along with how the radio signal gets to the antenna determines the antenna's pattern.