# How did old WW2-era radars accurately measure time delay and integrate this into an oscilloscope?

The speed of light is about 300,000 km per second. An error of just 1 ms would result in being off by about 300 km, which is far too much error for a radar. I would guess it needs accuracy on the order of 10 microseconds in order to get range accuracy of 3 km.

What I want to know, though, is how microsecond accuracy is integrated into an oscilloscope so that a human operator could visually notice a difference of 1 ms. What was the translation? E.g., 1 microsecond difference puts the blip 10 millimeters away? I understand an oscilloscope translates a signal into voltage, but what I don't get is, how is the time delay processed and shown on the screen? Did this require vacuum tubes?

• I visited the Dover chalk caves a few years back and there were many radar installations around the coast that overlapped - so a combination of signals and also they were backed up by the observers on the ground as well... Apparently we had a good grip on the technology then! and sorry I deviated from the direct point of the question. – Solar Mike Oct 1 '17 at 19:23
• Yes, vacuum tubes were used. When I was in the Navy in the early 80's we had radars whose design went back to the early 1950's (AN/SPS-10) which were originally designed using lots of vacuum tubes. By the time I saw them the vacuum tubes had for the most part been replaced with solid-state modules which fitted into the same sockets and did the same job, but which contained solid-state componentry for greater reliability. – Bob Jarvis - Reinstate Monica Oct 2 '17 at 3:20
• There are already some good answers here, but I'd just like to add that perhaps, with modern radars in mind, you are underestimating just how useful any kind of early warning would have been at the time, however inaccurate, even from the earliest installations (which I believe used a simple fixed antenna). It was crucial to get the intercepting fighters - with limited fuel - to altitude at the right time. Also I suspect that an experienced operator would learn how to glean a surprising amount of information even from a primitive display such as the one shown in Barry's link. – peterG Oct 2 '17 at 13:04
• Surprisingly, the Germans never used the rotating area display that the British did. They used separate disatance and angle displays - an inferior system in most cases as the rotating display better allows the eye-brain system to add value. – Russell McMahon Oct 4 '17 at 2:49

The basic PPI (plan position indicator) radar display — the kind that has a bright line that sweeps around a circular screen like the second hand on a clock — works on the principle that the electronics produces the "sweep" of the electron beam in a radial path, while the signal from the radar receiver controls its intensity. Whenever a strong signal is received, a bright spot is created on the display. The position of the "blip" corresponds directly to the position of the target that created it in the real world.

Analog circuitry of that era could easily have a bandwidth of 10 MHz or more, allowing range resolution on the order of 15 meters (50 feet) or so. (Keep in mind that the signal has to make two trips, so you get twice the resolution that you might otherwise expect.) Say that the range is set to 75 km (about 45 miles). The signal will take about 0.5 ms to return to the receiver at maximum range, which means that for each pulse transmitted, the electron beam on the display must move from the center to the edge of the display in that amount of time. The circuitry to do this is no more complicated than the horizontal sweep generator of an ordinary oscilloscope. Shorter range settings require faster sweeping, but still within reason.

The output of a pulse generator could also be added to the intensity signal to create range "markers" on the display — concentric circles that gave the operator a better way to judge the distance to a target.

A sawtooth generator provides the basic sweep signal from the center to the edge of the display. There were a number of ways to get it to rotate in sync with the physical position of the antenna. The very earliest versions actually mechanically rotated the deflection coils around the neck of the CRT display. Later models used a special potentiometer that had sine and cosine functions built into it — the sweep signal (and its complement) was applied to the end terminals, the wiper was turned by a synchronous motor, and the the two taps provided the signals to the (now fixed) X and Y deflection plates. Later still, this sine/cosine modulation was done entirely electronically.

One issue was that these displays were not very bright, mainly because of the long-persistence phosphors used to produce an image that "lingered" long enough to be useful. They had to be used in a darkened room, sometimes with hoods over them that the operator could peer into. I wasn't alive during WWII, but I did do some work in the early 1980s on a chip that could digitize and "rasterize" the signal from a radar set so that it could be displayed on a conventional TV monitor. Such a monitor could be made much brighter (short-persistence phosphors) — bright enough to be used directly in the control tower of an airport, for example, so that the tower operator did not need to rely on verbal messages from a separate radar operator in another room. The chip even simulated the "slow decay" function of the analog display. Nowadays, every cheap digital oscilloscope has this "variable persistence" feature. :-)

Naturally, I had to simulate the radial scan of the analog display when writing the receiver signal into the video frame buffer. I used a ROM to convert the reported angular position of the antenna into sine/cosine values, which got fed to a pair of DDS generators to produce a sequence of X and Y memory addresses for each sweep.

• Did the RADAR devices of the era actually use plan-position indicators? Most of the videos and photos I've seen show a traditional oscilloscope display. – AndrejaKo Oct 2 '17 at 6:45
• @AndrejaKo they were available as early as 1940, but definitely not universal. Systems without them, as far as I understand, would have manual control of the antenna direction so that an operator could find the pointing that gave the maximum blip strength. – hobbs Oct 2 '17 at 7:32
• Early sets did indeed use single axis displays. Great answer though. – Trevor_G Oct 2 '17 at 14:33

Did this require vacuum tubes?

A traditional analog scope is essentially a vacuum tube (the CRT) with the timebase sawtooth and signal being applied directly to the horizontal and vertical plates to direct the beam to a moving location on the screen.

Vacuum tubes would also have been used in the amplifier circuits to produce the large voltages needed on the plates to move the beam.

AFAIK, every scope of the WWII era worked on this principle, so vacuum tubes were an inherent part of the scope design.

What I want to know, though, is how millisecond accuracy is integrated into an oscilloscope so that a human operator could visually notice a difference of 1 ms.

The horizontal deflection was driven by a sawtooth wave. The slew rate of this sawtooth determined the scaling between time and horizontal position on the screen. In a current day scope, the scaling can be anywhere from a few picoseconds per centimeter of screen space to hours per centimeter. In the 1940's, the highest scale would not have been picoseconds per centimeter, but it could well have been microseconds per centimeter.

Obviously there's a bit of extra complexity in the traditional radar display where the "horizontal" (timebase, corresponding to range in a radar system) axis is rotated around the center of the screen to indicate the heading of the antenna as it rotated, and I'm not sure how this was accomplished (I can imagine a couple of different possibilities). But this doesn't change the fundamental point that the "range" resolution of the radar on the screen would just be determined by how quickly the voltage of the "horizontal" deflection plate was ramped.

• The rotation was handled by simply having the deflection coil itself rotate around the screen. – supercat Oct 2 '17 at 22:39
• @supercat, Dave's answer says that was done in early systems but later ones applied sine and cosine signals to the X and Y deflectors. If you disagree, you should probably comment on his answer, not mine. – The Photon Oct 2 '17 at 22:49
• As electronics became more sophisticated, it became practical to generate XY signals, but rotating the deflection coil was a simple and practical approach to producing a polar display using 1940s-era electronics. – supercat Oct 3 '17 at 0:30
• @supercat, this comment probably makes more sense on Dave's answer than mine. – The Photon Oct 3 '17 at 0:39
• I was responding to your last paragraph. – supercat Oct 3 '17 at 2:29

The SCR-270 radar that was present at Pearl Harbor on December 7, 1941 had the following characteristics:

• Transmit Frequency: 105 MHz
• Pulse width: 10-25 µsec
• Repetition rate: 621 Hz
• Power Level: 100 kW
• Maximum range : 250 miles
• Accuracy: 4 miles, 2 degrees

It used a large number of vacuum tubes including a CRT (The entire radar occupied 4 large trailers). The following link shows the actual oscilloscope trace when the approaching Japanese planes were detected:

Consider the 12SK7 vacuum tube: gm of 0.002, plate resistance of 0.8MegOhms, grid capacitance of 6pF, output(plate) capacitance of 7pF.

Predict bandwidth by gm/C. Assume nodal C is 6p + 7p + 7p parasitic = 20pF.

Bandwidth is 0.002 / 20e-12 = 0.0001 * e+12 = 1e+8 = 100MegaRadians/second or 16MHz; using the Tektronix rule-of-thumb of 0.35/bandwidth for the response of multi-stage systems, or 0.35/16MHz, the Trise is 20nanoseconds; 20nS providing 20 feet one way, 10 feet 2-way, resolution.

http://www.r-type.org/pdfs/6sk7.pdf

• ....Let there be cascode : and there was bandwidth . – carloc Oct 3 '17 at 19:19

If I understand correctly, the question is about how the radar display electronics can accurately cope with light speeds. Here I will show that the radar display electronics can run slower than you might expect.

Let's say the radar is designed for a range of 100 miles. Rounding for convenience, this is about 160km.

As you noted, the radar wave travels at about 3e8 meters per second. So the time it takes the radar wave to travel out to its maximum range is: $$160{\rm{k m}} \times \frac{{\rm{s}}}{{3{\rm{e}}8{\rm{ m}}}} = 0.53{\rm{ ms}}$$ Double that to get round-trip time, and you get about 1 millisecond.

As you also noted, the X and Y deflections of the scope display are controlled by independent voltage inputs. Let's consider a simple a-scope setup. Run the X deflection from a circuit that generates a sweep from -V to +V (leftmost to rightmost on the display). (This was most likely a tube circuit.) The circuit is designed so that the total time taken to go from rail to rail is 1ms. This sweep would likely be triggered by the same timing signal that triggers the radar's transmit.

The Y deflection is fed by the radar receiver. The blip will appear at whatever the sweep position is when the reflection is received. As a result, the later a reflection is sensed by the receiver, the farther to the right the blip appears on the display.

The thing to note is that while the radar wave travels 200 miles (there and back again), the dot on the scope display only has to travel a few inches! In this sense, the display electronics can run much slower than "speed of light." A 1ms sweep is readily achieved in tube electronics. It is the same class of technology as amplifying audio signals. For comparison, the horizontal sweep period used in every old NTSC television set was about 0.064 ms.

The radar system can be calibrated by putting a target at a known range and adjusting the circuits so that the displayed quantities match the ground truth. (Calibrating the system must have been an art form!)

It's $300000\frac{\mathrm{km}}{\mathrm{s}}$.

One way is to modulate the radar signal with a sine wave, and then measure the phase difference of the modulation signal between transmitted and returned signal — this difference is always proportional to the distance. The downside is that the return from multiple echos will interfere, and create a return signal that shows a distance somewhere in the middle between both.

Later models would use a radar "chirp", where the modulation frequency would be a sawtooth, allowing different echos to be distinguished and the distance to each measured accurately.

• a radar "chirp", where the modulation frequency would be a sawtooth That is not so, the sawtooth is what you'd get if you plotted the frequency over time curve. – Bimpelrekkie Oct 1 '17 at 18:56
• Yes, sorry if that was unclear. It's FM with a sawtooth input signal. Phase change is quadratic, so each return will have its own peak in the spectrum. – Simon Richter Oct 1 '17 at 20:09
• @Bimpelrekkie he said "frequency is a sawtooth" not "signal is a sawtooth" – user253751 Oct 1 '17 at 23:54