One of the more impressive presentations of a gadget at a recent Maker Fair was a floor-mounted four-hoop device with LEDs along each hoop. The hoops were circular in shape as though they were the longitude lines on a globe. When the contraption was rotated and the LEDs driven under computer-based control, a 3D display appeared. The resolution was visibly low but at inventor shows, it is more the idea that counts than its immediate refinement. The idea was simple and perspicuous : you could quickly see how it worked.
This article presents another idea, that of a perspicuous (to engineers of ordinary perspicacity ) desktop-sized LED electromechanical display like that of an oscilloscope display, avoiding custom mechanics and using items found in the usual household electronics shop and kitchen. Our starting reference is the well-established oscilloscope display. It is two-dimensional and oscilloscope makers have conventionally settled upon a format of 8 vertical by 10 horizontal major divisions with 5 (Tektronix) or 4 (generic H-P) minor divisions, or “divs”. Then the aspect ratio of oscilloscope CRT screens is H/V = 10/8 = 1.25 and its inverse is 8/10 or 0.8. Some artists, including Leonardo da Vinci in painting Mona Lisa, have thought that the golden ratio was the optimum aspect ratio:(1+ √ 5)/2 ≅ 1.618 ≅ 1/0.618. For NTSC television it is 1/0.75. The trace resolution of some Tek oscilloscopes (those with shorter and hence lower-performance CRTs) is about a half a minor div, resulting in a resolution of about 80 lines vertical and 100 horizontal. This resolution will be used as a basis for assessing alternative displays.
A first thought at a simple perspicuous electromechanical display is a matrix of LEDs. Small LEDs are cheap – about $0.04 US in any quantity – and can populate a circuit board to form a matrix with a resolution comparable to a CRT with 80 × 100, or 8000 LEDs. That seems excessive, and a display of half the resolution per axis, or 2000 LEDs, is still an arduous task to assemble. The LEDs alone would cost about $80 US.
A variation on this theme is to use instead 5 × 7 LED dot matrix displays. They are more costly per pixel because of the assembly and encapsulation. A matrix of them could be formed by rotating them horizontally to better fit the aspect ratio and stacking them 10 high (50 pixels vertical) by 10 wide (70 horizontal pixels), or 100 LED matrices. At $1.50 each surplus, the cost would be around $150 US – a formidable amount resulting in a rather large display and a large (and costly) circuit-board.
The LED solution does not appear to meet the design constraints for a low-cost display. Indeed, Samsung and others are now selling large LED displays, and at large prices. Dot-matrix LCDs are an alternative, and for cost and size feasibility, graphic LCD displays are a good solution. However, they require a display driver and have high levels of digital integration that for some might violate the perspicuity criterion. I leave LCDs as the default possibility, one which has been chosen for most DSO products nowadays. It is not a bad choice for a low-cost display but is very different from a CRT.
Thinking beyond the usual with low cost, simple mechanics, and perspicuity in mind, the old Nipkow (pronounced “nip-cough”) disk of mechanical television from the late 1800s comes to mind. This is a simple, fascinating display technology with inherent limitations. Yet it is food for thought. Spin a disk with holes that let a light source behind the disk shine through them. The light is varied in intensity as the disk spins to illuminate the pixels. For each horizontal display line there is a concentric circle on the disk. Define an arc angle for the display screen – say 60°. The top line – the outermost circle on the disk – has one hole the size of a pixel. It traverses the screen as the disk spins, and if the light is modulated, the resolution is continuous, limited by the bandwidth of the modulator and the hole size. Then when the top hole (line 1) reaches the right edge of the screen, the hole of line 2 (one line closer to the disk center) enters the left edge and scans the second line. The sequential scan is a mechanical raster scan like that of television displays. The number of lines is limited by the decreasing horizontal length of the screen arc toward the disk center, and this limits screen location (and size) to the outer portion of the disk. A more basic limitation is that if there is one hole per line, then the maximum number of lines is
This rather severe limitation can be circumvented by using multiple vertical sectors, each with its own light and hole pattern. This display multiplexing requires parallel light modulation but it extends L .
The display is not rectilinear because of the scanned arc lines. The curvature thus also limits the horizontal extent of the display. This can be compensated by allowing the arc width of the screen to increase at the screen bottom. However, as the display angle increases with display height, the number of lines decreases according to the above formula for L . For disk radius R , then at r = R /2, the screen angle doubles to maintain the same arc length of r x (2 x θ ).
Consider a disk with a radius of R = 5 cm. Then for a screen arc of 2 x θ = 60o (or π/3) at the screen top and 16 sectors, at 6 lines/sector the total vertical lines, V = 96. For a 30 Hz frame rate, the disk must spin at a mechanical frequency of 30 Hz (1800 rpm). The screen scan geometry is shown below with points labeled.
The disk radius is R and screen-top arc angle is ∠AOC = 2 x θ . Then the screen top is the arc sector of length ABC = R x (2 x θ ) ≈ (5 cm) x (1.047) ≈ 5.236 cm. The top two rectilinear display lines are shown with equal height (trace thickness) W , that of the line segment lengths BE = ED . The top scanned arc will begin in line 2, then rise to sweep within line 1, and finish again in line 2. The curved path can be partially corrected by multiplexing the top arc to display segments of both lines 1 and 2.
To solve the geometry, begin by finding chord length AC using the Law of Cosines:
Then The length and OF ≈ 0.9282 x R ≈ 4.641 cm. Because OF < OE , the fraction of time, f , that the scanned arc of line l is in line l and not line l – 1 is not constant. The fraction of line length that the top scan forms line 1 is
or f ≈ 0.7197 or about 72 % of the screen width. The fraction of time (for constant rotational speed) that the arc within line 1 is swept out over the screen arc width is φ /θ
If the screen is to be rectangular, then θ must vary with r , the distance from O along a radial of the disk. The sequence of pixel holes thus forms a discrete spiral. For an oscilloscope aspect ratio of 0.8, then with a screen width, H , equal to the length of the top chord, AC = 5 cm, and the screen height, V = 4 cm. Then the angle of the screen that subtends the bottom vertices is
However, the number of lines in a wider screen angle must be reduced from that of the top line spacing.
For a rectilinear display, the total lines for a given H and V can be derived as follows. The radius, r , and screen angle, θ , vary with line number, l , counting from line 1 at the top to the bottom line, L . The arc length, r x θ , must remain constant to maintain constant screen width. If for the top line, r = R and θ = Θ , then the constraint is
Arc l has a radius of r (l ) = R – l x W , where W is the line height (thickness), as previously derived, and thus the number of lines is L = R/W . Then the sequence of the angles is
For the given parameters, a plot connecting the holes is shown below. It assumes a constant line height, taken as that of the line at the top of the screen where curvature is least and the thinnest line is produced. Even at the top, the curvature for Θ = 60o is so much that only 15 lines can span the vertical range and require 965o /360o → 3 sectors. Thus, the dominating limitation of the Nipkow disk is curvature in the horizontal dimension. A better mechanical scanning method is needed to alleviate the problems of generating a rectilinear screen on a polar disk.
In Part 2 of this article, we will continue the search for better alternative low-cost, perspicuous display schemes, including the one I think is most attractive, though it has a raster scan that (like the LED array) works better for DSOs than real-time analog ’scope displays: the “Nipkow drum”.