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The Art of the Helicopter John Watkinson - Karatunov.net

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296 <strong>The</strong> <strong>Art</strong> <strong>of</strong> <strong>the</strong> <strong>Helicopter</strong><br />

Fig. 7.32 A linear encoder in which <strong>the</strong> position <strong>of</strong> <strong>the</strong> moving part determines <strong>the</strong> binary code created.<br />

single wire can be used where successive digits from each sample are sent serially. This<br />

is <strong>the</strong> definition <strong>of</strong> pulse code modulation. Clearly <strong>the</strong> clock frequency must now be<br />

higher than <strong>the</strong> sampling rate.<br />

Whilst control samples can be obtained by digitizing <strong>the</strong> output <strong>of</strong> an analog control<br />

such as a potentiometer, it is preferable to obtain samples directly in a digital encoder.<br />

Digital encoders are a form <strong>of</strong> displacement transducer in which <strong>the</strong> mechanical position<br />

<strong>of</strong> <strong>the</strong> shaft or pushrod is converted directly to a digital code. Figure 7.32 shows<br />

an absolute linear encoder. A grating is moved with respect to several light beams, one<br />

for each bit <strong>of</strong> <strong>the</strong> control word required. <strong>The</strong> interruption <strong>of</strong> <strong>the</strong> beams by <strong>the</strong> grating<br />

determines which photocells are illuminated. It is not possible to use a pure binary<br />

pattern on <strong>the</strong> grating because this results in transient false codes due to mechanical<br />

tolerances. Figure 7.33 shows some examples <strong>of</strong> <strong>the</strong>se false codes. For example, on<br />

moving <strong>the</strong> fader from 3 to 4, <strong>the</strong> MSB goes true slightly before <strong>the</strong> middle bit goes<br />

false. This results in a momentary value <strong>of</strong> 4 + 2 = 6 between 3 and 4.<br />

<strong>The</strong> solution is to use a code in which only one bit ever changes in going from one<br />

value to <strong>the</strong> next. One such code is <strong>the</strong> Gray code first devised to overcome timing<br />

hazards in relay logic but is now used extensively in position encoders. Gray code can<br />

be converted to binary in a suitable look-up table or gate array or by s<strong>of</strong>tware in a<br />

processor.<br />

For digital signalling, <strong>the</strong> prime purpose <strong>of</strong> binary numbers is to express <strong>the</strong> values <strong>of</strong><br />

<strong>the</strong> samples representing <strong>the</strong> original control position. Figure 7.34 shows some binary<br />

numbers and <strong>the</strong>ir equivalent in decimal. <strong>The</strong> radix point has <strong>the</strong> same significance in<br />

binary: symbols to <strong>the</strong> right <strong>of</strong> it represent one-half, one-quarter and so on. Binary<br />

is convenient for electronic circuits, which do not get tired, but numbers expressed in<br />

binary become very long, and writing <strong>the</strong>m is tedious and error-prone. <strong>The</strong> octal and<br />

hexadecimal notations are both used for writing binary since conversion is so simple.<br />

Figure 7.34 also shows that a binary number is split into groups <strong>of</strong> three or four digits<br />

starting at <strong>the</strong> least significant end, and <strong>the</strong> groups are individually converted to octal<br />

or hexadecimal digits. Since 16 different symbols are required in hex, <strong>the</strong> letters A–F<br />

are used for <strong>the</strong> numbers above nine.<br />

<strong>The</strong>re will be a fixed number <strong>of</strong> bits in a control sample, which determines <strong>the</strong> size <strong>of</strong><br />

<strong>the</strong> quantizing range. In a ten-bit sample <strong>the</strong>re may be 1024 different numbers. Each

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