The Art of the Helicopter John Watkinson - Karatunov.net

296 The Art of the Helicopter
Fig. 7.32 A linear encoder in which the position of the moving part determines the binary code created.
single wire can be used where successive digits from each sample are sent serially. This
is the definition of pulse code modulation. Clearly the clock frequency must now be
higher than the sampling rate.
Whilst control samples can be obtained by digitizing the output of an analog control
such as a potentiometer, it is preferable to obtain samples directly in a digital encoder.
Digital encoders are a form of displacement transducer in which the mechanical position
of the shaft or pushrod is converted directly to a digital code. Figure 7.32 shows
an absolute linear encoder. A grating is moved with respect to several light beams, one
for each bit of the control word required. The interruption of the beams by the grating
determines which photocells are illuminated. It is not possible to use a pure binary
pattern on the grating because this results in transient false codes due to mechanical
tolerances. Figure 7.33 shows some examples of these false codes. For example, on
moving the fader from 3 to 4, the MSB goes true slightly before the middle bit goes
false. This results in a momentary value of 4 + 2 = 6 between 3 and 4.
The solution is to use a code in which only one bit ever changes in going from one
value to the next. One such code is the Gray code first devised to overcome timing
hazards in relay logic but is now used extensively in position encoders. Gray code can
be converted to binary in a suitable look-up table or gate array or by software in a
processor.
For digital signalling, the prime purpose of binary numbers is to express the values of
the samples representing the original control position. Figure 7.34 shows some binary
numbers and their equivalent in decimal. The radix point has the same significance in
binary: symbols to the right of it represent one-half, one-quarter and so on. Binary
is convenient for electronic circuits, which do not get tired, but numbers expressed in
binary become very long, and writing them is tedious and error-prone. The octal and
hexadecimal notations are both used for writing binary since conversion is so simple.
Figure 7.34 also shows that a binary number is split into groups of three or four digits
starting at the least significant end, and the groups are individually converted to octal
or hexadecimal digits. Since 16 different symbols are required in hex, the letters A–F
are used for the numbers above nine.
There will be a fixed number of bits in a control sample, which determines the size of
the quantizing range. In a ten-bit sample there may be 1024 different numbers. Each