GB1570045A - Digital circuits - Google Patents

Description

(54) DIGITAL CIRCUITS (71) We, LITTON INDUSTRIES, INC., a corporation organised and existing under the laws of the State of Delaware, United States of America, having an office at 360 North Crescent Drive, Beverly Hills, California 90210, United States of America, do hereby declare the invention, for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the following statement: This invention relates to digital circuits for determining altitude differences or rate of change of altitude.

Cross reference is made to the related patent applications No. 24862/77 (Serial No.

1567553) and No. 24864/77 (Serial No. 1567554).

In the determination of the difference in altitude between successive sampling intervals, the sine and cosine signals from a barometric altimeter may be employed. However, the sine and cosine signals may be modified by a scale factor which may vary. Accordingly, the logical method of determining altitude differences would involve the use of the tangent or cotangent, to eliminate the effect of the possibly varying scale factor. In performing operations on digital numbers, however, it is more cumbersome and time-consuming to perform division operations than multiplication operations.

According to the present invention, there is provided a circuit arranged to determine altitude changes from sine and cosine synchro output signals from an altimeter, the circuit comprising means for producing periodic samples of said sine and cosine signals in digital form, and an arrangement which defines a relationship which gives an approximation to the altitude change between successive sampling times as a function of the sine and cosine values of successive samples, that function including multiplication and addition operations but not a division operation, the arrangement being operable to receive the signals in digital form from successive samples and to combine those signals according to said relationship to provide an altitude difference output substantially corresponding to the altitude change between the sampling times of the combined signals.

In the above and in the claims an "addition operation" is to be understood as including not only algebraic addition but also subtraction.

In accordance with a preferred embodiment of the present invention, differences in altitude are determined from the sine and cosine signals through the use of trigonometric substitutions which are employed to approximate the tangent or cotangent function using only multiplications and addition (or subtraction). Further, a scale correction factor is introduced to avoid the adverse effects which might otherwise arise from changes in the magnitude of the input signals. This scale factor correction is also formulated and accomplished through multiplication and addition (or subtraction), with division operations being avoided. In very specific terms, the key formulas for establishing the approximation in the preferred embodiment are as follows: e - Oo = (SH * CHO - CH * SHO) * [(1 Y) .(2-Y) (2 - Y) + 1] (A) Y = CH *CHO + SH *SHO = K2 (cos H cos 0o + sin H sin 80) 72 (B) DHB = 5000 * (H - go) (C) 2# Where 8 is the angle of the barometric altimeter synchro output, 00 is the previously sampled angle of the barometric altimeter output, SH = Ksin 0, CH = Kcos 0, SHO = Ksin Bo, and CHO = Kcos ûo; where K is the scale factor which may vary between 1.0 and 0.8.

The difference in barometric altitude between successive sampling intervals is DHB.

incidentally, it may be noted that the approximation is possible in view of the fact that the angle 0 changes by an amount less than 1 from one sampling interval to the next.

For a better understanding of the invention and to show how the same may be carried into effect, reference will now be made, by way of example, to the accompanying drawings, in which: Figure 1 is a detailed circuit diagram of one implementation of the present invention; and Figure 2 is an alternative implementation of the present invention, using microprocessor technology.

With reference to the drawings, a barometric altimeter 12 has the normal three synchro leads 14 coupled to Scott T transformer 16 which provides a sine H output signal on leads 18 and a cosine 0 output on leads 20. The sine 0 and cosine 0 signals are sampled in accordance with sampling pulses provided by pulse circuit 22 on lead 24 to the conditioning and sample and hole circuit 26. The analog sine 8 and cosine 8 signals are converted to digital form in the analog-to-digital, or A-to-D converter 28. The register 30 stores the digital representations of sine #o and cosine #o for the prior sampling interval. The routing of the sine 0 and cosine o to register 30 and the delay of these signals so that the sine 00 and cosine 0o signals are always one sampling interval behind the sine 0 and cosine 0 values, may be accomplished in any suitable manner. In Figure 1, the delay circuits 32 and 34 are employed to accomplish this function. Alternatively, suitable shift or transfer registers may be employed into which the digital representations of sine 0 and cosine 8 could be stepped by the sampling pulses from circuit 22.

Prior to consideration of the remaining circuits of Figure 1, it is useful to shift over to the mathematical determination which is implemented by the circuit of Figure 1. Let HB and HBO be the barometric altitude samples at two real time interrupts, t and to, respectively.

For small angle differences, it is well known that: 0 H = # tan ( - 8 ) = tan 0 - tan Oo 0 - 0o 1 + tan 0 tan 0o (1) H # = HB X 2#; indicating that where: o = ; indicating that 5,000 feet of altitude is equal to 360 , or 27r radians HBO x 2# 5000 Let (SH=Ksin f), (CH = Kcos S), (SHO = Ksin 0o) and (CHO = Ksin #0) be the outputs from A/D converter at times t and to, respectively. K is the scale factor which could be varied between 1.0 and 0.8. Now, tan 8 and tan 80 can be written as: sin 0 - sin = Ksin 0 - tan # = = sin 8 = Kcos # CH (2) tan 80 = sin #o = Ksin 0o = SHO (3) cos 80 Kcos Oo CHO By substituting equations (2) and (3) into (1), we have SH SHO CH CHO SH * CHO - CH*SHO (4) 8 - 0o = -------- = 1 + SH SHO CH * CHO + SH * SHO CH CHO Due to the inconvenience of performing divide algebraic operations, an approximation is made so that only multiply operations are required to carry out equations (4). Let Y = CH *CHO + SH *SHO (5) - K2 (cos 0 cos 0o + sin 0 sin Ho) (6) - K2 For the range of K, 12 Ka 0.8, we can have 1 1 -- =k1-Y)(2-Y) + (2-)+ 1] (7) Y 1-(1-Y) Substituting equations (5) and (7) into equation (4), we have 0-0o = (SH * CHO - CH * SHO) [(1-Y) (2-Y) + 1] (8) Then, the barometric difference (DHB) can be obtained as 5000 DNB = * (H- oo) (9) 2# Note that if K = 1, then Y = 1 and equation (8) becomes 0-0o = (SH * CHO - CH * SHO) = sin 8 cos 00 - cos H sin 00 = sin (0 - Oo) (10) It may be seen that [(1-Y).(2-Y) + 1] takes care of the scale factor K.

Returning to Figure 1, the multiplication circuits 36, 38, 40 and 42, are employed to provide the indicated combinations of sines and cosines involving samples from adjacent sampling intervals. The adder/subtracter 44 provides the differences in angle between û and 00 set forth in equation (8) with the exception of the bracketed scale factor involving "Y". The value of Y as expressed in equation (5) is obtained by the adder/subtracter 46.

Logic circuit 48 yields the bracketed scale correction factor of equation (7), as indicated on output lead 50 from this circuit. The multiplication circuit 56 includes as inputs the scale correction factor on lead 50, the basic angular difference factor on lead 52, and a third input on lead 54. The third input is indicated by equation (9) and includes the factor 5000, which is approximately equal to 794. With these three input factors, the output from multiplier 56 on lead 58 is the difference in barometric altitude between successive sampling intervals.

With regard to the implementation of Figure 1, a number of separate multiplication, addition, subtraction, and logic circuits have been shown. In accordance with known techniques, if desired, the operations performed by these circuits may be handled by a single common circuit on a time-shared basis.

It is noted again that the angle 0 in the output representation from the barometric altimeter 12 involves 360O or 2ir radians being equal to 5,000 feet of altitude. With a maximum change in altitude per second for the aircraft being approximately 71 feet per second, and a sampling rate of 16 samples per second, the maximum change in the angle 0 between successive samples is slightly more than one-half of 1". It is in part because of this relatively small value of the difference in the angle 0 from sample to sample that the approximations in the present specification are practical.

It is noted in passing that the 5000/2it factor could if desired be implented as a scale factor in the course of the A/ D conversion in unit 28 or elsewhere in the circuitry.

An alternative implementation of the circuit of Figure 1 is shown in Figure 2. In Figure 2, the input from the barometric altimeter 12 and the Scott T transformer 16 are the same as in Figure 1, but the circuitry from this point on follows that which is set forth in the patent applications referenced at the beginning of the present specification. More specifically, the circuit of Figure 2 includes the input conditioning circuitry 66, the analog multiplexing circuit 68, the analog-to-digital converter 70 and the digital multiplexer 72. A data processing circuit 74 includes the microprocessor 76, a read only memory or ROM 78 and a random access memory or RAM 80. The circuitry may for example be an Intel 8080 microprocessor having a mode of operation which is described in detail in available literature. The sequence of the steps for implementing the equations set forth in the present specification are, of course, permanently stored in the read only memory 78 and are thus an essential and permanent part of the system, precisely duplicating the hard wired circuit structure shown in Figure 1 of the present specification.

The barometric rate determination may be accomplished as indicated below.

An incremental method is used to generate barometric rate from altitude differences at fixed time intervals (0.064 second in our case). Barometric rate is also filtered with a time constant which can easily be varied to take care of the noise resulting from the synchro input or the A/D converter.

The equation is as follows: HBDn = HBDn.1 + 1 +t(DHB-HBDn-1*DT) (11) where HBD is the computed barometric rate, t is the time constant, DHB is the calculated difference in altitude between successive sampling intervals as calculated above, and DT is the real time interrupt interval. In practice, the time constant t might be set equal to two seconds, and the interrupt rate is equal to 1/16 of a second. Assuming that DHB was calculated as equal to three feet (in 1/16 second, or 48 feet in one second) and the prior rate HBD,, l was equal to 32 feet per second, then: HBDn = 32 + 0.5 (3 - 32 .1/16) = 32.5 ft/sec. (12) In conclusion, an effective technique for determining altitude differences and change in altitude rates using only multiplication and addition or subtraction circuitry, and sine and cosine input signals, has been set forth. In the event scaling factors are not present, the scale correction procedure may be dispensed with.

WHAT WE CLAIM IS: 1. A circuit arranged to determine altitude changes from sine and cosine synchro output signals from an altimeter, the circuit comprising means for producing periodic samples of said sine and cosine signals in digital form, and an arrangement which defines a relationship which gives an approximation to the altitude change between sucessive sampling times as a function of the sine and cosine values of successive samples, that function including multiplication and addition operations but not a division operation, the arrangement being operable to receive the signals in digital form from successive samples and to combine those signals according to said relationship to provide an altitude difference output substantially corresponding to the altitude change between the sampling times of the combined signals.

2. A circuit according to claim 1, wherein the producing means comprises means for periodically sampling said sine and cosine output signals and analog-to-digital conversion means for converting the samples sine and cosine signals into digital form.

3. A circuit according to claim 1 or 2, wherein the arrangement comprises: means for storing the samples sine and cosine values whilst the next sample is being taken; multiplication means for combining said sine and cosine signals from successive sampling times; and addition means for combining the resultant products from said multiplication means to provide said altitude difference output.

4. A circuit according to claim 1, 2 or 3, wherein the relationship for altitude change is: e - 0o = (SH.CHO - CH.SHO), where 0 is proportional to altitude at one sampling time t, û0 is proportional to the altitude at the preceding sampling time to, SH = KsinB, CH = K cos 0, SHO = Ksin û0, CHO = Kcos û0 and K is a scaling factor.

5. A circuit according to any one of the preceding claims, wherein the relationship also includes a correction factor for variations in the scale of said sine and cosine signals and the arrangement includes means for determining the correction factor.

6. A circuit according to claims 4 and 5, wherein the altitude change is given bye,, where y is the correction factor and the arrangement is operable to determine on the basis of the expression: i=(t-Y)(2-Y) + 1, Y wheein Y = CH.CHO + SH.SHO.

**WARNING** end of DESC field may overlap start of CLMS **.

Claims (10)

**WARNING** start of CLMS field may overlap end of DESC **. An incremental method is used to generate barometric rate from altitude differences at fixed time intervals (0.064 second in our case). Barometric rate is also filtered with a time constant which can easily be varied to take care of the noise resulting from the synchro input or the A/D converter. The equation is as follows: HBDn = HBDn.1 + 1 +t(DHB-HBDn-1*DT) (11) where HBD is the computed barometric rate, t is the time constant, DHB is the calculated difference in altitude between successive sampling intervals as calculated above, and DT is the real time interrupt interval. In practice, the time constant t might be set equal to two seconds, and the interrupt rate is equal to 1/16 of a second. Assuming that DHB was calculated as equal to three feet (in 1/16 second, or 48 feet in one second) and the prior rate HBD,, l was equal to 32 feet per second, then: HBDn = 32 + 0.5 (3 - 32 .1/16) = 32.5 ft/sec. (12) In conclusion, an effective technique for determining altitude differences and change in altitude rates using only multiplication and addition or subtraction circuitry, and sine and cosine input signals, has been set forth. In the event scaling factors are not present, the scale correction procedure may be dispensed with. WHAT WE CLAIM IS:

1. A circuit arranged to determine altitude changes from sine and cosine synchro output signals from an altimeter, the circuit comprising means for producing periodic samples of said sine and cosine signals in digital form, and an arrangement which defines a relationship which gives an approximation to the altitude change between sucessive sampling times as a function of the sine and cosine values of successive samples, that function including multiplication and addition operations but not a division operation, the arrangement being operable to receive the signals in digital form from successive samples and to combine those signals according to said relationship to provide an altitude difference output substantially corresponding to the altitude change between the sampling times of the combined signals.

2. A circuit according to claim 1, wherein the producing means comprises means for periodically sampling said sine and cosine output signals and analog-to-digital conversion means for converting the samples sine and cosine signals into digital form.

3. A circuit according to claim 1 or 2, wherein the arrangement comprises: means for storing the samples sine and cosine values whilst the next sample is being taken; multiplication means for combining said sine and cosine signals from successive sampling times; and addition means for combining the resultant products from said multiplication means to provide said altitude difference output.

4. A circuit according to claim 1, 2 or 3, wherein the relationship for altitude change is: e - 0o = (SH.CHO - CH.SHO), where 0 is proportional to altitude at one sampling time t, û0 is proportional to the altitude at the preceding sampling time to, SH = KsinB, CH = K cos 0, SHO = Ksin û0, CHO = Kcos û0 and K is a scaling factor.

5. A circuit according to any one of the preceding claims, wherein the relationship also includes a correction factor for variations in the scale of said sine and cosine signals and the arrangement includes means for determining the correction factor.

6. A circuit according to claims 4 and 5, wherein the altitude change is given bye,, where y is the correction factor and the arrangement is operable to determine on the basis of the expression: i=(t-Y)(2-Y) + 1, Y wheein Y = CH.CHO + SH.SHO.

7. A circuit according to claim 6, when appended to claim 3, and including additional

multiplication means for calculating 1/Y times (0 - û0).

8. A circuit according to any one of the preceding claims and including means for converting said altitude difference output to predetermined units of distance.

9. A circuit for determining altitude changes from sine and cosine synchro output signals from an altimeter substantially as hereinbefore described with reference to Figure 1 or Figure 2 of the accompanying drawings.

10. A circuit according to any one of the preceding claims, in operable combination with an altimeter having sine û and cosine H outputs, where û is proportional to altitude as measured by the altimeter.