Patent GB-868196-A (GB)
Title: Improvements relating to electrical analogue co-ordinate conversion apparatus
Inventor: HARRIS ROBERT JOHN
IPC: G06G7/22
Filed: 1956-03-27
Abstract: 868,196. Electric analogue calculating systems. ELECTRIC & MUSICAL INDUSTRIES Ltd., BUCKINGHAM, J., and HARRIS, R. J. June 27, 1957 [March 27, 1956], No. 9610/56. Class 37. Co-ordinate conversion apparatus for converting (1) polar into cartesian, and (2) cartesian into polar co-ordinates comprises means for generating first and second carrier waves (or pairs of carrier waves) amplitude modulated to represent the initial co-ordinates of a point, means responsive to (1) one of said carrier waves or (2) both carrier waves to derive a pulse train, of high repetition frequency relative to the carrier-wave frequency, and having a duty cycle proportional to the range co-ordinate of the point, means for relatively gating or sampling said pulse train (or a sinusoidal signal or signals derived therefrom), with (1) said second carrier wave (or pair of carrier waves) representing the bearing co-ordinates of the point, (2) said second pair of carrier waves representing the cartesian co-ordinates of the point. Fig. 3 shows a circuit for converting polar coordinates R, # into cartesian co-ordinates The bearing (#) information in the form of threephase signals is fed into a multi-terminal network 30 which converts them into two phase output signals e 11  = E 1  cos #t cos # and e 12  = E 1  cos #t sin 6, and the required output potentials e x , e y  are e x  = E z k 3 R cos # cos #t, ey = E 2 k 3 R sin # #s #t (E 2  being the reference potential and k 3  a constant) so that e 11 , e 12  must be multiplied by a factor k 3 RE 2 /E 1 . This is achieved by first extracting E 1  by passing e 11 , e 12  through filters 33, 34 and thence to a summing amplifier 35, e 11  passing through a 90- degree phase-shifting device 36. The output of amplifier 35 is e r  = E 1  sin (#t + #). This is passed to peak rectifier 37 which extracts e r (= E 1 ) and thence to gate 38 controlled by a generator 40 the duty cycle of which is m 1  (i.e. pulse duration X pulse repetition frequency) and the mean potential m 1 E 1  of which is supplied through filter 39, to an amplifier 42 together with a signal from a bi-stable circuit 45. If the pulses derived from circuit 45 have a duty cycle m 2  then signal transmitted by gate 43 to amplifier 42 after filtering is -m 2 E 2  and since components 40, 38, 39 form a - ve feedback path for amplifier 42 m 1  can be adjusted so that m 1 E 1 -m 2 E 2 #O so that m 1 E 1  = M 2 E 2  - 7. Now signals e 11 , e l2  are also transmitted by gates 46, 47 (controlled by generator 40) so that outputs from filters 48, 49 are e x  = m 1 E 1  cos #t and ey = m 2 E 2  cos #t sin # (8) and # from 7) ex = m 2 E 2  cos #t cos # and e y  = m 2 E 2  cos #t sin #, and E x =m 2 E 2  cos #, Ey = m 2 F 2  sin # A A (9). Now in order that E x (=e x ) and Ey(=ey) should be the desired cartesian co-ordinates m 2  must equal k 3 R and to achieve this the range (R) information is fed into a matrix 31 and signals e 11 , e 12  (E 1  cos #t#s# 1 E 1  cos #t sin # 1 ), where # 1  = displacement of the magslip shaft transmitting range information) are fed to amplifier 52. The output is delayed relative to carrier wave by # 1  and converted into a spike at the leading edge of waveform from limiter 54 by differentiating element 55 which spike is applied to one input of circuit 45. The unmodulated carrier signal is applied to the other input of circuit 45 which then receives two pulses having a phase difference # 1  and this provides a pulse the duty cycle of which is # 1 /2# = m 2 . But # 1 αR # m 2  = k 3 R and from (9) E x  = E 2 k 3 R cos # and Ey = E 2 k 3 R sin #. Detailed circuits are described (Figs. 7A, 7B, not shown) the networks 30, 31 taking the form of Scott connected transformers, the gate 46 (formed by a double diode) and filter 48 being incorporated in a see-saw amplifier 35 as are gate 47 and filter 49. The phase-shift device 36 consists of a circuit in which e 11  is advanced by 45 degrees and e 12  retarded by 45 degrees and amplifier 35 is a see-saw amplifier. The output from this amplifier is rectified by a doubler type of rectifier circuit. The first part of the "range" circuit is similar to that described for the "bearing" circuit but the output from the summing amplifier 52 is controlled directly by the setting of the " range " magslip which will however be at - 45 degrees relative to the phase of the reference signal applied to filter 57, and a delay circuit must therefore be introduced for the output to delay it by 45 degrees. The limiter 54 is a valve and produces a rectangular waveform, the element 55 being a resistance condenser differentiating network. The bi-stable circuit is of conventional construction. The limiter 56 for the, timing reference signal is constituted by two diodes and then fed through a multivibrator producing a square wave which is differentiated by an (RC) element 58 to provide the second input to circuit 45. The pulse generator 40 is a mono-stable cathode-coupled flip-flop. In another embodiment (Fig. 4, not shown) the circuit components are largely similar to those of Fig. 3, but the output from amplifier 35 is a vector delayed by with respect to the carrier signal and is limited and differentiated to provide pulses each of which are of equal duration but the phase of which is variable in response to # and these pulses are applied to gates as gating signals for an input dependent on the range R. Fig. 5 shows an embodiment in which cartesian co-ordinates are converted into polar co-ordinates. Input potentials e x  = E R  cos #t#S#, ey = E R  cos #t sin # are fed to circuits 72, 73 respectively each comprising a high-gain amplifier and negative feedback loop (transmittance B) gate and filter, 74, 75 and 76 in the former case, gate 75 being controlled by a pulse generator 77 (duration cycle m). The I gain of the amplifier = - and since m must be 1 equal to # gain = -. The output from the m amplifiers applied to networks 78 (identical with that 30 of Fig. 3) is equal to E R  cos #t cos #/m, E R  cos #t sin #/m so that in order to obtain the bearing output, E R /m must be removed. This is achieved by extracting a signal representing Ep by a phase shifter 79, amplifier 80 and rectifier 81 and feeding it into one input of amplifier 84, the other input of which is a signal corresponding to a reference voltage (E 2  ...), the feedback circuit of amplifier 84 for controlling pulse generator 77 being similar to that for generator 40 of Fig. 3. The width of the pulses from 77 is therefore controlled in response to range R so that m = E R /E 2 , therefore removing E R /m. The range output is obtained by synchronizing generator 77 from a sine wave oscillator 86 the output of which is e m  = E m  cos pt. A pulse from generator 77 is timed to commence at t n1  = 2##/p and the trailing edge will thus occur at tn 2  = 2#/p (m + n). Sampling stores 87, 88 also receive the output of oscillator 86, through a phase shifter 89 in case of store 87, the sampling pulses being derived from generator 77 through 90 which produces a spike at the trailing edge of each pulse. The outputs of 87, 88 are respectively E m  sin pt and E m  cos pt and when t = t n2  the outputs are E m  sin 2#m and E m  cos 2#m, so that the output fed to network 93 (identical with 31 of Fig. 3) is directly proportional to E R  (since m = E R /E 2 ). Specification 859,942 is referred to.