Circuit for the conversion of a digital signal to an analog signal
This is a division, of application Ser. No. 579,868, filed May 22, 1975, abandoned. 
    
    
     The invention relates to a circuit for the conversion of a digital signal to an analog signal which can be obtained from the output of a comparator, in which comparator the value of the digital signal corresponding to a digital number (A = A n-1  . . . A O ) to be converted is compared to the value of a digital comparison signal which corresponds to a periodically occurring series of comparison numbers (C = C n-1  . . . C O ), produced by a generator. 
     From the British Patent Specification No. 1,314,449 a circuit of the abovementioned kind is known in which a signal corresponding to a periodically occurring series of comparison numbers is supplied to the comparator and in which each comparison number is a mirror image of a number of a monotonously increasing or decreasing series numbers which each time decrease or increase in value by a step of one. Then the comparator delivers a signal in which the number of pulses per period increases by the value of the digital number which corresponds to the digital signal until the digital number has reached half of its maximum convertible value. 
     Therefore such a circuit delivers a pulse signal which can be easily converted to an analog signal as the number of pulses per period increases by the value of the digital number to be converted. However, it was found that this increase is accompanied by an increase in the absolute value of the error in the conversion, until the value of the digital number to be converted has obtained half of its convertible maximum value. 
     The object of the present invention is to greatly reduce the error in the conversion and a circuit of the kind described above is therefore characterized in that the generator is suitable for the generation of a signal that corresponds to a series of digital comparison numbers of which in each next comparison number (C = C n-1  . . . C O ) the most significant first m figures (C n-1  . . . C n-m ) pass through a series of numbers (D = D n-1  . . . D O ) which each time monotonously increase or decrease in value by one, whereas the least significant last (n - m) figures form a digital number (E = E n-1  . . . E O ) whose figures form an inversion of the order of the figures of a number (B n-1  . . . B m ) of (n - m) figures, which each time increases or decreases respectively by one, when the number series (C n-1  . . . C n-  m) of the first m figures, reckoned in the order of decreasing significance of the comparison number (C), has been passed through, with the condition that n ≧ 3, m ≠ 1 and m ≠ n. 
     This ensures that the number of pulses per period can only increase to 2 n-m  so that the number of pulse edges which produce the abovementioned error in the conversion remain limited. An added advantage is that temperature variations which affect the shape of the pulse edges now have a less disturbing influence in the conversion. 
     A circuit according to the invention is particularly suitable for use in a tuning circuit of a receiver such as for example television receiver. In such a circuit as a rule the analog signal values corresponding to a digital number smaller than 2 n-m , which continue to show the largest relative error, are usually not used. 
    
    
     The invention will now be described with reference to the drawing. 
     FIG. 1 of the drawing shows a block diagram of a converter circuit according to the invention. 
     FIG. 2 is a graph showing how the digital comparison number C varies as a function of the counter position B, and 
     FIG. 3 shows a block diagram of a television receiver having a circuit according to the invention. 
    
    
     In FIG. 1 there is supplied to a comparator 1 a signal combination which corresponds to a digital number A = A n-1  . . . A O  to be converted, namely to an input A O  a signal corresponding to the least significant figure A, to an output A 1  a signal corresponding to the, in significance, next figure A 1  and so on. 
     Also supplied to the comparator is a signal combination corresponding to a digital comparison number C = C n-1  . . . C O  which is supplied by a counter 3 whose position B = B n-1  . . . B O  produces a signal combination of signals which correspond to the figures B O , B 1  and so on. To an input 5 of the counter 3 pulses are continuously supplied which are generated by a pulse generator 7. Each pulse causes the counter to advance by one position. 
     To avoid intricate formulae, hereinafter the indications for figures and numbers and the corresponding signals and signal combinations will be intermingled. 
     The comparator 1 has an output 9 at which an analog signal appears which can be converted by means of a low-pass filter to an analog signal corresponding to the signal combination A n-1  . . . A O . 
     For example the output 9 can become high when C ≦ A and remain low when C &gt; A. 
     In the comparator 1 C O  is compared to A O , C 1  to A 1  and so on. The figures of the comparison number C are derived from the figures of the counter position B in the following manner: 
     The first, least significant figure B O  of B is the figure C n-m  of C, which figure is the (n-m+1) th  figure in sequence of increasing significance of C; the second figure B 1  of B, reckoned in sequence of increasing significance, is the (n-m+2) th  figure C c-m+1  of C and the m th  figure B m-1  of B is the n th  figure C n-1  of C 1 . Here n is the number of figures of the numbers A, B and C and m has a value which is to be adapted to the purposes for which the circuit is intended. The next figures of B, i.e. the (m+1) th  figure B m , the (m+2) th  figure B m+1  to the last, most significant n th  figure B n-1 , form in the mirror image sequence the first (n-m) figures C O , C 1  . . . C n-m-1  of C. Thus C O  = B n-1 , C 1  = B n-2 , . . . , C n-m-2  = B m+1  and C n-m-1  = B m . 
     The m most significant figures of C, which are the least significant figures of B, form a number D = D m-1 , C m-2 , . . . D O  which increases (or decreases when the counter 3 counts down) monotonously in value when the counter 3 passes through its positions in which jumps occur at the transitions of 11 . . . 1 to 00 . . . 0. The (n-m) least significant figures of C form a number E = E n-m-1 , E n-m-2 , . . . E O  whose value changes in a more intricate manner because it is a mirror image of the sequence of a number B n-1 , . . . B m  which each time increases by one when the number series B m-1 , . . . B O  = D m-1 , . . . D O  has been passed through. 
     The table below shows for n = 5 and m = 3 an example of the relation between the various figures and numbers and in FIG. 2 between the values of the counter position B and those of the comparison number C. 
     
                       TABLE                                                       
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Counter Position                                                          
              Comparison number                                           
                   C.sub.4 C.sub.3 C.sub.2 C.sub.1 C.sub.0                
                  D.sub.2 D.sub.1 D.sub.0 E.sub.1 E.sub.0                 
B     B.sub.4 B.sub.3 B.sub.2 B.sub.1 B.sub.0                             
                  B.sub.2 B.sub.1 B.sub.0 B.sub.3 B.sub.4                 
                               C     D     E                              
______________________________________                                    
0     0 0 0 0 0   0 0 0 0 0    0     0     0                              
1     0 0 0 0 1   0 0 1 0 0    4     1     0                              
2     0 0 0 1 0   0 1 0 0 0    8     2     0                              
3     0 0 0 1 2   0 1 1 0 0    12    3     0                              
4     0 0 1 0 0   1 0 0 0 0    16    4     0                              
5     0 0 1 0 1   1 0 1 0 0    20    5     0                              
6     0 0 1 1 0   1 1 0 0 0    24    6     0                              
7     0 0 1 1 1   1 1 1 0 0    28    7     0                              
8     0 1 0 0 0   0 0 0 1 0    2     0     2                              
9     0 1 0 0 1   0 0 1 1 0    6     1     2                              
10    0 1 0 1 0   0 1 0 1 0    10    2     2                              
11    0 1 0 1 1   0 1 1 1 0    14    3     2                              
12    0 1 1 0 0   1 0 0 1 0    18    4     2                              
13    0 1 1 0 1   1 0 1 1 0    22    5     2                              
14    0 1 1 1 0   1 1 0 1 0    26    6     2                              
15    0 1 1 1 1   1 1 1 1 0    30    7     2                              
16    1 0 0 0 0   0 0 0 0 1    1     0     1                              
17    1 0 0 0 1   0 0 1 0 1    5     1     1                              
18    1 0 0 1 0   0 1 0 0 1    9     2     1                              
19    1 0 0 1 1   0 1 1 0 1    13    3     1                              
20    1 0 1 0 0   1 0 0 0 1    17    4     1                              
21    1 0 1 0 1   1 0 1 0 1    21    5     1                              
22    1 0 1 1 0   1 1 0 0 1    25    6     1                              
23    1 0 1 1 1   1 1 1 0 1    29    7     1                              
24    1 1 0 0 0   0 0 0 1 1    3     0     3                              
25    1 1 0 0 1   0 0 1 1 1    7     1     3                              
26    1 1 0 1 0   0 1 0 1 1    11    2     3                              
27    1 1 0 1 1   0 1 1 1 1    15    3     3                              
28    1 1 1 0 0   1 0 0 1 1    19    4     3                              
29    1 1 1 0 1   1 0 1 1 1    23    5     3                              
30    1 1 1 1 0   1 1 0 1 1    27    6     3                              
31    1 1 1 1 1   1 1 1 1 1    31    7     3                              
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     The figure shows that for A = 0 a high value of the output signal of the comparator will occur at the counter position B = 0, for A = 1 at the counter positions B = 0 and B = 16, for A = 2 at the counter position B = 0, B = 8 and B = 16, for A = 3 at the counter positions B = 0, B = 8, B = 16 and B = 24. When the values A are still higher a number of pulses per counter cycle at the output 9 of the comparator does no longer increase, but the width of the pulses increases so that the number of pulse edges does no longer increase. These pulse edges are the cause of errors in the conversion which are, besides, temperature dependent. These errors are now limited because the number of pulses per counter cycle remains limited to 2 n-m . The increase of the frequency of the output signal at an increase in value of A from 0 is favorable for the choice of the values of the components of the low-pass filter mentioned above, following the comparator. 
     In FIG. 3 the same reference numerals have been used as in FIG. 1 for corresponding components. 
     The comparator 1 comprises three integrated 4-bit magnitude comparator circuits of the type SN 7485 and the counter 3 comprises three integrated 4-bits counter circuits SN 7493. 
     The digital number A to be converted is delivered by a two-way counter 11 which comprises three integrated 4-bits counter circuits SN S84193. This counter 11 has an upcounting input 13 and a downcounting input 15 which are connected to a switch 17, whose other side is connected to an output of a pulse generator 19. By operating the switch 17 the position of the counter 11 can be increased or decreased whereby the output signal of a comparator 1 delivers a pulse pattern which corresponds to that position and which is converted by a low pass filter 21 to a direct voltage which is supplied to a tuning unit 25. 
     The tuning unit 25 has an input 27 to which a signal received is fed. To an intermediate frequency detector 29 an I.F. signal is supplied which is determined by the tuning of the tuning unit 25. The intermediate frequency and detector unit 29 then supplies a signal to a separating circuit 31 which delivers sound, picture and synchronization signals to reproducing unit 33. 
     For the counters 3 and 11 and the comparator 1 m = 9 and n = 11 has been chosen. The maximum number of pulses which appear at the output 9 of comparator 1 per cycle of the counter 3 then is 2 n-m  = 2 2  = 4. 
     The output voltage of the filter 21 may have 2 n  = 2 11  = 2048 steps. 
     C O  of the comparator is connected to B 10 , of the counter C, to B 9 , C 2  to B O , C 3  to B 1 , C 4  to B 2 , C 5  to B 3 , C 6  to B 4 , C 7  to B 5 , C 8  to B 6 , C 9  to B 7 , and C 10  to B 8 . 
     It will be clear that the comparator 1 may also be in the form of a half-adder as described in the abovementioned British Patent. 
     Furthermore it is of course possible to use for the supply of the comparison members C a conventional counter 3, connected in a special manner which supplies the desired signal C at its output, in which case special gate circuits for the counter sections are then required. A shift register, having a special feedback, can also be used. 
     If desired a signal corresponding to a binary coded decimal number can also be converted to an analog signal in a manner which corresponds to a manner indicated in the British Patent. 
     In the extreme case that n-m = 1 is chosen the sequence inversion mentioned is of no practical significance. It will be clear that m ≠ n and m &gt; 1 must be chosen and n ≦ 3. 
     For n - m = 1 the circuit of FIG. 1 delivers a maximum of two output pulses per counter cycle.