Phase modulator having individually placed edges
RELATED APPLICATIONS 
     This application is related to application Ser. No. 08/339,420, filed Nov. 14, 1994 now U.S. Pat. No. 5,481,230, which is incorporated herein in its entirety. 
     BACKGROUND OF THE INVENTION 
     Clock signals are square waves used for timing digital systems. Spurious phase modulation of clock signals can lead to problems in system operation. Therefore, it is useful to simulate this spurious modulation with a clock phase modulator to test system performance under stressed conditions. 
     One technique for phase modulation is illustrated in FIG. 1. A phase-locked loop (PLL) 10 includes a voltage-controlled oscillator (VCO) 12 that is locked to a carrier signal v c  from an oscillator 14. A modulating signal v m  added after a phase detector 16 causes the output signal v o  to be phase-modulated. 
     One disadvantage of the PLL method is the limited dynamic range of the phase detector 16 and its possible non-linearity. This limits the amplitude of the phase modulation and may cause amplitude distortion. Another disadvantage is the limited frequency range of the closed-loop design and its likely non-flat frequency response. This limits the frequency of the phase modulation and possibly causes frequency distortion. A more thorough treatment of phase modulation using PLLs is discussed in Phase-Locked Loop Circuit Design, by D. H. Wolaver, Section 9-1 (Prentice-Hall, 1991). 
     Another known technique for phase modulation is a direct digital synthesizer (DDS) as shown in FIG. 2. A DDS 18 may have a numerical input N m  that controls the phase of the output signal v o . At each pulse of a clock signal v c  from an oscillator 19, a number N.sub.ƒ  is added to an accumulator 20, forming a number N p  representing the phase. A number N m  proportional to the phase modulation is added to N p  at summer 22. The sum N p  +N m  serves as the address for a look-up table 24 that provides a number N s . N s  is the value of a sine wave for the phase represented by the sum N p  +N m . A digital-to-analog converter (DAC) 26 and a low-pass filter (LPF) 28 produce a sinusoidal voltage v o  proportional to N s . The Stanford Telecommunications STEL-2173 device is an example of such a DDS. 
     A disadvantage of the DDS method is the complexity of the circuitry and its resulting high cost, especially for high-speed operation. In particular, the accumulator 20, the sine wave look-up table 24, and the DAC 26 each require large circuits. The size of the circuitry results in delays that slow the speed of operation. Therefore, high-speed operation requires expensive technology such as gallium arsenide semiconductors. 
     SUMMARY OF THE INVENTION 
     The previously mentioned drawbacks are overcome and other advantages achieved with the invention disclosed in copending application Ser. No. 08/339,420. In one form, that invention comprises an apparatus and method for generating an output signal having individually positionable edges. The phase modulator of that invention comprises a programmable pulse generator, such as an interval counter or a delay, for producing an output signal and a control value source for delivering a sequence of control values to the generator. The control values determine the time between successive output pulses. 
     More specifically, the position of each edge of the output signal relative to an input waveform such as a square wave clock signal is determined in response to a control value. By providing succeeding control values in response to edges of the output signal, each next control value in the sequence is made available to the programmable pulse generator within the time between successive edges of the output signal. Accordingly, the pulse generator is set up at a time which avoids any spurious, misplaced, or missing edges resulting from changing the control values independent of the output signal. 
     The present invention provides improvements to the apparatus and method of Ser. No. 08/339,420 by reducing required circuitry, improving calibration of the resolution and achieving finer resolution of edge positioning. 
     In a preferred embodiment of the present invention, a programmable interval counter includes a free running counter, the output of which is compared to a control value in memory to generate an output pulse. The control value can be a modulo data value to conserve memory. 
     In another embodiment, a programmable delay circuit comprises a ring oscillator having plural delay line outputs for fine control of edge positioning. To fully synchronize the delay line to a coarse control programmable interval counter, the clock input to the interval counter may be taken from the ring oscillator. The dual functioning ring oscillator automatically calibrates the fine control based upon the coarse control. 
     In yet another embodiment, a programmable delay circuit uses interpolation to achieve finer resolution between two time positions. The delay circuit includes pulse shaping circuitry to shape two adjacent pulses from a programmable interval counter. A combiner circuit combines portions of the shaped pulses weighted according to a control value. The output of the combiner circuit is formed into a square output pulse by a slicer circuit. The interpolating programmable delay can provide fine resolution to the output of the ring oscillator. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing and other objects, features, and advantages of the invention will be apparent from the following more particular description of preferred embodiments of the drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. 
     FIG. 1 is a block diagram of a prior art phase modulator with a phase-locked loop. 
     FIG. 2 is a block diagram of a prior art phase modulator using a direct digital synthesizer. 
     FIG. 3 is a block diagram of a general embodiment of the invention. 
     FIG. 4 is a timing diagram illustrating the edge positions in time produced by a system embodying the present invention. 
     FIG. 5 is a block diagram of an embodiment of the present invention. 
     FIG. 6 is a block diagram of another embodiment of the present invention. 
     FIG. 7 is a timing diagram of the modulated output signal produced by the phase modulator of FIG. 6. 
     FIG. 8 is a block diagram of the embodiment of FIG. 6 with a flip-flop to position the rising and falling edges. 
     FIG. 9 is a timing diagram of the modulated output signal produced by the phase modulator of FIG. 8. 
     FIG. 10 is a block diagram of a preferred embodiment of the present invention. 
     FIG. 11 is a timing diagram of the fine resolution achievable with the phase modulator of FIG. 10. 
     FIG. 12 is a block diagram of an embodiment of the present invention without a count-down circuit. 
     FIG. 13 is a timing diagram of the modulated output signal produced by the phase modulator of FIG. 12. 
     FIG. 14 is a schematic block diagram of a programmable delay comprising two delay lines. 
     FIG. 15 is a block diagram of the programmable delay circuit of FIG. 12. 
     FIG. 16 is a timing diagram of the modulated output signal produced by the programmable delay circuit of FIG. 15 having correct transition timing and bounded phase slope. 
     FIG. 17 is a timing diagram similar to FIG. 16 except the phase slope is unbounded. 
     FIG. 18 is a timing diagram similar to FIG. 16 except the transition timing is incorrect. 
     FIG. 19 is a timing diagram of the modulated output signal produced by the programmable interval counter of FIG. 6 having correct transition timing. 
     FIG. 20 is a timing diagram similar to FIG. 19 except the transition timing is incorrect. 
     FIG. 21 is a block diagram of an embodiment of the present invention for providing coarse phase modulation. 
     FIG. 22 is a timing diagram of the modulated output signal produced by the phase modulator of FIG. 21. 
     FIG. 23 is a block diagram of an embodiment of the present invention having a ring oscillator as a programmable delay. 
     FIG. 24 is a timing diagram of the modulated output signal produced by the phase modulator of FIG. 23. 
     FIG. 25 is a block diagram of the ring oscillator circuit of FIG. 23. 
     FIG. 26 is a timing diagram of the ring oscillator circuit of FIG. 25. 
     FIG. 27 is a block diagram of another embodiment of the present invention using interpolation to obtain fine resolution. 
     FIG. 28 is a timing diagram of the time resolution achievable with the phase modulator of FIG. 27. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The preferred system of the present invention modulates a square wave in a novel way; it governs the position of each edge of the output signal rather than governing the phase or frequency directly. The result is the same as phase or frequency modulation, but the method is simpler and, therefore, faster and less expensive. It uses edge-control circuits in an architecture that allows individual placement of each edge based upon a sequence of control values provided sequentially in response to the output signal. The control values may correspond to the time difference between successive edges of the output signal. They may be, or may be obtained from, values representing the time difference between an edge of the output signal and a corresponding edge of the input signal. 
     In accordance with the present invention, FIG. 3 illustrates a phase modulator 100 which has a programmable pulse generator 110 and a control value source 112. An external oscillator 114 generates an input signal v c  with frequency ƒ c  which is an input to programmable pulse generator 110. Programmable pulse generator 110 generates an output waveform v o . Control value source 112 outputs a control value signal 116 to programmable pulse generator 110. The programmable pulse generator 110 uses the input signal v c  and the control value signal 116 from the control value source 112 in order to generate the output waveform v o . Output waveform v o  can be generated so that its edges (rising, falling, or both) are individually positioned relative to each other or to the input signal v c  as determined by the value of the control value signal 116. 
     The control value source 112 outputs a new control value on the control value signal 116 in response to an edge of the output signal v o  which forms an input to the control value source 112. The control values output by the control value source 112 may form an arbitrary or ordered sequence such that the result is a square wave clock signal v o  with edges placed in any desired pattern. Since the transition to a new control value is made in response to the edges of v o , the generation of spurious, misplaced, or missing edges in the output v o  may be avoided as described further below. The sequence of control values is dynamic because the rate at which control value transitions occur is on the order of the nominal frequency of edges in the output signal; preferably, control value transitions occur with each edge. Since the sequence of control values is dynamic, the phase modulation achieves wide bandwidth and wide dynamic range. The circuitry is also simpler and cheaper than that of the prior art. 
     For a given phase modulation, it is possible to calculate the positions in time of the edges of a square wave as illustrated in FIG. 4. An algorithm for this calculation is given below. Let the position of the nth edge be t n , which is a sequence of monotonically increasing times. To bound the control values, it is usually convenient to calculate the difference Δt n  between each t n  and its position if the square wave had not been phase-modulated. Let the constant interval between unmodulated edges be 1/ƒ o . Then 
     
         Δt.sub.n =t.sub.n -n/f.sub.o 
    
     If time is quantized into increments of T, these edge positions can be stored in a memory as values N n , where 
     
         N.sub.n =Δt.sub.n /T                                 (Eq. 1) 
    
     rounded to the nearest integer. A new value may be provided from memory for each edge. Where the programmable pulse generator 110 is a delay circuit, the value N n  can be read from memory and used directly to control the delay of an input pulse and thus locate an output edge. However, the pulse generator may also be an interval counter which counts input pulses to locate an edge some number of input pulses after a prior edge. In that case, the values N n  may be converted into values M n  representing the difference between succeeding N n  : M n  =N n  -N n-1 . The M n  values may then be added to a constant K, where K=ƒ c  /ƒ o , resulting in values L n  representing the spacing t n  -t n-1  between successive edges of the output signal: ##EQU1## L n  can be read from a control value memory and applied to a programmable interval counter to control edge positions in time. Alternatively, the N n  values can be read from memory, and the values can be converted into edge positions in time (L n ) using simple circuitry that is fast and inexpensive. 
     In the embodiment of FIG. 5, the programmable pulse generator comprises both a programmable interval counter 210 and a programmable delay 220. The control value source comprises memory devices 214 and 224 and may include numerical processors 212 and 222. The Programmable Interval Counter generates pulses spaced L cycles of the oscillator apart. A Programmable Delay changes its delay in response to N1. 
     The advantage of using a programmable interval counter is that it allows a wide range of a nominal frequencies in v o . The programmable interval counter divides down the input frequency f c  of input signal v c  , so the output frequency can be anywhere from f c  divided by the maximum interval of the counter up to f c  itself. However, to provide high phase resolution or a high output frequency, a very high speed clock would be required. The use of a programmable delay allows for a higher phase resolution. On the other hand, if only the programmable delay line were used, the length of the delay line might have to be too great to provide a sufficient dynamic range. 
     The delay may even provide a frequency output higher than that of the input clock by sequentially decreasing the delay time as an input clock pulse passes through the delay. This results in multiple output pulses from the delay for each input pulse. 
     In the discussion of frequency and phase, it should be recognized that any change in frequency can be seen as a change in phase and any change in phase can be seen as a change in frequency. Accordingly, a phase modulator can be seen to modulate both frequency and phase. 
     The memories of FIG. 5 are stepped in response to the delayed outputs they respectively produce. The numerical processing may be omitted, and either the Programmable Interval Counter or the Programmable Delay may be omitted. The memories 214, 224 storing the N1&#39; n  and the N2 n  may share the same physical device and even share the same addresses. It is usually preferable to have Memory 224 step to the next address in response to the signal v l , but it may be simpler in some cases to have it respond to signal v o  instead. Similarly, it is usually preferable to have Memory 214 step to the next address in response to the signal v o , but it may be simpler in some cases to have it respond to signal v l  instead. The result is a square-wave clock signal v o  with edges placed in any desired pattern. 
     One particular embodiment of the present invention is shown in FIG. 6. Here, an input signal v c  from an oscillator 32 has a frequency ƒ c  chosen so that ƒ c  =1/T, and ƒ o  =ƒ c  /K, where ƒ o  is the nominal frequency of the output signal, v o . The values N n  located in memory 38 are converted by differentiator 40 into values M n  representing the difference between succeeding N n  : M n  =N n  -N n-1 . The values M n  are added to a constant K (where K=ƒ c  /ƒ o ) by summer 42, resulting in values L n  representing the spacing t n  -t n-1  between successive edges of the output signal as shown in the equations above. Each L n  is loaded into a count-down circuit 34, such as a Motorola MC10136 programmable interval counter, which is clocked at a frequency of ƒ c  =1/T. After L n  clock cycles, the count-down circuit 34 reaches the terminal count (one), the output of which steps an address counter 36 on counter signal 35 for fetching the next N n  in memory 38. The output signal v o  also prepares the count-down circuit 34 for a load on the next clock cycle on load signal 37. 
     It should be noted that there are known techniques for phase shifting that use count-down circuits. In one technique, the output signal is used to prepare a count-down circuit for loading a delay value L. This loading alone, however, does not change the value of L. Any changes in the delay value L are made independent of the output signal, unlike the present invention which steps a sequence of control values in response to the output signal. Thus, the known techniques produce relatively static phase shifting and do not achieve the high frequency, dynamic phase modulation of the present invention. 
     The modulated square wave output v o  consists of the terminal counts output from the count-down circuit 34, as shown in FIG. 7. The terminal counts, which are spaced T×L n  apart, are represented here as narrow pulses. These pulses can be widened easily by a one-shot multivibrator or by another count-down circuit (not shown). 
     The implementation in FIG. 6 positions only the rising edges. Both rising and falling edges can be positioned by using v o  to clock a toggle flip-flop as shown in FIG. 8. The alternate embodiment of FIG. 8 operates in the same manner as the embodiment of FIG. 6, except that the output of count-down circuit 34 serves as the input to toggle flip-flop 39. As shown in FIG. 9, the rising and falling edges of the flip-flop output signal v o  &#39; are positioned based upon the rising edges of signal v o . 
     The resolution of the phase modulator 30 shown in FIG. 6 is T=1/ƒ c . For the resolution to be less than a nanosecond, the oscillator frequency must be greater than 1 GHz, which requires more expensive circuitry. A less expensive way to make the resolution smaller without increasing ƒ c  is shown in FIG. 10. In this preferred embodiment, a phase modulator 50 achieves fine resolution by using a programmable delay 52 with delay τ n  =T1×N1 n , where the fine-resolution values N1 n  are preferably stored in a memory 60. The coarse resolution is achieved with a count-down circuit 54 clocked at ƒ c  =1/T2, based on the coarse-resolution values N2 n  also stored in the memory 60. These values are derived from the original position values N n  by: 
     
         N.sub.n =Δt.sub.n /T1 
    
     
         N1.sub.n =N.sub.n mod R, 
    
     
         N2.sub.n =(N.sub.n -N1.sub.n)/R.                           (Eq. 2) 
    
     where R=T2/T1, and the &#34;mod&#34; operation adds or subtracts R from N n  until N1 n  lies in the range from 0 to R-1. Then N n  =R×N2 n  +N1 n . Since the stored values are binary, this calculation is made easier if R is a power of two. 
     Here, an input signal v c  from an oscillator 62 has a frequency ƒ c  chosen so that ƒ c  =1/T2. The values N2 n  located in memory 60 are converted by differentiator 56 into values M n  representing the difference between succeeding N2 n  : M n  =N2 n  -N2 n-1 . The values M n  are added to a constant K by summer 55, where K=ƒ c  /ƒ o , resulting in values L n  representing the spacing between successive edges of an intermediate signal v l . Each L n  is loaded into the count-down circuit 54, which is clocked at a frequency of ƒ c  =1/T2. After L n  clock cycles, the count-down circuit 54 reaches the terminal count, which steps an address counter 58 on counter signal 57 and prepares the count-down circuit 54 for a load on the next clock cycle on load signal 59. The address counter 58 steps the memory 60 to output the next values N2 n  and N1 n . The modulated intermediate signal v l  consists of the terminal counts output from the count-down circuit 54 and are spaced T2×L n  apart, as shown in FIG. 11. 
     Referring again to FIG. 10, the intermediate signal v l  forms an input to the programmable delay circuit 52. The falling edge of each delayed terminal count on register signal 63 steps the next N1 n  from register 64 for producing the delay τ n  =T1×N1 n  in the programmable delay circuit 52. The fine resolution T1 can be made arbitrarily small, limited only by the accuracy and stability of the delays. In a variation of this embodiment, the difference and summation processes can be performed before the values are stored in memory; the L n  can be stored rather than the N2 n . 
     An algorithm to determine edge positions will now be described. For an unmodulated square wave, the phase p(t) in cycles increases linearly with time: p(t)=ƒ o  t. The phase of a modulated square wave is p(t)=ƒ o  t+Δp(t), where Δp(t) is the desired phase modulation in cycles. A rising edge will occur when p(t) is an integer (0, 1, 2, . . . ). Then the time t n  of the nth rising edge is found by solving Eq. 3 for t n . 
     
         ƒ.sub.o t.sub.n +Δp(t.sub.n)=n, 
    
     
         Δt.sub.n =t.sub.n -n/ƒ.sub.o.               (Eq. 3) 
    
     This equation cannot be solved in general, and the t n  must be found by trial and error. However, a good approximation to t n  can be found with an iterative equation. Without loss of generality, let p(0)=0. Then ##EQU2## Taking a specific example of nominal frequency ƒ o  =16 and a sinusoidal phase modulation of Δp(t)=(6/2π)·sin(2πt), then Δƒ(t)=6·cos(2πt), and the Δt n  found from Eq. 4 are shown in the table below. Also shown in the table are the ideal values for Δt n  determined from Eq. 3. For this case, the difference between the Δt n  determined from Eq. 4 and the ideal Δt n  is less than 6%. If the resolution is T=0.0001, then the numbers stored in memory are found by Eq. 1 (see the N n  in the table). If the phase modulator is to be implemented with a delay line as in FIG. 10 with T1=0.0001, T2=0.0005, R=5, and K=125, then the fine-resolution numbers and the coarse-resolution numbers are found by Eq. 2 (see N1 n  and N2 n  in the table). 
     
         ______________________________________                                    
n    Δt.sub.n (ideal)                                               
                 Δt.sub.n                                           
                          N.sub.n N1.sub.n                                
                                       N2.sub.n                           
______________________________________                                    
0    0.0000      0.0000   0       0    0                                  
1    -0.0169     -0.0168  -168    2    -34                                
2    -0.0327     -0.0324  -324    1    -65                                
3    -0.0463     -0.0456  -456    4    -92                                
4    -0.0560     -0.0548  -548    2    -110                               
5    -0.0597     -0.0581  -581    4    -117                               
6    -0.0538     -0.0524  -524    1    -105                               
7    -0.0340     -0.0340  -340    0    -68                                
8    0.0000      -0.0012  -12     3    -3                                 
9    0.0340      0.0352   352     2    70                                 
10   0.0538      0.0570   570     0    114                                
______________________________________                                    
 
    
     If either |Δp(t)|&lt;&lt;1 or |Δƒ|&lt;&lt;ƒ o , then there is an even simpler algorithm to approximate Δt n  : ##EQU3## 
     If the phase slope is bounded by |N2 n  -N2 n-1  |&lt;K/2, then N n  can be reduced to conserve memory. Replace N2 n  with 
     N3 n  =N2 n  mod K, and replace the operation 
     L n  =N2 n  -N2 n-1  +K with: 
     
         L.sub.n =N3.sub.n -N3.sub.n-1 +2K for N3.sub.n -N3.sub.n-1 &lt;-K/2 
    
     
         L.sub.n =N3.sub.n -N3.sub.n-1 +K for -K/2≦N3.sub.n -N3.sub.n-1 &lt;K/2 
    
     
         L.sub.n =N3.sub.n -N3.sub.n-1 for K/2≦N3.sub.n -N3.sub.n-1.{Eq. 6) 
    
     This operation is easily implemented when K=2 k  by performing the subtraction in k-bit signed numbers and always adding only K. 
     When the desired output frequency ƒ o  is very high, it is desirable to make the oscillator frequency ƒ c  equal ƒ o  to avoid an expensive high-frequency count-down circuit. Then all of the phase modulation is done with the programmable delay, and N n  =N1 n  (there is no N2 n ). Let T2 ≡1/ƒ o , and R≡T2/T1, where T1 is the resolution of the delay. If the phase slope is bounded by |N1 n  -N1 n-1  |&lt;R/4, then N1 n  can be reduced to conserve memory and to reduce the size of the programmable delay. Replace N1 n  with N3 n  =N1 n  mod R. 
     An embodiment without a count-down circuit is shown in FIG. 12. It is usually convenient for the duty cycle of v 1  to be 50%, especially for higher frequency operation to allow for greater range. The falling edge of the delayed signal v o  output from a programmable delay 74 advances an address counter 76 after an additional delay of T2/4. Given the bound on the phase slope, this additional delay assures that the waveform of v o  is low both immediately before and immediately after the change in N3 n . The address counter 76 steps the memory 78 to output the next N3 n . The waveforms for v l  and v o  shown in FIG. 13 are for an example where R=8 and the N3 sequence is 2, 1, 0, 7, 6, 5, 4. Note that the third rising edge of v l  appears twice in v o , delayed first by T1N3 2  =0 and then by T1N3 3  =T1×7. 
     If the programmable delay 74 has significant set-up time (compared to T2) before the delayed waveform is available after applying a new N3 n , then two programmable delays may be necessary. FIG. 14 illustrates a possible implementation of alternating delay line circuit 75 in place of block 75 from FIG. 12. The delay lines 74a and 74b each receive the input signal v l  and the control values N3 n . The delay line 74a handles the odd-ordered N3 n  while the delay line 74b handles the even-ordered N3 n . The next succeeding control value N3 n  is placed in registers 82a or 82b for being alternately loaded into the respective delay lines 74a and 74b. Output logic comprising AND gates 84a and 84b, OR gate 86, and type D flip-flop 88 performs a multiplexing function on the output of the delay lines 74a and 74b. The output logic also controls the alternating operation of the delay lines. 
     Specifically, the delay line output signal 83a forms an input to AND gate 84a and delay line output signal 83b is an input to AND gate 84b. The Q and Q output signals of flip-flop 88 form the other inputs to AND gates 84a and 84b. The OR gate 86 combines the output of AND gates 84a and 84b to form the modulated output signal v o . The output of OR gate 86 is also inverted to serve as the clock input to flip-flop 88. With each cycle of input signal v l , the delayed outputs of delay lines 74a and 74b are alternately selected through the operation of flip-flop 88. The outputs of AND gates 84a and 84b are also inverted to enable respective registers 82a and 82b. 
     As noted above, the aspect of the invention whereby the transition to a new control value is made in response to the edges of the output signal allows the generation of spurious, misplaced, or missing edges in the output signal to be avoided. Having described several embodiments of the present invention, the following discussion focuses on the additional conditions required to avoid the undesired edges in the output signal. 
     FIG. 15 shows the detail of the programmable delay 74 of FIG. 12. The programmable delay 74 includes a series of delay sections, D, each delay section adding a fixed delay of T2/16, where T2=1/ƒ o , to the input signal v l . A series of taps, P0 through P15, are coupled in parallel between the delay sections D and a multiplexer 73 to produce the output signal v o , dependent on the delay value N3 n  input to the multiplexer 73. 
     The timing diagram of FIG. 16 shows the relationship between the delay taps, P0 to P15, and the output signal v o  of the delay 74. As can be seen from the diagram, the value N3 n  changes a time T2/4 after the falling edge of v o . Since the phase slope is bounded by |N3 n  -N3 n-1  |&lt;R/4, where R=T2/T1 and T1 is the resolution of the programmable delay, the rising edges of v o  are correctly placed. 
     In contrast, FIG. 17 illustrates the undesirable result produced when the phase slope is not bounded. An unbounded phase slope, i.e., too large a phase change, results in both spurious and misplaced edges in the output signal v o . A similar undesirable output results when the transition time to a new control value is incorrect. The correct transition time assures that the output signal v o  is low both immediately before and immediately after the change in N3 n . FIG. 18 shows the spurious and misplaced edges resulting from incorrect transition times of T2/8 and T2/2.7, for example. 
     An embodiment of the invention in which the programmable pulse generator is a count-down circuit was shown earlier in FIG. 6. The timing diagram of FIG. 19 shows that such an embodiment correctly places edges of the output signal v o  when the control values L n  are changed a transition time T/2 after the falling edge of v o . The transition time of T/2 allows for greatest flexibility in changing phase. 
     In contrast, FIG. 20 illustrates the undesirable results produced when the control values L n  are changed independent of the output signal v o . In this example, the values L n  are changed instead every 5T, where T is the period of the oscillator signal v c . The timing diagram of FIG. 20 shows an extra &#34;spurious&#34; edge produced when L n  =3. An edge associated with L n  =4 is missed because by the time the count-down circuit has finished counting down from the previous value of L n-1  =8, the next value, L n+1  =5, has been loaded. 
     The previous examples illustrate that making the transition timing of the control values responsive to the output signal of the programmable pulse generator is necessary to be able to avoid spurious, misplaced, or missing edges. In addition, phase slope bounding and correct transition timing are also necessary to achieve desirable results. 
     A particular embodiment of a programmable interval counter 300 of the present invention is shown in FIG. 21. Here, an input signal υ c  from an oscillator 310 has a frequency ƒ c  chosen so that ƒ c  =1/T, and K=ƒ c  /ƒ o , where ƒ o  is the nominal frequency of the output signal, υ 1 . The values N n  located in memory 322 are converted by modulo K function block 314 into values N&#39; n , where N&#39; n  =N n  mod K. The modulo function adds or subtracts K from N n  until N&#39; n  lies in the range from 0 to K-1. A counter 312 runs continuously through K counts. At each count, the count M n  is compared to the current value of N&#39; n  in comparator 316. When the count M n  in counter 312 equals the value for N&#39; n , a pulse is generated on the output υ l . An edge of output signal υ l  advances an address counter 320 for retrieving the next N n  in memory 322 after a delay of TK/2 inserted by delay line 318. The delay TK/2 avoids ambiguity by ensuring that the next value of N&#39; n  is applied to the correct count cycle of TK in the comparator 316 as described further below. 
     This scheme works properly as long as the phase slope is bounded by: 
     
         |N.sub.n+1 -N.sub.n |&lt;K/2 
    
     This embodiment is desirable because the modulo K function is easier to realize than the differentiator 40 and summer 42 of the circuitry in FIG. 6. Alternatively, the modulo K values N&#39; n  can be stored in memory 322 to reduce the memory size required. It should be noted that the programmable interval counter 300 can perform the function of elements 202, 210, 212 and 214 of the general embodiment of FIG. 5. 
     The modulated output υ l  consists of the pulses output from the comparator 316, as shown in FIG. 22. The time line for υ c  indicates tick marks corresponding to each interval T. The time line C indicates the continuous cycle of counting to K by counter 312 where each count interval equals T and a count cycle of TK corresponds to the nominal output pulse period. As indicated in FIG. 22, the output pulses occur at a time difference TN n  (as indicated for TN 4  and TN 5 ) and TN&#39; n  relative to the start of each count cycle TK. As noted above, the delay TK/2 ensures that the next value of N&#39; n  is presented to the comparator 316 at the proper time. This can be appreciated by noting that the first pulse output on υ l  occurs when the count M n  =N n  &#39; which has an initial value of N n  &#39;=2. Without a delay of TK/2, the next value of N n  &#39; equal to 4 would be compared with M n  and a pulse output would occur two counts later when M n  =4 as indicated in phantom at 400 on timeline υ l . Instead, the change to the next N n  &#39; value =4 is delayed TK/2 during which time the counter 312 has counted to a count M n  &gt;4. When the M n  count reaches K, it resets to 0 and the new count in the next count cycle TK is compared to the new N n  &#39;=4 to generate the correct pulse at 402. 
     The implementation in FIG. 15 illustrates one type of programmable delay 74. An alternative embodiment programmable delay 340 is shown in FIG. 23. In this embodiment, the programmable delay 340 comprises a ring oscillator 350, a multiplexer 352, and AND gate 354. The ring oscillator 350, shown in more detail in FIG. 25 comprises a crystal oscillator 357, phase detector 359, and ring oscillator circuit 350a. The ring oscillator circuit 350a includes a series of delay sections 356, each delay section adding a fixed delay of T1 to the base clock signal υ c , where T1=T2/R and T2=1/ƒ c  and R equals the total number of delay sections 356. A tap from each delay section 356 is coupled with the tap from the previous section to an XOR gate 358 to produce a series of signals υ0 c , υ1 c , υ2 c , υ3 c  having the same frequency but offset in time by 1/R of a cycle from each other (see FIG. 24). 
     The oscillator circuit 350a is made to cycle repeatedly through its output pattern by feeding an inverted output of the final delay section 356d to the input of the first delay section 356a. Referring to the timeline of FIG. 26, the input to the first delay section 356a is shown as a pulse signal υ o  which is high for a time T2. This pulse moves through the delay line sections 356 with each delay line section adding a delay of T1, as is shown for delay line signals υ 1 , υ 2 , and υ 3 . The delay line signal υ 3  is also delayed for T1 and inverted, which corresponds to the falling edge of υ o . Signal υ o  then remains low for another time T2 until the low signal moves again through the delay line sections 356 and is inverted to a high after delay line section 356d. As can be seen in FIG. 26, the delay line output signal υ0 c  results from the XOR function performed on υ 0  and υ 1 . The other delay line output signals υ1 c , υ2 c  and υ3 c  are produced by an XOR function on υ 1  and υ 2 , υ 2  and υ 3 , and υ 3  and υ 0 , respectively. 
     A problem with programmable delays such as the type described in FIG. 15 is that temperature variations over time can cause the delay line periods to shift, resulting in a mismatch between the delay periods and the period of the input signal υ 1 . The natural calibration inherent in the structure of the ring oscillator 350 avoids this period mismatch. Because the structure of the ring oscillator 350 is a series of R delay sections 356 of fixed delay T1, the period T2 of output υ c  is assured to be T2=R×T1. 
     In addition, to avoid drift of the frequency ƒ c  with time and temperature, the ring oscillator 350a is slaved off of crystal oscillator 357. The phase detector 359 compares the crystal oscillator input to υ0 c  to yield a control signal υ d  which controls the delay T1 of the delay sections 356. 
     Referring again to FIG. 23, the multiplexer 352 selects one of the delayed signals υ0 c , υ1 c , υ2 c , υ3 c  based on a delay value N1 n  input to the multiplexer 352. The ring oscillator 350 also produces the clock signal υ c  that can be used as the input to a programmable interval counter (such as counter 54 in FIG. 10). The coarse resolution output υ l  of count-down circuit 54 of FIG. 10 can be coupled to AND gate 354 (FIG. 23) to resolve a fine resolution output υ o  as shown in the timing diagram of FIG. 24. Note that the pulses on output υ o  are delayed T1×N1 n  from the edge of the input signal υ l  from the count-down circuit 54 (FIG. 10). One advantage of this embodiment is that the fine delay T1=T2/R is automatically calibrated to the input oscillator, ring oscillator 350. An edge of output υ o  can be used to retrieve the next N1 n  from a memory such as memory 60 in FIG. 10. It should be noted that the programmable delay 340 can perform the functions of elements 202 and 220 of the general embodiment of FIG. 5. 
     Another alternative embodiment of a programmable delay is shown in FIG. 27. This embodiment 360 uses interpolation to achieve finer resolution between two time positions. The two time positions are two adjacent positions comprising a pulse output from a programmable interval counter at υ l  and that pulse delayed by T2 by a D-type flip-flop 362 at υ l  &#39;. A first pulse shaping circuit 364 forms a triangular pulse y from υ l  such that the pulse y has a rising slope that is about 2×T2 wide, as shown in FIG. 28. Similarly, a second pulse shaping circuit 366 forms a triangular pulse y&#39; from υ l  &#39; that is delayed T2 from y. A delay value N1 n  from memory is converted by a digital-to-analog converter 372 to yield a weighing factor, a, where a=N1 n  /R and R=T2/T1. The weighing factor a is used to weight portions of y and y&#39; through multipliers 368, 370 respectively, which are then combined in summing junction 374 to form a pulse z that is positioned in time between pulses y and y&#39;. The resultant summed signals z for four different weighting values defined by N1=0, 1, 2 and 3 are shown in FIG. 28. A thresholding slicer circuit 376 then forms a rectangular pulse at υ o  from the z pulse by initiating the pulse where the summed signal reaches the slice level. 
     An edge of output υ o  can be used to retrieve the next N1 n  from a memory such as memory 60 in FIG. 10. As shown in FIG. 28, the delay value N1 n , which determines the weighting for combining y and y&#39;, also determines the delay N1×T1 in the output υ o . The resolution T1 is limited only by noise and timing skew. Though the circuitry of this embodiment is more complex than that of other programmable delay embodiments, a finer delay resolution is made possible. 
     It should be noted that the embodiment of FIG. 27 can also be applied to two adjacent phases of the ring oscillator of FIG. 23. Further, it should be noted that the programmable delay 360 can be applied to the programmable delay 220 of FIG. 5. It should be further noted that the counter embodiment of FIG. 21 can be combined with both delay embodiments (FIGS. 23 and 27) to achieve succeeding stages of coarse, fine and very fine resolution, respectively. 
     The algorithms and numerical processes described herein to determine the control values do not restrict the invention to the use of those algorithms and processes. They are cited only to show that it is possible to achieved practical phase modulation with the embodiments described. 
     EQUIVALENTS 
     While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.