Abstract:
A dual-modulus digital prescaler circuit having an extended period in which responses to a divider control indicating a possible modulus change must be made, such extended period permitting higher speed operation while suffering no penalty in manufacturing cost or increased power use. In embodiments comprising a dual modulus divider, a fixed-modulus divider and interconnected control logic, dual modulus divider state transitions giving rise to incrementing of fixed-modulus divider states are selected to be independent of short-term instabilities in divider control inputs. Identified critical state transitions associated with output signals from the dual modulus divider are constrained to occur at times prior to periods of insensitivity to stability of the dual-modulus control signal. Thus, timing of such output signals is determined so that there will be following time interval sufficient to provide desired stability of the modulus control signal for the next divide cycle.

Description:
RELATED APPLICATIONS 
     The present application is related to concurrently filed non-provisional applications: 
     (i) Ser. No. 09/879,806, still pending, by A. W. Hietala entitled Fractional-N Modulation with Analog IQ Interface; 
     (ii) Ser. No. 09/879,672, still pending by S. R. Humphreys and A. W. Hietala entitled Fractional-N Synthesizer with Improved Noise Performance; 
     (iii) Ser. No. 09/879,808, still pending, by S. R. Humphreys and A. W. Hietala entitled Accumulator with Programmable Full-Scale Range; and 
     (iv) Ser. No. 09/879,671, still pending, by B. T. Hunt and S. R. Humphreys entitled True Single-Phase Flip-Flop; 
     which non-provisional applications are assigned to the assignee of the present invention, and are hereby incorporated in the present application as if set forth in their entirety herein. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to circuitry for counting or dividing. More particularly, the present invention relates to frequency prescaler circuits. Still more particularly, the present invention relates to dual modulus prescaler circuits for use in frequency synthesizers. 
     BACKGROUND OF THE INVENTION 
     Prescaler circuits for use in high-speed dividers, frequency synthesizers and the like are well known in the art. A dual modulus prescaler is a divider whose division ratio or modulus can be switched from one value to another by a control signal. Commonly known implementations of prescalers utilize a counter circuit consisting of series-coupled flip-flop circuits that are used to obtain an output whose frequency is a fraction of that of a clock signal. Thus, a prescaler can divide by a first factor when a control signal has a first state or by a second factor when the control signal has a second state. Aspects of prescaler circuits and component dual modulus dividers used in a variety of RF contexts are described generally in B. Razavi, RF Microelectronics , Prentice-Hall PTR, 1998, especially pp. 269-297. 
     Many electronic devices, including mobile radiotelephones operating in the 800-900 MHz and higher frequency bands require prescalers operating at correspondingly high frequencies under a variety of conditions. Further, many such applications of prescaler circuits place low power dissipation requirements for to enhance portability and extend period of use between battery recharges. In addition, prescalers for use in many portable devices advantageously operate at low supply voltage levels. 
     FIG. 1 shows a typical prior art prescaler circuit  100  comprising three sub-circuits: a synchronous dual-modulus divider (illustratively a divide by 4/5 divider)  105 ; a fixed-modulus divider (illustratively divide by 8)  110 ; and decode logic  115 . 
     As suggested by its name, synchronous dual-modulus divider  105  will, depending on the state of divider control signal divc on path  135 , divide an input frequency clock signal fin (applied on path  120  to each of three D-type flip-flops  145 ,  150  and  157 ) by either 4 or 5. Each of flip-flops  145 ,  150  and  157  has a Q and a/Q (Q-bar) output, and feedback paths from the Q outputs of flip-flops  150  and  157  to the D input to flip-flop  145  (input D 1 ). 
     Fixed modulus divider  110  in FIG. 1 receives divided clock pulses fb from dual-modulus divider  105  over path  130  to flip-flop  180 - 1  and counts them in standard fashion using flip-flops  180 -i, i=1, 2, 3. In particular, transitions of flip-flop  180 - 1  are triggered by rising edges of divided clock pulses on fb. Output fout appearing on path  125  is the desired divided output frequency signal. In selectively supplying binary state signals for divc, decode logic  115 , including AND gates  160  and  165 , receives inputs from flip-flops  180 -i in fixed modulus divider  110  and a modulus control signal mc on lead  170 . 
     In one application of the circuit of FIG. 1, operation as either a divide-by-32 or divide-by-33 circuit is achieved. Divide-by-32 operation is obtained if the dual-modulus divider  105  operates in divide-by-4 mode for eight cycles, accounting for 32 cycles of the input clock signal fin on path  120 . These eight cycles of dual-modulus divider  105  comprise one full cycle of the fixed modulus divider  110  and, therefore, of prescaler  100 . Divide-by-33 operation is obtained if dual-modulus divider  105  operates in divide-by-5 mode for one cycle (five cycles of input clock fin), and in divide-by-4 mode for seven cycles (28 cycles of fin), for a total of 33 cycles of fin. The eight cycles of dual-modulus divider  110  again comprise one full cycle of the fixed-modulus divider  100 , and therefore of prescaler  100 . 
     The divc signal on path  135  determines the mode of operation of the dual-modulus divider  105 . If divc is in a first state, then dual-modulus divider  105  operates in a divide-by-4 mode, and if divc is in a second state, then dual-modulus divider  105  operates in a divide-by-5 mode. For proper operation, divc must be held in one of its two states for approximately one cycle of dual-modulus divider  105 . In typical applications of prescaler  100  selection of divide-by-32 or divide-by-33 mode is performed by a circuit external to prescaler  100 . This external circuit may be a programmable divider that receives output signal fout as its clock and generates modulus control signal mc on path  170 . The mc signal will appear in one or the other of its states for the duration of one or more periods of fout. Decode logic  115  uses the mc signal and decodes the state of fixed modulus divider  110  to generate divc in a state corresponding to the state of mc for the required duration (approximately one cycle of dual-modulus divider  105 ). 
     FIGS. 2A and 2B are state transition diagrams for the divide-by-4 and divide-by-5modes of operation of divide circuit  105  of FIG.  1 . In particular, each of these state transition diagrams show eight states represented by a three-bit sequence (Q 1  Q 2  Q 3 ) associated with flip flops  145 ,  150  and  157 , with the most significant bit (MSB) corresponding to the Q output of flip-flop  145  (Q 1 ), the next bit corresponding to the Q output of flip-flop  150  (Q 2 ), and the least significant bit (LSB) corresponding to the Q output of flip-flop  157  (Q 3 ). The state machine reflected by FIGS. 2A and 2B is clocked by input clock signal fin on path  120  to synchronous divider  105 . 
     Input control to the state machine is provided by divider control signal, divc, on path  135 , with state machine transitions from one state to another during each clock period of the input signal occurring in response to the one-bit divc signal. Transitions are indicated in the FIGS. 2A and 2B by directional arrows labeled with divc values x, 0, or 1, where divc=x indicates “don&#39;t care,” divc=0 indicates divide-by-4 mode, and divc=1 indicates a divide-by-5 mode. Thus, for example, if divc=0 and flip-flops  145 ,  150  and  157  are in respective states 1,0,0 (Q 1 =1; Q 2 =Q 3 =0), then /Q 2 =1, the output of NAND gate  155  is 1, and a 1 is clocked into flip-flop  157  while flip-flops  145  and  150  have  1 &#39;s clocked in—thus giving rise to a new state of 111. But, if flip-flops  145 ,  150  and  157  exhibit a  110  state (Q 1 =1, Q 2 =1, and Q 3 =0), then the next state will be 111 regardless of whether divc is a 0 or a 1. 
     In the state transition diagrams of FIGS. 2A and 2B, crosshatched states are those from which transitions occur for the respective mode (divide by 4/5). The normal state transition path for the divide-by-4 mode (FIG. 2A) is: 111=&gt;011=&gt;001=&gt;101. Similarly, normal sequence of state transitions in the divide-by-5 mode is: 111=&gt;011 =&gt;001=&gt;100=&gt;110. Two of the eight states (010 and 000) are start-up states that are not present in the normal divide by 4 or divide by 5 paths. 
     FIG. 3 is a timing diagram for operation of prescaler  100  of FIG. 1 illustrating clocking inputs (fin), states traversed in respective divide-by-5 and divide-by-4 operating modes and the state of each of the fb and divc signals. The waveform for divc in FIG. 3 shows a maximum allowable delay for the transition from one state to another. In particular, it will be appreciated that, because divc is generated, in part, in response to states of fixed modulus divider  115 , and because states of divider  115  depend, in turn, on fb, a maximum of one input clock cycle can be counted on as the period in which the divc signal will settle after a rising edge occurs in the fb signal. 
     Since divide-by-4/5 circuits are important elements of prescaler operation, considerable effort has been devoted to insure that reliable high-speed operation is achieved in this sub-circuit. It has also proven desirable to employ relatively lower performance circuit structures for the fixed-modulus divider  110  and decode logic  115  to realize advantages in current drain and, in some cases, reduced circuit area and manufacturing costs. Nevertheless, optimum operation of dual-modulus dividers can be degraded by timing limitations of these lower performance elements. Moreover, simply speeding up performance of fixed modulus divider and decoding elements will not only incur increased fabrication costs, but will also incur increased power usage. 
     Accordingly, there exists a need for high-speed prescaler architectures operating at low power levels and low supply voltage that realize benefits of optimized performance of high-speed dual modulus dividers. 
     SUMMARY OF THE INVENTION 
     Limitations of the prior art are overcome and a technical advance is made in accordance with the present invention, typical embodiments of which are described below. 
     In accordance with one illustrative embodiment of the present invention prior prescaler organizations are modified by avoiding reliance on transitions in a divider control signal occurring within relatively narrow tolerances. Moreover, such modifications are accomplished at no penalty in manufacturing costs or increased power consumption. 
     In accordance with an aspect of illustrative embodiments of the present invention dual modulus divider state transitions giving rise to incrementing of fixed-modulus divider states are selected to be independent of possible short-term changes in divider control inputs to the dual modulus divider. Thus, for example, it proves possible to constrain state transitions from certain critical states in a dual modulus divider to occur only prior to a period of insensitivity to short-term instabilities in a dual-modulus divider control signal. 
     In realizing such improved operation it proves advantageous to select an output signal from a dual modulus divider that ensures that there will be a subsequent time interval sufficient to realize desired stability of a modulus selection signal for the dual-modulus divider in its next divide cycle. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING FIGURES 
     The above-summarized invention will be more fully understood upon consideration of the following detailed description and the attached drawing wherein: 
     FIG. 1 shows a prior art prescaler circuit. 
     FIGS. 2A and 2B show state transition diagrams associated with the circuit of FIG.  1 . 
     FIG. 3 is a timing diagram illustrating the timing of certain operations in the circuit of FIG.  1 . 
     FIG. 4 is a diagram showing the relationship between certain time delays in the circuit of FIG.  1 . 
     FIG. 5 is improved prescaler in accordance with an illustrative embodiment of the present invention. 
     FIG. 6 is a timing diagram illustrating the timing of certain operations in the circuit of FIG.  5 . 
    
    
     DETAILED DESCRIPTION 
     The following detailed description and accompanying drawing figures depict illustrative embodiments of the present invention. Those skilled in the art will discern alternative system and method embodiments within the spirit of the present invention, and within the scope of the attached claims, from consideration of the present inventive teachings. 
     A further consideration of timing aspects of the prescaler circuit  100  of FIG. 1, as reflected in FIG. 3, shows that desired operation of the prescaler depends on modulus transitions in dual-modulus divider  105  occurring in a timely fashion. Specifically, synchronous divider  105  must receive a divc signal for a new divide cycle from decode logic  115  in time to determine whether the divide cycle should be a divide-by-4 cycle or a divide-by-5. Since the fixed modulus divider is clocked by the output signal, fb, of the synchronous divider, an update in the divc signal will appear some time delay, τ, after a rising clock edge on fb. Therefore, for purposes of timing between sub-circuits of the circuit of FIG. 1, fixed modulus divider  110  and the decode logic  115  may be collectively viewed as a delay block  410  inserted between signal fb and divc as illustrated FIG.  4 . In FIG. 4, block  405  represents the general case (Q/Q+1) dual modulus divider corresponding to the specific (4/5) dual modulus divider  105  in FIG.  1 . 
     As the desired frequency of operation for prescaler circuits increases, inherent delay of fixed divider  110  and decode logic  115  becomes more important in determining the maximum operating frequency of a prescaler. In a typical applications, such as fractional-N synthesizers, various aspects of which are described in incorporated patent applications (i) through (iv) cited above, synchronous divider  105  in FIG. 1 operates at a VCO output frequency, here fin, the highest frequency signal in the prescaler. It will be seen from the arrangement of FIG. 1 that the highest possible frequency for the input, fb, to fixed modulus divider is fin divided by Q. Thus circuit architectures for fixed-modulus divider  110  and decoder  115  need not be speed-optimized to the extent as high-speed dual-modulus divider  105 . 
     However, while maximum operating speeds of the individual sub-circuits  110  and  115  in FIG. 1 need not be as high as that for the high-speed dual modulus divider  105 , overall frequency performance of prescalers having the general arrangement of that in FIG. 1 are a function of these operating speeds and tolerance for signal delays between the several units. In particular, in accordance with one aspect of illustrative embodiments of the present invention, it proves desirable to provide maximum tolerance in a dual-modulus divider to signal delay through other elements, such as fixed modulus divider  110  and decode logic  115  in FIG.  1 . This ensures that a dual-modulus synchronous divider will have maximum flexibility in adapting to a change of state in sub-circuits such as fixed divider  110  caused by an output signal fb output from the dual modulus divider. 
     In particular, it has proven desirable to extend the time between a positive change in fb and the time by which a synchronous divider such as  105  in FIG. 1 must receive an updated divc signal in time to switch divider  105  from a divide by Q mode to a divide by Q+1 mode (or vice versa). Any such change in divc will occur (for a given externally applied value of mc) by a change in state of fixed modulus divider  110  in response to the indicated positive change in fb. 
     To better understand the manner of introducing present inventive modifications to prescaler circuits generally of the form shown in FIG. 1 it proves useful to more fully examine state transition diagrams shown in FIGS. 2A and 2B and the timing diagram of FIG.  3 . Upon closer examination of these, it becomes clear that certain state transitions are more critical to improved operation of a dual modulus prescaler of the type shown in FIG. 1 than others. Specifically, it will be noted that transitions from states 001 and 101 (for the divide-by-4 sequence of states, and states 001 and 100 (for the divide-by-5 sequence of states) require that the divc signal be maintained at a stable desired level to ensure that the desired sequence of states is achieved. Overall, then, transitions from 001, 100, and 101 are critical transitions. Other transitions, those for which a don&#39;t-care (x) value for the divc signal is shown in FIGS. 2A and 2B, are less critical because these state transitions are the same regardless of the value of divc. 
     This critically of transitions from states 001, 100, and 101 is further illustrated in the timing diagram of FIG. 3, where, after a desired divide-by-5 state cycle has commenced with a positive transition of the fb signal—upon a transition in divider  105  to state 101 in response to a divc logical input of 0 from a prior state 001. In particular, if the divc signal has not become stable as a logical 1, an erroneous transition to state 111 (corresponding to a divc=0) could occur. At most, therefore, the time for settling of the divc=1 level, corresponding to a divide-by-5 state, is one clock cycle after the positive transition of fb. 
     Similar errors can potentially occur upon the beginning of a divide-by-4 cycle, also associated with a positive transition of fb as a transition occurs from the 001 state to the 100 state. In particular, state 100 can transition to either erroneous state 110 (divc=1) or, (with divc=0) to state 111, the correct next state for a divide-by-4 cycle. Thus, it is important that the correct divc state be settled by the time the next transition can occur, i.e., by the end of one input clock cycle in the circuit of FIG.  1 . 
     By further examination of the state transition diagram of FIGS. 2A and 2B, it is seen. that the Q 1  signal (the source of the fb signal in FIG. 1) changes from a 0 to a 1 on state transitions from 001=&gt;101 and from 001=&gt;100. Consequently, the 101 and 100 states can be termed the output states for the circuit of FIG.  1 . For a zero delay in the divc signal, i.e., τ=0 in FIG. 4, the circuit of FIG. 1 would switch from the divide by 4 path to the divide by 5 path at the 101 critical state and from the divide by 5 path to the divide by 4 path at the 100 critical state. The 101 and 100 states are, therefore, the critical states where the divc signal must be updated and stable before the next state transition. In this architecture, the output states that generate an update to the fb signal are the same as the critical states that must receive the updated, delayed divc signal. 
     For example, assume dual-modulus divider  405  is currently in the 001 state with a 0 on the divc signal line. On the next fin clock cycle, the divider will move to the 101 state. At this time, a 0 to 1 transition will occur on the Q 1  output signal (fb). Assume this transition causes the fixed modulus divider to output a signal to the decode logic which, in combination with a 1 signal on the prescaler modulus control line (mc), causes the divc signal to transition from 0 to 1. This indicates that the next cycle in the synchronous divider should be a divide-by-5 path. However, the divider must decide before leaving the 101 state to transition to the 110 state instead of the 111 state. The divider state will change on the next input frequency clock cycle, regardless of whether or not the divc signal has been updated from a 0 to a 1. If the 1 on the divc signal is not received before the next fin clock cycle, the synchronous divider will progress to the 111 state and miss the 110 state transition. 
     Therefore, in the conventional prescaler architecture of FIG. 1, the acceptable time delay for the update of the divc signal is less than one state transition. The time delay between each state transition is the inverse of the input frequency (fin) to the prescaler. As the operating frequency of the prescaler increases, the acceptable time delay τ, for the updated divc signal to be available and stable is reduced. 
     FIG. 5 shows an improved prescaler  500  in accordance with one embodiment of the present invention. Again, a dual modulus divider  505  receives input signals at frequency fin and performs either a divide-by-4 or divide-by-5 function depending on the state of divc. The latter input is again derived in decode logic unit  515  from a desired modulus control input on path  570  and by inputs derived from the state of fixed-modulus divider  510 . Fixed-modulus divider  510  and decode logic  515  illustratively comprise the same components as in the prescaler of FIG.  1  and function in the same way as corresponding sub-circuits in that circuit. 
     Dual modulus divider  505  is also arranged as in FIG. 1, except divided output signal fb used to increment fixed-divider  510  is derived as an output from Q 2 , rather than from Q 1 . While this adaptation, amounting to a selection of a time of occurrence for the above-noted critical states, is readily achieved, its effect on the manner of operation of fast reliable prescaler operation is significant. In particular, the modifications embodied in FIG. 5 extends the time by which the divc signal need be sufficiently settled to ensure the correctness of critical state transitions as described above. 
     The manner in which such extended time for settling of divc may be achieved will be better understood by consideration of FIG. 6, a timing diagram for the improved prescaler circuit of FIG.  5 . From the foregoing discussion a maximum delay margin between the occurrence of a positive transition on fb and reliance on a settled divc will occur when the number of non-critical states immediately following occurrence of this positive transition of fb should be maximized. 
     By analyzing the position of non-critical states relative to the position of critical states in the state transition diagram, maximum delay margin path can be located. In particular, examination of the state diagrams of FIGS. 2A and 2B reveals that state 110 in the divide-by-5 path and state 111 in the divide-by-4 path are immediately followed by the maximum number of non-critical states. To select the optimal output states, it is recognized that the second bit in the state code changes from 0 to 1 on state transitions from 101=&gt;111 and 100=&gt;110. Using the second bit in the state code as the fb signal places the new output states immediately prior to a maximum number of non-critical states, resulting in a vastly increased time delay margin. 
     Therefore, by selecting the Q 2  output of FF 2  as the fb signal to a positive-edge sensitive fixed modulus divider (or one of the equivalent implementations discussed below) the acceptable time delay is increased to three state transitions in divide-by-four mode and four state transitions in divide-by-five mode. This is an improvement over the prior art arrangement of FIG. 1 (where fb=Q 1 ) and similar prior art prescaler circuits (where fb=/Q 1 ). Though a four-state-transition delay margin is the maximum achievable time delay for a divide-by-4/5 dual modulus divider, other particular maximum delay cycles are achieved in higher-order dual modulus dividers. 
     To illustrate improved time delay margins achieved using embodiments of the present invention, the following example is offered in connection with FIG.  6 . Assume a divide-by-4/5 synchronous dual-modulus divider is currently in the 101 state with a 0 on the divc signal line. On the next fin clock cycle, the divider will move to the 111 state. At this time, a 0 to 1 transition will occur on the Q 2  output signal (fb). Assume this transition causes the fixed modulus divider to output a signal to the decode logic which, in combination with a 1 signal on the prescaler modulus control line (mc), causes the divc signal to transition from 0 to 1. This indicates that the next cycle in the synchronous divider should be a divide-by-5 cycle, and state transitions should be those associated with a divide-by-5 transition path. 
     Ideally, the dual-modulus divider of the current example would receive a stable updated value of divc=1 before transitioning from the 111 state to the next state, 011. However, since the path including the maximum number of immediately following noncritical states follows state of 111, a time delay in the arrival of the divc=1 signal will have no effect on the operation of the synchronous divider. In particular, the dual-modulus divider will transition from 111=&gt;011 and from 011=&gt;001 regardless of the value of the divc signal. The update to divc need only occur before the 101 state transitions to its next state. Therefore, the acceptable time delay on the divc signal for dual-modulus prescaler  500  has increased from less than one state transition (&lt;1/fin seconds) to less than three state transitions (&lt;3/fin seconds) in divide-by-four mode and less than four state transitions (&lt;4/fin) in divide-by-five mode. 
     Implementations of embodiments of the present invention will illustratively employ high-speed, enhanced functionality building blocks in speed-critical circuit contexts. For example, flip-flops  545  and  557  in dual-modulus divider  505  will advantageously be Modified Full-Latch TSPC- 1  Flip-Flops with corrective circuitry to prevent glitches and integrated NAND gate functionality as described in incorporated related patent application (iv) cited above. Flip-Flop  550  is advantageously a Modified Full-Latch TSPC- 1  Flip-Flops with the corrective circuitry and added complementary outputs as described in incorporated related patent application (iv) cited above. Flip-flops  580 -i in FIG. 5 are illustratively of a type described in J. Yuan and C. Svensson, “High-Speed CMOS Circuit Technique,” in IEEE  J. Solid-State Circuits , vol. 24, pp. 62-70, Feb. 1989, which flip-flops are well-known in the art. These latter flip-flops designs are sufficient for less demanding a synchronous ripple-counter implementations of a fixed modulus divider, such as divider  510  in FIG.  5 . Decode logic  515  is advantageously implemented using standard CMOS logic circuitry. Those skilled in the art will recognize and apply other particular implementation technologies in realizing aspects of the present invention. 
     Thus, an improved dual-modulus prescaler embodying principles of the present invention allows the prescaler to continue proper operation at a higher input frequency than the conventional prescaler architectures for a given time delay between the fb and divc signals. 
     While specific embodiments of the present invention described above in connection with FIGS. 5 and 6 enjoy particular advantages as compared with prior prescalers, it will be realized that numerous alternative configurations based on the above inventive teachings will occur to those skilled in the art. So, for example, fixed modulus divider  510  can be made sensitive to either rising edges (using positive edge-triggered flip-flops) or falling edges (using negative edge-triggered flip-flops) of an fb signal. Then, either of the Q 2  or /Q 2  flip-flop outputs from synchronous dual-modulus divider  505  can be used in supplying the fb output signal to fixed-modulus divider  510  in particular cases. That is, Q 2  will advantageously be used to supply the fb output when fixed modulus divider  510  employs positive edge-triggered flip-flops, while /Q 2  will advantageously be used to supply the fb output signal when fixed modulus divider  510  employs negative edge-triggered flip-flops. 
     Other combinations of output sources for fb and edge-triggering polarities of fixed modulus dividers may be employed using additional well-known circuit modifications. Thus, for example, an inverter may be inserted in the fb path between one of the Q 2  or /Q 2  outputs of dual-modulus divider  505  and the input of the fixed modulus divider to accommodate the particular type of flip-flops used in fixed-modulus divider  510  while adhering to the inventive teachings above. In any of these cases, the state diagram for the divide-by-4/5 configuration does not change. 
     Overall, it proves advantageous to select optimal output states from state diagrams such as those in FIGS. 2A and 2B, viz., those output states that are followed by a sufficient number of don&#39;t care transitions to allow for useful increased delay margin. Of course, less than maximum delay margins can be chosen in particular cases. For example, it may proved desirable or expedient in some cases where Q&gt;4 where the state diagram has a sufficient number of don&#39;t care transitions to select an output state that is followed by two (or more) don&#39;t-care transitions in particular cases, provided that the resulting extended settling period is sufficient for divc in a prescaler operating under particular speed and frequency conditions. 
     Further, prescalers employing a variety of dual-modulus dividers (generically Q/Q+1) in addition to 4/5 dividers discussed by way of illustration above, a variety of fixed-modulus dividers in addition to divide-by-8 dividers used by way of illustration above, and combinations of various Q/Q+1 and fixed dividers will apply the present inventive teaching to advantage. 
     While the above detailed description has illustratively employed a dual-modulus divider and consequent dual-modulus prescaler, it will be recognized by those skilled in the art that the same inventive principles described above may be applied to N-modulus dividers and prescalers, for N&gt;2. In such N-modulus circuits will employ a divc signal having one of N values for the period appropriate to control a divide-by-Q i  cycle, where Q i   i =1,2, . . . , N.