Latched Accumulator Fractional N Synthesis With Residual Error Reduction

This invention relates generally to frequency synthesizers and more particularly to a latched accumulator fractional-N frequency synthesizer employing more than one latched accumulator configuration, in which the remaining noise components from the fractionalization process are coupled to a digital to analog converter and subsequently applied to the phase detector output for cancellation of the residual noise. The latched configuration operates synchronously and enables the system to operate at higher frequencies thereby reducing spurious signals. Reference is made to copending U.S. patent application Ser. Nos. 516,993, "Multiaccumulator Sigma-Delta Fractional-N Synthesis", filed in behalf of Hietala et al., on Apr. 30, 1990 and 516,897, "Fractional N/M Synthesis", filed in behalf of Black et al. on Apr. 30, 1990, each assigned to the assignee of the present invention. Reference is also mode to U.S. patent application Ser. No. 576,342, "Multiple Latched Accumulator Fractional-N Synthesis", filed on the same date herewith in behalf of Hietala et al.

Phase-locked loop (PLL) frequency synthesis is a well known technique for generating one of many related signals from a voltage controlled oscillator (VCO). In a single loop PLL, an output signal from the VCO is coupled to a programmable frequency divider which divides by a selected integer number to provide a frequency divided signal to a phase detector which compares the frequency divided signal to a reference signal from another fixed frequency oscillator which, often, is selected for stability of frequency over time and environmental changes. Any difference in phase between the frequency divided signal and the reference signal is output from the phase detector, coupled through a loop filter, and applied to the VCO in a manner which causes the output signal from the VCO to change in frequency such that the phase error between the frequency divided signal and the reference signal is minimized. Since the programmable divider divides by integers only, the output frequency step size is constrained to be equal to the reference signal frequency. With the single loop PLL, an engineering compromise must be struck between the competing requirements of loop lock time, output frequency step size, noise performance, and spurious signal generation.

In order to overcome the limitations of the single loop PLL, programmable frequency dividers capable of dividing by non-integers have been developed. Output frequency step sizes which are fractions of the reference signal frequency are obtained while maintaining a high reference frequency and wide loop bandwidth. A discussion of fractional-N synthesis may be found in U.S. Pat. No. 4,816,774. As described therein, two accumulators are employed to simulate the performance of fractional synthesis of the switching between different integer values of divisors without the attendant spurious signals generated by such switching. The two accumulator technique acts to reduce the unwanted spurious signals by cancellation and loop filter rejection. Furthermore, residual noise cancellation by application of the ripple accumulator contents to a digital to analog converter connected to the loop filter has been disclosed in U.S. pat. No. 4,204,174 but this implementation suffers from the problem of not providing an exact correction to the residual noise waveform. A modification to a two ripple-accumulator structure with accurate correction was disclosed in U.S. Pat. No. 4,758,802 but the implementation is not amenable to higher order accumulator networks.

The reference signal frequency for the fractional-N frequency synthesizer is, therefore, determined by the step size of the VCO output frequency multiplied by the denominator of the programmable divider divisor. Fractional-N synthesis allows the use of a reference frequency which is much higher than the actual channel spacing and allows designs to use wider bandwidths due to the reduction of low frequency spurious outputs. Wider bandwidths allow fast lock times and the possibility of wideband modulation applied to the reference input or the fractional division scheme.

Unfortunately, the system is not perfect and generates some spurious signals output at a frequency equal to the channel spacing. The desired signal output purity is better than the non-fractional system, but by itself may still be insufficient for some high quality systems.

In order to minimize the effects of this spurious output, two accumulator fractional-N synthesis systems have been developed which spread out the spurious signals to frequencies at which filtering is inexpensive and simple. By using systems with more than two accumulators this benefit can be dramatically increased.

The present multiple accumulator systems all have a drawback in that the accumulators "ripple" the data. In other words, on every clock pulse the data must act on the entire digital network structure. This results in a relatively low upper frequency limit of operation for a multiple accumulator system due to propagation delays in the digital circuitry used to build the system.

The basic structure of a one-accumulator fractional N system is shown in the block diagram of FIG. 1. A VCO 101 generates an output signal which, typically is coupled to a programmable frequency divider 103 which has an output to a phase detector (.phi.) 105. The control input is a summation of a coarse channel setting and the output of the digital network which provides the fractional part of the division. The phase detector 105 conventionally compares the phase of the divided frequency, f.sub.v, to the phase of the reference signal frequency f.sub.r output from a reference oscillator 107 to produce a signal which is applied to a loop filter 109 and subsequently to the VCO 101 to phase-lock the VCO output signal.

The selection of the divisor value of variable frequency divider 103 is made by digital network 111 which, in previously known implementations such as described in Z-transform equivalent in U.S. Pat. No. 4,758,802, comprises a conventional adder 113, a comparator 115 (which produces a "carry out" signal when the input to the comparator 115 exceeds a given numerical value), and feedback logic 117 which subtracts the denominator (if a carry output occurs) from the digital number representation output from adder 113 and comparator 115 before applying the digital number representation to the adder 113. A second digital number representation, which in a fractional-N synthesizer is the digital equivalent of the first differential of the offset phase with respect to time (the offset frequency), is applied to another input of the digital network 111. The overall effect of the digital network 111 is to integrate the differential phase and to apply to the PLL a control signal (in the form of a carry-out digital signal) which is a first order equivalent of the phase offset. The adder 113 sums the previous contents of the adder 113 with a d.phi./dt (a numerator) on each occurrence of the reference frequency signal f.sub.r. As described in U.S. Pat. No. 4,816,774, the adder 113 output is compared to a number (a denominator of a desired fractional part of the divisor when the divisor of frequency divider 103 is expressed as a sum of a whole number and ##EQU1## If the contents of adder 113 exceed the denominator then the carry output is set true and the contents of the adder is reduced by the denominator in feedback logic 117 before the next reference pulse occurs.

As an example, assume the denominator is 13 and the numerator is 1. On every thirteenth reference pulse the adder 113 exceeds the denominator and generates a carry output which will increase the divisor of the frequency divider 103 by one for one reference signal, f.sub.r, pulse. This removes one pulse from the VCO 101 output signal and thus reduces the accumulated phase error by 360 degrees. This corresponds to a 1/13 division added to the nominal loop division number.

Shown in the Z-transform diagram of FIG. 2, is a Z-transform equivalent digital network 111' of this one accumulator system consistent with that disclosed in U.S. Pat. No. 4,758,802. The Z-transform equation for the single accumulator system is: ##EQU2## The Z-transform adder 201 is fed from the numerator (minus the denominator if an overflow occurs) and the previous adder contents represented by a z.sup.-1 (delay) block 203, 205. The comparison is considered to be a digital slicer with quantization error Q added at 207. The output from adder 207 is the digital number fed back to adder 201 and the carry out signal is taken as the output signal. For Z-transform analysis, however, no difference need be made between the output and the feedback signals.

At point B an equation can be written as follows.

But Data out=B(z)+Q and A(z)=Data in -B(z)-Q

Substituting this in and solving for B(z) then:

And solving for Data out:

This equation may now be converted to the frequency domain (Note that "v" is frequency normalized to the folding frequency): ##EQU3##

Thus, the data into adder 201 is slightly low pass filtered and the quantization noise introduced by the digital network 111' is high pass filtered. The high pass filtering of the quantization noise has the effect of reducing the spurious signals occurring at the frequency of the channel to channel frequency spacing of the transceiver if the spurious occurs at a frequency much below the corner of the high pass. By selecting a PLL response with a low pass corner frequency much lower in frequency than the high pass corner it is possible to reject almost all of the noise. In a single accumulator system, the high pass roll-off is 20 dB/decade. Thus the reference frequency must be large to push the high pass corner to large frequencies if sufficient noise suppression is to be obtained. (Or the PLL low pass must be very low in frequency and thus lose the benefits of wide bandwidth.)

To improve the high pass filtering of the basic fractional-N structure, it has been known to use fractional-N synthesis for systems using more than one accumulator. A two accumulator fractional-N synthesizer is disclosed in U.S. Pat. No. 4,204,174. Also, an example of a multiaccumulator fractional-N synthesizer is shown in the block diagram of FIG. 3, where the single digital network 111 of FIG. 1 is augmented by additional accumulators, in this instance, accumulator 303, accumulator 304, and accumulator 307.

In a multiaccumulator system, the contents of the first accumulator 111 becomes the Data input to the second accumulator 303. The contents of the second accumulator 303 becomes the data input to the third accumulator 305. Once the data is set at the output of adder 113 of accumulator 111, it must be transferred to the data input of adder 113 of accumulator 303. Once the data is set at the output of adder 113 of accumulator 303, it must be transferred to the data input of accumulator 305, etc. All of the transfer must be accomplished in one clock pulse (which is typically derived from the output of frequency divider 103). This process has been termed a "ripple" process, and the accumulators are known as "ripple" accumulators. Obviously, an upper limit on the speed and/or the number of accumulators is imposed by the ripple process.

The second accumulator 303 has its own Z-transform quantization error, Q2, in addition to the error of, Q1, the first accumulator. However the combination of these errors will be greatly reduced from the single accumulator case. The carry-output from the second accumulator 303 is applied to a delay logic element 309 and, after the differentiation produced by delay element 309, is applied to adder 311. The carry output from the comparator of accumulator 305 is twice differentiated by delay logic elements 313 and 315 and input to adder 311. The carry output from the comparator of accumulator 307 is thrice differentiated by delay logic elements 317, 319, and 321 and input to adder 311. The carry outputs, differentiated as described are added and output as an effective carry-out signal to be applied to frequency divider 103. Thus, the effect produced by the multiple accumulator system is to add the first order phase offset of the carry-output of accumulator 111 and the second order phase offset of the differentiated carry-output of accumulator 303, the third order phase offset of the twice differentiated carry output of accumulator 305, and the fourth order phase offset of the thrice differentiated carry output of accumulator 307 for the effective carry-out signal.

For simplicity, the Z-transform model of the first and second accumulators is shown in the diagram of FIG. 4. DO1 is the Data out of the first accumulator. From the above calculation: ##EQU4##

Di2 is the accumulator contents of the first accumulator: ##EQU5##

A similar equation to that above for DO2 is: ##EQU6##

Substituting in the expression for Di2 and the substituting in for DO1: ##EQU7##

But: DO3=DO2(1-z.sup.-1) and Data out=DO1+DO3

Thus after some algebra: ##EQU8##

This representation is then converted to the frequency domain (Once again "v" is the frequency normalized to the folding frequency): ##EQU9##

In this case the high pass corner occurs at about the same frequency as in the one accumulator case but the frequency response of the high pass characteristic to the quantization noise is 40 db/decade. This allows the PLL to have a wider bandwidth, i.e., allows the fractional system to operate at a lower frequency, than in the one accumulator case while still maintaining the desired noise suppression.

The number of accumulators can theoretically be increased to any desired order. The resulting slope of the response of the high pass characteristic to the quantization noise will be the number of accumulators times 20 db/decade. The accumulators are "recombined" in what is known as a "Pascal's triangle method" as disclosed in U.S. Pat. No. 4,609,881. In general the higher order accumulators are recombined as (1-Z.sup.-1).sup.(n-1).

The aforementioned systems require that the data must ripple through all of the accumulators upon a clock pulse. For a higher order system this requirement limits the maximum accumulator clock rate and thus limits the noise suppression which can be obtained. The reason for this limit is that the propagation delay of each accumulator will add until the data cannot ripple through the system in one clock pulse period. Furthermore, even after processing by multiple accumulators, a residual noise term will still remain which may cause excessive spurious signals in some applications.

A fractional-N latched accumulator synthesizer having reduced residual error accepts a digital number to select a controllable oscillator output signal frequency. The output signal frequency is frequency divided with a variable divisor divider controlled by carry output signals from latched accumulator networks and a control signal, which is filtered by a loop filter, is applied to the controllable oscillator. A first latched output signal related to the digital number is generated and a second latched output signal, which is an integral of said first latched output signal, is generated. The first latched output signal and the second latched output signal are combined to generate a residual error correction signal. The residual error signal is then coupled to the loop filter.

FIG. 1 is a block diagram of a first order fractional-N synthesizer.

FIG. 2 is a Z-transform diagram equivalent of the digital network in FIG. 1. FIG. 3 is a block diagram of a multiple order ripple fractional-N synthesizer.

FIG. 4 is a Z-transform diagram equivalent of the digital network of a second order ripple accumulator.

FIG. 5 is a block diagram of a radio transceiver which may employ the present invention.

FIG. 6 is a block diagram of a multiple latched accumulator fractional-N synthesizer in accordance with the present invention.

FIG. 7 is a block diagram detail of a delay adding, or ripple, accumulator structure.

FIG. 8 is a block diagram detail of a non delay adding or latched accumulator structure which may be employed in the present invention.

FIG. 9 shows a Z-transform diagram equivalent of the latched accumulator in FIG. 8.

FIG. 10 is the Z-transform diagram equivalent of a three accumulator system in accordance with the present invention.

FIG. 11 shows the attenuation due to the digital network of the data in and the quantization noise terms for a three accumulator system in which the input data is not distorted at higher frequencies.

FIG. 12 is a block diagram of a fractional-N synthesizer in accordance with the present invention and in which a digital correction term is derived and applied to the phase detector output through an analog differentiation network.

FIG. 13 is a block diagram of an alternative embodiment of a fractional-N synthesizer in accordance with the present invention and in which a digital correction term is derived and applied to the phase detector output through a digital differentiation network.

A basic block diagram of a radio transceiver which may employ the present invention is shown in FIG. 5. Such a radio transceiver, preferably, is a digital radio transceiver useful in a digital radiotelephone system. The output of the synthesizer 503 is used by both the receiver 505 and the transmitter 507 to produce a local oscillator and a transmit signal, respectively. Control over functions of the transceiver, such as channel of operation frequency, is provided by control logic 509 function and is input to the first accumulator of a fractional-N synthesizer as Numerator data in.

A multiple latched accumulator fractional-N synthesizer is shown in FIG. 6. The frequency synthesizer utilizes a voltage controlled oscillator, VCO 101, which provides the desired output frequency fo, as well as feeds the input to a variable digital frequency divider circuit 103. The output of the variable frequency divider 103 feeds one input of a phase comparator circuit 105 with the other input being fed from a reference oscillator 107. The output of the phase comparator 105 is filtered to remove extraneous noise components by loop filter 109. The output of the loop filter 109 is then fed back to the control input of the VCO 101 such that the VCO 101 will adjust its output frequency f.sub.o to be equal to the frequency of the reference oscillator 107 times the digital division ratio of the frequency divider 103.

In the preferred embodiment, the division ratio, N, of the frequency divider 103 is varied with a periodic sequence such that the output frequency f.sub.o of the VCO 101 may be adjusted in frequency steps equal to a fraction of the frequency of the reference oscillator 107. This periodic sequence is generated by a multiple accumulator digital network 611. A digital network of four accumulators is shown in FIG. 6.

Numerator data, which corresponds to frequency offset and which may include modulation information, is input from frequency selection circuitry (not shown) and applied to the first adder 113 of accumulator 615. The data output from the first accumulator 615 is taken at the output of feedback logic 117 after processing by comparator 115. This data output is available after the clock input signal, derived from frequency divider 103, has clocked the accumulator 615. It is an important feature of the present invention that the data presented from one accumulator to the next is only transferred to the next accumulator in the string during one clock cycle thereby avoiding the problem of having to ripple through all accumulators during one clock pulse. Each accumulator beyond the first is fed with the contents of the next lower order accumulator. Each accumulator performs a digital integration of the contents of the accumulator of next lower order with the first accumulator 615 performing a digital integration of the input Numerator data. The second accumulator 617 performs a double integral of the input Numerator data, the third accumulator 619 performs a triple integral of the input Numerator data, and the fourth accumulator 621 performs a quadruple integral of the input Numerator data.

The output of each accumulator is the carry or overflow output. For the first accumulator 615 this output signifies that the output frequency f.sub.o of the VCO 101 has acquired 360 degrees of phase error relative to the frequency of the signal output from the reference oscillator 107. In order to correct this, the division ratio of the frequency divider 103 is increased by one integer for the next clock interval and the internal contents of accumulator 615 is reduced by it's capacity. This action effectively removes one cycle of the output frequency f.sub.o from the phase detector 105 input and thus results in a phase correction of 360 degrees at the VCO 101 output. This correction will occur only at the point the output frequency f.sub.o would achieve 360 degrees of phase error without a loop filter 109. Such a condition will results in a sawtooth type of waveform at the output of the phase detector 105 which must then be filtered by the loop filter 109. The average value of this sawtooth waveform is the correct control signal to select frequencies which are spaced at fractional increments of the reference frequency output from reference oscillator 107.

However, the internal contents of the first accumulator 615 represent the intermediate phase error. Higher order accumulators are included to operate on the internal contents of the first accumulator 615 to provide intermediate corrections to the phase error with the result that the sawtooth type of waveform can be subdivided in frequency of the lower noise output at the fundamental frequency of the original sawtooth waveform.

The output of the higher order accumulators are fed through digital delay networks (623, 625, 627, 629 respectively), which perform derivatives of the carry outputs. Since these carry outputs of the accumulators are digital integrations of the Numerator data input, the net result is higher order corrections to the desired phase.

For example, the carry output of the second accumulator 617 is applied to digital delay network 625 where it is delayed by conventional delay elements 631, 632, and 633 prior to being fed to a conventional digital adder 635. In adder 635, the delayed output of second accumulator 617 is added to the negative of its previous value obtained from the output of conventional delay element 637. This is a first derivative in a digital sense. Since the output of the second accumulator 617 is the second integral of the input Numerator data, the net output of this arrangement is a second order phase correction of the fractional frequency offset. (Note that the Numerator data is a frequency offset which is the derivative of phase.)

The carry output of the third accumulator 619 is applied to digital delay network 627 where it is delayed by delay elements 639 and 640 and added to twice the negative of its previous value plus its second previous value. These previous values are obtained from the outputs of delay elements 641 and 643 respectively. This corresponds to a second order digital derivative. Since the output of the third accumulator 619 represents the third integral of the Numerator data input, the overall effect is a third order correction to the phase of the fractional frequency offset.

The digital delay network 629 of the latched accumulator 621 comprises three delay elements (651, 653, and 655) coupled to adder 635 in a manner which yields three differentiators.

This technique may be carried out to the desired order of corrections by adding more accumulator sections to the digital network 611. The coefficients of the addition of each sequence correspond to the factors in the expansion of (1-z.sup.-1).sup.x, where X is the order of the accumulator under consideration. It is also possible to introduce other coefficients in which the sum of the coefficients are one for the first accumulator and zero for all higher order accumulators. However, any choice other than the above coefficients will result in less than optimum noise rejection performance. The number of delay elements in the first digital delay network 623 (i.e., delay elements 645, 646, 647, and 649 in the preferred embodiment) is equal to the number of accumulators in the system.

In FIG. 7 a block diagram of a ripple accumulator is shown. If a plurality of these accumulators were cascaded, as illustrated in FIG. 3, such that the data output of one fed the data input of the next, then the resulting circuit would have a group of cascaded adders of depth equal to the number of accumulators. Such an arrangement would require a settling time equal to the delay of the addition process for one accumulator, times the number of accumulators. If a high order correction to the phase is desired, then a large number of accumulators will be required with a corresponding decrease in the maximum rate of operation.

In the preferred embodiment a latched accumulator configuration such as shown in FIG. 8 for accumulator 615, 617, 619, and 621 is employed. The data to signal 801 of each accumulator is taken as the latched output from conventional latch circuit 803. A cascade of such accumulators will only have a single adder delay upon the occurrence of each clock pulse (which is applied via 805 to latch circuit 803) since the latch 803 isolates the associated adder 807. This arrangement results in each accumulator carry output sequence from adder 807 being delayed by one clock cycle from the output sequence of the next lower order accumulator.

Referring again to FIG. 6 in a four accumulator system, for example, the fourth accumulator 621 carry output sequence applied to digital network 629 will be delayed three cycles from the first accumulator 615 carry output sequence, the third accumulator 619 carry output sequence will be delayed two cycles from the first accumulator 615 carry output sequence, and the second accumulator 617 carry output sequence will be delayed on cycle from the first accumulator 615 carry output sequence. In order to align the sequences in time, the output of the first accumulator 615 is delayed three times by the delay elements 645, 647, and 649, the output of the second accumulator 617 is delayed twice by delay elements 631 and 633, and the output of the third accumulator 619 is delayed once by delay element 639. In addition, delay elements 646, 632, and 640 are added to the lower order accumulators in order to obtain an all pass response to the input data and to obtain a residual noise term which may be easily reconstructed in digital form for D to A conversion and application to the loop filter. All other delays are associated with the digital differentiation processes.

In order to demonstrate the necessity for speed of operation, an equivalent model 900 of a latched accumulator and associated digital delay network suitable for analyzing the noise performance of the digital network is presented in FIG. 9. This model, based on conventional Z transform theory, represents the latch operation as a digital delay or z.sup.-1 gain block 901. The adder in the accumulator is represented by the adder block 903 associated with the delay block 901. A second adder block 905 is used in the outer loop to represent the subtraction of the accumulator capacity which occurs every time the accumulator overflows. Finally a third adder block 907 is used to represent the noise caused by the quantization of the phase error.

Two transfer functions can be defined for this accumulator structure:

The four latched accumulators and associated delay networks, representing the accumulators of FIG. 6, are shown in the Z-transform diagram equivalent of FIG. 10. The carry output of each higher order accumulator is passed through a corresponding number of digital derivatives and then recombined in a common adder 1001. Each lower order accumulator output is delayed to realign all sequences. An overall transfer function for this system may be derived as shown below:

This expression may be converted back to the frequency domain by the substitution e.sup.j.pi..nu. =z. This results in the following expression for DO.(Note that this is a term-by-term magnitude expression.)

In the above expression .nu. is frequency normalized to the folding frequency. The folding frequency is equal to one half the rate at which the accumulator clocks operate

The frequency versus attenuation curve of FIG. 11 shows the output of each term of this expression. Note that the DI(or data in) is passed with no distortion to the data out (DO) and each of the quantization noise terms (Q) are high pass filtered. The high pass term rolls off with a slope of 60 db/decade and the corner of the high pass occurs at about one half the folding frequency.

Two results can be interpreted from FIG. 11. First of all the desired frequency offset data is passed through the digital network with no distortion. Secondly, it can be seen that for each added accumulator the noise rejection of the digital network at low frequencies is improved since the slope of the high pass characteristic to the quantization noise will be 20 times the number of accumulators in db per decade. In addition the digital network should be operated at as high a rate as possible such that the corner of the high pass characteristic will be at as high a frequency as possible. If the low frequency noise is properly rejected in the digital network then the overall synthesizer can be made low noise because the phase locked loop which the digital network feeds is a low pass network which will reject any residual higher frequency noise components which are note rejected by the digital network.

Note that in the previously presented expression for DO, the only quantization noise term which is passed to the output sequence is that due to the highest order accumulator. Due to the simple form of this noise term it is now possible to construct this noise term in digital form by operating on the contents of the two highest order accumulator internal contents.

In a general N.sup.th order system the carry output sequence can be derived in the Z transform model as:

The internal contents of any accumulator may be derived as:

where X is the order of the accumulator.

If the contents of this accumulator are subtracted from the contents of the next lowest order accumulator then the following term is obtained:

Therefore the residual error term can be recreated in a digital form by subtracting the delayed contents of the second highest order accumulator from the contents of the highest order accumulator and differentiating the result N-1 times.

FIG. 12 is a block diagram of a four accumulator system, such as that shown in FIG. 6, in which the internal contents of the second highest order latched accumulator 619 are utilized in the subtraction of the residual noise term at the loop filter 109. The internal contents of latched accumulator 619 are delayed once by delay element 1203 and then subtracted from the internal contents of the highest order latched accumulator 621 in conventional add function 1205. This results in a term equal to -z.sup.-1 Q4 at the output of adder 1205. Delay element 1207 and adder 1209 form a digital derivative network. The output of adder 1209 will be -z.sup.-1 (1-z.sup.-1)Q4. Delay element 1211 and adder 1213 form a second digital derivative network. The output of adder 1213 will be -z.sup.-1 (1-z.sup.-1).sup.2 Q4. A conventional digital to analog converter 1215 then converts this to an analog form and scales the amplitude. Capacitor 1217 is then used as an analog derivative network to convert the voltage output of D/A converter 1215 to a current suitable for application to the loop filter 109 in which the phase comparator drive is a current source. (The current through a capacitor is the time derivative of the voltage.)

The correction term has an additional delay as compared to the data output path. This delay is compensated by adding another delay 1219 in the data output path to the frequency divider (+N) 103. Thus the data sequence at the input of the frequency divider (+N) 103 is:

Since the phase detector 105 compares phase and not frequency, the signal is effectively integrated upon passing through the phase detector 105. Thus the phase term at the phase detector output can be represented in the Z transform domain as: ##EQU10## where .sup.K.sbsp..phi. is the phase detector conversion gain.

The phase correction term generated by the D/A converter 1215 and capacitor 1217 can be represented in the Z transform domain as:

where A.sub.D/A is the D to A converter gain and C is the capacitance of capacitor 1217.

If the value of capacitor 1217 is chosen to be equal to the phase detector gain divided by the D/A conversion gain then a cancellation of any residual noise terms is achieved.

Additional delay elements 646, 632, and 640 are added in the carry output signals from latched accumulators 615, 617, and 619, respectively, in order that the data output sequence noise term will depend only on the highest order accumulator. This allows the noise sequence to be easily reconstructed for use in a D to A converter which provides error correction at the loop filter input. Without these delay elements the output noise term would involve factors from all accumulators. It would be difficult to derive a correction waveform from this type of output.

FIG. 13 shows an alternative embodiment of the present invention in which the residual noise cancellation is realized without a capacitor being used as a derivative element. In this embodiment an extra delay element 1303 and adder 1305 are used to perform the derivative which was accomplished by the capacitor in the embodiment of FIG. 12. For cancellation, the gain of the D/A converter 1215 must equal the phase detector 105 gain.

In the preferred embodiment, modulation information is applied to the multiaccumulator digital network 611 of the fractional-N synthesizer as the sixteen least significant bits of a twenty-four bit number Numerator data input from the transceiver control logic 509. Since a transceiver which employs the present invention may be effectively utilized in the GSM pan-European digital radiotelephone system, rapid frequency changes, modulation, and low spurious and noise levels are realized with a fractional-N synthesizer. For modulation, the fractional-N synthesizer employs a look-up table to convert the data stream to be transmitted into frequency offsets for the fractional-N synthesizer. The loop division of the synthesizer is adjusted in accordance with the input data stream to follow the instantaneous frequency offset required for the GMSK modulated signal. This can be at the offset frequency or directly at the main frequency.

The latched accumulator fractional-N synthesizer configuration is operated upon with large accumulators to eliminate spurious signals, to provide D/A correction to reduce discrete spurious signals, and to provide direct digital modulation to the PLL. In the GSM system, the data rate is 270.83333 kb with a BT product of 0.3. This results in in a frequency of about 81 kHz which must be passed with low distortion through the PLL as modulation.

The actual frequency offset components of the GMSK signal range from 10 Hz to about 70 kHz. This range determines the length of the accumulators as it will be necessary to synthesize steps of less than 10 Hz. In the preferred embodiment of the GSM system, with a reference frequency of 26 mHz, the accumulator length is 24 bits but, as a minimum, must be at least 22 bits.

Obviously, the desired instantaneous frequency offsets due to the modulation are well below the cutoff of the loop filter. Therefore the frequency synthesizer loop does not attenuate any of the fundamental frequency "channelization" spurious signals due to the modulation. However, with a multiple accumulator system this problem is overcome.

It is possible, and preferable, to increase the fractionalization (the value of the denominator of the fractional part of the division) such that all spurious outputs are moved to very low frequencies where the combined effects of using many accumulators at a high rate of clock speed results in a large attenuation of the quantization noise of the fractional process. Thus, a large denominator effectively divides the frequency of the reference oscillator such that spurious signals which are produced fall well below the three decibel corner of the loop high pass characteristic. Using many accumulators increases the slope of the high pass filtering action. Increasing the rate of operation moves the corner frequency of the high pass filter up in frequency.

Referring again to the block diagram of the latched accumulator fraction-N synthesizer of FIG. 6, the output of the fractional-N multiple accumulator digital network 611 is fed to the division control input of the frequency divider 103. When network 611 causes the division to increase by one for one cock reference period, one output pulse of the VCO 101 is effectively removed by the frequency divider 103. This action corresponds to a phase shift of 2 .pi. radians at the output frequency of the VCO 101. This phase shift is then divided by phase detector 105 in put is 2 .pi. radians divided by the divisor or the frequency divider 103. In general the network 611 generates a time-varying division ratio. Thus in the general case the input to the phase detector 105 may be represented as follows: ##EQU11## where: N.sub.L is the nominal loop division ratio

c(n) is the Fourier component of the digital sequence at the offset frequency

and: 1/s is introduced to convert frequency to phase

The Fourier components of the digital sequence are calculated as follows: ##EQU12## where: N is the total number of points in one period of the sequence

.theta.(i) is the time waveform of the digital sequence

i is the time component

and: n is the frequency component.

After passing through the phase detector 105 the signal is then input to the loop filter 109. The output of the loop filter 109 feeds the control input of the VCO 101. The magnitude of the controlling error voltage at the input of the VCO 101 is expressed as follows: ##EQU13## where: .sup.K.sbsp.100 is the phase detector conversion gain

and: .vertline.R(.omega.).vertline. is the magnitude of the filter response a the offset frequency

This control voltage will cause the VCO 101 to output a spurious component as follows: ##EQU14## where: .sup..omega. m is the spurious frequency component of the digital sequence

and: K.sub.v is the conversion gain of the variable oscillator.

The feedback nature of the phase locked loop will correct this such that the spurious component will be as follows: ##EQU15##

for small spurious components the spur level may be approximated as .beta./2 where .beta. is the phase corresponding to the frequency derived above

The spurious levels may thus be approximated as follows: ##EQU16## for low frequencies .sup.F(.omega.).fwdarw..infin. and .OMEGA..sbsp.m .fwdarw.0. Thus the spurious level can be approximated as follows:

Thus, if the Fourier components of the multiple accumulator digital network 611 are shaped such that all spurious components are small valued, then the output of the phase locked loop will also contain small spurious values. The network 611 behaves as a high pass filter to the quantization noise. By increasing the fractionalization to a very large number all spurious signals will be located at frequency offsets where the fractional sequence generator attenuates the spurious levels to below that of the noise floor of the phase locked loop. After passing to the phase locked loop output, the spurious signals still retain the level established by the fractional sequence generator.

In the preferred embodiment, the phase detector operates at 26 MHz supplied by reference oscillator 107, and fractionalization is by a large number. (2.sup.24 =16,777,216.) The fractional-N spurious signals occur at harmonics and subharmonics of 1,54972 Hertz. Since the reference is at a very high frequency, the high pass corner of the fractional-N multiple accumulator digital network 611 occurs at about 6.5 MHz. The attenuation of spurious signals caused by the fractionalization is, therefore, extremely large.

Elimination of spurious signals by the use of network 611 high pass nature has important advantages. First, the channel spacing is much smaller than the minimum required frequency step for low distortion modulation. Second, the loop bandwidth is extremely wide since there are no discrete spurious signals above the noise floor of the phase locked loop which need to be rejected. (Except for the spur at the actual reference which is 26 MHz). In the preferred embodiment, an open loop unity gain frequency of 400 kHz causes a 5 degrees peak and 3.5 degrees RMS phase error to the GMSK signal. This is a reasonable limit given the GSM specifications of 20 degrees peak and 5 degrees RMS. The RMS value of 3.5 degrees is very reliable in that it is determined by the wide loop bandwidth.

A problem could develop with a system designed for very high fractionalization in that some channel offsets would result in a common factor of the numerator and denominator. This would result in an effective fractionalization which is much less than that desired and the discrete spurious signals would re-appear. This situation can be avoided by setting the least significant bit of the accumulator. As an example consider the above situation in which a channel requires a fractional offset of 1/4. This would result in spurious outputs at harmonics and subharmonics of 6.5 MHz. If the LSB Is set the fractionalization will become 4,194,305/16,777,216 which will move the spurious signals back to the 1 Hz region. This will result in a small frequency error, but for most cases this kind of error is insignificant.

A second method of ensuring high fractionalization is to initially offset the accumulators with a number, or group of numbers, and then input the desired frequency data. This initial offset will cause a fractional-N accumulator which contains two or more internal accumulators to generate a spurious pattern corresponding to that of its full accumulator length for almost any value of the input data. In a multiple accumulator system the initial offset of the bottom bit (or bits) will result in an essentially random pattern imposed on the offset data. This method will not cause a frequency error since the initial offset is removed once the data is fed into the system. Note that this method will not work for a single accumulator system because in a single accumulator system the waveform corresponds to a simple sawtooth which will return to the same waveform regardless of the initial offset. With many accumulators the offset will set up a multitude of patterns which will interact to form very long time sequences with correspondingly low frequency spectral components which will be rejected in the digital network 111.

Thus, given an n.sup.the order fractional N system, the accumulators may be "latched" resulting in a synchronous system in which data does not need to ripple through more than one accumulator in one clock cycle. The first, or lowest order, accumulator output to the variable loop divider is delayed by n clock units, the next lowest level accumulator is delayed by n-1 clock units and so on until the next to last accumulator is delayed by two clock units and the last, or highest level, accumulator which is not delayed. This realigns the time sequences to allow the noise performance of a non-latched system.

Because of the synchronous nature of the system, it is able to operate at higher frequencies and thus allow the PLL bandwidth to be larger. This allows faster lock times and wideband digital modulation through the fractional divider (or analog modulation through the reference oscillator input to the phase detector.) while maintaining superior and predictable spurious performance. A digital representation of the remaining error is obtained in a form suitable to be used in a digital to analog conversion scheme. The analog output of this conversion is applied to the phase detector output to cancel any residual noise.