Nested digital delta-sigma modulator

[0001] The present application claims priority to U.S. Provisional Patent Application No. 61/576,411, filed Dec. 16, 2011, titled “NESTED DIGITAL DELTA-SIGMA MODULATOR,” the entirety of which is hereby incorporated herein by reference.

[0002] The disclosure relates to synthesizing radio frequencies using a frequency synthesizer in order to output a desired frequency.

[0003] Wireless communication devices communicate by sending and receiving information in particular radio frequencies. These particular radio frequencies can be communication channels, just like channels on a radio. In order to receive a particular station on a radio, it is important to tune to the radio frequency that station is broadcast on. If one does not tune directly onto the proper frequency that the radio station is being broadcast on, then the radio will likely receive static or a signal that is not as clear.

[0004] Wireless communication devices typically use a frequency synthesizer to set the frequency of the communication channel. Just like the radio example above, it can be important for reliable and efficient wireless communications to have accurate and precise generation of specific radio frequencies. In order to generate the specific radio frequencies the frequency synthesizer often needs to create the desired frequency using reference frequencies. It can be difficult to produce a frequency synthesizer that is precise without the design of the frequency synthesizer becoming very complicated.

[0005] The present disclosure provides methods and systems for a radio frequency synthesizer to generate precise frequencies over a large radio frequency range in some embodiments. The radio frequency synthesizer can provide a high resolution of frequency generation and still provide precise frequencies over a range of radio frequencies. In some embodiments, a fractional-N synthesizer system can be adapted to generate a signal at an output frequency from a reference frequency, wherein said output frequency is generated using a first modulus and a second modulus adapted to ensure that the output frequency can be set to an exact value.

[0006] In certain embodiments, the radio frequency synthesizer uses a programmable second modulus M₂ (which may or may not be a power of two) to define f_VCO=(N₀+(N₁+N₂/M₂)/M₁)f_PD. The resolution in this case is set by the product M₁×M₂ rather than by M₁ alone. With appropriate choices of M₂ and M₁, desired practical values of the output frequency f_VCO can be set exactly.

[0007] In some embodiments, a fractional-N frequency synthesizer is provided that allows the frequency f_VCO to be set exactly while maintaining the spur performance of a power-of-two-modulus divider. Furthermore, the spectral performance of the nested fractional-N frequency synthesizer can be improved by careful selection of the clocking frequencies of the first DDSM and the second DDSM.

[0017] The present disclosure provides methods and systems for a radio frequency synthesizer to generate precise frequencies over a large radio frequency range in accordance with some embodiments. Typically, with radio frequency synthesizers, there is a trade-off between resolution and range of a frequency synthesizer. It is similar to the situation of choosing a measurement scale in order to measure something. While a ruler may be good at measuring small objects such a paper clip, it is not ideal for measuring the dimensions of a large room. The range of the ruler can be limited by its inherent resolution chosen beforehand.

[0018] In the same way, radio frequency synthesizers can have difficulty generating precise frequencies that also cover a number of frequencies in a range of frequencies. This is because radio frequency synthesizers use a reference frequency that is scaled to provide the output frequencies. Generally, past efforts to solve resolution and range problem have ended up with complex systems and/or performance issues.

[0019] The most widely used type is called a fractional-N synthesizer, whose output frequency is defined by f_VCO=(N₀+N₁/M₁) f_PD, where f_PD is a very precise frequency that is typically defined by a crystal oscillator, and N₀, N₁, and M₁ are integers. M₁ is called the modulus and determines the frequency resolution f_res=f_PD/M₁.

[0020] f_PD is typically a multiple of ten Hz and M₁ is a power of two. In the case of many desired practical values of f_VCO, it is impossible to set f_VCO exactly because of the inevitable remainder when powers of two divide into multiples of ten.

[0021] A fractional-N frequency synthesizer generates a frequency f_VCO which is a rational multiple of a precise reference frequency. The precision of f_VCO is determined by the modulus which, for reasons of speed and ease of implementation, is usually a power of two. When the modulus is a power of two, f_VCO has an inherent error and cannot be set exactly; this is a problem.

[0022] In an integer-N frequency synthesizer, the relationship between the output and reference frequencies is
f_VCO=N₀f_PD;
where N₀ is a positive integer. The smallest frequency step is defined by
f_res=f_PD

[0023] In a system that requires a channel spacing of f_CS, one could set f_CS=f_PD. To attenuate the reference spur (at frequency f_PD) at the output of the phase detector, the loop filter requires a bandwidth that is much less than f_PD (typically one tenth of f_PD or more). This has two important consequences:

[0024] 1) the transient response of the loop is relatively slow, and

[0025] 2) the energy storage elements in the loop filter are physically large.

[0026] An improved solution is the so-called fractional-N frequency synthesizer; this has a larger loop bandwidth, resulting in a faster transient response and a smaller loop filter.

[0027] An integer-N synthesizer has a fixed division ratio N. By contrast, in a fractional-N frequency synthesizer, the division ratio is updated at a frequency f_s, as illustrated in FIGS. 1 and 2. The instantaneous value of the division ratio is determined by a divider controller. A typical implementation of a divider controller comprises a Digital Delta-Sigma modulator (DDSM) with input N₁, modulus M₁, and output Y₁ and a summing element. The DDSM is clocked at a frequency f_s by the output of the divider. N₁ and M₁ are chosen such that the average of Y₁ is N₁/M₁. The relationship between the output and reference frequencies is

[0028] $f_{\mathrm{VCO}}=\left(N_O+\frac{N_1}{M_1}\right)f_{\mathrm{PD}},$
where M₁ is called the modulus of the DDSM. M₁ is typically a large power of two. N₀ and N₁ are positive integers and N₁<M₁. The frequency resolution is defined by

[0029] $f_{\mathrm{res}=}\frac{1}{M_1}{f}_{\mathrm{PD}}$

[0030] For example, if M₁=2²⁰(=1048576) and f_PD=1.048576 MHz, then f_res=1 Hz. To achieve a resolution of 1 Hz, an integer-N synthesizer would require f_PD=1 Hz and the bandwidth of the loop filter would have to be much less than 1 Hz. By contrast, to attenuate the reference spur from the phase detector in the fractional-N synthesizer, the loop filter will require a bandwidth that is less than 1.048576 MHz but much larger than 1 Hz. The use of a significantly higher value of f_PD has two important consequences:

[0031] 1) the transient response of the loop is much faster than in the integer-N case, and

[0032] 2) the energy storage elements in the loop filter are physically smaller.

[0033] FIG. 3 shows an implementation of a MASH 1-1-1 DDSM₁ architecture for a fractional-N frequency synthesizer, where each accumulator has a modulus M₁.

[0034] The fractional-N synthesizer suffers from a number of problems that are related to this modulus M₁:

• • [0035] 1) when M₁ is a power of two and f_PD is not, it can be impossible to set a desired output frequency exactly.
  • [0036] 2) undesirable tones appear in the output spectrum that are multiples of f_res. The smaller the numerator and denominator of the fraction N₁/M₁, and the larger the greatest common divisor (gcd) of N₁ and M₁, the larger the spurs.

[0037] One way to correct the first problem is to use a value of M₁ that is not a power of two. While this solves the first problem, it requires more complex circuitry to implement a programmable modulus, and it can make the second problem (spurs) worse.

[0038] In the simplest nested fractional-N frequency synthesizer, as shown in FIG. 4, the relationship between the output and reference frequencies is:

[0039] $f_{\mathrm{VCO}}=\left(N_0+\frac{\left(N_1+\frac{N_2}{M_2}\right)}{M_1}\right)f_{\mathrm{PD}},$
where M₁ and M₂ are the moduli of two distinct Digital Delta Sigma Modulators (DDSMs), as shown in FIG. 5. The frequency resolution is defined by:

[0040] $f_{\mathrm{res}=}\frac{1}{M_1{M}_2}{f}_{\mathrm{PD}}.$

[0041] By adding additional DDSMs with moduli M₃; M₄; : : : , etc the relationship becomes

[0042] $f_{\mathrm{VCO}}=\left(N_0+\frac{\left(N_1+\frac{\left(N_2+\frac{\left(N_3+\frac{\left(N_4+\dots \right)}{M_4}\right)}{M_3}\right)}{M_2}\right)}{M_1}\right)f_{\mathrm{PD}}.$

[0043] In the simplest nested fractional-N structure, which has two moduli, M₂ is programmable but M₁ can be a power of two. The divider controller comprises a nested DDSM structure, as shown in FIG. 5 in accordance with some embodiments. The divider controller comprises two DDSMs, labelled DDSM1 and DDSM2, clocked at rates f_s1 and f_s2; respectively. These rates could be different, as described below. For simplicity, it is easier to consider the simplest case when they are equal.

[0044] In order to illustrate an example operation the performance of integer-N, fractional-N and nested fractional-N frequency synthesizers can be compared in the context of a specific design problem. The specifications are as shown in Table I.

[0045] The output frequency of the integer-N synthesizer is an integer multiple of the reference frequency, namely:
f_VCO=N₀f_PD

[0046] Unfortunately, 2000.20 MHz is not an integer multiple of 61.44 MHz; therefore the specification cannot be met with an integer-N architecture.

[0047]

TABLE I
SPECIFICATIONS
	Parameter	Value	Units
	fVCO	2000.20	MHz
	fPD	61.44	MHz
	fCS	100	kHz

[0048] In the fractional-N divider,

[0049] $f_{\mathrm{VCO}}=\left(N_0+\frac{N_1}{M_1}\right)f_{\mathrm{PD}1}$

[0050] Consider two cases: power-of-two modulus M₁ and programmable (not a power of two) modulus M₁.

[0051] 1) Power-of-two modulus M₁: From Table II,

[0052] $\begin{array}{c}{f}_{\mathrm{VCO}}=\left(32+\frac{582315}{1048576}\right)61.44\mathrm{MHz}\\ =2000.20001953\mathrm{MHz}\end{array}$

[0053] Note that the power-of-two modulus results in a frequency error. The size of the error can be reduced by increasing the value of M₁, but it cannot be eliminated.

[0054]

TABLE II
FRACTIONAL-N FREQUENCY SYNTHESIZER
WITH POWER-OF-TWO MODULUS DIVIDER
	Parameter	Value
	M1	1048576
	N0	32
	N1	582315

[0055] 2) Programmable modulus M₁: From Table III,

[0056] $\begin{array}{c}{f}_{\mathrm{VCO}}=\left(32+\frac{3412}{6144}\right)61.44\mathrm{MHz}\\ =2000.200000\mathrm{MHz}\end{array}$

[0057] Note that the use of a programmable modulus results in no frequency error in this case.

[0058]

TABLE III
FRACTIONAL-N FREQUENCY SYNTHESIZER
WITH PROGRAMMABLE MODULUS
	Parameter	Value
	M1	6144
	N0	32
	N1	3412

[0059] Note that M₁ is typically much smaller in the case of a programmable modulus compared to the power-of-two case (6144 versus 1048576 in this example). Indeed, the main problem associated with using a small modulus M₁ is that short cycles, and consequently large spurs, may occur.

[0060] Consider what happens when f_VCO=1996.80 MHz. In this case, N₁=3072 and

[0061] $\begin{array}{c}{f}_{\mathrm{VCO}}=\left(32+\frac{3072}{6144}\right)61.44\mathrm{MHz}\\ =1996.800000\mathrm{MHz}\end{array}$

[0062] With an even initial condition, a third-order MASH 1-1-1 DDSM has a cycle of length 4 and therefore produces a very strong spur at an offset from f_VCO of 6144/4 MHz, namely 15.36 MHz. In the best case, the cycle length is 2×6144 and the quantization noise is spread over 12288 tones, the lowest of which is 5 kHz from f_VCO.

[0063] Next consider the nested fractional-N architecture, from Table IV,

[0064]

TABLE IV
NESTED FRACTIONAL-N FREQUENCY SYNTHESIZER
	Parameter	Value
	M1	1048576
	M2	3072
	N0	32
	N1	582314
	N2	2048

[0065] $\begin{array}{c}{f}_{\mathrm{VCO}}=\left(32+\frac{582314+\frac{2048}{3072}}{1048576}\right)61.44\mathrm{MHz}\\ =2000.200000\mathrm{MHz}\end{array}$

[0066] Note that the use of multiple moduli, at least one of which is programmable, can result in zero frequency error. The programmable modulus associated with each modulator can be an integer with factors other than 2.

[0067] When the input to a DDSM is fixed or periodic, the system cycles through a finite number of states repeatedly. Consequently, its output signal contains a quantization noise component that is periodic. The length of the cycle determines the number of tones over which the quantization noise is spread in the frequency domain. The shorter the cycle, the fewer the tones and consequently the larger the average power per tone.

[0068] By contrast with the single programmable modulus case, the nested fractional-N synthesizer in this example has a very large effective modulus, namely 3072×1048576 (being the product of a first programmable modules which has 3 as a factor and a second modulus which is a large power of two). In this case, the cycle length is greater than 6×10⁶, and the power in each tone of the quantization noise is extremely low.

[0069] Referring to FIGS. 5 and 6, an embodiment of a two-level nested DDSM divider controller is described in more detail. The controller comprises a first DDSM (DDSM₁) which can be a third order MASH 1-1-1 with fixed modulus M1, signal transfer function STF₁=1/M₁, and noise transfer function NTF₁=(1−z⁻¹)³. A second DDSM (DDSM₂) which is a first order Error Feedback Modulator (EFM) with programmable modulus M₂, signal transfer function STF₂=1/M₂, and noise transfer function NTF₂=(1−z⁻¹).

[0070] DDSM₁ is comprised of a cascade of three first order EFMs and a noise cancellation network. Each EFM can be a digital accumulator which has a primary input X and a secondary “carry in” input, and a “carry out” output Y.

[0071] N₂ is applied to the primary input of DDSM₂; its carry in input is zero. The output Y₂ of DDSM₂ is summed with N₁ and applied to the input of DDSM₁. Because Y₂ is a single bit, the sum can be performed implicitly by applying N₁ to the primary input of DDSM₁ and Y₂ to the secondary input.

[0072] The output Y₁ of DDSM₁ is summed with N₀ to produce the signal Y₀.

[0073] In FIG. 5, DDSM₁ and DDSM₂ are clocked at frequencies f_s1 and f_s2, respectively. In a conventional fractional-N frequency synthesizer, f_s1=f_PD. In the nested structure, one can choose f_s2=f_s1 or use a lower clock rate, such as f_s2=f_s1/2. DDSM₁ and DDSM₂ can be clocked synchronously at different rates f_s1 and f_s2, where f_s2<f_s1, or at the same rate f_s1=f_s2=f_s. This is advantageous as speed bottlenecks in the system are typically attributed to the comparator in the programmable modulus DDSM and the summer in DDSM₁. If the former is the problem, it can be alleviated by clocking DDSM₂ at a lower frequency than DDSM₁.

[0074] M₁ determines the attenuation of spurs and quantization noise from the second DDSM, as well as the worst case spur performance and quantization noise of the first DDSM. The value of M₁ should be chosen to satisfy constraints on the quantization noise and spurs.

[0075] Cycle lengths in DDSM₁ are influenced by N₁ and M₁. A variety of stochastic and deterministic techniques are available to maximize cycle lengths in DDSM₁. These include adding dither, setting an initial condition (called “seeding”), setting the LSB of the input, using prime modulus quantizers, and architectures such as a known HK-MASH structure. It is necessary to fix the problem of inherent spurs in the DDSMs when the inputs are constant. This can be done by adding dither, setting the initial condition (seeding), using prime modulus quantizers, or architectures such as the HK-MASH structure. A HK-MASH structure in DDSM₁ obviates the need for dither and seeding, for example using a HK MASH structure published by K. Hosseini and M. P. Kennedy, ‘A sigma-delta modulator’, 10 Apr. 2008. Patent no. WO2008041216-A1, and the entire disclosure of which is incorporated herein by reference.

[0076] These considerations also apply to conventional fractional-N frequency synthesizers. In order to maximize the simplicity and speed of DDSM₁, a power-of-two modulus can be used. Furthermore, architectures such as pipelined nested bus-splitting can be used to maximize the throughput of DDSM1. In the nested fractional-N synthesizer, the contribution of Y₂ to the output Y₀ is weighted by STF₁. The value of M₁ determines the attenuation of the shaped quantization noise component from DDSM₂.

[0077] Cycle lengths in DDSM2 are influenced by N₂ and M₂. As in DDSM₁, a variety of stochastic and deterministic techniques are available to maximize cycle lengths in DDSM₂. The range of options is restricted in this case because modulus M₂ is programmable and the required frequency correction is predetermined. Consequently cycle length maximization through architectural modifications such as prime modulus quantizers and HK-MASH (which put restrictions on M₂) cannot be used. By choosing M₁ sufficiently large, the potentially poor spectral performance of DDSM₂ can be spectrally masked by that of DDSM₁ using techniques such as those described in a paper entitled ‘Recent Advances in the analysis, design and optimization of Digital Delta-Sigma Modulators’, NOLTA, Jul. 1, 2012, IEICE, vol. 3, no. 3 pp 258-286.

[0078] FIG. 7 shows the spectral performance obtained by employing the two modulator nested structure of FIGS. 4 to 6. The conventional fractional-N modulator has the noise component S₁. The nested fractional-N modulator has similar spectral performance if the additional noise component S₂ is spectrally masked by S₁. FIG. 7 shows typical contributions of quantization noise to the signal Y₀. The jagged curve is the simulated power spectral density of Y₀. The solid curves S₁ and S₂ are estimates of the contributions from DDSM₁ and DDSM₂, respectively. S₀ indicates the noise floor associated with quantization at the input of DDSM₁.

[0079] FIG. 8 illustrates results obtained for a radio frequency synthesizer incorporating the two modulus nested structure of FIGS. 4 to 6 implemented in silicon. The peak shown in the center to the right shows an exact output frequency using the implementation of FIGS. 4 to 6 to provide an output precise frequency over a range of radio frequencies.

[0080] In some embodiments, a modified fractional-N frequency synthesizer is provided that allows the frequency step to be set exactly while maintaining the spur performance of a power-of-two-modulus divider. Furthermore, the spectral performance of the nested fractional-N frequency synthesizer is no worse than a conventional fractional-N synthesizer with a power-of-two divider. It will be appreciated that the above description describes the simplest DDSM structures. More complicated DDSMs with more complex transfer functions and multilevel quantizers can be used in accordance with the implementations shown in FIGS. 4 to 6.

[0081] An advantage of the radio frequency synthesizer is that a large value of f_PD can be obtained. This allows use of smaller components in the loop filter and improves the transient response. For a given f_res, f_PD in the nested fractional-N frequency synthesizer can be a factor of M₂ higher than in the conventional fractional-N.

[0082] The nested fractional-N architecture allows one to set the output frequency exactly while maintaining the architectural advantages and spur performance of a power-of-two modulus, overcoming the aforementioned problems.

[0083] Using a single power of two modulus M₁ alone permits high speed operation but produces an inexact frequency f_VCO. Using a modulus M₁ that is not a power of two produces an exact frequency but also unwanted tones (spurs) in the output signal. Using the first and second modulus M₁ and M₂ together has the advantage of both high speed and an exact frequency, without the spurs associated with a modulus that is not a power of two.

[0084] In one embodiment the first modulus comprises a value set at a power of two.

[0085] In one embodiment the first modulator is clocked to operate at a first frequency.

[0086] In one embodiment the second modulator is clocked to operate at a second frequency.

[0087] In one embodiment the second frequency is set to operate at a lower frequency than the first frequency adapted to eliminate speed bottlenecks in the system. The speed bottlenecks in the system are the comparator and/or summer in the programmable modulus DDSM2 and the summer in DDSM1. This is alleviated by clocking DDSM2 at a lower frequency than DDSM1.

[0088] In one embodiment the second modulus is programmable.

[0089] In one embodiment the frequency resolution of the system is governed by the equation:
f_res=f_PD/(M₁,M₂)

[0090] In one embodiment the relationship between the output frequency and reference frequency is governed by the equation:

[0091] $f_{\mathrm{VCO}}=\left(N_0+\frac{\left(N_1+\frac{N_2}{M_2}\right)}{M_1}\right)f_{\mathrm{PD}1}$

[0092] In one embodiment the first and second frequency are equal in value.

[0093] In one embodiment the output of the second modulus is weighted by a transfer function associated with the first modulus.

[0094] In another embodiment there is provided a fractional-N synthesizer system comprising an oscillator adapted to generate a signal at an output frequency from a reference frequency set by said oscillator, said output frequency is generated using a modulus having a value set at a power of two; and a second modulus adapted to ensure the output frequency equals the reference frequency.

[0095] In a further embodiment there is provided a divider controller for use in a nested fractional-N frequency synthesizer, said controller adapted to generate a signal at an output frequency from a reference frequency, wherein said output frequency is generated using a first modulus and a second modulus adapted to ensure the output frequency can be set to an exact value.

[0096] It will be appreciated that a computer program comprising program instructions for causing a computer program to control the operation of the first or second modulus or divider controller, which may be embodied on a record medium, carrier signal or read-only memory.

[0097] The embodiments in the disclosure described with reference to the drawings comprise a computer apparatus and/or processes performed in an integrated circuit. This disclosure also extends to computer programs, particularly computer programs stored on or in a carrier adapted to control operation of the frequency synthesizer as described herein. The program may be in the form of source code, object code, or a code intermediate source and object code, such as in partially compiled form or in any other form suitable for use in the implementation of the method according to the invention. The carrier may comprise a storage medium such as ROM, e.g. CD ROM, or magnetic recording medium, e.g. a floppy disk or hard disk. The carrier may be an electrical or optical signal which may be transmitted via an electrical or an optical cable or by radio or other means.

[0098] In the specification the terms “comprise, comprises, comprised and comprising” or any variation thereof and the terms “include, includes, included and including” or any variation thereof are considered to be totally interchangeable and they should all be afforded the widest possible interpretation and vice versa.

[0099] The invention is not limited to the embodiments hereinbefore described but may be varied in both construction and detail.