INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS

[0001] Any and all applications for which a foreign or domestic priority claim is identified in the Application Data Sheet as filed with the present application are hereby incorporated by reference under 37 CFR 1 .57.

BACKGROUND

[0002] Fractional-N frequency synthesizers are essential parts of any modern multi-band and multi-standard wireless transceiver systems. These synthesizers make use of digital delta-sigma noise shaping modulators to generate the fractional division ratios. Deita-sigma modulators, however, comprise a finite state machine that generates cyclic train of division ratios. These introduce fractional spurious tones. In general, dithering and or seeding are used to alleviate the presence of delta-sigma fractional spurs. In high performance application, however, dither and seeding techniques are not useful since they significantly increase in-band noise and introduce large frequency errors.

SUMMARY

[0003] Embodiments reduce or eliminate fractional spurious tones present in deita-sigma based fractional-N frequency synthesizers without the use of dither or seeding in the modulator. In certain embodiments, the Fractional-N divider of the frequency synthesizer is driven by dither-less and seed-less modulators. In one embodiment, the dither-iess and seed-less modulator comprises a Dither-Less Error Feedback Modulator (DS-EFM) and an exemplary 3 ^rd order Dither-Less Error Feedback Modulator (DS-EFM3) is provided. In another embodiment, the dither-less and seed-less modulator comprises a Dither-iess Seed-less MASH architecture modulator (DS-MASH) and an exemplary three 1 ^st order stage Dither-iess Seed-less MASH Modulator (DS- MASH 1 1 1 ) is provided. In other embodiments, these modulators can be of any order and are not limited to 1 ^st order or 3 ^rd order modulators. Further embodiments comprise modifications to implement approximately static zero error over time,

[0004] in an embodiment, a pbase-iocked loop (PPL) circuit is disclosed. The PLL circuit comprises a phase frequency detector (PFD) configured to generate a first signal representative of a phase difference between a reference signal and a PLL feedback signal, an adjustment circuit in communication with the PDF and configured to generate a control voltage based on the first signal, a voltage-controlled oscillator (VCO) in communication with the adjustment circuit and configured to generate an output signal based on the control voltage, and a PLL feedback circuit in communication with the VCO and the PFD and configured to generate the PLL feedback signal based on the output signal.

[0005] in an embodiment, the PLL feedback circuit includes a divider circuit configured to receive the output signal and to generate an updated version of the PLL feedback signal, and a dither-less delta-sigma modulator in communication with the divider circuit that allows the output signal to have an output frequency that is a non-integer multiple of the frequency of the reference signal. The dither-less delta-sigma modulator receives the output of the divider circuit and generates a cyclic code sequence, which is fedback to the divider circuit. The dither-less delta-sigma modulator includes a first summing circuit configured to receive the output of the divider circuit and a modulator feedback signal and to provide a first summed signal, a quantizing circuit configured to receive the first summed signal and generate the cyclic code sequence, a first modulator feedback loop that generates the modulator feedback signal and includes a second summing circuit and a first filter. The second summing circuit is configured to receive the first summed signal and the cyclic code sequence and to provide a second summed signal, and the first filter is configured to filter the second summed signal and to provide the modulator feedback signal.

[0006] The dither-less delta-sigma modulator further includes a second modulator feedback loop that introduces a scaled version of the cyclic code sequence into the first feedback loop and includes a gain component configured to receive the cyclic code sequence and to provide a scaled code sequence. The second summing circuit is further configured to receive the scaled code sequence to introduce a small amount of error to the modulator feedback signal such that fractional spurious tones are disrupted.

[0007] The dither-less delta-sigma modulator further includes a third modulator feedback loop that periodically cancels the gain from the scaled code sequence in the second feedback loop and includes a filter configured to receive the scaled code sequence and to provide a filtered gain signal. The second summing circuit is further configured to receive the filtered gain signal to average error in the modulator feedback signal to approximately zero such that the dither- less delta-sigma modulator provides approximately zero static error. In an embodiment, one or more of the first and second filters comprises a delay,

[0008] In another embodiment, a dither-less delta-sigma modulator comprises a first summing circuit configured to combine an output of a divider circuit and a modulator feedback signal to provide a first summed signal, a quantizing circuit configured to generate a cyclic code sequence based on the first summed signal, a first modulator feedback loop including a second summing circuit configured to combine the first summed signal and the cyclic code sequence to provide a second summed signal, and a first filter configured to filter the second summed signal to provide the modulator feedback signal, and a second modulator feedback loop including a gain component configured to receive the cyclic code sequence and to provide a scaled code sequence based on the cyclic code sequence, where the second summing circuit is further configured to receive the scaled code sequence and combine the scaled code sequence and the second summed signal. The dither-less delta-sigma modulator further comprises a third modulato feedback loop that periodically cancels gain from the scaled code sequence in the second feedback loop and includes a filter configured to filter the scaled code sequence and to provide a filtered gain signal based on the scaled code sequence, the second summing circuit further configured to receive the filtered gain signal in order to average error in the modulator feedback signal so that the dither-less delta-sigma modulator provides approximately zero static error.

[0009] In a further embodiment, a phase-locked loop (PPL) circuit comprises a phase frequency detector (PFD) configured to generate a first signal representative of a phase difference between a reference signal and a PLL feedback signal, an adjustment circuit in communication with the PFD and configured to generate a control voltage based on the first signal, and a voltage- controlled oscillator (VCO) in communication with the adjustment circuit and configured to generate an output signal based on the control voltage, and a divider circuit configured to receive the output signal and to generate an updated version of the PLL feedback signal. The PLL circuit further comprises dither-less de!ta-sigma modulator in communication with the divider circuit and including a first summing circuit configured to combine the output of the divider circuit and a modulator feedback signal to provide a first summed signal, a quantizing circuit configured to quantize the first summed signal to generate a cyclic code sequence, a second summing circuit configured to combine the first summed signal and the cyclic code sequence to provide a second summed signal, a first filter configured to filter the second summed signal to provide the modulator feedback signal, and a gain component configured to receive the cyclic code sequence to provide a scaled code sequence, where the second summing circuit further configured to receive the scaled code sequence and combine the scaled code sequence with the first summed signal and the cyclic code sequence to provide the second summed signal. The dither-less delta-sigma modulator further includes a filter configured to filter the scaled code sequence and to provide a filtered gain signal based on the scaled code sequence, the second summing circuit further configured to combine the filtered gain signal with the scaled code sequence, the first summed signal, and the cyclic code sequence to provide the second summed signal. The dither-less delta-sigma modulator furthe includes a first modulator feedback loop that generates the modulato feedback signal and that includes the second summing circuit and the first filter, a second modulator feedback loop that introduces a scaled version of the cyclic code sequence into the first feedback loop and that includes the gain component, and a third modulator feedback loop that periodically cancels the gain from the scaled code sequence in the second feedback loop and that includes a filter configured to receive the scaled code sequence and to provide a filtered gain signal based on the scaled code sequence, the second summing circuit furthe configured to receive the filtered gain signal in order to average error in the modulator feedback signal so that the dither-less delta-sigma modulator provides approximately zero static error. [0010] In a yet further embodiment, a wireless device comprises an antenna configured to facilitate reception of a radio frequency (RF) signal, a receiver in communication with the antenna, the receiver configured to process the RF signal, and a frequency synthesizer in communication with the receiver, the frequency synthesizer circuit having a phase-locked loop (PLL) circuit having a divider circuit and a dither-less delta-sigma modulator including a first summing circuit configured to combine an output of the divider circuit and a modulator feedback signal to provide a first summed signal, a quantizing circuit configured to quantize the first summed signal to generate a cyclic code sequence, a second summing circuit configured to combine the first summed signal and the cyclic code sequence to provide a second summed signal, a first filter configured to filter the second summed signal to provide the modulator feedback signal, a gain component configured to receive the cyclic code sequence to provide a scaled code sequence, the second summing circuit further configured to receive the scaled code sequence.

[0011] Certain embodiments relate to a dither-less delta-sigma modulator configured to generate a cyclic output code, The dither-less delta- sigma modulator comprises a feedback filtering network including a first feedback loop and a second feedback loop that includes a summing circuit and a gain circuit configured to introduce a small erro signal into the first feedback loop to disrupt tonal behavior due to the cyclic output code. In an embodiment, the feedback filtering network further includes a third feedback loop that includes a filter configured to periodically cancel the small error signal in the second feedback loop to reduce static error.

[0012] According to a number of embodiments, the disclosure relates to a phase-locked loop (PPL) circuit comprising a phase frequency detector (PFD) configured to generate a first signal representative of a phase difference between a reference signal and a PLL feedback signal, an adjustment circuit in communication with the PFD and configured to generate a control voltage based on the first signal, a voltage-controlled oscillator (VCO) in communication with the adjustment circuit and configured to generate an output signal based on the control voltage, a divider circuit configured to receive the output signal and to generate an updated version of the PLL feedback signal, and a dither-less delta- sigma modulator in communication with the divider circuit and including a feedback filtering network including a first feedback loop and a second feedback loop that includes a gain circuit configured to introduce a small error signal into the first feedback loop to disrupt tonal behavior due to the cyclic output code. In an embodiment, the first feedback loop includes a first summing circuit configured to provide a first summed signal based on an output of the divider circuit and a modulator feedback signal, a quantizing circuit configured to quantize the first summed signal to generate the cyclic output code, a second summing circuit configured to combine the first summed signal and the cyclic output code to provide a second summed signal, and a first filter configured to filter the second summed signal to provide the modulator feedback signal. In another embodiment, the second feedback loop includes a gain component configured to receive the cyclic output code to provide a scaled output code, where the second summing circuit further configured to combine the scaled output code with the first summed signal and the cyclic output code to provide the second summed signal, in a further embodiment, the dither-less delta-sigma modulator further includes a third feedback loop that periodically cancels gain from the scaled output code in the second feedback loop and that includes a second filter configured to receive the scaled output code and to provide a filtered gain signal based on the scaled output code, where the second summing circuit is further configured to receive the filtered gain signal in order to average error in the modulator feedback signal so that the dither-less delta-sigma modulator provides approximately zero static error. In a yet further embodiment, the second filter includes a delay element.

[0013] In accordance with various embodiments, a wireless device comprises an antenna configured to facilitate reception of a radio frequency (RF) signal, a receiver in communication with the antenna, the receiver configured to process the RF signal, and a frequency synthesizer in communication with the receiver, where the frequency synthesizer circuit has a phase-locked loop (PLL) circuit having a divider circuit and a dither-less delta-sigma modulator in communication with the divider circuit and includes a feedback filtering network including a first feedback loop and a second feedback loop that includes a gain circuit configured to introduce a small error signal into the first feedback loop to disrupt tonal behavior due to the cyclic output code. In an embodiment, the first feedback loop includes a first summing circuit configured to provide a first summed signal based on an output of the divider circuit and a modulator feedback signal, a quantizing circuit configured to quantize the first summed signal to generate a cyclic output code, a second summing circuit configured to combine the first summed signal and the cyclic output code to provide a second summed signal, and a first filter configured to filter the second summed signal to provide the modulator feedback signal, In another embodiment, the second feedback loop includes a gain component configured to receive the cyclic output code to provide a scaled output code, the second summing circuit further configured to combine the scaled output code with the first summed signal and the cyclic output code to provide the second summed signal. In a further embodiment, the dither-less delta-sigma modulator further includes a third feedback loop that periodically cancels the gain from the scaled output code in the second feedback loop and that includes a second filter configured to receive the scaled output code and to provide a filtered gain signal based on the scaled output code, where the second summing circuit is further configured to receive the filtered gain signal in order to average error in the modulator feedback signal so that the dither-less deita-sigma modulator provides approximately zero static error. In a yet further embodiment, the second filter includes a delay element.

[0014] Other embodiments relate to a method to operate a phase- locked loop (PLL) circuit in a frequency synthesizer of a wireless device. The method comprises generating a first signal representative of a phase difference between a reference signal and a PLL feedback signal, generating a control voltage based on the first signal, generating an output signal based on the control voltage, generating an updated version of the PLL feedback signal based on the output signal and a cyclic output code provided by a dither-less deita-sigma modulator including a modulator feedback loop that provides an updated version of the cyclic output code, and introducing a small error signal into the modulator feedback loop to disrupt tonal behavior due to the cyclic output code. In an embodiment, the method further comprises combining a divided signal based on the output signal and a modulator feedback signal to provide a first summed signal. In another embodiment, the method further comprises quantizing the first summed signal to generate the cyclic output code. In a further embodiment, the method further comprises scaling the cyclic output code. In a yet further embodiment, the method further comprises combining the first summed signal, the cyclic output code, and the scaled cyclic output code to provide a second summed signal, where the scaled cyclic output code provides the small error signal. In an embodiment, the method further comprises filtering the second summed signal to provide the modulator feedback signal. In another embodiment, the method further comprises filtering the scaled cyclic output code to provide a filtered gain signal and combining the first summed signal, the cyclic output code, the scaled cyclic output code, and the filtered gain signal to provide the second summed signal. In another embodiment, the filtered gain signal periodically cancels gain from the cyclic output code to reduce static error.

[0015] In another embodiment, the PLL feedback circuit includes a divider circuit configured to receive the output signal and to generate an updated version of the PLL feedback signal, and a multi-stage noise shaping (MASH) modulator that allows the output signal to have an output frequency that is a non- integer multiple of the frequency of the reference signal. The MASH modulator receives the output of the divider circuit and generating a cyclic code sequence, which is fedback to the divider circuit. The MASH modulator includes a first dither-less delta-sigma modulator, a second dither-less deita-sigma modulator, and a combining circuit.

[0016] The first dither-less delta-sigma modulator includes a first summing circuit configured to receive the output of the divider circuit and a first modulator feedback signal and to provide a first summed signal, a first quantizing circuit configured to receive the first summed signal and to generate a first code sequence, and a first modulator feedback loop that generates the first modulator feedback signal and includes a second summing circuit and a first filter. The second summing circuit is configured to receive the first summed signal and the first code sequence and to provide a first error signal. The first filter is configured to filter the first error signal and to provide the first modulator feedback signal. ;

[0017] The first dither-less delta-sigma modulator furthe includes the second modulator feedback loop that introduces a scaled version of the first code sequence into the first modulator feedback loop and includes a first gain component configured to receive the first code sequence and to provide a first scaled code sequence. The second summing circuit is furthe configured to receive the first scaled code sequence to introduce a first smali amount of error to the first modulator feedback signal such that fractional spurious tones are disrupted.

[0018] The first dither-less delta-sigma modulator further includes the third modulator feedback loop that periodically cancels the gain from the first scaled code sequence in the second modulator feedback loop and includes a second filter configured to receive the first scaled code sequence and to provide a first filtered gain signal. The second summing circuit is further configured to receive the first filtered gain signal to average error in the modulator feedback signal to approximately zero such that the first dither-less delta-sigma modulator provides approximately zero static error.

[0019] The second dither-less delta sigma modulator includes a third summing circuit configured to receive the first error signal and a second modulator feedback signal and to provide a third summed signal, a second quantizing circuit configured to receive the third summed signal and generate a second code sequence, and a fourth modulator feedback loop that generates the second modulator feedback signal and includes a fourth summing circuit and a third filter. The fourth summing circuit is configured to receive the third summed signal and the second code sequence and to provide a second error signal, and the third filter is configured to filter the second error signal and to provide the second modulator feedback signal.

[0020] The second dither-less delta sigma modulator furthe includes a fifth modulator feedback loop that introduces a scaled version of the second code sequence into the second feedback loop and includes a second gain component configured to receive the second code sequence and to provide a second scaled code sequence. The fourth summing circuit is further configured to receive the second scaled code sequence to introduce a second small amount of error to the second modulator feedback signal such that fractional spurious tones are disrupted.

[0021] The second dither-less delta sigma modulator further includes a sixth modulator feedback loop that periodically cancels the gain from the second scaled code sequence in the fifth modulator feedback loop and includes a fourth filter configured to receive the second scaled code sequence and to provide a second filtered gain signal. The fourth summing circuit is further configured to receive the second filtered gain signal to average error in the second modulator feedback signal to approximately zero such that the second dither-less deita- sigma modulator provides approximately zero static error.

[0022] The combining circuit includes a fifth filter configured to receive the second code sequence and provide a filtered second code sequence and a fifth summing circuit configured to combine the filtered second code sequence, the second code sequence, and the first code sequence to provide the cyclic code sequence. In an embodiment, the fifth summing circuit configured to combine the filtered second code sequence, the second code sequence, the first code sequence and the integer code sequence to provide the cyclic code sequence. In an embodiment, one or more of the first, second, third, fourth and fifth filters comprises a delay.

[0023] In an embodiment, a multi-stage noise shaping (MASH) modulator comprises at least two of dither-less delta-sigma modulators configured such that an error signal from a first dither-less delta-sigma modulator includes an input signal to a second dither-less delta-sigma modulator, and a summation circuit configured to combine at least outputs from each of the plurality of dither-less delta-sigma modulators, where each dither-less delta- sigma modulato includes a first summing circuit configured to combine the input signal and a modulator feedback signal to provide a first summed signal, a quantizing circuit configured to generate a cyclic code sequence based on the first summed signal, a second summing circuit configured to combine the first summed signal and the cyclic code sequence to provide the error signal, a first filter configured to filter the error signal to provide the modulator feedback signal, and a gain component configured to receive the cyclic code sequence and to provide a scaled code sequence based on the cyclic code sequence, the second summing circuit further configured to receive the scaled code sequence and combines the scaled code sequence and the error signal to provide the modulator feedback signal such tonal behavior due to the cyclic code sequence is disrupted. Each dither-less delta-sigma modulator further includes a third modulator feedback loop that periodically cancels gain from the scaled code sequence in a second feedback loop and includes a filter configured to filter the scaled code sequence and to provide a filtered gain signal based on the scaled code sequence, the second summing circuit further configured to receive the filtered gain signal in order to average error in the modulator feedback signal to provide approximately zero static error.

[0024] In another embodiment, a phase-locked loop (PPL) circuit comprises a phase frequency detector (PFD) configured to generate a first signal representative of a phase difference between a reference signal and a PLL feedback signal, an adjustment circuit in communication with the PDF and configured to generate a control voltage based on the first signal, a voltage- controlled oscillator (VCO) in communication with the adjustment circuit and configured to generate an output signal based on the control voltage, a divider circuit configured to receive the output signal and to generate an updated version of the PLL feedback signal, and a MASH modulator in communication with the divider circuit and including multiple dither-less delta-sigma modulators configured such that an error signal from a first dither-less deita-sigma modulator includes an input signal to a second dither-!ess delta-sigma modulator, and a summation circuit, where each dither-less delta-sigma modulator including a first summing circuit configured to combine the input signal and a modulator feedback signal to provide a first summed signal, a quantizing circuit configured to quantize the first summed signal to generate a cyclic code sequence, a second summing circuit configured to combine the first summed signal and the cyclic code sequence to provide the error signal, a first filter configured to filter the error signal to provide the modulator feedback signal, a gain component configured to receive the cyclic code sequence to provide a scaled code sequence, and where the second summing circuit further configured to receive the scaled code sequence and combine the scaled code sequence with the first summed signal and the cyclic code sequence to provide the error signal. Each dither-less delta- sigma modulator further includes a filter configured to filter the scaled code sequence and to provide a filtered gain signal based on the scaled code sequence, where the second summing circuit further configured to combine the filtered gain signal with the scaled code sequence, the first summed signal, and the cyclic code sequence to provide the error signal.

[0025] In a yet further embodiment, a wireless device comprises an antenna configured to facilitate reception of a radio frequency (RF) signal, a receiver in communication with the antenna and configured to process the RF signal, and a frequency synthesizer in communication with the receiver, the frequency synthesizer circuit having a phase-locked loop (PLL) circuit having a divider circuit and a MASH modulator including a plurality of dither-less delta- sigma modulators, each dither-less delta-sigma modulator including a first summing circuit configured to combine an input and a modulator feedback signal to provide a first summed signal, a quantizing circuit configured to quantize the first summed signal to generate a cyclic code sequence, a second summing circuit configured to combine the first summed signal and the cyclic code sequence to provide an error signal, a first filter configured to filter the error signal to provide the modulator feedback signal, and a gain component configured to receive the cyclic code sequence to provide a scaled code sequence, the second summing circuit further configured to receive the scaled code sequence,

[0026] Certain embodiments relate to a multi-stage noise shaping (MASH) modulator configured to generate a cyclic code sequence. The MASH modulator comprises a first dither-less delta-sigma modulator and a second dither-less delta-sigma modulator configured such that an error signal from the first dither-less delta-sigma modulator includes an input to the second dither-less delta-sigma modulator, and each of the dither-less delta-sigma modulators includes a first feedback loop and a second feedback loop that includes a summing circuit and a gain circuit configured to introduce a small error signal into the first feedback loop to disrupt tonal behavior due to the cyclic code sequence. In an embodiment, each of the dither-less delta-sigma modulators further includes a third feedback loop that includes a filter configured to periodically cancel the small error signal in the second feedback loop to reduce static error. In another embodiment, the MASH modulator further comprises a combining circuit configured to delay an output of the second delta-sigma modulator and to combine at least an output from the first delta-sigma modulator, the output from the second delta-sigma modulator, and the delayed output from the second delta- sigma modulator to provide the cyclic code sequence.

[0027] According to a number of embodiments, the disclosure relates to a phase-locked loop (PPL) circuit comprising a phase frequency detector (PFD) configured to generate a first signal representative of a phase difference between a reference signal and a PLL feedback signal, an adjustment circuit in communication with the PDF and configured to generate a control voltage based on the first signal, a voltage-controlled oscillator (VCO) in communication with the adjustment circuit and configured to generate an output signal based on the control voltage, a divider circuit configured to receive the output signa! and to generate an updated version of the PLL feedback signal, and a multi-stage noise shaping (MASH) modulator in communication with the divider circuit and configured to generate a cyclic code sequence. The MASH modulator includes a first dither-iess deita-sigma modulator and a second dither-iess delta-sigma modulator configured such that an error signal from the first dither-less delta- sigma modulator includes an input to the second dither-less deita-sigma modulator, and each of the dither-less deita-sigma modulators providing a cyclic output code and including a first feedback loop and a second feedback loop that includes a gain circuit configured to introduce a scaled version of the cyclic output code into the first feedback loop to disrupt tonal behavior due to the cyclic output code. In an embodiment, each of the dither-less delta-sigma modulators further includes a third feedback loop that includes a filter configured to periodically cancel the scaled version of the cyclic output code in the second feedback loop to reduce static error. In another embodiment, the PLL circuit further comprises a combining circuit configured to delay an output of the second deita-sigma modulator and to combine at least an output from the first deita-sigma modulator, the output from the second deita-sigma modulator, and the delayed output from the second deita-sigma modulator to provide the cyclic code sequence. In a further embodiment, each dither-less deita-sigma modulator includes a first summing circuit configured to combine the input and a modulator feedback signal to provide a first summed signal and a quantizing circuit configured to quantize the first summed signal to generate the cyclic output code. In a yet further embodiment, each dither-less delta-sigma modulator further includes a second summing circuit configured to combine the first summed signal and the cyclic output code to provide the error signal, and a first filter configured to filter the error signal to provide the modulator feedback signal. In an embodiment, each dither-iess delta-sigma modulator further includes a second filter configured to scale the cyclic output code, the second summing circuit further configured to combine the first summed signal, the cyclic output code, and the scaled cyclic output code to provide the error signal. [0028] In accordance with various embodiments, a wireless device comprises an antenna configured to facilitate reception of a radio frequency (RF) signal, a receiver in communication with the antenna and configured to process the RF signal, and a frequency synthesizer in communication with the receiver. The frequency synthesizer circuit has a phase-locked loop (PLL) circuit having a divider circuit and a multi-stage noise shaping (MASH) modulator in communication with the divider circuit and configured to generate a cyclic code sequence, where the MASH modulator includes a first dither-less delta-sigma modulator and a second dither-less delta-sigma modulator configured such that an error signal from the first dither-less delta-sigma modulator includes an input to the second dither-less delta-sigma modulator. Each of the dither-less delta- sigma modulators provides a cyclic output code and includes a first feedback loop and a second feedback loop that includes a gain circuit configured to introduce a scaled version of the cyclic output code into the first feedback loop to disrupt tonal behavior due to the cyclic output code. In an embodiment, each of the dither-less delta-sigma modulators further includes a third feedback loop that includes a filter configured to periodically cancel the scaled version of the cyclic output code in the second feedback loop to reduce static error. In another embodiment, the wireless device t further comprises a combining circuit configured to delay an output of the second delta-sigma modulator and to combine at least an output from the first delta-sigma modulator, the output from the second delta-sigma modulator, and the delayed output from the second delta- sigma modulator to provide the cyclic code sequence. In a further embodiment, each dither-less delta-sigma modulator includes a first summing circuit configured to combine the input and a modulator feedback signal to provide a first summed signal and a quantizing circuit configured to quantize the first summed signal to generate the cyclic output code. In a yet further embodiment, each dither-less delta-sigma modulator further includes a second summing circuit configured to combine the first summed signal and the cyclic output code to provide the error signal, and a first filter configured to filter the error signal to provide the modulator feedback signal. In another embodiment, each dither-less delta-sigma modulator further includes a second filter configured to scale the cyclic output code, and the second summing circuit is further configured to combine the first summed signal, the cyclic output code, and the scaled cyclic output code to provide the error signal

[0029] Other embodiments relate to a method to operate a phase- locked loop (PLL) circuit in a frequency synthesizer of a wireless device, The method comprises generating a first signal representative of a phase difference between a reference signal and a PLL feedback signal, generating a control voltage based on the first signal, generating an output signal based on the control voltage, generating an updated version of the PLL feedback signal based on the output signal and a cyclic code sequence provided by a multi-stage noise shaping (MASH) modulator including a plurality of dither-less delta-sigma modulators arranged such that an error signal of a first dither-less delta-sigma modulato comprises an input signal to a second dither-less delta-sigma modulator, where each of the dither-less delta-sigma modulators providing a cyclic output code and including a first feedback loop and a second feedback loop that includes a summing circuit and a gain circuit configured to introduce a scaled version of the cyclic output code into the first feedback loop to disrupt tonal behavior due to the cyclic output code, and combining at least the cyclic code output from each of the dither-less delta-sigma modulators to provide the cyclic code sequence, in an embodiment, each of the dither-less delta-sigma modulators further includes a third feedback loop that includes a filter configured to periodically cancel the scaled version of the cyclic output code in the second feedback loop to reduce static error, in another embodiment, the method furthe comprises delaying an output of the second delta-sigma modulator. In a further embodiment, the method further comprises combining at least an output from the first delta-sigma modulator, the output from the second delta-sigma modulator, and the delayed output from the second delta-sigma modulator to provide the cyclic code sequence. In a yet further embodiment, each dither-less delta-sigma modulator is configured to combine the input signal and a modulator feedback signal to provide a first summed signal, quantize the first summed signal to generate the cyclic output code, scale the cyclic output code, combine the first summed signal, the cyclic output code, and the scaled cyclic output code to provide the error signal, and filter the error signal to provide the modulator feedback signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 schematically depicts a phase-locked loop (PLL) comprising a delta-sigma modulator, according to certain embodiments.

[0031] Figure 2 illustrates a wireless device in which the PLL of Figure 1 can be implemented, according to certain embodiments.

[0032] Figure 3 illustrates that in some embodiments, the PLL of Figure 1 can be implemented in a frequency synthesizer that facilitates processing of a received radio frequency (RF) signal.

[0033] Figure 4 illustrates an exemplary PLL frequency synthesizer that is capable of operating as a fractional-N PLL, according to certain embodiments.

[0034] Figure 5 is an exemplary 3 ^rd order Error Feedback Modulator (EFM3) including dither that can be implemented in the frequency synthesizer of Figure 4, according to certain embodiments.

[0035] Figure 8 is a plot of the Fast Fourier Transform (FFT) of the output code sequence of the 3 ^rd order Error Feedback Modulator (EFM3) with and without dithering, according to certain embodiments.

[0036] Figure 7 illustrates an embodiment of a Dither-less Seed-less Error Feedback-based fractional-N frequency synthesizer, according to certain embodiments.

[0037] Figure 8 illustrates an exemplary 3 ^rd order Dither-less Seed-less Error Feedback Modulator (DS-EFM3) that can be implemented in the frequency synthesizer of Figure 7, according to certain embodiments.

[0038] Figure 9 is a plot of the FFT of the output code sequences of the 3 ^rd order Error Feedback Modulator (EFM3) of Figure 5 and the 3 ^rd order Dither- less Seed-less Error Feedback Modulator (DS-EFM3) of Figure 8, according to certain embodiments.

[0039] Figure 10 illustrates plots of an exemplary synthesized output frequency for a PLL Frequency Synthesizer including the dithered EFM3 of Figure 5 and including the DS-EFM3 of Figure 8, according to certain embodiments.

[0040] Figure 1 1 illustrates an exemplary 1 ^st order Error Feedback Modulator (EFM1 ), according to certain embodiments. [0041] Figure 12 illustrates an exemplary Dither-less Seed-less 1 order Error Feedback Modulator (DS-EFM1 ), according to certain embodiments.

[0042] Figure 13 illustrates an exemplary 3 ^rd order Dither-less Seedless MASH architecture modulator (DS-MASH 1 1 1 ), according to certain embodiments.

[0043] Figure 14 illustrates the simulated noise output performance for the DS-MASH1 1 1 modulator of Figure 13, according to certain embodiments.

[0044] Figure 15 illustrates an exemplary 3 ^rd order Dither-less Seedless Error Feedback Modulator with approximately zero static error implemented with a 50% duty cycle, according to certain embodiments.

[0045] Figure 16 illustrates an exemplary 3™ order Dither-less Seedless MASH architecture modulator (DS-MASH1 1 1 ) with approximately zero static error implemented with a 50% duty cycle, according to certain embodiments.

DETAILED DESCRIPTION

[0048] in some embodiments, a radio frequency (RF) device such as a wireless device can include a frequency synthesizer having a phase-locked loop (PLL). Figure 1 schematically depicts a PLL 100 that can be configured to receive a reference signal and generate an output signal having a desired output frequency. Such a PLL can include a delta-sigma modulator having one or more desirable features as described herein.

[0047] in some embodiments, a PLL having one or more features of the present disclosure can be implemented in a radio frequency (RF) device such as a wireless device. Such a wireless device can include, for example, a cellular phone, a smart-phone, a hand-held wireless device with or without phone functionality, a wireless tablet, etc. Although described in the context of a wireless device, it will be understood that one or more features of the present disclosure can also be implemented in other RF systems, including, for example, a base-station.

[0048] Figure 2 schematically depicts an example of a wireless device 1 10 having one or advantageous features described herein. The wireless device 1 10 is shown to include an antenna 140 configured to facilitate transmission (TX) and/or reception (RX) of RF signals. Such TX and/or RX operations can be performed simultaneously by use of a duplexer 138, Although described in the context of such duplex functionality and common antenna, other configurations are also possible.

[0049] A received signal is shown to be routed from the antenna 140 to a receiver circuit 120 via the duplexer 138 and a low-noise amplifier (LNA) 130. For transmission, a signal to be transmitted is shown to be generated by a transmitter circuit 126 and routed to the antenna 140 via a power amplifier (PA) 136 and the duplexer 1 18. The receiver circuit 120 and the transmitter circuit 126 may or may not be part of a same component (e.g., a transceiver). In some embodiments, a wireless device 1 10 can include both of the receiver and transmitter circuits, or just one circuit (e.g., receiver or transmitter).

[0050] The wireless device 1 10 is shown to further include a frequency synthesizer circuit 122 having a phase-locked loop (PLL) 100. Such a circuit (122) can include one or more features as described herein to provide advantages for either or both of RX and TX functionalities associated with the wireless device 1 10.

[0051] The receiver circuit 120, the transmitter circuit 126, and the frequency synthesizer circuit 122 are shown to be in communication with a baseband subsystem 1 14 which can include, for example, a processor 1 16 configured to control a number of operations associated with the wireless device 1 10, and a memory 1 18 configured to store data, executable instructions, etc. The baseband subsystem 1 14 is also shown to be in communication with a user interface 1 12 to allow interfacing of various functionalities of the wireless device 1 10 with a user.

[0052] As shown in Figure 2, at least some of the one or more features associated with the frequency synthesizer 122 can be implemented in an RF module 102. Such a module can include a packaging substrate configured to receive a plurality of components. The module 102 can include one or more semiconductor die mounted on the packaging substrate. Such one or more die can include some or ail of the circuit that provides various functionalities associated with the frequency synthesizer 122.

[0053] Figure 3 shows an example of a configuration 150 where one or more frequency synthesizers can be implemented in a receiver chain of a wireless device. Although described in such a receiver chain context, it will be understood that one or more features of the present disclosure can also be implemented in other parts of a wireless device.

[0054] A signal received by the antenna 140 can be passed through a preselect filter 152 configured to pass a desired receive band. The preselect filter 152 can work in conjunction with an image filter 156 to further isolate the receive band. Both of these filters can pass substantially the entire receive band, since channel selection does not occur until more downstream of the receiver chain.

[0055] A low-noise amplifier (LNA) 130 can be implemented to boost the incoming signal. Such an LNA can be configured to provide this gain while degrading the signai-to-noise ratio (SNR) as little as possible. An automatic gain control (AGC) circuit 154 can be configured to allow the wireless device to handle a wide range of expected input power levels. Fo example, a low powered incoming signal can require a greater boost than a higher powered incoming signal.

[0056] A first mixer 158a can be configured to convert the RF channels down to lower frequencies and center a desired channel at a specific intermediate frequency (IF). Such a specific IF can be provided to the first mixer 158a from a first frequency synthesizer 122a.

[0057] At this stage, the entire received-and-filtered band is now mixed down to the IF. An IF filter 160 can be configured to isolate the channel of interest from the receive band. An AGC circuit 162 can be configured to allow the wireless device to handle a wide range of expected input power levels associated with the isolated channel of interest.

[0058] A second mixe 158b can be configured to convert the foregoing isolated channel signal down to a baseband signal. Such down-conversion can be facilitated by a second frequency synthesizer 122b configured to generate and provide a desired baseband frequency to the second mixer 158b.

[0059] An AGC circuit 164 can be configured to allow the wireless device to handle a wide range of expected input power levels associated with the output of the second mixer 158b. A baseband filter 166 can be configured to filter the selected baseband-frequency signal before having the signal sampled by an analog-to-digital converter (ADC) 188. A digital signal resulting from such an ADC can be passed to a baseband sub-system (not shown in Figure 3).

[0060] In the context of the example signal processing configuration of Figure 3, the first frequency synthesizer 122a generates a clock signal that facilitates the down-conversion of a received signal to an IF signal. Similarly, the second frequency synthesizer 122b generates a clock signal that facilitates the down-conversion of the IF signal to a baseband signal.

[0061] As described in reference to Figures 1 and 2, a frequency synthesizer can include a PLL. In some embodiments, a PLL can be implemented as a negative feedback control system designed to generate an output at a particular frequency. Such an output can be utilized as an output of the frequency synthesizer.

[0062] Figure 4 shows an example configuration of a PLL circuit 400, which can be a part of the frequency synthesizer 122. As shown, a crystal oscillator 170 outputs a clock signal to a 1/R divider 174 which divides the clock signal by R (or multiplies the frequency of the clock signal from the crystal oscillator 170 by R) to provide a reference clock signal to a phase frequency detector (PFD) 172. Sn some embodiments, the PFD 172 can be configured to compare the rising edges of the reference clock signal and a feedback signal (in path 196) and determine if the feedback signal is leading or lagging with respect to the reference clock signal.

[0063] Based on this comparison, the PFD 172 can output a phase error information signal to a charge pump 176. The phase error information signal can be either an UP signal indicating that the feedback signal is too slow when compared with the reference clock signal or a DOWN (DN) signal indicating that the feedback signal is too fast when compared with the reference signal. In response, the charge pump 176 can output a current that is related to the phase difference between the reference and feedback signals.

[0064] The foregoing charge pump current can be provided to a loop filter 180 comprising capacitors C1-C3 and resistors R2, R3. The loop filter 180 can be configured to convert the charge pump current into a voltage suitable for driving a voltage controlled oscillator (VCO) 184. The loop filter 180 can also be configured to control loop dynamics of the PLL 400 (e.g., bandwidth, settling time, etc.).

[0065] The VCO 184 can be configured to output a signal having a frequency that is related to the driving voltage from the loop filter 180. In some embodiments, the output of the VCO 184 is buffered by buffer 182.

[0068] The buffered VCO output is fed into divider circuit 192 (1/N). The divider circuit 192 can be configured to divide the buffered VCO output frequency back down to the reference frequency. A feedback signal from the divider circuit 192 can be fed back into the PFD 172 through path 196 to thereby complete the PLL loop.

[0067] The foregoing feedback mechanism allows the output frequency of the PLL 400 to lock on to a frequency that is a multiple of the reference signal frequency. If the multiple is an integer (N), the PLL 400 is considered to be an Integer-N PLL. if the multiple contains a fractional component (1/M), as indicated by divider circuit 188, the PLL 400 is considered to be a Fractional~N PLL.

[0068] Figure 4 further shows a deita-sigma modulator (DSM) 500 in communication with the feedback loop. As described herein, such a DSM can be configured as an additional feedback loop with the divider circuit 192 to allow the PLL 400 to operate as a delta-sigma based fractional-N frequency synthesizer.

[0069] In some embodiments, the DSM 500 can be configured to generate a signal that instructs the divider circuit 192 with which integer value to divide the frequency of the VCO output signal. By way of an example, suppose that a PLL has a reference signal frequency of 40 MHz, and it is desired to output a signal having a frequency of 2.41 GHz. Such a configuration yields a divide ratio of 60 and 1/4. One way the PLL can achieve this divide ratio is to implement dividing by 60 for three reference cycles, then dividing by 61 for one cycle. This pattern can then repeat. Over each repetition the average divide value, Navg, is 60 and 1/4 as expected.

[0070] In the context of the foregoing example, the DSM 500 can instruct the divider circuit 192 to divide by 60 or 61. Such dithering between two integer divide ratios can allow the divider circuit 192 to be implemented even if the circuit 192 is only capable of integer division. Accordingly, the output frequency of such a fractional-N PLL frequency synthesizer 400 can be an averaged result of a plurality of integer divide values.

[0071] A fractional-N PLL frequency synthesizer is used to synthesize a reference that is higher than the channel spacing. This is important in multi- bands and multi-standards applications where the channel spacing is different from standard to standard. Equation 1 shows the relationship of the reference frequency (fREp) and the synthesized VCO frequency (f ^' vco) at the output of the divider 188.

CD

wher* jig® & the is the rzf er ee- freq e cy,

N &— GTg the mtsf-ger & f roe pert af ike division wak e-

[0072] Embodiments of some fractional-N PLL frequency synthesizers 400 make use of higher order multi-stage noise shaping structure (MASH) and Single Loop delta-sigma modulators, such as a 3rd order Error Feedback Modulator (EFM3) 500, shown in Figure 5, to generate divider value sequences that on average yieid the required division ratios as discussed above. The EF 3 500 comprises a finite state machine that generates cyclic train of division ratios. These introduce fractional spurious tones due to the cyclic output code.

[0073] In the illustrated embodiment of Figure 5, a first summing circuit 502 receives the input signal and a dithering signal from a dither component 504. A second summing circuit 514 receives the dithered input signal and a feedback signal. A quantizer 506 receives the summed signal and outputs a quantized output signal. A 3 ^rd order feedback loop 508 comprises a third summing circuit 510 and a 3 ^rd order filter 512. The third summing circuit 510 receives the summed signal and the output signal and generates an error signal. The filter 512 receives the error signal and outputs the feedback signal.

[0074] in general, dithering and or seeding are used to alleviate the presence of delta-sigma fractional spurs. Dithering disturbs the tonal behavior by randomizing the code sequence but inherently adds significant in-band noise. Seeding or initial condition setting may help with a limited number of fractional channels. Randomization due to this technique is input dependent and may not remove all fractional spurs in most frequency channels. Another issue with seeding is it generates unwanted static frequency errors. Thus, in high performance applications, dither and seeding techniques may not be useful since they significantly increase in-band noise and introduce large frequency errors.

[0075] Figure 6 illustrates a Fast Fourier Transform (FFT) 600 of the output code sequence of a typical 3rd order deita-sigma modulator with and without dithering. Curve 810 shows the modulator output without dither and curve 620 shows the modulator output with dither for a frequency synthesizer As shown in Figure 6, curve 620 (with dither) has fewer spurious frequencies than curve 610 (without dither), but the in-band noise of curve 620 (with dither) is significantly higher than curve 610 (without dither).

Delta-Sigma Based Fractionai-N Frequency Synthesizer

[0078] Figure 7 illustrates an embodiment of a Dither-less Seed-less EF -based Fractiona!-N Frequency Synthesizer 700 which can be a part of the frequency synthesizer 122. Frequency synthesizer 700 comprises the crystal oscillator 170, the 1/R divider 174, the phase detector 172, the charge pump 176, the loop filter 180, the VCO 184, the buffer 182, and dividers 188, 192 as described above with respect to Figure 4. The frequency synthesizer 700 further comprises a Dither-less Seed-less Error Feedback Modulator (DS-EFM) 800. in the illustrated embodiment, the DS-EFM 800 comprises a 3 ^rd order Dither-less Seed-less Error Feedback Modulator (DS-EFM3) 800. The DS-EFM3 800 does not use dithering to remove fractional-N spurious tones.

[0077] Figure 8 illustrates an embodiment of the DS-ESM3 800 comprising a 3rd order single Loop EFM with an additional feedback loop comprising a scaled version of the output sequence summed into the feedback filtering network.

[0078] in the illustrated embodiment of Figure 8, a first summing circuit 802 receives an input signal and a feedback signal and combines them to generate a summed signal. A quantizer 806 receives the summed signal and outputs a quantized output signal. A 3 ^rd order feedback loop 808 comprises a second summing circuit 810 and a 3 ^rd order filter 812 including an additional feedback loop. The additional feedback loop comprises a gain component 820 and a third summing circuit 822. [0079] The second summing circuit 810 receives the summed signal and the quantized output signal and generates an error signal. The gain component 820 receives the quantized output signal and scales the quantized output signal to generate a scaled version of the output signal/output sequence. The filter 812 receives the error signal and the scaled version of the output signal/output sequence. This scaled version of the output sequence is added to the feedback network of filter 812 at the third summing circuit 822. The additional feedback based on the scaled version of the output signal/output sequence adds a small amount of error to the feedback signal such that the fractional spurious tones are disrupted.

[0080] Embodiments of the DS-EF 3 800 without the additional feedback will suffer from fractional spurious tones unless dithering or seeding is used. The Signal and Noise Transfer Functions of the EF 3500, such as in Figure 5, are given in equation 2.

[0081] A mathematical derivation of the Signal Transfer Function (SFT) and the Noise Transfer Function (NTF) of the DS-EFM3800 are:

V[n] = -E[n -3] + g-Y[n-\] + 3E[n - 2] - 3E[n - 1] + X[n] (3) -E[n] = V[n]-M -Y[n] (4) Sub (4) in (3)

M ^■ Y[n] -g-Y[n-l] = X[n] - E[n - 3] + 3E[n - 2] - 3E[n - 1] + E[n] (5) Using Z-Transform:

M ^■ Y(z) -g Z ^{l ■} Y(z) = X(∑) - Z ^{3 ■} Eq(z) + 3Z ^{~2 ■} Eq(z) - 3Z ^_1 · Eq(z) + Eq(z) (6)

) = X(z) + Eq(z)-(l-3Z ¹ +3Z ² -Z ³ ) (7)

^X(! > , ₊ m- <'- ^z ">; (9)

M ( -S Z ^l ) (1- δ-Ζ- ¹ )

where δ =— and E(z) = ¾^ (10)

M M

STF = & NTF =— ^J — (11)

Μ-(\-δ-Ζ- ) (Ι-δ-Ζ ¹ ) Setting δ = 0, the STF and the NTF are:

STF =— & NTF = (l - Z ¹ ) ³

M

[0082] From equations 1 1 and 12, it is very easy to notice that the additional error introduced in the system is so small that it does not alter the noise shaping characteristics of the modulator and yet it is large enough to continuously disrupt the tonal behavior of traditional high order modulators 500.

[0083] Figure 9 is a plot of the FFT of the output code sequences of an embodiment of the EFM3 500 of Figure 5 including dithering and an embodiment of the DS-EFM3 800 of Figure 8. Curve 910 shows the FFT for the DS-EFM3 800 and curve 920 shows the FFT for the Dithered EFM3 500. Referring to equations 2 and 12, the Signal and Noise transfer functions for the DS-EF 3 800 and the Dithered EFM3 500 are approximately the same. As illustrated in Figure 9, the output signal of the DS-EFM3 800 has no out-of~band spurious tones, similar to the output signal of the dithered EFM3 500, without any impact on the in-band noise floor.

[0084] Figure 10 is a plot 1000 illustrating exemplary synthesized output frequencies for a PLL Frequency Synthesizer including the dithered EF 3 500 of Figure 5 (curve 1 102) and including the DS-EFM3 800 of Figure 8 (curve 1 104). Curve 1004 for the DS-EFM3 shows a superior noise performance in- band, below 100 KHz offset frequency.

[0085] Embodiments of the Dither-less and Seed-less EFMs can be implemented on other high order single loop modulators and hence are not restricted to 3rd order modulators.

[0086] Figure 1 1 illustrates an exemplary 1 ^st order Error Feedback Modulator (EFM1 ) 1 100. In the illustrated embodiment, a first summing circuit 1 102 receives the input signal and a feedback signal and outputs a summed signal. A quantizer or quantizing circuit 1 104 receives the summed signal and outputs a quantized output signal to an amplifier 1 106. A second summing circuit 1 108 receives the summed signal and the amplified output signal from the amplifier 1 108 and generates an error signal. Sn an embodiment, the second summing circuit 1 108 generates the error signal by subtracting the amplified output signal from the summed signal. A first order filter 1 1 10 receives the error signal, filters the error signal, and outputs the feedback signal. Dither-less Seed-less MASH Architecture Error Feedback Modulator

[0087] Figure 12 illustrates an exemplary Dither-less Seed-less 1 ^st order Error Feedback Modulator (DS-EFM1 ) 1200 comprising the EFM1 1 100 of Figure 1 1 with an additional feedback loop comprising a scaled version of the output sequence added into the feedback filtering loop. The additional feedback loop comprises a gain component 1220. The gain component 1220 receives the output sequence from the quantizing circuit, indicated as 1 104 in Figure 1 1 , and outputs a scaled version of the output sequence. The output of the gain component 1220 is added into the feedback filtering loop at a summing circuit 1222.

[0088] Figure 13 illustrates an embodiment of a modulator 1300 having a multi-stage noise shaping (MASH) architecture comprising three DS-EF 1 stages 1200a, 1200b, 1200c and a summing circuit 1302. This new architecture is termed DS-MASH1 1 1. Each stage 1200a, 1200b, 1200c operates similarly to the DS-EFM1 1200 of Figure 12. The three DS-EFM1 stages 1200a, 1200b, 1200c are cascaded such that the first DS-EFM1 stage1200a receives the input signal and the first stage feedback signal and outputs a first stage summed signal. The first stage quantizer or quantizing circuit receives the first stage summed signal and outputs a first stage quantized output signal to the first stage amplifier. A first stage second summing circuit receives the first stage summed signal and the first stage amplified output signal from the first stage amplifier and generates the first stage error signal. The first stage gain component receives the first stage output sequence from the first stage quantizing circuit and outputs a first stage scaled version of the first stage output sequence. The output of the first stage gain component 1220 is combined with the first stage error signal and input to the first stage filter. The filtered output signal from the first stage filter comprises the feedback signal for the first stage of the DS-MASH1 1 1 modulator 1300.

[0089] The second stage 1200b receives the error signal from the first stage 1200a and the second stage feedback signal and operates similarly to the first stage 1200a. Likewise, the third stage 1200c receives the error signal from the second stage 1200b and the third stage feedback signal and operates similarly to the first stage 1200a. [0090] The summing circuit 1302 comprises a first summing circuit 1304, a second summing circuit 1308, a third summing circuit 1308, a first filter 1310, and a second filter 1312. The second filter 1312 filters the third stage quantized output. The third summing circuit 1308 combines the third stage quantized output signal, the filtered version of the third stage quantized output signal, and the second stage quantized output signal to produce a first combined signal. The first filter 1310 filters the first combined signal. The second summing circuit 1308 combines the first combined signal, the filtered version of the first combined signal, and the first stage quantized output signal to produce a second combined signal. The first summing circuit 1304 combines the second combined signal and an output of a divider circuit from the PLL feedback loop comprising the DS-MASH1 1 1 modulator 1300.

[0091] Beginning with the 1 st order DS-EF 1 1200 from Figure 12, the mathematical derivation of the Signal and Noise Transfer Functions of the DS- ASH1 1 1 1300 are:

V[n] = X[n] + S _Q [n - l] (13) S ₀ [n] = -E[n] + g. Y[n] (14) M. Y[n] = V[n] + E[n] (15) V[n] = X[n] + g. Y[n - 1] - E[n - 1] (16)

Substituting equation 18 in equation 15,

M. Y\n] - g. Y\n - 1] = X\n] - E\n E[n] (17)

Using a Z-transform

y(z). [M - g. Z ^"1 ] = x(z) + Eq z) - Eq(z). Z ^"1 (18)

1 1 1 - Z ^-1 g Eq(z)

Assuming that the quantization noise on each DS-EFM1 1200 is additive, the 3 ^rd order DS- ASH1 1 1 output can be written as: The 3 ^rd order DS-MASH Signal Transfer Function and Noise Transfer Function are:

l (l - z- ¹ ) ³

^STF = M. (l - ^- ⁱ ) ^{& NTF} = (ϊ^ϊ) W

Setting 5 = 0, the 3 ^rd orde DS-MASH Signal Transfer Function and Noise Transfer Function become:

STF =— & NTF = (l - Z- ⁱ y (23) M

Referring to equations 12 and 23, the DS-MASH1 1 1 1300 behaves similar to the DS-EFM3 800 of Figure 8.

[0092] Figure 14 plot 1400 of the FFT of the output code sequences of an embodiment of the DS-MASH1 1 1 1300. Referring to Figures 9 and 14, the simulated noise output performance for the DS-MASH1 1 1 1300 is approximately the same as the simulated noise performance (curve 910) for the DS-EF 3 800. Zero Static Frequency Error

[0093] Referring to equations 1 1 and 22, the architecture of the Dither- less Seed-less Error Feedback Modulator (DS-EFM) and the Dither-iess Seedless MASH modulator (DS-MASH) provide a very small static error. This error may be insignificant. However, to provide approximately zero static frequency error, embodiments of the DS-EFM and the DS-MASH can be modified to cancel the gain g every other clock cycle.

[0094] Figure 15 illustrates an embodiment of a 3 ^rd order Dither-less Seed-less Error Feedback Modulator (DS-EFM3) 1500 with approximately zero static error. The zero static error DS-EFM3 1500 comprises the DS-EFM3 800 of Figure 8 and an additional feedback loop 1502. The feedback loop 1502 comprises a filter 1504 receiving a scaled output from the gain component 820 and outputting a filtered gain signal to the summing circuit 822 in the 3 ^rd order feedback loop 812.

[0095] Figure 16 illustrates an embodiment of a Dither-iess Seed-less MASH architecture modulator (DS-MASH1 1 1 ) 1600 with approximately zero static error. The DS-MASH1 1 1 comprises three cascaded 1 ^st order DS-EFM1 modulators 1804a, 1604b, 1604c, each comprising an additional feedback loop comprising a filter 1606a, 1606b, 1606c, respectively, configured to reduce the static error. The zero static error DS-MASH1 1 1 1800 further comprises a summing circuit 1802, The summing circuit 1602 is similar to the summing circuit 1302 in Figure 13 and operates as described above with respect to the summing circuit 1302. The DS-EFM1 modulators 1604a, 1604b, 1604c operate similarly to the DS-EFM3 modulator 1500 in Figure 15 as described above, taking into account that the DS-EF 1 modulators 1804a, 1804b, 1804c are first order modulators and the DS-EFM3 modulator 1500 is a third order modulator.

[0096] Referring to Figures 15 and 16, the filtering of the gain g averages out the error to approximately zero and forces the signal transfer function to approximately unity, providing approximately absolute zero static error. The effect of the periodic gain cancellation in both the zero static error DS- EF 3 1500 and the zero static error DS- ASH1 1 1 1600 modulators is mathematically shown:

Setting δ = 0 in equations 1 1 and 22, the Signal Transfer Function and the Noise Transfer Function become, as described above:

l (l - z- ¹ ) ³

STF =— & NTF = — (12 & 23)

M M

For simplicity, if written in terms of clock cycles, equation 5 can be written as:

At cycle 1 ==> M. y[n] - g. y[n - 1] = x[n] - E[n - 3] + 3E[n - 2] - 3E[n - 1] + E[n]

At cycle 2 ==> M. y [n - 1] + g. y [n - 2]

= x[n - 1] - E[n - 4] + 3E[n - 3] - 3E[n - 2] + E[n - 1] (24)

Add and then divide by 2 for the mean ove two cycles in this example. The Z- transform representation is:

Y[z] = X[z] + E _q z). (1 - 3Z ^"1 + 3Z ^~2 - Z ^~3 ) (25)

The Signal and Noise Transfer Functions over the two cycles are then given by:

1

STF =— & NTF = (1 - ^-1 ) ³ (26) M

[0097] Equation 26 shows that the Signal Transfer Function is unity over time. This provides approximately zero static frequency error.

[0098] Embodiments of the Dither-less and Seed-less EFMs and MASHs with and without zero frequency error can be implemented on other high order loop modulators and hence are not restricted to 1 ^st order or 3 ^rd order modulators,

[0099] The present disclosure describes various features, no single one of which is solely responsible for the benefits described herein. It will be understood that various features described herein may be combined, modified, or omitted, as would be apparent to one of ordinary skill. Other combinations and sub-combinations than those specifically described herein will be apparent to one of ordinary skill, and are intended to form a part of this disclosure. Various methods are described herein in connection with various flowchart steps and/or phases, it will be understood that in many cases, certain steps and/or phases may be combined together such that multiple steps and/or phases shown in the flowcharts can be performed as a single step and/or phase. Also, certain steps and/or phases can be broken into additional sub-components to be performed separately. In some instances, the order of the steps and/or phases can be rearranged and certain steps and/or phases may be omitted entirely. Also, the methods described herein are to be understood to be open-ended, such that additional steps and/or phases to those shown and described herein can also be performed.

[0100] Some aspects of the systems and methods described herein can advantageously be implemented using, fo example, computer software, hardware, firmware, or any combination of computer software, hardware, and firmware. Computer software can comprise computer executable code stored in a computer readable medium (e.g., non-transitory computer readable medium) that, when executed, performs the functions described herein. In some embodiments, computer-executable code is executed by one or more general- purpose computer processors. A skilled artisan will appreciate, in light of this disclosure, that any feature or function that can be implemented using software to be executed on a general purpose computer can also be implemented using a different combination of hardware, software, or firmware. For example, such a module can be implemented completely in hardware using a combination of integrated circuits. Alternatively or additionally, such a feature or function can be implemented completely or partially using specialized computers designed to perform the particular functions described herein rather than by general purpose computers. [0101] Multiple distributed computing devices can be substituted for any one computing device described herein. In such distributed embodiments, the functions of the one computing device are distributed (e.g., over a network) such that some functions are performed on each of the distributed computing devices.

[0102] Some embodiments may be described with reference to equations, algorithms, and/or flowchart illustrations. These methods may be implemented using computer program instructions executable on one or more computers. These methods may also be implemented as computer program products either separately, or as a component of an apparatus or system. In this regard, each equation, algorithm, block, or step of a flowchart, and combinations thereof, may be implemented by hardware, firmware, and/or software including one or more computer program instructions embodied in computer-readable program code logic. As will be appreciated, any such computer program instructions may be loaded onto one or more computers, including without limitation a general purpose computer or special purpose computer, or other programmable processing apparatus to produce a machine, such that the computer program instructions which execute on the computer(s) or other programmable processing device(s) implement the functions specified in the equations, algorithms, and/or flowcharts. It will also be understood that each equation, algorithm, and/or block in flowchart illustrations, and combinations thereof, may be implemented by special purpose hardware-based computer systems that perform the specified functions or steps, or combinations of special purpose hardware and computer-readable program code logic means.

[0103] Furthermore, computer program instructions, such as embodied in computer-readable program code logic, may also be stored in a computer readable memory (e.g., a non-transitory computer readable medium) that can direct one or more computers or other programmable processing devices to function in a particular manner, such that the instructions stored in the computer- readable memory implement the function(s) specified in the block(s) of the flowchart(s). The computer program instructions may also be loaded onto one or more computers or other programmable computing devices to cause a series of operational steps to be performed on the one or more computers o other programmable computing devices to produce a computer-Implemented process such that the Instructions which execute on the computer or other programmable processing apparatus provide steps for implementing the functions specified in the equation(s), algorithm(s), and/or block(s) of the flowchart(s).

[0104] Some or all of the methods and tasks described herein may be performed and fully automated by a computer system. The computer system may, in some cases, include multiple distinct computers or computing devices (e.g., physical servers, workstations, storage arrays, etc.) that communicate and interoperate over a network to perform the described functions. Each such computing device typically includes a processor (or multiple processors} that executes program instructions or modules stored in a memory or other non- transitory computer-readable storage medium or device. The various functions disclosed herein may be embodied in such program instructions, although some or all of the disclosed functions may alternatively be implemented in application- specific circuitry (e.g., ASICs or FPGAs) of the computer system. Where the computer system includes multiple computing devices, these devices may, but need not, be co-located. The results of the disclosed methods and tasks may be persistently stored by transforming physical storage devices, such as solid-state memory chips and/or magnetic disks, into a different state.

[0105] Unless the context clearly requires otherwise, throughout the description and the claims, the words "comprise," "comprising," and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of Including, but not limited to." The word "coupled", as generally used herein, refers to two or more elements that may be either directly connected, or connected by way of one or more intermediate elements. Additionally, the words "herein," "above," "below," and words of similar import, when used in this application, shall refer to this application as a whole and not to any particular portions of this application. Where the context permits, words in the above Detailed Description using the singular or plural number may also include the plural or singular number respectively. The word "or" in reference to a list of two or more items, that word covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list. The word "exemplary" is used exclusively herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations,

[0108] The disclosure is not intended to be limited to the implementations shown herein. Various modifications to the implementations described in this disclosure may be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other implementations without departing from the spirit or scope of this disclosure. The teachings of the invention provided herein can be applied to other methods and systems, and are not limited to the methods and systems described above, and elements and acts of the various embodiments described above can be combined to provide further embodiments. Accordingly, the novel methods and systems described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions, and changes in the form of the methods and systems described herein may be made without departing from the spirit of the disclosure. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the disclosure.