Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M3/00—Conversion of analogue values to or from differential modulation
  • H03M3/30—Delta-sigma modulation
  • H03M3/322—Continuously compensating for, or preventing, undesired influence of physical parameters
  • H03M3/368—Continuously compensating for, or preventing, undesired influence of physical parameters of noise other than the quantisation noise already being shaped inherently by delta-sigma modulators
  • H03M3/37—Compensation or reduction of delay or phase error
  • H03M3/374—Relaxation of settling time constraints, e.g. slew rate enhancement
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M3/00—Conversion of analogue values to or from differential modulation
  • H03M3/30—Delta-sigma modulation
  • H03M3/39—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators
  • H03M3/436—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators characterised by the order of the loop filter, e.g. error feedback type
  • H03M3/438—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators characterised by the order of the loop filter, e.g. error feedback type the modulator having a higher order loop filter in the feedforward path
  • H03M3/454—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators characterised by the order of the loop filter, e.g. error feedback type the modulator having a higher order loop filter in the feedforward path with distributed feedback, i.e. with feedback paths from the quantiser output to more than one filter stage

Definitions

• Embodiments of the subject matter described herein relate generally to mixed- signal circuits, and more particularly, embodiments of the subject matter relate to continuous- time sigma-delta modulators.
• ADCs analog-to-digital converters
• sigma-delta modulation (or alternatively, delta-sigma modulation) is used to reduce the effect of quantization error and improve signal-to-noise ratio (SNR).
• Sigma-delta modulation (alternatively referred to as delta-sigma modulation) adds or subtracts quantization error to a forward signal path using feedback loops and integrator circuits. The quantization error is oversampled at a frequency greater than the analog input signal frequency, thereby allowing it to be filtered at the integrators without noticeably impacting the signal.
• Many systems utilize continuous-time sigma-delta modulators, that is, sigma-delta modulators constructed using continuous-time circuitry.
• Continuous-time sigma-delta modulators can be clocked at higher sampling frequencies which improves the performance of the sigma-delta modulator.
• high-speed sigma-delta modulators generally sigma-delta modulators with sampling frequencies in the MHz range or higher
• exhibit delay referred to as excess loop delay, which can lead to instability and degrade performance (e.g., SNR) of the modulator.
• the loop delay results from, for example, the nonzero switching time of transistors and/or comparators utilized in the quantizer and/or digital-to-analog converter (DAC).
• DAC digital-to-analog converter
• the loop delay is further compounded by other factors, such as, for example, metastability in the comparators (or other components) and/or dynamic element matching. While the loop delay may be reduced with improvements to the hardware and/or electrical components, such improvements generally come at the cost of increased power consumption and larger area requirements, both of which are undesirable.
• the sigma-delta modulator may compensate for loop delay by adjusting the gain coefficients in the main feedback path.
• RZ return-to-zero
• NRZ no-return-to-zero
• some systems utilize digital differentiation to move the additional feedback path from the input of the quantizer to the input of the integrator that precedes the quantizer. While this eliminates the analog summer and reduces the voltage swing at the output of the integrator, the digital differentiation results in a bipolar RZ pulse at the input of the integrator. This causes the output of the integrator to move in the wrong direction during the first half of the clock period before switching direction in the second half of the clock period, resulting in a large slew rate requirement for the integrator. To satisfy the slew rate requirement, the integrator consumes additional power and area, which offsets the power and area saving from eliminating the analog summer.
• Other systems utilize proportional-integral (PI) compensation or other techniques which degrade the frequency response of the integrator and may lead to out-of-band peaking and other undesirable effects.
• PI proportional-integral
• FIG. 1 is a block diagram of a sigma-delta modulator in accordance with one embodiment
• FIG. 2 is a block diagram of a sigma-delta modulator in accordance with another embodiment.
• FIG. 3 is a block diagram of a sigma-delta modulator in accordance with yet another embodiment.
• a "node” means any internal or external reference point, connection point, junction, signal line, conductive element, or the like, at which a given signal, logic level, voltage, data pattern, current, or quantity is present.
• two or more nodes may be realized by one physical element (and two or more signals can be multiplexed, modulated, or otherwise distinguished even though received or output at a common mode).
• the following description refers to elements or nodes or features being “connected” or “coupled” together.
• “connected” means that one element/node/feature is directly joined to (or directly communicates with) another element/node/feature, and not necessarily mechanically.
• “coupled” means that one element is directly or indirectly joined to (or directly or indirectly communicates with) another element, and not necessarily mechanically.
• a compensation feedback path is implemented with a different delay than the delay in the main feedback path, and the delay in the compensation feedback path is independent of the delay in the main feedback path.
• the compensation feedback path may each be implemented using non-return-to-zero (NRZ) digital-to-analog converters (DACs), and the gain coefficients of the DACs and the delay in the compensation feedback path may be adjusted to relax slew-rate requirements for analog components and eliminate the need for a high-speed analog summing junction (or analog summer) before the input of the quantizer.
• NRZ non-return-to-zero
• DACs digital-to-analog converters
• FIG. 1 depicts an exemplary embodiment of a sigma-delta modulator 100 suitable for use in an analog-to-digital converter (ADC) or another analog-to-digital conversion application.
• the sigma-delta modulator 100 is realized as a continuous-time sigma-delta modulator comprising suitably configured continuous-time circuitry.
• the sigma-delta modulator 100 may include, without limitation, an input node 102 for receiving an input signal, a forward signal arrangement 104 configured to establish a forward signal path, a quantizer 106, a main feedback arrangement 108 configured to establish a main feedback signal path, a compensation feedback arrangement 110 configured to establish a compensation feedback signal path, and a digital output 112.
• FIG. 1 is a simplified diagram of the sigma-delta modulator 100 depicted in single-ended form, and practical embodiments of the sigma-delta modulator 100 may include additional or alternative components, and/or be implemented in a differential manner (e.g., as a differential circuit adapted for differential input signals).
• the sigma-delta modulator 100 may be configured for single-bit operation or multi-bit operation, depending on the particular needs of a given application. It should also be understood that FIG.
• FIG. 1 depicts a second-order feedback sigma-delta modulator 100 for purposes of explanation, and the subject matter described herein is not intended to be limited to any particular sigma-delta topology.
• the subject matter can be adapted for a forward signal arrangement 104 having any order, and may be implemented using any suitable sigma- delta topology, as will be appreciated in the art.
• the input node 102 is coupled to the forward signal arrangement 104 which, in turn, is coupled to the analog input 114 of the quantizer 106.
• the quantizer 106 converts an analog signal at the quantizer input 114 to a digital value at the quantizer output 116 which, in turn, is coupled to the digital output 112.
• the main feedback arrangement 108 (or main feedback path) comprises a combination of functional, hardware, and/or logical elements coupled between the digital output 112 and the forward signal arrangement 104, wherein the main feedback arrangement 108 defines a feedback signal path for one or more main feedback signals, as described in greater detail below.
• the main feedback arrangement 108 is configured to delay the digital value at the digital output 112 by a first delay period (t d ) and generate one or more main feedback signals based on the delayed value. It should be noted that the main feedback arrangement 108 provides at least a first main feedback signal at the input of the sigma-delta modulator 100, that is, the main feedback arrangement 108 includes at least one feedback path coupled to the input node 102 as described below.
• the compensation feedback arrangement 110 (or compensation feedback path) comprises a combination of functional, hardware, and/or logical elements coupled between the digital output 112 and the forward signal arrangement 104, wherein the compensation feedback arrangement 110 defines a feedback signal path for one or more compensation feedback signals.
• the compensation feedback path 110 is configured to delay the digital value at the digital output 112 by a second delay period (t c ) and generate one or more compensation feedback signals based on the delayed value.
• the forward signal arrangement 104 (or forward signal path) comprises a combination of functional, hardware, and/or logical elements which are suitably configured to produce the analog signal at the quantizer input 114 based on the input signal at the input node 102, the main feedback signals from the main feedback arrangement 108, and the compensation feedback signals from the compensation feedback arrangement 110.
• the first delay period ( t d ) represents an intentional delay inserted into the main feedback arrangement 108 to compensate for the loop delay caused by the analog components of the sigma-delta modulator 100.
• the second delay period (t c ) represents a delay used to create compensation feedback signals that compensate for the difference between the value of the first delay period and the actual loop delay exhibited by the analog components of the sigma-delta modulator 100.
• the forward signal path 104 may be realized with any order and using any suitable sigma-delta circuit topology, such as, for example, a lowpass topology, a bandpass topology, a highpass topology, a feedback topology, a feedforward topology, a feedforward-feedback topology or another hybrid topology, a cascade topology, a quadrature or complex topology, and the like.
• the forward signal path 104 is realized as a second-order sigma-delta feedback topology including, without limitation, a first summing junction 118, a first integrator 120, a second summing junction 122, and a second integrator 124.
• the first summing junction 118 is coupled between the input node 102 and the input of the first integrator 120.
• the second summing junction 122 is coupled between the output of the first integrator 120 and the input of the second integrator 124.
• the output of the second integrator 124 is connected to the quantizer input 114 and the second integrator 124 produces an analog signal at the quantizer input 114.
• the quantizer 106 is configured to generate a digital value at the quantizer output 116 that comprises one or more bits which are representative of the analog signal (or analog voltage level) at the quantizer input 114.
• the quantizer 106 generates the digital value at by sampling the analog signal at the quantizer input 114 with a particular sampling frequency (f s ). For example, a continuous-time sigma-delta modulator
• the sampling frequency of the quantizer 106 ranges from about 200 MHz to about 400 MHz or more.
• the sampling frequency of the quantizer 106 will vary depending on the needs of a particular application (e.g., the desired effective number of bits).
• the sampling period or sampling interval e.g., the time between samples
• the quantizer 106 may utilize a flash analog-to-digital conversion architecture or another suitable conversion architecture, and may be configured for any number of output bits or any noise shaping.
• the main feedback path 108 includes a main feedback delay element 126 and at least one digital-to-analog converter (DAC) 128, 130.
• DAC digital-to-analog converter
• the input of the main feedback delay element 126 is connected to the digital output 112 (or quantizer output 116) and the main feedback delay element 126 is configured to delay the digital value at the digital output 112 by the first delay period (t d ).
• the first delay period represents an intentional delay inserted into the main feedback path 108 which is intended to compensate for the loop delay of the sigma-delta modulator 100 (e.g., the delays introduced by the forward signal path 104, the quantizer 106, and/or DACs 128, 130).
• the first delay period may be any arbitrary time period between zero and length of one sampling period (e.g., ).
• the first delay period is intended to absorb the loop delay of the sigma-delta modulator 100, that is, the value of the first delay period is greater than or equal to the actual delay associated with the analog components of the modulator 100.
• the main feedback delay element 126 is realized as a digital delay element, such as, for example, a flip-flop, a latch, and the like). Various implementation aspects of delaying a signal are well known, and as such, will not be described in detail herein.
• the main feedback DACs 128, 130 are each realized as a NRZ DAC that uses a NRZ pulse scheme to generate the respective feedback signal, such that the respective feedback signal generated by the DAC 128, 130 is substantially constant (e.g., within practical and/or realistic operating tolerances) for the duration of the sampling period. It should be noted, however, that in alternative embodiments, the main feedback DACs 128, 130 may be realized using return-to-zero (RZ) DACs or DACs having non-square or non-rectangular waveforms (e.g., DACs with a damping exponential waveform).
• RZ return-to-zero
• the first DAC 128 has a digital input connected to the output of the main feedback delay element 126 and an analog output coupled to the input node 102, that is, the input of the sigma-delta modulator 100.
• the analog output of the first DAC 128 is connected to the first summing junction 118.
• the first DAC 128 generates a first main feedback signal at the input of the sigma-delta modulator 100 (e.g., at the first summing junction 118) by converting the digital value at the output of the main feedback delay element 126 (e.g., the digital value at the digital output 112 which has been delayed by the first delay period) into an analog signal with a first gain coefficient ( ⁇ 1 ).
• the second DAC 130 has a digital input connected to the output of the main feedback delay element 126 and an analog output connected to the second summing junction 122.
• the second DAC 130 generates a second main feedback signal at the second summing junction 122 by converting the digital value at the output of the main feedback delay element 126 into an analog signal with a second gain coefficient (a 2 ).
• the compensation feedback path 110 includes a compensation feedback delay element 132 and at least one DAC 134, 136.
• the input of the compensation feedback delay element 132 is connected to the digital output 112 (or quantizer output 116) and the compensation feedback delay element 132 is configured to delay the digital value at the digital output 112 by the second delay period (t c ).
• the second delay period represents a delay inserted into the compensation feedback path 110 which is intended to compensate for the effect of the excess loop delay resulting from the first delay period.
• the length of time of the second delay period may be chosen to be any arbitrary time period between zero and length of one sampling period (e.g., where f s is the sampling frequency).
• the second delay period is preferably chosen to be greater than the excess loop delay, and is different than the first delay period, as described in greater detail below.
• the compensation feedback delay element 132 is preferably realized as a digital delay element as described above in the context of main feedback delay element 126.
• the first DAC 134 of the compensation feedback path 110 has a digital input connected to the output of the compensation feedback delay element 132 and an analog output connected to the first summing junction 118.
• the first DAC 134 generates a first compensation feedback signal at the first summing junction 118 by converting the digital value at the output of the compensation feedback delay element 132 (e.g., the digital value at the digital output 112 which has been delayed by the second delay period) into an analog signal with a third gain coefficient (b ⁇ ).
• the second DAC 136 of the compensation feedback path 110 has a digital input connected to the output of the compensation feedback delay element 132 and an analog output connected to the second summing junction 122, wherein the second DAC 136 generates a second compensation feedback signal at the second summing junction 122 by converting the digital value at the output of the compensation feedback delay element 132 into an analog signal with a fourth gain coefficient (b 2 ).
• the compensation DACs 134, 136 are realized as NRZ DACs, although in alternative embodiments, the compensation DACs 134, 136 may be realized as return-to-zero (RZ) DACs, as described in greater detail below.
• the compensation DACs 134, 136 may also be realized using DACs having non-square or non-rectangular waveforms (e.g., DACs with a damping exponential waveform).
• the first summing junction 118 is configured to subtract the first main feedback signal (from DAC 128) and the first compensation feedback signal (from DAC 134) from the input signal at the input node 102 and provide the result to input of the first integrator 120.
• the first integrator 120 integrates the resultant signal at the first summing junction 118 in a conventional manner, as will be appreciated in the art.
• the second summing junction 122 is configured to subtract the second main feedback signal (from DAC 130) and the second compensation feedback signal (from DAC 136) from the output of the first integrator 120 and provide the result to the second integrator 124.
• the second integrator 124 integrates the resultant signal at the second summing junction 122 to produce the analog signal at the quantizer input 114.
• each integrator 120, 124 may be realized using active circuitry components, passive circuitry components, or a suitable combination thereof.
• the analog signal at the quantizer input 114 is based on the input signal, the main feedback signals, and the compensation feedback signals.
• FIG. 1 depicts multiple DACs 134, 136 in the compensation feedback path 110 for producing multiple compensation feedback signals, in practice, only a single compensation feedback signal is needed to compensate for the intentional delay (t d ) inserted in the main feedback path 108, as described in greater detail below. However, the use of additional compensation feedback signals as shown in FIG.
• the second delay period is structurally independent of the first delay period, that is, the second delay period is not influenced by the first delay period and the first delay period is not influenced by the second delay period.
• the delay elements 126, 132 are in distinct feedback paths and are not cascaded (or non-cascaded) or otherwise interconnected, for example, the output of one delay element does not feed the input of another.
• the first delay period and the second delay period are uncorrelated as the second delay period is not influenced or affected by the components and/or embedded delays in the main feedback path 108 and the first delay period is not influenced or affected by the components and/or embedded delays in the compensation feedback path 110.
• the first delay period and the second delay period are not equal.
• the value of the second delay period is not chosen to be equal to the first delay period or vice versa.
• the first delay period and the second delay period are each chosen to be a value greater than the actual loop delay of the analog components of the modulator 100.
• the second delay period may be less than the first delay period or greater than the first delay period, as described in greater detail below.
• FIG. 2 depicts a sigma-delta modulator 200 in accordance with another embodiment.
• the sigma-delta modulator 200 is realized as a continuous-time sigma-delta modulator including, without limitation, an input node 202 for receiving an input signal, a forward signal arrangement 204 (or forward signal path), a quantizer 206, a main feedback arrangement 208 (or main feedback path), a compensation feedback arrangement 210 (or compensation feedback path), and a digital output 212.
• the elements of the sigma-delta modulator 200 are similar to counterpart elements discussed above in the context of sigma- delta modulator 100 of FIG. 1, and as such, these common elements will not be redundantly described in detail here in the context of FIG. 2. In the illustrated embodiment of FIG.
• FIG. 3 depicts a sigma-delta modulator 300 in accordance with another embodiment.
• the sigma-delta modulator 300 is realized as a continuous-time sigma-delta modulator having a feedforward topology.
• the sigma-delta modulator 300 includes, without limitation, an input node 302 for receiving an input signal, a forward signal arrangement 304 (or forward signal path), a quantizer 306, a main feedback arrangement 308 (or main feedback path), a compensation feedback arrangement 310 (or compensation feedback path), and a digital output 312.
• Various elements of the sigma-delta modulator 300 are similar to counterpart elements discussed above in the context of sigma-delta modulator 100 of FIG. 1, and as such, these common elements will not be redundantly described in detail here in the context of FIG. 3.
• the forward signal path 304 is realized as a feedforward sigma-delta topology including, without limitation, a first summing junction 318, a first integrator 320, a second summing junction 322, a second integrator 324, an amplifier 338, and a third summing junction 340.
• the first summing junction 318 is connected between the input node 302 and the input of the first integrator 320.
• the first summing junction 318 is configured to subtract the main feedback signal (from DAC 328) from the input signal at the input node 302 and provide the result to input of the first integrator 320 which integrates the resultant signal at the first summing junction 318 in a conventional manner.
• the second summing junction 322 is connected between the output of the first integrator 320 and the input of the second integrator 324.
• the second summing junction 122 is configured to subtract the compensation feedback signal (from DAC 336) from the output of the first integrator 320 and provide the result to the input of the second integrator 324.
• the output of the first integrator 320 is also connected to an input of the amplifier 338, and the output of the amplifier 338 is connected to the third summing junction 340.
• the amplifier 338 amplifies the output of the first integrator 320 by a gain factor (q ) and provides the result to the third summing junction 340.
• the output of the second integrator 324 is also connected to the third summing junction 340.
• the third summing junction 340 is configured to add the output of the second integrator 324 and the amplified output of the first integrator 320 (e.g., via amplifier 338) to produce the analog signal at the quantizer input 314.
• the analog signal at the quantizer input 314 is based on the input signal, the main feedback signal, and the compensation feedback signal.
• an NRZ DAC 336 there are smaller voltage variations at the input of the second integrator 324, and as a result, the slew rate requirement for the second integrator 324 is relaxed compared to an integrator with a bipolar RZ feedback pulse at its input.
• the third summing junction 340 is realized as a summing amplifier (or analog summer)
• the speed requirement e.g., the gain-bandwidth for small-signal implementations, slew-rate for large-signal implementations
• the speed requirement of the summing amplifier is relaxed by virtue of only two signals being present at the third summing junction 340.
• the sigma-delta modulator 100, 200, 300 may achieve any desired noise transfer function using NRZ compensation feedback signals. Furthermore, it should be noted that any desired noise transfer function may be achieved using only a single DAC in the compensation feedback path.
• the second delay period e.g., t c or ⁇
• the first delay period may be less than the first delay period
• the first delay period may be chosen to be equal to one sample
• the second delay period may be chosen to be equal
• the sigma-delta modulator 200 may provide the desired noise transfer function with a single compensation feedback signal (i.e., only a single DAC 236 in the compensation feedback path 210).
• the delay periods in the feedback paths may be adjusted by an offset delay, with the offset delay being allocated to analog components in the forward signal path and/or quantizer.
• the offset delay represents a settling time margin which may be allocated to the analog components, thereby allowing them to be designed for a lower speed to save power.
• the delay periods of the feedback paths 208, 210 may adjusted by an offset delay of a quarter sample (or ), which has been identified as the optimal
• the offset delay is then allocated to analog components in the forward signal path 204 and/or quantizer 206, such as, for example, the integrators 220, 224 or preamplifiers within the quantizer 206.
• the second delay period may be greater than the first delay period. For example, referring again to FIG.
• the sigma- delta modulator may also achieve a desired noise transfer function using NRZ main feedback signals with a single RZ compensation feedback signal.
• the compensation feedback DAC 236 may be realized as a RZ DAC that uses a RZ pulse scheme to generate the compensation feedback signal, such that the compensation feedback signal generated by the DAC 236 is substantially constant (e.g., within practical and/or realistic operating tolerances) for the duration of one half of the sampling period.
• the use of the RZ compensation feedback signal results in increased voltage steps at the input of the integrator 224 relative to the voltage steps experienced when a NRZ compensation feedback signal is used.
• NRZ feedback signals may be used to compensate for excess loop delay resulting from the intentional delay inserted in the main feedback loop for a sigma-delta modulator.
• the NRZ feedback signals may be implemented in a manner that provides multiple degrees of freedom, which may be utilized to vary the delay and/or gain coefficients for the main feedback signals and the compensation feedback signals to relax slew-rate requirements for integrators and/or amplifiers or eliminate the need for a high-speed analog summing junction (or analog summer).
• the area, power, cost and design time of the sigma-delta modulator are reduced without sacrificing the performance of the modulator.
• the sigma-delta modulator comprises an input node for receiving an input signal and a quantizer configured to convert a first analog signal to a digital value.
• a main feedback arrangement is coupled to the quantizer and is configured to delay the digital value by a first delay period to obtain a first delayed value and generate a main feedback signal based on the first delayed value.
• a compensation feedback arrangement is coupled to the quantizer and configured to delay the digital value by a second delay period to obtain a second delayed value and generate a compensation feedback signal based on the second delayed value.
• a forward signal arrangement is coupled between the input node and the quantizer, the forward signal arrangement being coupled to the main feedback arrangement and the compensation feedback arrangement.
• the forward signal arrangement produces the first analog signal at the quantizer based on the input signal, the main feedback signal, and the compensation feedback signal.
• the second delay period is not influenced by the first delay period and the compensation feedback signal compensates for the first delay period.
• the compensation feedback arrangement comprises a non-return-to-zero digital-to-analog converter configured to generate the compensation feedback signal.
• the compensation feedback arrangement comprises a return-to-zero digital-to-analog converter configured to generate the compensation feedback signal.
• the second delay period is not equal to the first delay period.
• the main feedback arrangement comprises a first non-return-to-zero digital-to-analog converter configured to generate the main feedback signal and the compensation feedback arrangement comprises a second non-return-to-zero digital-to-analog converter configured to generate the compensation feedback signal.
• the main feedback arrangement generates the main feedback signal with a first gain and the compensation feedback arrangement generates the compensation feedback signal with a second gain, wherein the magnitude of the second gain is not equal to the magnitude of the first gain.
• the main feedback arrangement comprises a non-return-to-zero digital-to-analog converter configured to generate the main feedback signal and the compensation feedback arrangement comprises a return-to-zero digital-to-analog converter configured to generate the compensation feedback signal.
• the forward signal arrangement comprises a circuit topology selected from a group consisting of a lowpass topology, a bandpass topology, a highpass topology, a feedback topology, a feedforward topology, a mixed feedforward-feedback topology, a cascade topology, a quadrature topology, and a complex topology.
• an apparatus for an analog-to-digital converter comprises an input node for receiving an input signal and a quantizer configured to convert a first analog signal to a digital value.
• a forward signal path is coupled between the input node and the quantizer.
• a first delay element is coupled to the quantizer, and the first delay element is configured to delay the digital value by a first delay period resulting in a first delayed value.
• a first digital-to-analog converter is coupled between the first delay element and the forward signal path, and the first digital-to-analog converter generates a first feedback signal based on the first delayed value.
• a second delay element is coupled to the quantizer, and the second delay element is configured to delay the digital value by a second delay period resulting in a second delayed value.
• the first delay element and the second delay element are non-cascaded, such that the first delay period and the second delay period are uncorrelated.
• a second digital-to-analog converter is coupled between the second delay element and the forward signal path, and the second digital-to-analog converter generates a second feedback signal based on the second delayed value.
• the forward signal path produces the first analog signal at the quantizer based on the input signal, the first feedback signal, and the second feedback signal, such that the second feedback signal compensates for the first delay period.
• the first digital-to-analog converter generates the first feedback signal with a first gain and the second digital-to-analog converter generates the second feedback signal with a second gain, wherein the second gain is not equal to the first gain.
• the second digital-to-analog converter comprises a non-return-to-zero digital-to-analog converter.
• the second digital-to-analog converter comprises a return-to-zero digital-to-analog converter.
• the second delay period is less than the first delay period. In accordance with yet another embodiment, the second delay period is greater than the first delay period.
• the forward signal path comprises a circuit topology selected from a group consisting of a lowpass topology, a bandpass topology, a highpass topology, a feedback topology, a feedforward topology, and a mixed feedforward-feedback topology.
• an apparatus for a sigma-delta modulator comprises an input node for receiving an input signal and first integrator having a first input coupled to the input node and a first output.
• a quantizer has a quantizer input coupled to the first output, wherein the quantizer is configured to convert a first analog signal at the quantizer input to a digital value at a quantizer output.
• a first delay element is coupled to the quantizer output, and the first delay element is configured to delay the digital value by a first delay period resulting in a first delayed value.
• a first digital-to- analog converter is coupled between the first delay element and the first input, and the first digital-to-analog converter converts the first delayed value to a first analog value at the first input.
• a second delay element is coupled to the quantizer output, and the second delay element is configured to delay the digital value by a second delay period resulting in a second delayed value. The second delay period is not equal to the first delay period and the second delay period is independent of the first delay period.
• a second digital-to-analog converter is coupled between the second delay element and the first input, and the second digital-to- analog converter converts the second delayed value to a second analog value at the first input.
• the sigma-delta modulator further comprises a second integrator coupled between the input node and the first integrator.
• the second integrator has a second input coupled to the input node and a second output coupled to the first input.
• a third digital-to-analog converter is coupled between the first delay element and the second input, and the third digital-to-analog converter converts the first delayed value to a third analog value at the second input.
• the second delay period is less than the first delay period.
• the quantizer has a sampling period associated therewith, wherein the second delay period is equal to one half of the sampling period and the first delay period is equal to the sampling period.
• the second delay period is equal to one quarter of the sampling period and the first delay period is equal to three quarters of the sampling period.

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