US20110043398A1 - Cascaded dac architecture with pulse width modulation - Google Patents
Cascaded dac architecture with pulse width modulation Download PDFInfo
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- US20110043398A1 US20110043398A1 US12/546,521 US54652109A US2011043398A1 US 20110043398 A1 US20110043398 A1 US 20110043398A1 US 54652109 A US54652109 A US 54652109A US 2011043398 A1 US2011043398 A1 US 2011043398A1
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- 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
- H03M3/50—Digital/analogue converters using delta-sigma modulation as an intermediate step
- H03M3/502—Details of the final digital/analogue conversion following the digital delta-sigma modulation
- H03M3/506—Details of the final digital/analogue conversion following the digital delta-sigma modulation the final digital/analogue converter being constituted by a pulse width modulator
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- 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
- H03M3/412—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators characterised by the number of quantisers and their type and resolution
- H03M3/414—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators characterised by the number of quantisers and their type and resolution having multiple quantisers arranged in cascaded loops, each of the second and further loops processing the quantisation error of the loop preceding it, i.e. multiple stage noise shaping [MASH] type
- H03M3/416—Structural details of delta-sigma modulators, e.g. incremental delta-sigma modulators characterised by the number of quantisers and their type and resolution having multiple quantisers arranged in cascaded loops, each of the second and further loops processing the quantisation error of the loop preceding it, i.e. multiple stage noise shaping [MASH] type all these quantisers being multiple bit quantisers
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- 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
- H03M3/50—Digital/analogue converters using delta-sigma modulation as an intermediate step
- H03M3/502—Details of the final digital/analogue conversion following the digital delta-sigma modulation
- H03M3/504—Details of the final digital/analogue conversion following the digital delta-sigma modulation the final digital/analogue converter being constituted by a finite impulse response [FIR] filter, i.e. FIRDAC
Definitions
- DACs Digital-to-Analog converters
- PDAs Personal Digital Assistant
- cellular phones cellular phones
- computers video players
- CD players Compact Disc Players
- DACs convert a digital signal into an analog signal.
- Analog signals include music and voice.
- noise may be created.
- Noise may be any electrical contribution added to a signal that was not part of the original source that created the signal.
- some sources of noise are thermal noise, phase noise, quantization noise and switching noise.
- the original signal may be distorted. There are many types of distortion such a harmonic distortion, and intermodulation distortion.
- noise-shaping filters shift quantization noise from in-band (typically from 20 Hz to 20,000 Khz, the frequency range of human hearing) to out-of-band quantization noise (typically from 20 KHz and above).
- AFIR Analog Finite Impulse Response filters are used to reduce out-of-band noise (OBN).
- FIG. 1 is a plot of an ideal analog output versus the magnitude of eight 3-bit binary words.
- FIG. 2A is a plot of quantization noise as a function of frequency when using 1-bit Nyquist sampling.
- FIG. 2B is a plot of quantization noise as a function of frequency when using an oversampling rate of f a .
- FIG. 2C is a plot of quantization noise as a function of frequency when first order noise-shaping is used.
- FIG. 3 is a plot of the magnitude of a sample frequency, harmonic distortion, in-band noise and folding noise as a function of frequency when a noise-shaping filter is used.
- FIG. 4 is a plot of the output level of a DAC when switching from a first level to a second level when using a 2-bit binary word.
- FIG. 5 is a schematic showing a digital SDM (Sigma Delta Modulation) filter, a thermometer encoder, and an N-tap AFIR (Analog Finite Impulse Response) Filter DAC (Prior Art).
- a digital SDM Sigma Delta Modulation
- thermometer encoder thermometer encoder
- N-tap AFIR Analog Finite Impulse Response Filter DAC
- FIG. 6 is a plot of attenuation out-of-band noise when using 8-tap and a 16-tap AFIR (Analog Finite Impulse Response) Filter DACs.
- AFIR Analog Finite Impulse Response
- FIG. 7 is an exemplary embodiment of a cascaded circuit which includes a first cascade circuit, a second cascade circuit and a third cascade circuit.
- FIG. 8 is an exemplary embodiment of a PCM (Pulse Code Modulation)-to-PWM (Pulse Width Modulation) converter.
- PCM Pulse Code Modulation
- PWM Pulse Width Modulation
- FIG. 9 is an exemplary embodiment of a 1-bit P-tap AFIR (Analog Finite Impulse Response) Filter DAC.
- AFIR Analog Finite Impulse Response
- FIG. 10 is a plot of spectral density versus frequency when using a 1-bit P-tap AFIR Filter DAC.
- FIG. 11 is a plot of noise versus frequency when using a 1-bit P-tap AFIR Filter DAC.
- FIG. 12 is an exemplary embodiment of a cascaded circuit using at least four cascade circuits.
- the drawings and description disclose one or more cascade circuits that are cascaded together to form a cascaded circuit.
- the cascaded circuit reduces out-of-band quantization noise at an analog output of the cascaded circuit.
- Each of the cascade circuits contain a noise-shaping circuit, a PCM (Pulse Code Modulation)-to-PWM (Pulse Width Modulation) converter and a 1-bit P-tap AFIR (Analog Finite Impulse Response) filter DAC.
- Out-of-band quantization noise at the output of the cascaded circuit may be further reduced by increasing the number of cascade circuits.
- out-of-band quantization noise may be reduced to a level that is at or below the thermal noise level with minimum silicon area.
- the noise-shaping circuit shifts, for example, quantization noise from within the audible range (often called “in-band”, typically 20 Hz to 20 KHz), to a frequency range outside the audible range (often called “out-of-band”, typically 20 KHz and higher).
- the noise-shaping circuit in this example converts PCM M-bit digital words to PCM N-bit digital words where M and N are integers and M is greater than N.
- the sampling frequency of the PCM M-bit digital words and the PCM N-bit digital words, in this example, is Fs.
- the PCM-to-PWM converter converts PCM N-bit digital words sampled at a frequency of Fs to PWM 1-bit words at a frequency of (2 N )*Fs.
- the PWM 1-bit words are then input into the P-tap AFIR filter 1-bit DAC.
- Pulse width modulation reduces sensitivity to to analog glitch energies and an P-tap AFIR filter in each cascade circuit reduces mismatch errors.
- Each tap in each AFIR filter is a small 1-bit DAC and an analog output is formed by summing the outputs of all such 1-bit DACs of the AFIRs in all the cascade circuits.
- FIG. 1 is a plot of an ideal analog output versus the magnitude of eight 3-bit binary words.
- the eight 3-bit binary words, 104 , 106 , 108 , 110 , 112 , 114 , 116 and 118 do not end at line 102 , the ideal analog output.
- INL (Integrated Non-Linear) and DNL (Differential Non-Linear) distortion is created because these eight 3-bit binary words, 104 , 106 , 108 , 110 , 112 , 114 , 116 and 118 do not end at line 102 .
- INL and DNL distortion may be caused by static element mismatch. For example, if current sources used in the DACs are not matched, INL and DNL distortion may occur.
- Pulse width modulation coupled with an N-tap AFIR filter in each cascade circuit reduces sensitivity to analog glitch energies and mismatch errors
- FIG. 2A is a plot of quantization noise as a function of frequency when using N-bit Nyquist sampling.
- the quantization noise in FIG. 2A is contained in the audio band.
- FIG. 2B is a plot of quantization noise as a function of frequency when using an over-sampling rate of Fa.
- the quantization noise in FIG. 2B is spread from DC (0 Hz) to Fa/2.
- quantization noise is reduced in the audio band, improving the signal-to-noise ratio.
- the same quantization noise is “spread thinner” due to over-sampling. However, in this case more quantization noise is found in the out-of-band frequency range.
- the Nyquist case will have more quantization noise due to the images (repetitions of the spectrum) unless a sharp low-pass filter is applied.
- FIG. 2C is a plot of quantization noise as a function of frequency when first order noise-shaping is used.
- most of the quantization noise is removed from the audio band into the out-of-band frequency range. Because most of the quantization noise is removed from the audio band, the signal-to-noise ratio is improved. However, in this case more quantization noise is found out-of-band.
- FIG. 3 is a plot of the magnitude of a sample frequency 302 , harmonic distortion 304 , in-band noise quantization 306 and folding quantization noise 308 as a function of frequency when noise-shaping is used.
- out-of-band quantization noise 312 is folded back into the audible band as folding quantization noise 308 .
- the noise-shaping filter shapes quantization noise as shown by curve 310 .
- FIG. 4 is a plot of the output level of a DAC when switching from a first level to a second level when using a 2-bit binary word.
- the output level switches from level 1 to level 6 for a short time instead of the correct level 2 due to differences in rise and fall times. This “glitch” when switching from level 1 to level 2 causes dynamic distortion and noise.
- the “glitch” shown in FIG. 4 may be reduced using thermometer encoding.
- Table 1 shows an example of thermometer encoding. In this example a 2-bit word is used. Thermometer encoding allows only one bit to switch at any time. Allowing only one bit to switch at any time for a single LSB step change in the input code reduces the number of glitches that is may have occurred.
- thermometer encoding t 3 , t 2 , t 1 , is used as shown in Table 1, only one bit changes at a time. Because only one bit changes at a time, dynamic errors are reduced.
- FIG. 5 shows a digital GDM (Sigma Delta Modulation) modulator 528 , a thermometer encoder 530 , and an N-tap AFIR (Analog Finite Impulse Response) filter DAC 500 .
- the digital SDM 528 shifts quantization noise from the audible range to the out-of-band range and the thermometer encoding 530 reduces INL and DNL distortion.
- the N-tap AFIR filter DAC 500 reduces out-of-band quantization noise and sensitivity to non-linearities and phase noise.
- Matching between M-level DACs, 544 , 546 , 548 is typically not needed because it only affects the filter response. However, matching with an individual M-level DAC is usually necessary.
- M-level rotation, 538 , 540 , 542 is used to create first order noise-shaping. The rotation insures that all M ⁇ 1 segments inside one M-level DAC are used with the same average density/frequency. This causes the INL linear and shifts mismatch induced errors to be out of the audio band. This M-level rotation may be accomplished using barrel (circular) shifters.
- FIG. 6 is a plot of attenuation of out-of-band quantization noise when using an 8-tap and a 16-tap AFIR filter DAC (unit coefficients giving a sinc response).
- An 8-tap AFIR filter DAC 602 attenuates out-of-band quantization noise on average for a white noise signal by 18 db.
- a 16-tap AFIR filter DAC 604 attenuates out-of-band quantization noise on average by 22 db. Neither of these N-tap AFIR filter DACs provides enough stop-band suppression.
- the M-level rotation, 538 , 540 , 542 may create tonal distortion at small signal levels.
- FIG. 7 is an exemplary embodiment of a cascaded circuit 700 including a first cascade circuit 702 , a second cascade circuit 704 and a third cascade circuit 706 .
- a digital signal 742 is input to the cascaded circuit 700 .
- the digital signal 742 is an M-bit PCM digital word received at a frequency of Fs.
- the analog differential output 772 and 774 of the cascaded circuit 700 are connected to the differential input of an amplifier 708 .
- the output 766 of the first cascade circuit 702 is connected to the input 766 of the second cascade circuit 704 .
- Signal 766 is the quantization noise of the noise-shaping circuit 710 .
- Signal 766 is fed into cascade circuit 704 in the digital domain and then subtracted in the analog domain in order or reduce the resulting quantization noise.
- the differential input 754 and 756 of the first cascade circuit 702 is connected to the differential output 754 and 756 of the second cascade circuit 704 .
- the output 768 of the second cascade circuit 704 is connected to the input 768 of the third cascade circuit 706 .
- the differential input 758 and 770 of the second cascade circuit 704 is connected to the differential output 758 and 770 of the third cascade circuit 704 .
- the first cascade circuit 702 comprises a noise-shaping circuit 710 , for example a SDM, a PCM-to PWM converter 716 and a 1-bit P-tap AFIR filter DAC 722 .
- the input 742 of the noise-shaping circuit 710 is summed with the output 744 of the noise-shaping circuit 710 .
- the sum of the input 742 and the output 744 of the noise-shaping circuit is the output 766 of the first cascade circuit 702 .
- the output 744 of the noise-shaping circuit 710 is also connected to the input 744 of the PCM-to-PWM converter 716 .
- the output 744 of the noise-shaping circuit 710 is, in this example, an N-bit PCM word with a sampling frequency of Fs where M is greater than N.
- the differential output Bp 1 and Bm 1 of the PCM-to-PWM converter 716 is connected to the differential input Bp 1 and Bm 1 of the 1-bit P-tap AFIR filter DAC 722 .
- the differential output Bp 1 and Bm 1 of the PCM-to-PWM converter 716 is a 1-bit PWM word with a sampling frequency of (2 N )*Fs.
- the effects of analog glitch energies are reduced due to the use of pulse width modulation; the glitches for each segment are now repeated periodically due to PWM and this concentrates the error near harmonics of the PWM switching rate.
- Static mismatches inside the 1-bit P-tap AFIR DAC ( 722 ) only affect the AFIR filter response (linear error which does not produce distortion or noise).
- the N-tap AFIR filter has notches at the harmonics of the PWM rate which aligns with the spectrum of the PWM signal thus reducing the out-of-band energy to a level similar to an N-level DAC.
- the reduction of the out-of-band energy is done with significantly reduced sensitivity to both static and dynamic mismatches.
- the analog output Ip 1 and Im 1 are summed with the differential input 754 and 756 of the first cascade circuit 702 respectively.
- the sum 772 and 774 of the analog output Ip 1 and Im 1 and the differential input 754 and 756 of the first cascade circuit 702 provides the analog differential output 772 and 774 of the cascaded circuit 700 .
- the second cascade circuit 704 comprises a first gain circuit 728 , a first gain attenuation circuit 732 , a second gain attenuation circuit 734 , a noise-shaping circuit 712 , a PCM-to-PWM converter 718 and a 1-bit P-tap AFIR filter DAC 724 .
- the first gain attenuation circuit 732 may be implemented, for example, by reducing the reference inputs to the 1-bit DACs inside the 1-bit P-tap AFIR filter DAC 724 .
- the output 746 of the first gain circuit 728 is connected to the input 746 of the noise-shaping circuit 712 .
- the input 746 of the noise-shaping circuit 712 is summed with the output 748 of the noise-shaping circuit 712 .
- the sum of the input 742 and the output 744 of the noise-shaping circuit 712 is the output 768 of the second cascade circuit 704 .
- the output 748 of the noise-shaping circuit 712 is also connected to the input 748 of the PCM-to-PWM converter 718 .
- the output 748 of the noise-shaping circuit 710 is, in this example, an N-bit PCM word with a sampling frequency of Fs where M is greater than N.
- the differential output Bp 2 and Bm 2 of the PCM-to-PWM converter 718 is connected to the differential input Bp 2 and Bm 2 of the 1-bit P-tap AFIR filter DAC 724 .
- the differential output Bp 2 and Bm 2 of the PCM-to-PWM converter 718 is a 1-bit PWM word with a sampling frequency of (2 N )*Fs.
- the effects of analog glitch energies and mismatch errors are reduced by including pulse width modulation with an N-tap AFIR filter in each cascade circuit.
- the analog output Ip 2 and Im 2 are summed with the differential input 758 and 770 of the second cascade circuit 704 respectively.
- the sum 776 and 760 of the analog output Ip 2 and Im 2 and the inputs 776 and 760 of the second cascade circuit 704 provides the analog inputs 776 and 760 of the first 732 and second 734 gain attenuation circuits.
- the outputs of the first 732 and second 734 gain attenuation circuits are connected to the differential output 754 and 756 of the second cascade circuit 704 .
- the third cascade circuit 706 comprises a first gain circuit 730 , a first gain attenuation circuit 736 , a second gain attenuation circuit 738 , a noise-shaping circuit 714 , a PCM-to PWM converter 720 and a 1-bit P-tap AFIR filter DAC 726 .
- the output 750 of the first gain circuit 730 is connected to the input 750 of the noise-shaping circuit 714 .
- the output 752 of the noise-shaping circuit 714 is also connected to the input 752 of the PCM-to-PWM converter 720 .
- the output 752 of the noise-shaping circuit 714 is, in this example, an N-bit PCM word with a sampling frequency of Fs where M is greater than N.
- the differential output BpN and BmN of the PCM-to-PWM converter 720 is connected to the differential input BpN and BmN of the 1-bit P-tap AFIR filter DAC 726 .
- the differential output BpN and BmN of the PCM-to-PWM converter 720 is a 1-bit PWM word with a sampling frequency of (2 N )*Fs. The effects of analog glitch energies and mismatch errors are reduced by including pulse width modulation with an P-tap AFIR filter in each cascade circuit.
- the analog output IpN and ImN are the analog inputs IpN and ImN of the first 736 and second 738 gain attenuation circuits respectively.
- the outputs of the first 736 and second 738 gain attenuation circuits are connected to the differential output 758 and 770 of the third cascade circuit 706 .
- the amplifier 708 comprises an op-amp 740 , two capacitors Cf 1 and Cf 2 , and two resistors Rf 1 and Rf 2 .
- the resistor Rf 1 and the capacitor Cf 1 are connected between the first leg 772 of the differential input to the op-amp 740 and the first leg 762 of the differential output of the op-amp 740 .
- the resistor Rf 2 and the capacitor Cf 2 are connected between the second leg 774 of the differential input to the op-amp 740 and the second leg 764 of the differential output of the op-amp 740 .
- the noise-shaping circuits 710 , 712 and 714 are SDM (Sigma Delta Modulated) circuits.
- FIG. 12 is an exemplary embodiment of a cascaded circuit 1200 using at least four cascade circuits.
- the first cascade circuit 1226 is a copy of the cascade circuit 702 shown in FIG. 7 .
- the second cascade circuit 1228 is a copy of the cascade circuit 704 shown in FIG. 7 .
- the second cascade circuit 1230 is a copy of the cascade circuit 704 shown in FIG. 7 .
- the third cascade circuit 1232 is a copy of the cascade circuit 706 shown in FIG. 7 .
- any number of second cascade circuits may be included as part of the cascaded circuit 1200 . As more second cascade circuits are added, more noise is attenuated on the output 1222 and 1224 of the noise attenuation circuit 1200 . As more second cascade circuits are added to the cascaded circuit, filtering capacitors Cf 1 and Cf 2 may no longer be needed in the amplifier 708 . Capacitors Cf 1 and Cf 2 are typically large and expensive.
- FIG. 11 is a plot 1100 of out-of-band quantization noise versus frequency when using a cascaded circuit 1200 .
- a signal 1104 centered around 1 kHz is input to the cascaded circuit 1200 .
- a thermal noise floor 1102 is shown at around ⁇ 120 db.
- the out-of-band quantization noise level on the output, 1222 and 1224 , of the cascaded circuit 1200 drops as shown by out-of-band quantization noise measurements 1106 , 1108 , 1110 and 1112 .
- the out-of-band quantization noise measurement 1112 is below the thermal noise floor 1102 .
- Out-of-band quantization noise may be reduced to a level that is at or below the thermal noise level with minimum silicon area.
- FIG. 8 is an exemplary embodiment of a PCM-to-PWM converter 800 .
- an N-bit word at a sampling is frequency of Fs is input to the input Din of the comparator 806 and the input Dinof the inverter 804 .
- a waveform generator 802 provides a signal 810 to the second input of the first comparator 806 and the second input of the second comparator 808 .
- the output 812 of the inverter 804 is connected to the first input of the second comparator 808 .
- the signal 810 provided by the waveform generator 802 is a triangle waveform having a frequency of Fc.
- the carrier frequency Fc may be, for example, 385 kHz or 768 kHz. However, other frequencies are anticipated.
- the outputs, Bp and Bm of the PCM-to-PWM converter 800 are 1-bit words at sampling frequency of (2 N )*Fs. The effects of analog glitch energies and mismatch errors are reduced by including pulse width modulation with an P-tap AFIR filter in each cascade circuit.
- FIG. 9 is an exemplary embodiment of a 1-bit P-tap AFIR filter DAC 900 .
- All of the registers in this exemplary embodiment are D-type flip-flops. Other types of registers are may be used.
- a clock signal CLK is connected to an input of each of the registers, REG 0 , REG 1 , REG 2 , REGN and REG 1 B, REG 2 B, REGNB.
- Current sources, I 1 , I 2 , IN, I 1 B, I 2 B, INB are connected to the inputs 942 , 944 , 946 , 964 , 966 , 968 of each of the differential amplifiers 970 , 972 , 974 , 976 , 978 , and 980 respectively.
- the differential outputs from each differential amplifier are connected to the outputs Ip and Im of the 1-bit P-tap AFIR filter DAC 900 .
- a barrel shifter is not needed in this embodiment of the 1-bit P-tap AFIR filter
- Input Bp of the 1-bit P-tap AFIR filter DAC 900 is connected to input D of the REG 1 .
- Outputs Q and QN of REG 1 are connected to inputs 926 and 928 of differential amplifier 970 respectively.
- Output Q of REG 1 is also connected to input D of REG 2 .
- Outputs Q and QN of REG 2 are connected to inputs 930 and 932 of differential amplifier 972 respectively.
- Output Q of REG 2 is also connected to input D of REGN.
- the dotted lines and dashed lines in FIG. 9 indicate that any number of taps may be used.
- Outputs Q and QN of REGN are connected to inputs 938 and 940 of differential amplifier 974 respectively.
- PFETs P-type Field Effect Transistors
- Input Bn of the 1-bit P-tap AFIR filter DAC 900 is connected to input D of the REG 0 .
- Output Q of REG 0 is connected to the D input of REG 1 B.
- Outputs Q and QN of REG 1 B are connected to inputs 948 and 950 of differential amplifier 976 respectively.
- Output Q of REG 1 B is also connected to input D of REG 2 B.
- Outputs Q and QN of REG 2 B are connected to inputs 952 and 954 of differential amplifier 978 respectively.
- Output Q of REG 2 B is also connected to input D of REGNB.
- the dotted lines and dashed lines in FIG. 9 indicate that any number of taps may be used.
- Outputs Q and QN of REGNB are connected to inputs 960 and 962 of differential amplifier 980 .
- PFETs P-type Field Effect Transistors
- FIG. 10 is a plot of spectral density versus frequency when using a 1-bit P-tap AFIR filter DAC.
- Waveform 1002 shows the out-of-band quantization noise for an 8-tap AFIR.
- Waveform 1004 shows the out-of-band quantization noise for an 8-tap AFIR. Because the switching rate of the DAC segments is a function of the PWM carrier frequency Fc, the notches of the AFIR filter are located a integer values of the carrier frequency Fc.
- a first notch is shown in FIG. 10 between 1018 and 1020 with the audio information 1006 located in the middle of the first notch.
- a second notch is shown in FIG. 10 between 1022 and 1024 with the audio information 1008 located in the middle of the second notch.
- the cascaded circuit 700 relies on the notches of the AFIR filter. As a result, the out-of-band quantization noise is greatly attenuated as shown in FIG. 11 .
- the cascaded circuit also reduces the impact of static mismatch error because the 1-bit DACs used are substantially linear. Dynamic errors are also reduced because the distortion of the carrier frequency Fc is outside the audible range.
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Abstract
Description
- Digital-to-Analog converters (DACs) are found in many electronic devices. For example, DACs are used in PDAs (Personal Digital Assistant), cellular phones, computers, video players and CD players. DACs convert a digital signal into an analog signal. Analog signals include music and voice.
- In the process of converting a digital signal to an analog signal, noise may be created. Noise may be any electrical contribution added to a signal that was not part of the original source that created the signal. For example, some sources of noise are thermal noise, phase noise, quantization noise and switching noise. During the process of converting a digital signal to an analog signal, the original signal may be distorted. There are many types of distortion such a harmonic distortion, and intermodulation distortion.
- At low signal levels, the human ear is very sensitive to low level noise and distortion. Because the human ear is very sensitive to noise and distortion at low signal levels, methods have been devised to attenuate noise and distortion at low signal levels. For example, noise-shaping filters shift quantization noise from in-band (typically from 20 Hz to 20,000 Khz, the frequency range of human hearing) to out-of-band quantization noise (typically from 20 KHz and above). AFIR (Analog Finite Impulse Response) filters are used to reduce out-of-band noise (OBN).
- Due to manufacturing variance, current segments in a DAC array will have slightly different values from each other. This variance in the current segments of a DAC array may cause harmonic distortion and may raise the noise level in a DAC. Inter-symbol interference due to uneven rise and fall times and parasitic capacitances may cause distortion and noise as well.
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FIG. 1 is a plot of an ideal analog output versus the magnitude of eight 3-bit binary words. -
FIG. 2A is a plot of quantization noise as a function of frequency when using 1-bit Nyquist sampling. -
FIG. 2B is a plot of quantization noise as a function of frequency when using an oversampling rate of fa. -
FIG. 2C is a plot of quantization noise as a function of frequency when first order noise-shaping is used. -
FIG. 3 is a plot of the magnitude of a sample frequency, harmonic distortion, in-band noise and folding noise as a function of frequency when a noise-shaping filter is used. -
FIG. 4 is a plot of the output level of a DAC when switching from a first level to a second level when using a 2-bit binary word. -
FIG. 5 is a schematic showing a digital SDM (Sigma Delta Modulation) filter, a thermometer encoder, and an N-tap AFIR (Analog Finite Impulse Response) Filter DAC (Prior Art). -
FIG. 6 is a plot of attenuation out-of-band noise when using 8-tap and a 16-tap AFIR (Analog Finite Impulse Response) Filter DACs. -
FIG. 7 is an exemplary embodiment of a cascaded circuit which includes a first cascade circuit, a second cascade circuit and a third cascade circuit. -
FIG. 8 is an exemplary embodiment of a PCM (Pulse Code Modulation)-to-PWM (Pulse Width Modulation) converter. -
FIG. 9 is an exemplary embodiment of a 1-bit P-tap AFIR (Analog Finite Impulse Response) Filter DAC. -
FIG. 10 is a plot of spectral density versus frequency when using a 1-bit P-tap AFIR Filter DAC. -
FIG. 11 is a plot of noise versus frequency when using a 1-bit P-tap AFIR Filter DAC. -
FIG. 12 is an exemplary embodiment of a cascaded circuit using at least four cascade circuits. - The drawings and description, in general, disclose one or more cascade circuits that are cascaded together to form a cascaded circuit. The cascaded circuit reduces out-of-band quantization noise at an analog output of the cascaded circuit. Each of the cascade circuits contain a noise-shaping circuit, a PCM (Pulse Code Modulation)-to-PWM (Pulse Width Modulation) converter and a 1-bit P-tap AFIR (Analog Finite Impulse Response) filter DAC. Out-of-band quantization noise at the output of the cascaded circuit may be further reduced by increasing the number of cascade circuits. In addition, out-of-band quantization noise may be reduced to a level that is at or below the thermal noise level with minimum silicon area.
- In this exemplary embodiment, the noise-shaping circuit shifts, for example, quantization noise from within the audible range (often called “in-band”, typically 20 Hz to 20 KHz), to a frequency range outside the audible range (often called “out-of-band”, typically 20 KHz and higher). In addition, the noise-shaping circuit in this example converts PCM M-bit digital words to PCM N-bit digital words where M and N are integers and M is greater than N. The sampling frequency of the PCM M-bit digital words and the PCM N-bit digital words, in this example, is Fs.
- In this exemplary embodiment, the PCM-to-PWM converter converts PCM N-bit digital words sampled at a frequency of Fs to PWM 1-bit words at a frequency of (2N)*Fs. The PWM 1-bit words are then input into the P-tap AFIR filter 1-bit DAC. Pulse width modulation reduces sensitivity to to analog glitch energies and an P-tap AFIR filter in each cascade circuit reduces mismatch errors. Each tap in each AFIR filter is a small 1-bit DAC and an analog output is formed by summing the outputs of all such 1-bit DACs of the AFIRs in all the cascade circuits.
-
FIG. 1 is a plot of an ideal analog output versus the magnitude of eight 3-bit binary words. In this example, the eight 3-bit binary words, 104, 106, 108, 110, 112, 114, 116 and 118 do not end atline 102, the ideal analog output. INL (Integrated Non-Linear) and DNL (Differential Non-Linear) distortion is created because these eight 3-bit binary words, 104, 106, 108, 110, 112, 114, 116 and 118 do not end atline 102. INL and DNL distortion may be caused by static element mismatch. For example, if current sources used in the DACs are not matched, INL and DNL distortion may occur. Pulse width modulation coupled with an N-tap AFIR filter in each cascade circuit reduces sensitivity to analog glitch energies and mismatch errors - One source of noise is quantization noise.
FIG. 2A is a plot of quantization noise as a function of frequency when using N-bit Nyquist sampling. The quantization noise inFIG. 2A is contained in the audio band. As a result, the quantization noise is added to the audio signal.FIG. 2B is a plot of quantization noise as a function of frequency when using an over-sampling rate of Fa. The quantization noise inFIG. 2B is spread from DC (0 Hz) to Fa/2. In this case, quantization noise is reduced in the audio band, improving the signal-to-noise ratio. The same quantization noise is “spread thinner” due to over-sampling. However, in this case more quantization noise is found in the out-of-band frequency range. The Nyquist case will have more quantization noise due to the images (repetitions of the spectrum) unless a sharp low-pass filter is applied. -
FIG. 2C is a plot of quantization noise as a function of frequency when first order noise-shaping is used. InFIG. 2C , most of the quantization noise is removed from the audio band into the out-of-band frequency range. Because most of the quantization noise is removed from the audio band, the signal-to-noise ratio is improved. However, in this case more quantization noise is found out-of-band. - Due to analog nonlinearities such as mismatch errors and glitch energy, the out-of-
band quantization noise 312 may be folded back into the audio band increasing the noise floor.FIG. 3 is a plot of the magnitude of asample frequency 302,harmonic distortion 304, in-band noise quantization 306 andfolding quantization noise 308 as a function of frequency when noise-shaping is used. In this example, out-of-band quantization noise 312 is folded back into the audible band as foldingquantization noise 308. The noise-shaping filter shapes quantization noise as shown bycurve 310. - Dynamic error may be generated due to differences in rise and fall times, clock skew distribution, memory effects at the switching nodes, glitches and parasitic coupling between switching nodes between DAC elements. All of these dynamic errors can lead to distortion and noise.
FIG. 4 is a plot of the output level of a DAC when switching from a first level to a second level when using a 2-bit binary word. InFIG. 4 , the output level switches fromlevel 1 tolevel 6 for a short time instead of thecorrect level 2 due to differences in rise and fall times. This “glitch” when switching fromlevel 1 tolevel 2 causes dynamic distortion and noise. - The “glitch” shown in
FIG. 4 may be reduced using thermometer encoding. Table 1 shows an example of thermometer encoding. In this example a 2-bit word is used. Thermometer encoding allows only one bit to switch at any time. Allowing only one bit to switch at any time for a single LSB step change in the input code reduces the number of glitches that is may have occurred. -
TABLE 1 b1 b0 t3 t2 t1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 - When b1=0 and b0=1 changes to b1=1 and b0=0, both b1 and b0 change. Because both b1 and b0 change, a dynamic error may occur as shown in
FIG. 4 . However, when thermometer encoding, t3, t2, t1, is used as shown in Table 1, only one bit changes at a time. Because only one bit changes at a time, dynamic errors are reduced. - The effects of analog glitch energies and mismatch errors may be reduced by including pulse width modulation with an N-tap AFIR filter in each cascade circuit.
FIG. 5 shows a digital GDM (Sigma Delta Modulation)modulator 528, athermometer encoder 530, and an N-tap AFIR (Analog Finite Impulse Response)filter DAC 500. As previously discussed thedigital SDM 528 shifts quantization noise from the audible range to the out-of-band range and thethermometer encoding 530 reduces INL and DNL distortion. - The N-tap
AFIR filter DAC 500 reduces out-of-band quantization noise and sensitivity to non-linearities and phase noise. The N-tapAFIR filter DAC 500 is implemented by dividing L-DAC segments into N-tap M-bit AFIR structures with equal coefficients where L=M*N. Matching between M-level DACs, 544, 546, 548 is typically not needed because it only affects the filter response. However, matching with an individual M-level DAC is usually necessary. In order to reduce the effects of mismatching, M-level rotation, 538, 540, 542 is used to create first order noise-shaping. The rotation insures that all M−1 segments inside one M-level DAC are used with the same average density/frequency. This causes the INL linear and shifts mismatch induced errors to be out of the audio band. This M-level rotation may be accomplished using barrel (circular) shifters. -
FIG. 6 is a plot of attenuation of out-of-band quantization noise when using an 8-tap and a 16-tap AFIR filter DAC (unit coefficients giving a sinc response). An 8-tapAFIR filter DAC 602 attenuates out-of-band quantization noise on average for a white noise signal by 18 db. A 16-tapAFIR filter DAC 604 attenuates out-of-band quantization noise on average by 22 db. Neither of these N-tap AFIR filter DACs provides enough stop-band suppression. In addition, the M-level rotation, 538, 540, 542 may create tonal distortion at small signal levels. It is more efficient from an out-of-band noise perspective to use a single L-level DAC instead of the AFIR version shown inFIG. 5 (prior art) because RMS out-of-band noise scales down inversely proportionally with L for the single stage versus only −3 db/doubling for the AFIR case shown inFIG. 5 (prior art). -
FIG. 7 is an exemplary embodiment of a cascadedcircuit 700 including afirst cascade circuit 702, asecond cascade circuit 704 and athird cascade circuit 706. In this exemplary embodiment adigital signal 742 is input to the cascadedcircuit 700. Thedigital signal 742 is an M-bit PCM digital word received at a frequency of Fs. In this exemplary embodiment the analogdifferential output circuit 700 are connected to the differential input of anamplifier 708. - The
output 766 of thefirst cascade circuit 702 is connected to theinput 766 of thesecond cascade circuit 704.Signal 766 is the quantization noise of the noise-shaping circuit 710.Signal 766 is fed intocascade circuit 704 in the digital domain and then subtracted in the analog domain in order or reduce the resulting quantization noise. Thedifferential input first cascade circuit 702 is connected to thedifferential output second cascade circuit 704. Theoutput 768 of thesecond cascade circuit 704 is connected to theinput 768 of thethird cascade circuit 706. Thedifferential input second cascade circuit 704 is connected to thedifferential output third cascade circuit 704. - In this exemplary embodiment, the
first cascade circuit 702 comprises a noise-shaping circuit 710, for example a SDM, a PCM-toPWM converter 716 and a 1-bit P-tapAFIR filter DAC 722. In this example, theinput 742 of the noise-shaping circuit 710 is summed with theoutput 744 of the noise-shaping circuit 710. The sum of theinput 742 and theoutput 744 of the noise-shaping circuit is theoutput 766 of thefirst cascade circuit 702. Theoutput 744 of the noise-shaping circuit 710 is also connected to theinput 744 of the PCM-to-PWM converter 716. Theoutput 744 of the noise-shaping circuit 710 is, in this example, an N-bit PCM word with a sampling frequency of Fs where M is greater than N. - In this exemplary embodiment, the differential output Bp1 and Bm1 of the PCM-to-
PWM converter 716 is connected to the differential input Bp1 and Bm1 of the 1-bit P-tapAFIR filter DAC 722. The differential output Bp1 and Bm1 of the PCM-to-PWM converter 716 is a 1-bit PWM word with a sampling frequency of (2N)*Fs. The effects of analog glitch energies are reduced due to the use of pulse width modulation; the glitches for each segment are now repeated periodically due to PWM and this concentrates the error near harmonics of the PWM switching rate. Static mismatches inside the 1-bit P-tap AFIR DAC (722) only affect the AFIR filter response (linear error which does not produce distortion or noise). - The N-tap AFIR filter has notches at the harmonics of the PWM rate which aligns with the spectrum of the PWM signal thus reducing the out-of-band energy to a level similar to an N-level DAC. The reduction of the out-of-band energy is done with significantly reduced sensitivity to both static and dynamic mismatches. The analog output Ip1 and Im1 are summed with the
differential input first cascade circuit 702 respectively. Thesum differential input first cascade circuit 702 provides the analogdifferential output circuit 700. - In this exemplary embodiment, the
second cascade circuit 704 comprises afirst gain circuit 728, a firstgain attenuation circuit 732, a secondgain attenuation circuit 734, a noise-shaping circuit 712, a PCM-to-PWM converter 718 and a 1-bit P-tapAFIR filter DAC 724. The firstgain attenuation circuit 732 may be implemented, for example, by reducing the reference inputs to the 1-bit DACs inside the 1-bit P-tapAFIR filter DAC 724. In this example, theoutput 746 of thefirst gain circuit 728 is connected to theinput 746 of the noise-shaping circuit 712. Theinput 746 of the noise-shaping circuit 712 is summed with theoutput 748 of the noise-shaping circuit 712. The sum of theinput 742 and theoutput 744 of the noise-shaping circuit 712 is theoutput 768 of thesecond cascade circuit 704. Theoutput 748 of the noise-shaping circuit 712 is also connected to theinput 748 of the PCM-to-PWM converter 718. Theoutput 748 of the noise-shaping circuit 710 is, in this example, an N-bit PCM word with a sampling frequency of Fs where M is greater than N. - In this exemplary embodiment, the differential output Bp2 and Bm2 of the PCM-to-
PWM converter 718 is connected to the differential input Bp2 and Bm2 of the 1-bit P-tapAFIR filter DAC 724. The differential output Bp2 and Bm2 of the PCM-to-PWM converter 718 is a 1-bit PWM word with a sampling frequency of (2N)*Fs. The effects of analog glitch energies and mismatch errors are reduced by including pulse width modulation with an N-tap AFIR filter in each cascade circuit. The analog output Ip2 and Im2 are summed with thedifferential input second cascade circuit 704 respectively. Thesum inputs second cascade circuit 704 provides theanalog inputs differential output second cascade circuit 704. - In this exemplary embodiment, the
third cascade circuit 706 comprises afirst gain circuit 730, a firstgain attenuation circuit 736, a secondgain attenuation circuit 738, a noise-shaping circuit 714, a PCM-toPWM converter 720 and a 1-bit P-tapAFIR filter DAC 726. In this example, theoutput 750 of thefirst gain circuit 730 is connected to theinput 750 of the noise-shaping circuit 714. Theoutput 752 of the noise-shaping circuit 714 is also connected to theinput 752 of the PCM-to-PWM converter 720. Theoutput 752 of the noise-shaping circuit 714 is, in this example, an N-bit PCM word with a sampling frequency of Fs where M is greater than N. - In this exemplary embodiment, the differential output BpN and BmN of the PCM-to-
PWM converter 720 is connected to the differential input BpN and BmN of the 1-bit P-tapAFIR filter DAC 726. The differential output BpN and BmN of the PCM-to-PWM converter 720 is a 1-bit PWM word with a sampling frequency of (2N)*Fs. The effects of analog glitch energies and mismatch errors are reduced by including pulse width modulation with an P-tap AFIR filter in each cascade circuit. The analog output IpN and ImN are the analog inputs IpN and ImN of the first 736 and second 738 gain attenuation circuits respectively. The outputs of the first 736 and second 738 gain attenuation circuits are connected to thedifferential output third cascade circuit 706. - In this exemplary embodiment, the
amplifier 708 comprises an op-amp 740, two capacitors Cf1 and Cf2, and two resistors Rf1 and Rf2. The resistor Rf1 and the capacitor Cf1 are connected between thefirst leg 772 of the differential input to the op-amp 740 and thefirst leg 762 of the differential output of the op-amp 740. The resistor Rf2 and the capacitor Cf2 are connected between thesecond leg 774 of the differential input to the op-amp 740 and thesecond leg 764 of the differential output of the op-amp 740. - In this exemplary embodiment, the noise-shaping
circuits -
FIG. 12 is an exemplary embodiment of a cascadedcircuit 1200 using at least four cascade circuits. Thefirst cascade circuit 1226 is a copy of thecascade circuit 702 shown inFIG. 7 . Thesecond cascade circuit 1228 is a copy of thecascade circuit 704 shown inFIG. 7 . Thesecond cascade circuit 1230 is a copy of thecascade circuit 704 shown inFIG. 7 . Thethird cascade circuit 1232 is a copy of thecascade circuit 706 shown inFIG. 7 . In this exemplary embodiment, any number of second cascade circuits may be included as part of the cascadedcircuit 1200. As more second cascade circuits are added, more noise is attenuated on theoutput noise attenuation circuit 1200. As more second cascade circuits are added to the cascaded circuit, filtering capacitors Cf1 and Cf2 may no longer be needed in theamplifier 708. Capacitors Cf1 and Cf2 are typically large and expensive. -
FIG. 11 is aplot 1100 of out-of-band quantization noise versus frequency when using a cascadedcircuit 1200. Asignal 1104 centered around 1 kHz is input to the cascadedcircuit 1200. Athermal noise floor 1102 is shown at around −120 db. As additional cascade circuits are cascaded into the cascadedcircuit 1200, the out-of-band quantization noise level on the output, 1222 and 1224, of the cascadedcircuit 1200 drops as shown by out-of-bandquantization noise measurements quantization noise measurement 1112 is below thethermal noise floor 1102. Out-of-band quantization noise may be reduced to a level that is at or below the thermal noise level with minimum silicon area. -
FIG. 8 is an exemplary embodiment of a PCM-to-PWM converter 800. In this exemplary embodiment an N-bit word at a sampling is frequency of Fs is input to the input Din of thecomparator 806 and the input Dinof theinverter 804. Awaveform generator 802 provides asignal 810 to the second input of thefirst comparator 806 and the second input of thesecond comparator 808. Theoutput 812 of theinverter 804 is connected to the first input of thesecond comparator 808. - In this exemplary embodiment, the
signal 810 provided by thewaveform generator 802 is a triangle waveform having a frequency of Fc. The carrier frequency Fc may be, for example, 385 kHz or 768 kHz. However, other frequencies are anticipated. The outputs, Bp and Bm of the PCM-to-PWM converter 800 are 1-bit words at sampling frequency of (2N)*Fs. The effects of analog glitch energies and mismatch errors are reduced by including pulse width modulation with an P-tap AFIR filter in each cascade circuit. -
FIG. 9 is an exemplary embodiment of a 1-bit P-tapAFIR filter DAC 900. All of the registers in this exemplary embodiment are D-type flip-flops. Other types of registers are may be used. A clock signal CLK is connected to an input of each of the registers, REG0, REG1, REG2, REGN and REG1B, REG2B, REGNB. Current sources, I1, I2, IN, I1B, I2B, INB are connected to theinputs differential amplifiers AFIR filter DAC 900. A barrel shifter is not needed in this embodiment of the 1-bit P-tapAFIR filter DAC 900. - Input Bp of the 1-bit P-tap
AFIR filter DAC 900 is connected to input D of the REG1. Outputs Q and QN of REG1 are connected toinputs differential amplifier 970 respectively. Output Q of REG1 is also connected to input D of REG2. Outputs Q and QN of REG2 are connected toinputs differential amplifier 972 respectively. Output Q of REG2 is also connected to input D of REGN. The dotted lines and dashed lines inFIG. 9 indicate that any number of taps may be used. Outputs Q and QN of REGN are connected toinputs differential amplifier 974 respectively. PFETs (P-type Field Effect Transistors) are used in this exemplary embodiment; however other types of transistors may be used. - Input Bn of the 1-bit P-tap
AFIR filter DAC 900 is connected to input D of the REG0. Output Q of REG0 is connected to the D input of REG1B. Outputs Q and QN of REG1B are connected toinputs differential amplifier 976 respectively. Output Q of REG1B is also connected to input D of REG2B. Outputs Q and QN of REG2B are connected toinputs differential amplifier 978 respectively. Output Q of REG2B is also connected to input D of REGNB. The dotted lines and dashed lines inFIG. 9 indicate that any number of taps may be used. Outputs Q and QN of REGNB are connected toinputs differential amplifier 980. PFETs (P-type Field Effect Transistors) are used in this exemplary embodiment; however other types of transistors may be used. -
FIG. 10 is a plot of spectral density versus frequency when using a 1-bit P-tap AFIR filter DAC.Waveform 1002 shows the out-of-band quantization noise for an 8-tap AFIR.Waveform 1004 shows the out-of-band quantization noise for an 8-tap AFIR. Because the switching rate of the DAC segments is a function of the PWM carrier frequency Fc, the notches of the AFIR filter are located a integer values of the carrier frequency Fc. A first notch is shown inFIG. 10 between 1018 and 1020 with theaudio information 1006 located in the middle of the first notch. A second notch is shown inFIG. 10 between 1022 and 1024 with theaudio information 1008 located in the middle of the second notch. - Instead of relying on the absolute stop-band ripple size of a standard AFIR filter, the cascaded
circuit 700 relies on the notches of the AFIR filter. As a result, the out-of-band quantization noise is greatly attenuated as shown inFIG. 11 . The cascaded circuit also reduces the impact of static mismatch error because the 1-bit DACs used are substantially linear. Dynamic errors are also reduced because the distortion of the carrier frequency Fc is outside the audible range. - The foregoing description has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and other modifications and variations may be possible in light of the above teachings. The exemplary embodiments were chosen and described in order to best explain the applicable principles and their practical application to thereby enable others skilled in the art to best utilize various embodiments and various modifications as are suited to the particular use contemplated. It is intended that the appended claims be construed to include other alternative embodiments except insofar as limited by the prior art.
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