dnc, gec & non-linear interpolation
DESCRIPTION
DNC, GEC & Non-linear interpolation. A Review of ”A Digitally Enhanced 1.8V 15-bit 40-MSample/s CMOS Pipelined ADC”[1] & ”Background Digital Calibration Techniques for Pipelined ADC’s”[2]. Pipelined ADC review. Non-linearities in DAC levels cause harmonic distortion - PowerPoint PPT PresentationTRANSCRIPT
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DNC, GEC & Non-linear interpolation
A Review of ”A Digitally Enhanced 1.8V 15-bit 40-MSample/s
CMOS Pipelined ADC”[1] &
”Background Digital Calibration Techniques for Pipelined ADC’s”[2]
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Pipelined ADC review
• Non-linearities in DAC levels cause harmonic distortion– Common solution: Try to randomly distribute non-
linearities in DAC so energy is spread out in the frequency spectrum
• Interstage gain errors reduce SNDR/SNR– Solution: Apply correction gain digitally
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Detecting a known signal component in the output of an unknown system
Mean of td = 0
• Td with a mean of zero:– Periodic signal
• Pro: Can have a small N since power of td is evenly distributed in time
• Con: Delta function in the frequency domain
– White noise signal• Pro: Flat power density spectrum• Con: Need large N, ideally N=∞
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A Digitally Enhanced 1.8V 15-bit 40-MSample/s CMOS Pipelined ADC
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• Dynamic Element Matching (DEM)• DAC Noise Cancellation (DNC)• Gain Error Correction (GEC)• Bootstrapped Switches• Timing
Outline
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Pipeline ADC from [1]
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Dynamic Element Matching (1)
• Errors in DAC paths cause signal dependent error• Signal dependent error => Distortion
R
Vout
Bin
ary
to T
herm
omet
er
B0
B1
Iref
T = 0001 => Vout = RIref (1+ e0)
T = 1111 => Vout = RIref (4+ e0e1 e2 e3 )
Vout = RIref [T0 (1+ e0) + T1 (1+ e1)+ T2 (1+ e2)+ T3 (1+ e3 )]
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Dynamic Element Matching (2)
• Scrambler randomly selects a sequence of Sn such that Vout equals (1)
• The error, e, is uncorrelated with the input signal if it is done correctly
• This will effectively spread DAC noise power in the frequency spectrum
Bin
ary
to T
herm
omet
er
B0
B1
Iref
S0
S1
S2
S3
Scr
ambl
er
R
Vout
S4
S5
S6
S7
T0
T1
T2
T3
Random Sequence
(1)Vout = RIref [T0 + T1+ T2 +T3] + e
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• With DEM encoder from [1] it can be shown that DAC noise inherits statistical properties of the pseudorandom sequence used in DEM
• This can be used to estimate the mismatch in the DAC paths
• Each path error is related to a specific pseduorandom sequence
DEM encoder from [1]
DAC path errors
Known sequences
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DAC Noise Cancellation
• Detect presence of known pseduorandom signal, s[n], in output, u[n] + εs[n], by calculating the covariance
• Estimate DAC path error, ε, from covariance• Multiply psedurandom sequence by path error estimate and
subtract from output • Repeat for all DAC paths
u[n] + εs[n] - εs[n]
s[n]
Estimate errorε
s[n]
u[n] + εs[n]
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Gain Error Calibration (GEC) from [1]
• Estimate gain error from covariance of digitized residue and pseudorandom signal
• Assuming small ε =>(1 + ε ) ≈ 1, multiply digitized residue by gain estimate and subtract from output
r[n]
Estimate error
ε
(1 + ε)
u[n]
d1[n]
d2[n]
y[n]
d1[n] = u[n] + εu[n] + εr[n]
d2[n] = εu[n] + ε2u[n] + ε2r[n] ≈ εu[n]
y[n] = u[n] + εu[n] + εr[n] - εu[n] - εr[n] = u[n]
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Bootstrapped switches
• Used on continous-time input sampling switches – Increased linearity
• Used on switches connected to mid-supply or time-constant matching constrains – Reduced resistance
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Timing
• First stage amplification is most important• Steal time for first stage Flash from second stage
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Results from [1]
• SFDR is improved by 12dB with DNC and GEC enabled• SNDR is improved by 20dB with DNC and GEC enabled
Signal
Without calibration With calibration
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Background Digital Calibration Techniques for Pipelined ADC’s
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Outline
• Error Model• Calibration Method• Non-linear Interpolation• Quantization Effects on Interpolation
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Error Model
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Error measurement
• Measure gain error in each stage by applying known calibration voltage, Vcal-i
1 1_ (2 ) ( (2 ) )i i
gain error i cal i offset i i cal i offset iV e V V e V V
Positive calibration voltage Negative calibration voltage
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Simulation results
• Simulated performance (DNL & INL) with and without gain calibration
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Non-linear Interpolation
• Uses fitting of high order polynomials to estimate missing sample.
• Uses causal and noncausal taps
Normalized coefficients
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• Limits input bandwidth of converter below Nyquist
Non-linear Interpolation
Fin < ½ Nyquist Fin < Nyquist
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Non-linear Interpolation
• Interpolation error depends on the number of taps• Achieve higher bandwith with a certain error by using
more taps
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Quantization Effects on Interpolation
• Quantization noise limits performance of interpolation• Each tap adds quantization noise to total noise power• Limits the number of taps
Variance vs number of taps
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References
1. Eric Siragusa & Ian Galton; ”A Digitally Enhanced 1.8V 15-bit 40-MSample/s CMOS Pipelined ADC”; IEEE Journal of Solid State, Vol. 39, NO. 12, December 2004
2. Un-Ku Moon & Bang-Sup Song;” Background Digital Calibration Techniques for Pipelined ADC’s”; IEEE Transatctions on Circuits and Systems-II, Vol. 44, NO. 2, Febuary 1997