©Alex Doboli 2006 Analog to Digital Converters Alex Doboli, Ph.D. Department of Electrical and Computer Engineering State University of New York at.

©Alex Doboli 2006

Analog to Digital Converters

Alex Doboli, Ph.D.

Department of Electrical and Computer Engineering

State University of New York at Stony Brook

Email: [email protected]

©Alex Doboli 2006

ADC

The chapter introduces the following aspects:

• Basic concepts of ADC & 1sr and 2nd order ADCs

• ADC are main subsystems in any embedded system

ADC offer high resolution through two mechanisms:– Oversampling: reduces in-band quantization noise– Noiseshaping: eliminates in-band quantization noise

• PSoC implementation of ADC: modulator, decimator, API

©Alex Doboli 2006

Nyquist ADCs

Embedded system front end:

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Sampling

• Collect sufficient data for correctly representing a continuous-time signal

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Nyquist Sampling Theorem

• A bandlimited signal can be exactly reconstructed if the samplingFrequency is greater than twice the signal bandwidth

• Nyquist frequency is twice the signal bandwidth

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Sampling

aliasing

Xs(f) = X(f) + X(f+/-fs) + X(f+/-2fs) + X(f+/-3fs) + X(f+/-4fs) + …

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Quantization

• Quantization is the process of converting the sampled continuous-Valued signals into discrete-valued data

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Quantization

• Discretization range: = 2 / (2B - 1)

• Quantization error:er ε (-/2, /2)

White noise

xd = xs + er

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Quantization Error

• Bennett’s conditions:• Input does not overload quantizer• B is large• is small• Joint probability density function of the input at

various sampling moments is smooth

• Quantization error is white noise & is uncorrelated to the input

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Quantization Error

• Quantization noise power

• Power spectral density

2e = 2 / 12

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Analog to Digital Converter

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Oversampling

• Oversampling frequency• Oversampling Ratio (OSR)

• Advantages of high OSR:• simplifies elimination of the images• reduced in-band noise power

Pin-band = 2e / OSR

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Noiseshaping

Y(z) = H(z) / (1 + H(z)) X(z) + 1 / (1 + H(z)) E(z)

STF NTF

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ADC Performance

• Signal-to-noise ratio (SNR):

SNR (dB) = 10 log (signal power) / (in band quantization noise power)

– For sinusoidal input:SNR (dB) = 6.02 B + 1.76 (dB)

SNR (dB) = 6.02 B + 10 log OSR

• Dynamic range (DR):– Ratio between the output power for a sinusoidal input with full-

range amplitude and the output power of the smallest input signal that it can distinguish and quantize

DR (dB) = 10 log (2 / 8) / (in band quantization noise power)B (bits) = (DR (dB) – 1.76) / 6.02

©Alex Doboli 2006

First-order Modulator

yd(t) = z-1 x(t) + (1 – z-1) e(t)

STF = z-1

NTF = 1 – z-1

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First-order Modulator: STF & NTF

STF

NTF

High pass

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Power Spectrum Density

Frequency of the input signal

noise shaping

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Modulator Performance

• Signal to noise ratio for sinusoidal input:

• In-band quantization noise power:

Pin-band = 2 / (9 OSR3)

SNR = 10 log (9 A2 OSR3) / (2 2)

©Alex Doboli 2006

Dynamic Range

34 dB (5 bits)

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Dynamic Range vs. OSR

DR=34db (OSR=32)DR=38dB (OSR=64)

DR=42dB (OSR=128)DR=50dB (OSR=256)

(8 bits)

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PSoC Implementation

Vin (-Vref, Vref)Vref {VDD/2, 1.6 Vbandgap, Vexternal}OSR = 64Vin = (n – 128) / 128 Vref

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PSoC Implementation

modulator– Uses programmable SC blocks

• Decimator– Low pass filtering (eliminates high frequency images)– Downconversion by factor OSR– Sinc2 filter– Implementation: hardware (integration) – software

(differentiation)– Downconversion: timer produces an interrupt after OSR clock

cycles & ISR implements differentiations

• API routines

• Clocks

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Modulator Implementation

Single clock for entire design (4 x OSR)

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Measured PSD (OSR = 32)

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Measured PSD (OSR = 64)

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Sinc2 Decimator Filter (OSR=64)

H(z) = [1 / OSR x (1 – z-OSR) / (1 – z-1) ]2

fb/2 + m fs/2

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Sinc2 Decimator Filter

• Integration: in hardware using Type 1 decimator block• Differentiation: in software at downconversion rate (4 x

OSR)

• Interrupts at 4 x OSR / fs

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Timer ISR

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API Routines

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API Routines

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Example

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Modeling of jitter noise

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Switch Thermal Noise

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Switch Thermal Noise

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Switch Thermal Noise

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OpAmp Noise

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Modeling of Slew Rate & Saturation

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Second Order Modulator

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Second-order Modulator

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PSoC Implementation