Sampling Methods and Analog Filtering

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Sampling Methods and Analog Filtering

• The sampling process is of critical importance in
  radio receivers using digitization at the RF or
  IF.
• Common sampling techniques using a uniform
  spacing
• Nyquist Sampling
• Oversampling
• Quadrature Sampling
• Bandpass Sampling

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Nyquist Sampling

• Def A sampling rate of two times the highest
  frequency component of the analog signal
• Sampling a bandlimited signal at Nyquist
  rategtAnti-Aliasing

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Bandlimited Signal in a Practical Sense??

• SolutionThe relative amplitude of the undesired
  signals to the desired signal is important.
• QuestionWhat is the relative amplitude of the
  signals occurring above one-half of the sampling
  rate?
• SolutionUndesired signals appearing in the
  Nyquist band due to spectrum overlap must be
  lower in power than the largest spurious response
  of the ADC due to nonlinearity.

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Bandlimited Signal in a Practical Sense??(Cont.)

• To relax this requirement
• QHow much distortion of the desired signal is
  tolerable?
• AConsidering Communication System
• 1.source informationvoice, data, video, etc)
• 2.desired signal bandwidth
• 3.undesired signal characteristics(BW, power,
  signal type)

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Realizable Anti-Aliasing Filters

• More complicated filters are required to reduce
  the distortion in the sampled signal due to
  spectrum overlap for a given sampling rate.
• gtHigh Order
• gtPhase response tends to become more nonlinear.

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Oversampling

• Definition
• Sampling at rates greater than the Nyquist
  sampling rate is called oversampling.
• When sampling at a higher rate, a simpler
  anti-aliasing filter with less stop band
  attenuation can be used .
• Increasingly faster ADCs are required to
  digitize low frequency signals.

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Quadrature Sampling

• In quadrature sampling the signal to be digitized
  is split into two signals.
• One is in phase component the other is
  quadrature phase component.
• Be sampled at one-half the sampling rate
  required for the original signal.
• At expense of using two phase-locked ADCs
  instead of one.

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Bandpass Sampling

• For a bandpass signal, the sampling rate be at
  least two times the BW( ) of the signal.
• The sampling frequency must satisfied
• Bandpass sampling holds promise for radio
  receivers that digitize directly at the RF or IF,
  since the desired input signals to radio
  receivers are normally bandpass signals.

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Effects of Quantization Noise, Distortion, and
Receiver Noise

• Relationship among quantization noise, harmonic
  distortion, and receiver noise (thermal noise)
• Quantization
• Uniform quantization
• NonuniformA-law, u-law, adaptive, and
  differential quantization

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Uniform Quantization

• Statistically, the error signal is assumed to be
  uniformly distributed within a quantization
  level.
• Mean Squared Quantization Noise Power
  

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Noise and Solution

• DitheringgtHarmonic Distortion, Thermal
  Noise(Flat Noise)
• Boost Amp Gain
• Matching the Input Impedence between the ADC and
  Receiver Output(50-ohm)gt Quantization Noise
• To place a 50-ohm resistive load at the input of
  the ADC

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Noise and Solution

• The Receiver Noise
• Higher ResolutiongtSmaller Quantization Noise
  PowergtLess Gain

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Signal-to-Noise Ratio

• Theoretical S/N ratio due to quantization noise

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Signal-to-Noise Ratio

• Theoretical S/N ratio due to aperture jitter
  noise
• Sources
• Externally by jitter in the sampling clock
• Internally by sampling switches
• SNRSNRqSNRaj

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Residual Error

• Definition
• Residual error is the combination of quantization
  noise, random noise, and nonlinear distortion.
• Measure
• Output signal - input signal(sin wave)

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Spurious Free Dynamic Range

• Definition
• Ratio of the sinusoidal signal power to the peak
  power of the largest spurious signal in the ADC
  output spectrum.
• Application
• Desired signal BW less than Nyquist BW
• SRDRgtgtSNR

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Noise Power Ratio

• Definition
• PSD of noise outside BW of notch filter/PSD of
  noise inside BW of notch filter
• Measure
• By using a noise input signal into the ADC
• Application
• Desired signal spectrum with many channels

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Summay of ADC Specifications for Radio Receiver
Application
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Critical ADC Specification for Typical
Application
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Examples of current high-speed ADC technology