Natural vs Flat Top Sampling

Convert continuous audio into discrete pulses for digital conversion. Sample and hold circuits like the LF398 rely entirely on flat top sampling.

Core Concept

A sampling switch multiplies the analog signal with a periodic pulse train. Natural sampling leaves the top of each pulse matching the exact contour of the input signal. The voltage varies continuously during the pulse duration.

Analog to digital converters cannot work with a varying voltage. Flat top sampling solves this by holding the instantaneous voltage constant for the entire pulse duration. A hold capacitor briefly stores this sampled value.

While practical to build, holding the voltage causes distortion in the frequency domain. This rectangular pulse shape alters the high frequency content of the recovered audio. Engineers must correct this distortion before final output.

Key Equations

Flat top sampling introduces a sinc function envelope to the spectrum. H(f) = T * sinc(f * T) models this attenuation.

Here T represents the pulse duration. Longer pulses create worse high frequency roll-off. sinc(x) = sin(pi * x) / (pi * x) is the standard mathematical definition.

Given:\nFrequency (f) = 4000 Hz\nPulse width (T) = 50 us (0.00005 s)\n\nWhy this formula:\nThe sinc function envelope dictates the attenuation of the original signal.\n\nFormula:\nMagnitude = sinc(f * T)\n\nSubstitution:\nMagnitude = sinc(4000 * 0.00005)\n\nCalculation:\nProduct = 0.2\nMagnitude = sin(180 * 0.2 degrees) / (pi * 0.2)\nMagnitude = sin(36 degrees) / 0.628\nMagnitude = 0.587 / 0.628\nMagnitude = 0.934\n\nFinal Answer:\n0.934 (or 93.4 percent)

Exam Tip: Flat top sampling introduces aperture effect distortion. This severe high frequency roll-off requires an equalizer circuit at the receiver to flatten the spectrum back out.

Key Properties

• Natural sampling requires instantaneous switching but produces no frequency distortion.
• Flat top sampling dominates modern digital systems because ADCs require stable input voltages.
• A sample and hold amplifier performs flat top sampling perfectly.
• The hold capacitor dictates how flat the top remains during conversion.
• Wider sampling pulses worsen the aperture effect significantly.

Quick Revision

• Natural sampling retains the exact analog shape.
• Flat top sampling creates a staircase approximation.
• Aperture effect only happens with flat top sampling.
• Equalizers easily reverse aperture distortion.
• Practical switching circuits heavily favor flat top methods.
• Exam trap: Assuming natural sampling and flat top sampling have the exact same spectrum envelope.