Data acquisition & sampling worksheet with answers

Free printable Data acquisition & sampling worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
Vin​N = 82.5 V2ᴺ − 101 LSB

An 8-bit ADC that rounds to the nearest code has an input range of 0 to 2.5 V. With 1 LSB = VFSR/2ᴺ, find the largest quantisation error eq,max in mV.

N = 8VFSR = 2.5 V
eq,max = mV
2.Easy
Vin​N = 85 V2ᴺ − 101 LSB

An 8-bit ADC that rounds to the nearest code has an input range of 0 to 5 V. With 1 LSB = VFSR/2ᴺ, find the largest quantisation error eq,max in mV.

N = 8VFSR = 5 V
eq,max = mV
3.Medium
tTs​ = 1/fs​f = 4.4 kHzfs​ = 4 kHz

A 4.4 kHz sine wave is sampled at 4 kHz without an anti-aliasing filter. At which frequency fa does it appear in the samples? Give it in Hz.

f = 4.4 kHzfs = 4 kHz
fa = Hz
4.Medium
Vin​N = 10VFSR​2ᴺ − 101 LSB

Find the ideal signal-to-quantisation-noise ratio SQNR of a 10-bit ADC for a full-scale sine wave.

N = 10
SQNR = dB
5.Hard
SD0​D1​D2​D3​D4​D5​D6​D7​1/fbaud​20 MHz / (16·D)

A microcontroller with a 20 MHz clock sets its UART baud rate as fclk/(16·D), with D a whole number rounded to the nearest value. The target is 38400 baud. Find the percentage error of the real baud rate (positive when it is too fast).

fclk = 20 MHztarget = 38400 Bd
e = %
6.Hard
f0fs​/2fs​2fs​560 Hz7f₁?

A 560 Hz square wave is sampled at 2 kHz with no anti-aliasing filter. A square wave contains the odd harmonics 3f₁, 5f₁, 7f₁, … At which frequency fa does its harmonic 7f₁ appear in the sampled data? Give it in Hz.

f₁ = 560 Hzfs = 2 kHzharmonic: 7f₁
fa = Hz

Answer key

  1. 1. eq,max = 4.883 mV
  2. 2. eq,max = 9.766 mV
  3. 3. fa = 400 Hz
  4. 4. SQNR = 61.96 dB
  5. 5. e = −1.357 %
  6. 6. fa = 80 Hz

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