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 = 121 V2ᴺ − 101 LSB

A 12-bit ADC that rounds to the nearest code has an input range of 0 to 1 V. With 1 LSB = VFSR/2ᴺ, find the largest quantisation error eq,max in mV.

N = 12VFSR = 1 V
eq,max = mV
2.Easy
Vin​N = 810 V2ᴺ − 101 LSB = ?

An 8-bit ADC has an input range of 0 to 10 V. Taking 1 LSB = VFSR/2ᴺ, find the size of one LSB in mV.

N = 8VFSR = 10 V
1 LSB = mV
3.Medium
tTs​ = 1/fs​f = 23 kHzfs​ = 20 kHz

A 23 kHz sine wave is sampled at 20 kHz without an anti-aliasing filter. At which frequency fa does it appear in the samples? Give it in kHz.

f = 23 kHzfs = 20 kHz
fa = kHz
4.Medium
Vin​N = ?500 kPa2ᴺ − 10≤ 1 kPa

A sensor measures pressure over a span of 500 kPa, and its output fills the whole input range of an ADC. The reading must resolve 1 kPa. Find the smallest number of bits N the ADC needs.

span = 500 kParesolution = 1 kPa
N =
5.Hard
f0fs​/2fs​4.4 kHz5f₁?

A 4.4 kHz square wave is sampled at 20 kHz with no anti-aliasing filter. A square wave contains the odd harmonics 3f₁, 5f₁, 7f₁, … At which frequency fa does its harmonic 5f₁ appear in the sampled data? Give it in kHz.

f₁ = 4.4 kHzfs = 20 kHzharmonic: 5f₁
fa = kHz
6.Hard
T10 mV/°C×10∿01N = 8, 5 V? °C/LSB

A temperature sensor gives 10 mV/°C (0 V at 0 °C). Its signal is amplified 10 times and fed to an 8-bit ADC with a range of 0 to 5 V (1 LSB = VFSR/2ᴺ). Find the temperature change ΔTLSB that corresponds to one LSB.

S = 10 mV/°CG = 10N = 8VFSR = 5 V
ΔTLSB = °C

Answer key

  1. 1. eq,max = 0.1221 mV
  2. 2. 1 LSB = 39.06 mV
  3. 3. fa = 3 kHz
  4. 4. N = 9
  5. 5. fa = 2 kHz
  6. 6. ΔTLSB = 0.1953 °C

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