ADC resolution for an LM35 temperature sensor

LSB size = V_ref / 2^N. Convert it to °C using the sensor's 10 mV/°C.

Worked answer.

(a) Resolution with a 5 V reference

• LSB = V_ref / 2¹⁰ = 5 / 1024 ≈ 4.883 mV.
• Temperature per LSB = 4.883 mV / (10 mV/°C) ≈ 0.49 °C.
• Reading of 62: V = 62 × 4.883 mV ≈ 302.7 mV, so T ≈ 30.3 °C.

The sensor's full range is only 0–1.0 V, so it uses about 20% of the ADC's input range. Most of the codes are wasted.

(b) Getting about 0.1 °C

Option 1: Lower the reference. Many microcontrollers (for example the ATmega328P) have an internal 1.1 V reference.

• LSB = 1.1 / 1024 ≈ 1.074 mV, so resolution ≈ 0.107 °C.
• Maximum measurable temperature = 1.1 V / 10 mV/°C = 110 °C, which covers 0–100 °C.
• Trade-off: the internal reference has a tolerance of several percent, so it must be calibrated for good accuracy.

Option 2: Amplify the signal. Use a non-inverting op-amp with gain 5 so that 0–1 V becomes 0–5 V.

• Effective resolution = 4.883 mV / (10 mV/°C × 5) ≈ 0.098 °C.
• Trade-off: the op-amp's offset and gain errors add to the error budget, and a rail-to-rail op-amp is needed to reach close to 5 V.

(c) Ideal SQNR
SQNR = 6.02N + 1.76 dB = 6.02 × 10 + 1.76 ≈ 61.96 dB for a full-scale sine wave.

Check. With 1.1 V reference, 100 °C gives 1.0 V, which is code 1.0 / 1.074 mV ≈ 931, below the 1023 maximum, so there is no clipping.

Key point. Resolution is not accuracy. The LM35 itself is only guaranteed to within about ±0.5 °C to ±1 °C at room temperature, depending on the grade, so 0.1 °C resolution gives finer steps but not a more accurate reading unless you calibrate.

Likely follow-up. "How would you reduce noise in the reading?" Average or oversample several readings, add an RC filter at the ADC input, and keep the analog ground separate from noisy digital returns.