Analog Engineer's Circuit

Amplifiers

Design Goals

Design Description

This temperature sensing circuit uses a resistor in series with a positive-temperature-coefficient (PTC) thermistor to form a voltage-divider, which has the effect of producing an output voltage that is linear over temperature. The circuit uses an op amp in a non-inverting configuration with inverting reference to offset and amplify the signal, which helps to utilize the full ADC resolution and increase measurement accuracy.

Circuit Schematic Description: The circuit schematic shows a voltage divider formed by resistor R1 (10 kΩ) and a PTC thermistor. This divider is connected to the non-inverting input of an op-amp (U1 TLV9002). The op-amp is configured in a non-inverting amplifier configuration with feedback resistors R2 (510 Ω) and R4 (510 Ω) in parallel, and a series resistor R3 (3 kΩ) connected to VDD. The input voltage Vin is taken from the junction of R1 and the PTC. The output voltage Vout is taken from the op-amp's output. VDD is supplied at 3.3V.

Design Notes

1. Use the op amp in a linear operating region. Linear output swing is usually specified under the AOL test conditions. TLV9002 linear output swing 0.05 V to 3.25 V.
2. The connection, Vin, is a positive temperature coefficient output voltage. To correct a negative-temperature-coefficient (NTC) output voltage, switch the position of R₁ and PTC thermistor.
3. Choose R₁ based on the temperature range and the PTC's value.
4. Using high-value resistors can degrade the phase margin of the amplifier and introduce additional noise in the circuit. It is recommended to use resistor values around 10kΩ or less.
5. A capacitor placed in parallel with the feedback resistor will limit bandwidth, improve stability and help reduce noise.

Design Steps

The output voltage equation for the circuit is:

1. Calculate the value of R₁ to produce a linear output voltage. Use the minimum and maximum values of the PTC to obtain a range of values for R1.
   RPTCMax = RPTC @ 50°C = 11.611 kΩ
   RPTCMin = RPTC @ 0°C = 8.525 kΩ
   R₁ = √(RPTC @ 0°C × RPTC @ 50°C) = √8.525 kΩ × 11.611 kΩ = 9.95 kΩ ≈ 10 kΩ
2. Calculate the input voltage range.
   VinMin = Vdd × (RPTCMin / (RPTCMin + R1)) = 3.3 V × (8.525 kΩ / (8.525 kΩ + 10 kΩ)) = 1.519 V
   VinMax = Vdd × (RPTCMax / (RPTCMax + R1)) = 3.3 V × (11.611 kΩ / (11.611 kΩ + 10 kΩ)) = 1.773 V
3. Calculate the gain required to produce the maximum output swing.
   Gideal = (VoutMax - VoutMin) / (VinMax - VinMin) = (3.25 V - 0.05 V) / (1.773 V - 1.519 V) = 12.598 V/V
4. Solve for the parallel combination of R2 and R4 using the ideal gain. Select R3= 3 kΩ (Standard Value).
   (R2||R4)ideal = R3 / (Gideal - 1) = 3 kΩ / (12.598 V/V - 1) = 258.665 Ω
5. Calculate R2 and R4 based off of the transfer function and gain.
   R4 = (R3 × Vdd) / (VinMax × Gideal - VoutMax) = (3 kΩ × 3.3 V) / (1.773 V × 12.598 V/V - 3.25 V) = 518.698 Ω
   R2 = ((R2||R4)ideal × R4) / (R4 - (R2||R4)ideal) = (258.665 Ω × 518.698 Ω) / (518.698 Ω - 258.665 Ω) = 515.969 Ω
6. Calculate the actual gain with the standard values of R2 (510 Ω) and R4 (510 Ω).
   Gactual = ((R2||R4) + R3) / (R2||R4) = (255 Ω + 3 kΩ) / 255 Ω = 12.764 V/V

Design Simulations

DC Transfer Results Description: The DC Transfer Results plot shows the output voltage (Vout) in Volts on the Y-axis versus Temperature in Celsius on the X-axis. The plot is a nearly linear line from approximately 0°C to 50°C. Key points indicated are: at 0°C, Vout is 21.95mV; at 25°C, Vout is 1.63V; and at 50°C, Vout is 3.23V.

Design References

1. Analog Engineer's Circuit Cookbooks
2. SPICE Simulation File SBOMAV5
3. TI Precision Labs

Design Featured Op Amp

Design Alternate Op Amp

Design Featured Thermistor

Revision History

NOTE: Page numbers for previous revisions may differ from page numbers in the current version.

Changes from Revision A (May 2019) to Revision B (May 2021)

• Updated VREF with voltage divider, changed schematic, and equations.

Changes from Revision * (December 2018) to Revision A (May 2019)

• Added Design Featured Thermistor table.

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