Design Steps

V_{o u t} = V_{d d} \times \frac{R_{P T C}}{R_{P T C} + R_{1}} \times \frac{(R_{2} | | R_{4}) + R_{3}}{(R_{2} | | R_{4})} - (\frac{R_{3}}{R_{4}} \times V_{d d})

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.
$R_{P T C M a x} = R_{P T C @ 50 C} = 11.611 k Ω, R_{P T C M i n} = R_{P T C @ 0 C} = 8.525 k Ω$
$R_{1} = \sqrt{R_{P T C @ 0 C} \times R_{P T C @ 50 C}} = \sqrt{8.525 k Ω \times 11.611 k Ω} = 9.95 k Ω \approx 10 k Ω$
Calculate the input voltage range.
$V_{i n M i n} = V_{d d} \times \frac{R_{P T C M i n}}{R_{P T C M i n} + R_{1}} = 3.3 V \times \frac{8.525 k Ω}{8.525 k Ω + 10 k Ω} = 1.519 V$
$V_{i n M a x} = V_{d d} \times \frac{R_{P T C M a x}}{R_{P T C M a x} + R_{1}} = 3.3 V \times \frac{11.611 k Ω}{11.611 k Ω + 10 k Ω} = 1.773 V$
Calculate the gain required to produce the maximum output swing.
$G_{i d e a l} = \frac{V_{o u t M a x} - V_{o u t M i n}}{V_{i n M a x} - V_{i n M i n}} = \frac{3.25 V - 0.05 V}{1.773 V - 1.519 V} = 12.598 \frac{V}{V}$
Solve for the parallel combination of R₂ and R₄ using the ideal gain. Select R₃= 3 kΩ (Standard Value).
${(R_{2} | | R_{4})}_{i d e a l} = \frac{R_{3}}{G_{i d e a l} - 1} = \frac{3 k Ω}{12.598 \frac{V}{V} - 1} = 258.665 Ω$
Calculate R₂ and R₄ based off of the transfer function and gain.
$R_{4} = \frac{R_{3} \times V_{d d}}{V_{i n M a x} \times G_{i d e a l} - V_{o u t M a x}} = \frac{3 k Ω \times 3.3 V}{1.773 V \times 12.598 \frac{V}{V} - 3.25 V} = 518.698 Ω$
$R_{2} = \frac{{(R_{2} | | R_{4})}_{i d e a l} \times R_{4}}{R_{4} - {(R_{2} | | R_{4})}_{i d e a l}} = \frac{258.665 Ω \times 518.698 Ω}{518.698 Ω - 258.665 Ω} = 515.969 Ω$
Calculate the actual gain with the standard values of R₂ (510 Ω) and R₄ (510 Ω).
$G_{a c t u a l} = \frac{(R_{2} | | R_{4}) + R_{3}}{(R_{2} | | R_{4})} = \frac{255 Ω + 3 k Ω}{255 Ω} = 12.764 \frac{V}{V}$