# How can I determine the equation for the output voltage?

This is circuit is proposed for a thermomether based on the TSP102 sensor (linear PTC). How can I determine the equation for the output voltage? My main question is about the op amp. I know that two voltages dividers are the inputs of the op amp. What would the equation be for the op amp output?

• Have you done the current calculations yet? – Ignacio Vazquez-Abrams Jul 11 '16 at 2:45
• Yes, I have them. – Blue_Electronx Jul 11 '16 at 3:32
• Then calculate Vo/Vin and...done? – Daniel Jul 11 '16 at 4:33

One way to simplify the problem is to use the Thevenin equivalent circuits for those voltage dividers you have there. That is, you could draw the circuit in this manner:

simulate this circuit – Schematic created using CircuitLab

Here $$V_{th1}=\frac{R_1}{R_{sensor}+R_1}V_{cc}$$ $R_1$ is just your 680 ohm resistor in series with your 500 ohm potentiometer. $V_{cc}$ is the supply voltage.

Your $R_{th1}$ is simply: $$R_{th1}=R_1||R_{sensor}$$

The same procedure is done for $V_{th2}$ and $R_{th2}$.

You should get $V_{th2}=\frac{V_{cc}}{2}$ and $R_{th2}=\frac{R}{2}$. Where $R=1.2k\Omega$.

Now, you can use $V^-=V^+$ and start your opamp analysis. In the end, you should obtain the equation for the opamp as a differential amplifier. I'll let you do the math, but your final solution for $V_{out}$ should be (if I didn't mess up somewhere):

$$V_{out}=V_{th2}-\frac{R_f}{R_{th1}}(V_{th1}-V_{th2})$$

Where $R_f$ is your $5k\Omega$ feedback potentiometer.