How to solve for amplification and gain in a transducer (thermometer example)

Basic introduction to transducers and a quick example of amplifying a microphone signal to a computer speaker.

Below is the basic format:
Sensor to electric signal -- amplify electric signal and change bias – thermometer output

thermocouple -- amplify electric signal and change bias – thermometer output

2 to 4 mV corresponds to 0 to 100 degrees Celsius -- amplify electric signal and change bias – thermometer output, 0 to 5 V corresponds to 0 to 100 degrees Celcius

Here we can't just multiply by K because, say it's 0 degrees and we needed to translate 2 mV to 0 V, we would have to multiply by 0, but of course then every temperature would give us 0 output voltage. So we have to introduce a bias as well.

To do this it may help to create a little table:

V_out = K V_in + B

So you may notice this looks like an equation for a line, y=mx+b and we can just consider this like a graph with V_in as my x and V_out as my y

So we have two points we need to connect

And you notice if we a draw a line through these two points we get an intersection on the x axis at our B value.

Two find this equation we can first find the slope as the rise/run

Rise = (V_out2-V_out1) = (y_2-y_1)= (5-0) = 5

Run = (V_in2 – V_in1) = (x_2-x_1) = 0.004-0.002= 0.002

So our slope will be 5/0.002 = 2500, which will be our b value

Then use our point-slope formula

Y-y_1= m (x-x_1)

Y-0 = 2500 (x-0.002)

Y=2500x-5

So our m value of 2500 is our K

And our b value of –5 is our big B

And our diagram for the transducer would look like this: