SaM - Full Bridge

We have seen the quarter bridge, the half brige. Let’s see how we can design a full bridge with $4$ strain sensors, on a cantilever:

• $\epsilon$ : strain
• $w$ is the width.
• $E$ is the Young modulus.
• $F$ is the force, the force magnitude.

Design of a full bridge:

$\frac{V_{TH}}{V}$ is equal to:

• $R_1=R_3=R_0(1+G\epsilon )$
• $R_2=R_4=R_0(1-G\epsilon )$

Continuing:

So it is important to remember that:IMPORTANTE $\frac{V_{TH}}{V}=G\epsilon$Supposing that we have taken $K=1$, and remember that $K$ is defined as:$K=\frac{R_{40}}{R_{10}}=\frac{R_{30}}{R_{20}}$

==So this is a linear circuit, the voltage output is related to the strain in a linear way, always. It’s a differential sensor: that means that if I have variations, which are of the same sign like the ones due to temperature variation, they are cancelled by the structure of the brigdge==.

NOTE: I’ve put a zero in the subscript of the resitances to represent that they are sensors.

So ==the full bridge is always linear and it rejects common mode disturbances==.

What are the gains of using a full bridge instead of a half brige?

• If $(1+K)\gg x_1$ and $(1+K)\gg x_2$ the half bridge behaves linearly.
  While ==the full bridge always behave linearly==.
• It has higher sensitivity than the half bridge.
• However it requires four sensors, so requires more space, and has a higher cost.