Accelerometer Design

# Would you know to predict the phase of the output?

Why would you worry about this question. In practice if we need to determine that, we rather press on the piezo and see if the positive side is up or down.

Either way let’s try to find it out in theorie. First we have to decide what we call positive and negative. It’s all a question of conventions.

## The Physics of current flow

Electrical current is the flow of electrons. Metals or other electrical conductors are made of atoms with a lot of free electrons. When we apply an electromotive force along a wire, free electrons jump from one atom to the next, creating current flow. We know that the negative electrons are attracted by the positive charge so we can deduct that current is flowing from the negative side to the positive.

### Conventional (technical) current

It started all with Benjamin Franklin.

At the time very little was known about the mysterious force called electricity. Franklin was one of the first who made physical experiments about electrical charge. He found that when a glass rod was rubbed with silk the glass was loaded with electricity.

Franklin discovered that in a closed system the sum of the existing electrical charge remains constant. He raised the convention of assigning positive charge signs to the “things” that were moving in a circuit doing work.

It turns out that Franklin was wrong regarding the sign of the charges that move. Today we know that electrons are free to move and protons are not. The silk was producing negative charge on the glass.

So why do we mostly use conventional current flow if it’s wrong? In fact, most formulas used in electrical engineering such as Ohm’s Law presume that the current is flowing from positive to negative. That’s why we also presume for our calculations that the current flows from positive to negative.

### Pico Coulombs are positive

We have seen in the previous chapter that the magnitude of the charge of one electron is

e = 1.6 · 10⁻¹⁹ C (Coulomb)

Strictly speaking it should read e = - 1.6 · 10⁻¹⁹ C, because if we have a positive current (Coulombs per second) then positive charges are flowing from the positive pole to the negative pole.

So let’s agree that a pC (with no sign) shall be a positive charge.

### Convention on a positive force

Most text books on mechanics presume that a force out of a body (tension) is positive, while a force into the body (compression) shall be negative.

If we apply this to our piezoelectric constants we should get (with a positive d33 constant) a negative charge when we compress the element and a positive charge if we pull on it!

So the term «compression mode» is somewhat misleading and we better should use the expression longitudinal mode instead.

### Mounting of the piezo element

Of course we need also to consider the orientation of the piezo element. If we mount it upside down the positive charge will appear on the other side.

### Combination

If you combine now all this you should perfectly be able to tell the output sign of the accelerometer (dont forget in a sinusoidal motion the acceleration is inverse to the displacement).

If you still have concerns go back to first sentence at the top. ;-)

## Yet another worry

We have a positive charge Q on one side and the corresponding negative charge on the other side of a piezo element.

Question: Is the total charge from the positive to the negative pole then 2Q ?

We remember that charge cannot be produced but only separated (negative from positive).

A negative charge is due to a surplus of electrons, while the corresponding positive charge means a deficit of these electrons. So the total charge available from + to – is still only 1Q !

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