piezoelectric elements

7/29/2019 Piezoelectric Elements

1/15

The unit cell of crystal silicon dioxide

-

+

+

-

+

-

+ = Silicon

- = Oxygen

By definition: A unit cell is the smallest parallelepiped

(6 sided parallelogram) that will describe the molecule.


2/15

-

+

+

-

+

-

Unit Cell at Rest

-

+

+

-

+

-

Neutral Charge

Unit Cell Under Mechanical

Compression (pushing force):Electrical polarity as shown

-

+

+

-

+

-

Unit Cell Under mechanical

Tension (pulling force):

Electrical polarity reverses.

+ + +

- - -

+ + +

- - -

+


3/15

-

+

+

-

+

-

-

+

+

-

+

-

+ + +

- - -

Unit Cell at Rest

Neutral Charge

2 compression forces in

opposite directions...

Will also result in electrical energy!

This is called ashearforce, and is the most common mechanical

distortion in crystals we make: This is where the famous term:

Thickness Shearhas its origins.-AT, -BT, & SC crystals all are

shear mode devices (more on this later)


4/15

What we have learned so far.

The unique piezoelectricand converse piezoelectricproperties ofcrystalline quartzallow us to design anelectro-mechanical device (mechanical force = electrical

signal; electrical field = mechanical deformation)

By operating the device at its mechanical resonancefrequency, we can get a useful electrical signal out of it:The electrical signal will be at the same frequency as the

mechanical resonance frequency. If we know how to control the devices mechanical

resonance frequency, we ought to be able to design adevice at any frequency of interest..


5/15

For purposes of this class, the term frequencyrefers to amathematical description of a periodic (or repeating)signal.

Since all of the devices we build at VF are designed to

produce a very stable frequency signal, we can analyze a

typical output signal to get a general feeling how the signal

behaves.

Definition of Frequency.


6/15

Anatomy of a Sine Wave and a Square Wave

Sine Wave

Square Wave


7/15

Amplitude: A measure of how big the signal is. Usually expressed in

Electrical Units (voltage or current).Wavelength: How long the signal is (usually in meters).

Period: How much time it takes to complete 1 cycle (measured in seconds).

Frequency: The number of complete cycles in a 1 second chunk of time.

Frequency is equivalent to 1/Period, and is commonly measured in

Hertz; 1 Hz = 1 cycle per second

Amplitude,pk to pk

Time

Wavelength

Period


8/15

Now, we should have enough information to allow us to design a crystal.

We will build an y-cut extensional vibrational mode crystal that will

operate at a fundamental resonance frequency of 50 kHz...

Extensional Modeis the $5.00 term meaning the part gets longer when an electricalfield is applied (remember: E field = mechanical deformation!).

We also need a pair of electrodes to connect to a circuit:

These are simply a couple of conductive plates attached to the

major faces of the crystal.

Electrode

Wires for circuit

attachment

Crystal at restSame crystal with

driving signal applied,

operating in lengthextension mode.


9/15

First, you need to know how to reference the crystal out of the

raw crystal stone. Both X-cut and Y-cut crystals are simply

cut parallel to their respective axes (more complicated cuts

require x-ray technology to locate the crystal axis orientation)

z

y

x


10/15

For the case of an X-cut or Y-cut, the resonance frequency is related to the

geometry of the blank by a 1/2 wavelength ratio. This is similar in nature to the

xylophone, where each metal bar is tuned to an audible tone.

I offer the following mathematical relationship without proof so as to avoid

confusion. I have provided this proof in the class notes I sent out to everyone.

For now, just take my word for it...

tnkf xx

fx is the frequency in the x direction.

nis the harmonic order (dont worryabout this for now).

t is the thickness of the crystal.

kxis known as the frequency

constant in the x direction.

fy is the frequency in the y direction.nis the harmonic order (dont worry

about this for now).

l is the length of the crystal.

kyis known as the frequency

constant in the y direction.

l

nkf y

y


11/15

l

nk

f

y

y

t

nkf tx

fx We want 50 kHz.

n = 1, for fundamental mode.

l is the thickness of the crystal.

ky In the Y direction, this is 2600 kHz-mm

PROBLEM 1

fx: We dont want the crystal to vibrate in

the x (thickness) direction at all! This maycause interference with the vibration in the x

direction.

Also, the frequency constant is different in

the x direction (2870 kHz-mm) This is due to

the anisotropic nature of quartz: That is, dueto the crystalline molecular structure, some

physical properties of the device change with

direction.


12/15

One clever way around this dilemma is to change the aspect ratio so that the

dominant resonance is in the direction of interest.

Aspect ratio is engineer-ese for the length-to-thickness ratio, in this case.EXAMPLE: For an aspect ratio of 10:1, a 10 mm length has a 1 mm thickness.

Lets take a guess and make the length 10 times the width

And begin the design:


13/15

mml

kHzmmkHzl

or

l

mmkHzkHzff

ly

52

502600

,

260050

This is about 2 inches, so with an aspect ratio

of 10:1, the thickness will be 5.2 mm, or about

0.2


14/15

Since we have not put any restrictions on the Z axis (which is the width), we can

choose to go with a convenient value that will take other design aspects into

account. Lets say that the only electrodes available to us are 0.35

0.35 = 9 mm.

Now, we can simply make the Z width something slightly larger. Lets try a length

to width aspect ratio of 5 (eg: length is 5 times the width).

mmmm

mmw

lw

4.100.5

0.52

5

This width should work fine

for our 9 mm electrode.


15/15

Summary of the finished design

Length: 52.0 mm (2.05)

Width: 10.4 mm (0.41)

Thickness: 5.2 mm (0.20)

Electrode W.: 9.0 mm (0.35)

w

l

t

Elec.

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