Wheatstone Bridge Learning Module

Wheatstone Bridge Learning

Module

Wheatstone Bridge (WB) Unit

Pressure Sensor Model Activity

WB Derivation Activity

Participant Guide www.scme

nm.org

Southwest Center for Microsystems Education (SCME)

University of New Mexico

MEMS Introduction Topic

Wheatstone Bridge Overview

Primary Knowledge (PK)

Shareable Content Object (SCO)

This SCO is part of the Learning Module


Target audiences: High School, Community College.

Support for this work was provided by the National Science Foundation's Advanced Technological Education

(ATE) Program through Grants #0830384 and 092411.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and creators, and do not necessarily reflect the views of the National Science Foundation.

Copyright 2009 - 2011 by the Southwest Center for Microsystems Education and

The Regents of the University of New Mexico

Southwest Center for Microsystems Education (SCME)

800 Bradbury Drive SE, Ste. 235

Albuquerque, NM 87106-4346

Phone: 505-272-7150

Website: www.scme-nm.org

email contact: mpleil@unm.edu

Southwest Center for Microsystems Education (SCME)

Int_WheatB_PK01_PG_061411

Page 2 of 14

Wheatstone Bridge PK


Primary Knowledge

Participant Guide

Description and Estimated Time

This Wheatstone Bridge Overview provides information on the electronic circuitry of a Wheatstone

Bridge. This overview will help you to understand how a Wheatstone Bridge is used for sensing changes in pressure when used in a MEMS pressure sensor.

Estimated Time to Complete

Allow approximately 1 hour to complete.

Introduction

A Wheatstone bridge is an electrical circuit design dating back to the early 1800's. It is named for its most famous user, Sir

Charles Wheatstone. Sir Wheatstone never claimed to have invented it; however, he did develop multiple uses for it. The

Wheatstone bridge circuit was invented by Samuel Hunter

Christie (1784-1865) and first described in 1833

1

. Sir

Wheatstone actually called the circuit a “Differential Resistance

Measurer.”

The Wheatstone bridge is one of the most sensitive and precise methods of measuring small changes in resistance. This is possible through its use of transducers (devices which change one form of energy into another, such as mechanical to electrical or electrical to mechanical). The Wheatstone bridge incorporates one or more electrical transducers that change resistance as a result

Sir Charles Wheatstone

2

National Portrait Gallery, London of an environmental change or input (e.g., temperature, pressure, stress). This change is sensed by the circuitry of the Wheatstone bridge which provides a useable electrical output (voltage) representative of the input. The Wheatstone bridge is widely used today in both macro-sized and micro-sized sensors.

This unit will describe the basics of the Wheatstone bridge circuit.



Page 3 of 14


Objectives



Define the variable components of the Wheatstone bridge.



Describe how the Wheatstone bridge works.

Key Terms (These terms are defined in the glossary at this end of this unit.)

Calibration Curve

Electric circuit

Kirchhoff’s Voltage Law

Ohm’s Law

Resistance

Resistivity

Resistor

Signal to Noise Ratio

Transducer

Voltage

Wheatstone Bridge

The Wheatstone Bridge

A Wheatstone bridge is a simple circuit used to measure small changes in resistance of a transducer.

The classic Wheatstone bridge configuration consists of four resistors, three of which are of fixed value and a fourth which is variable, see R

4

in the diagram below. The variable resistor is the sensing element (transducer). Its design will allow its resistance to change due to a change in an environmental factor such as stress, pressure, or temperature.

Basic Wheatstone Bridge Configuration with one transducer or sensing element (R

4

)



Page 4 of 14


Some Wheatstone bridge designs include two variable resistors (sensing elements) to improve the sensitivity of the system, and to provide an enhanced voltage variation as a function of the changing input. When applied to a microsystems pressure sensor system, the bridge circuit has two fixed resistors (R

2

and R

3

below), and two variable resistors (R

1 and R

4

) that are the transducers (see diagram below) . A direct current (DC) voltage source such as a battery provides the input Voltage.

The Wheatstone bridge output is called the gap voltage (V g

) and is proportional to the difference in the transducers’ resistance values relative to the reference resistance in the bridge configuration.

This design allows for the measurement of very small changes in the environmental factor that affects the transducer resistance. The design of the circuit reduces the effects of noise on the output voltage. For example, if the input voltage varies, it does not influence the output voltage since it is related to the ratio of the resistances. Also, a variation in temperature affects all the resistor elements equally and therefore cancel each other out. Therefore, this circuit greatly suppresses electrical noise and thereby improves the signal to noise ratio.

Basic Wheatstone Bridge Configuration with two transducers or sensing elements (R

1

and R

4

)



Page 5 of 14


Background Circuits

The Wheatstone bridge is based on a simpler circuit element called the voltage divider. There are two basic concepts needed to understand how these circuit elements operate:

 Ohm’s Law (I=V/R)

 Kirchoff’s Circuit Laws

Resistor Voltage Dividers

The figure below is made up of two resistors placed in series labeled R

1

, R

2

, and a power supply V in

(battery).

Resistive Voltage Divider

The electron flow or current I in

is measured in Amperes (A), and travels from the negative terminal of the battery through the resistors to the positive terminal of the battery. As the electrons move through the resistors, they loss some of their energy, and this is measured as voltage drop (reduction) across the resistors.

Ohm's Law

Ohm's Law determines the voltage drop (or change) across a resistor R for a given current I . Ohm's

Law states: V = IR where V is the voltage difference across a resistor R that has current I flowing through it. In the Resistive Voltage Divider circuit above, the voltage drop, V

1

across resistor R

1

is written as and the voltage drop, V

2

across resistor R

2

is

V

1

= I in

R

1

V

2

= I in

R

2

.

To measure the V

2

across R

2

with reference to ground, a voltmeter is placed across the resistor. One lead is connected to the node located between R

1

and R

2

, and the other lead is connected to ground

(or the negative side of the voltage source). Ground reference voltage is 0 V. The voltmeter reads V

2

= I in

R

2

and this is the voltage difference which drives current through R

2

.



Page 6 of 14


Note that the current, I , is conserved, in other words, the amount of current flowing into the circuit is the same as the amount flowing out of the circuit. This is analogous to saying that the amount of water flowing into a houses’ plumbing circuit is equal to the amount of water flowing out of the same circuit. Water flow is analogous to electrical current flow. However, the water pressure measured coming into the house is higher than the pressure measured going out of the house. The water pressure is analogous to the voltage on a circuit. A thin pipe in a plumbing circuit will allow less water flow (current) and it will also result in a greater pressure drop (voltage change). This thinner pipe is analogous to a resistor having higher resistance.

Let's put some numbers to this Voltage divider circuit and check out our calculations.

V in

= 10V R

1

= R

2

= 500



The total circuit resistance R t

is equal to R

1

+ R

2

:

R t

= 500



+ 500



= 1000



or 1 k



Using Ohm's Law, calculate I in

.

I in



V in

R t



10 V

1 k





10 mA

Now you know I in

and can determine V

1

.

The voltage drop, V

1

across resistor R

1

is

V

1

= I in

R

1 or 10mA*500



= 0.01A*500



=5V

The voltage drop, V

2

across resistor R

2

is

V

2

= I in

R

2

or 10mA*500



= 0.01A*500



=5V



Page 7 of 14


Kirchoff’s Laws

Two of Kirchoff’s Laws can be applied to find out the voltages and currents in DC circuits.

Kirchoff’s current law, states that the sum of all currents entering a node in the circuit is zero.

Another way to look at this is that the current flowing into a node is equal to the current flowing out of it. Kirchhoff’s voltage law, states that the sum of the voltage drops across a collection of resistors arranged in series (in a line, one after the other) within a circuit is equal to the applied voltage across all the resistors ( V in

). In this example, it can then be written as

V in



I in

R

1



I in

R

2



I in



R

1



R

2



or

V in



V

1



V

2

Notice in that the previous problem shows this to be true:

10 v (V

in

) = 5 v + 5v

The voltage drop across a specific resistor in series with other resistors is the fraction of that resistor to the sum of the series resistors, multiplied by the applied voltage. (The formula is derived below.)

V

2



I in

R

2

I in



R

1

V in



R

2



R

1

V in



R

2

R

2



R

1

R

2



R

2

V in

Applying the values of the previous circuit, we get

V

2



500



500

 

500



10 V



5 V

The Wheatstone bridge has two such voltage dividers connected in parallel; therefore, the analysis of the resistive voltage divider circuit can be applied to the Wheatstone bridge circuit. Can you identify the two voltage divider circuits in the circuit below?

Wheatstone Bridge with two variable resistors



Page 8 of 14


Wheatstone Bridge and Difference Voltage

One Variable Resistor

Wheatstone Bridge with one variable resistor

The figure above shows the schematic circuit diagram of a Wheatstone bridge. The resistor pair R

1 and R

2

is a resistive voltage divider and resistors R

3

and R

4

form another voltage divider in parallel with R

1 and R

2

. The circuit is sensitive to the difference in voltage between nodea and nodeb . V a and V b can be found by

V a



R

1

R

2



R

2

V in

V b



R

3

R

4



R

4

V in so that

V a



V b



V ab

This can also be written as







R

1

R



2

R

2



R

3

R



4

R

4



 V in

𝑽 𝒂𝒃

= 𝐕 𝐢𝐧 𝑹

𝟏

𝑹

𝟐

+

𝑹

𝑹

𝟑

𝟐

− 𝑹

𝟏

𝑹

𝟑

𝑹

𝟒

+ 𝑹

𝟒

When R

2

R

3

= R

1

R

4

, the circuit output is zero, V ab

=0. The bridge is said to be balanced when V ab

=

0 volts. This occurs when R

1

/R

2

= R

3

/R

4

. In a typical sensing device, a variable resistor R

4

, is used.

The other three resistors are fixed. We will now refer to R

4

as R

S

. The Wheatstone Bridge is initially balanced with all of the R’s having the same resistance value by design, including R

S

(the resistance of the sensing element when there is nothing to sense). The value of R

S

changes when the external environment changes thus affecting V ab

as

V ab







R

1

R

2



R

2



R

3

R

S



R

S



 V in



Page 9 of 14


Assuming the input voltage, V in

= 10V and the transducer resistance R

S

is initially 100 Ohms (



), and R

1

= R

2

= R

3

= 100



, as well, then V ab

can be plotted as a function of R

S

:

Notice that when R

S

= 100



V ab

=0 volts and the bridge is balanced. Changes in the environment on the transducer affects its resistance, R s

, creating an unbalanced bridge which results in a voltage related to the resistance change. Based on the graph, if the resistance of R

S

increases, V ab

decreases.

A similar plot can be made plotting V ab

versus the environmental variable associated with the change in resistance.



Page 10 of 14


Two Variable Resistors

Looking carefully at the equations and the circuit diagrams, one can design a more sensitive circuit where R

1

and R

4

are both variable resistors. Such a circuit is shown below:

If the R

1

and R

4

resistors are both variable and react in the same manner to an external environmental change, then the effect on the output voltage, V ab

is amplified!

Reconsider the case where all resistances are initially at 100Ω each and V in

is 10 V. How would V ab be affected if both R

1

and R

4 both increased to 110 ohms? Graphing V ab

as a function of the variable resistances of R

1

and R

4

(in this case changing by the same amount while the other two, R

2 and R

3

remain constant at 100Ω) is shown in the following graph. Note: the variable resistors in the case of a strain gauge pressure sensor will only increase from the nominal value (why would this be?). In the graph below, the blue line represents the case when there is only one variable resistor.

The red line represents the transducer response when both R

1 and R

4 are variable.



Page 11 of 14


When the Wheatstone bridge is used in a pressure sensor, the resistors are oriented such that R

1

and

R

4 are variable under the stress of a flexible membrane on which they are made.

Membrane

(Diaphragm)

Wheatstone Bridge layout used in a Pressure Sensor

Actual pressure sensor photo showing the Wheatstone bridge circuit (gold) pattern on top of the silicon nitride membrane. This pattern is slightly different than the schematic.

[Image of a pressure sensor built at the Manufacturing Technology Training Center (MTTC) at the University of New

Mexico (UNM)]



Page 12 of 14


Calibration

To calibrate a Wheatstone bridge as a pressure transducer, a series of known pressure differences is applied to the sensing element(s). The output voltage ( V ab

) is measured using a voltmeter, and V ab versus pressure is plotted. Such a plot is referred to as a calibration curve. When an unknown pressure is subsequently applied and the output voltage read, the calibration curve of V ab vs.

Pressure can be used to determine the actual pressure.

The graph below is an example of a calibration curve based on an actual MEMS pressure sensor utilizing a Wheatstone bridge

5

. This graphic shows how to read the curve, for example, if an output voltage of .22 V is read, the corresponding pressure is approximately 82psi.

Summary

A Wheatstone bridge is a simple circuit used to measure transducer responses by measuring changes in voltage. Basic circuit analysis is used to determine the resistance, voltage and current when the bridge is balanced. Any change in transducer resistance causes the bridge output voltage to change corresponding to the change in pressure. A voltmeter measures the output of the Wheatstone bridge and the corresponding pressure is read off of the calibration curve. In a MEMS where the

Wheatstone bridge is part of the sensing circuit, its output can be amplified and processed to send information or to initiate a mechanical or electrical response.



Page 13 of 14


References

1 http://en.wikipedia.org/wiki/Wheatstone_bridge

2 http://www.britannica.com/EBchecked/topic/641626/Sir-Charles-Wheatstone

3

Dr. Chuck Hawkins, University of New Mexico , Wheatstone Bridge v3.doc

4

Wheatstone Bridge www.geocities.com/CapeCanaveral/8341/bridge.htm

5

Hsun-Heng Tsai*, Chi-Chang Hsieh, Cheng-Wen Fan, Young-Chang Chen and Wei-Te Wu

“Design and Characterization of Temperature-Robust Piezoresistive Micro-Pressure Sensor with Double Wheatstone

Bridge Bridge Structure”, DTIP of MEMS & MOEMS, 1-3 April, Rome, Italy, 2009.

Glossary of Key Terms

Calibration Curve – A plot of data acquired in the calibration of instrument or device. The curve is used to show how an instrument meets a standard or specification.

Electric circuit – A path or group of interconnected paths capable of carrying electric current.

Kirchhoff’s Voltage Law – The algebraic sum of all voltages in a closed loop of electric circuit must equal zero.

Ohm’s Law - The law stating that the direct current flowing in a conductor is directly proportional to the potential difference between its ends. It is usually formulated as V = IR, where V is the potential difference, or voltage, I is the current, and R is the resistance of the conductor.

Resistance – A component’s opposition to current passing through it,resulting in a change of electrical energy into heat or another form of energy.

Resistivity – The measure of how strongly a material opposes the flow of current.

Resistor – An electronic device designed with a specific amount of resistance; used to limit current flow or to provide a voltage drop.

Signal to Noise Ratio (SNR) – The ratio of the amplitude of a desired signal at any point to the amplitude of noise signals at that same point. (i.e., The ratio of a desired signal to the level of background noise.) A ratio less than 1:1 indicates that the background noise is greater than the desired (or reference) noise.

Transducer – A device that converts one form of energy to another form of energy. (e.g., A motor converts electrical energy to mechanical energy.)

Voltage – A representation of the electric potential energy per unit charge. A measurement of the energy contained within an electric field, or an electric circuit, at a given point.

Wheatstone Bridge – A four armed bridge circuit, each arm having a resistor (fixed or variable). It is used to measure an unknown resistance by balancing two arms of the bridge, one of which contains the unknown resistance.

Support for this work was provided by the National Science Foundation's Advanced Technological Education

(ATE) Program.



Page 14 of 14





Pressure Sensor Model Activity













Phone: 505-272-7150



Pressure Sensor Model Activity

Wheatstone Bridge Overview Learning Module


Description and Estimated Time to Complete

In this activity you will use basic materials to build a macro pressure sensor with a Wheatstone bridge sensing circuit (circuit right) on a flexible diaphragm. The results will simulate a MEMS pressure sensor (see Introduction) . To test your sensor, you will apply variable pressures to the diaphragm while monitoring the resistance change and resulting voltage output of the bridge.

The unit Wheatstone Bridge Overview, explains the operation of a Wheatstone bridge. If you haven’t already reviewed this unit, you should review it before you test your pressure sensor model. Complete this activity through “Making a conductive bridge pattern”. As your pattern dries, review the Wheatstone Bridge Overview. This will help you to better understand the workings of this device and the results of your testing.


Allow at least two hours to complete this activity.

Southwest Center for Microsystems Education (SCME)

Int_WheatB_AC02_PG_061511

Page 2 of 18

PS Model Activity

MEMS Pressure Sensor Applications

MEMS pressure sensors are designed to measure absolute or differential pressures. They convert physical quantities such as air flow and liquid levels into pressure values that are measured by an electronic system. MEMS pressure sensors can be used in conjunction with other sensors such as temperature sensors and accelerometers for multisensing applications or other components.

In the automotive industry, MEMS pressure sensors monitor the absolute air pressure within the intake manifold of the engine. MEMS are also being designed to sense tire pressure, fuel pressure, and air flow.

In the biomedical field, current and developing applications for MEMS pressure sensors include blood pressure sensors (see photo right) , single and multipoint catheters, intracranial pressure sensors, cerebrospinal fluid pressure sensors, intraocular pressure (IOP) monitors, and other implanted coronary pressure measurements. The photo shows three blood pressure sensors on the head of a pin. These sensors were developed by Lucas

NovaSensor to measure blood pressure and provide an electrical output representative of the pressure. RF elements are incorporated into the

MEMS device allowing the sensor to transmit its measurements to an external receiver.

MEMS Blood Pressure Sensors on the head of a pin. [Photo courtesy of Lucas

MEMS pressure sensors are also incorporated

NovaSensor, Fremont, CA] into endoscopes for measuring pressure in the stomach and other organs, infusion pumps for monitoring blockage, and noninvasive blood pressure monitors. Applications of MEMS pressure sensors within the biomedical field and other industries are numerous.

A MEMS Pressure Sensor

Many MEMS pressure sensors use a Wheatstone bridge configuration as the sensing circuit. In MEMS the Wheatstone bridge circuit is mounted on a membrane or diaphragm. The resistors in the

Wheatstone bridge are made of a piezoresistive material, a material which changes its resistance when mechanical stress is applied.



Page 3 of 18


In the example below, a conductive material such as gold is used for the bridge circuit. The pressure sensor diaphragm is a thin layer of material which is resistant to chemical change such as, in this case, silicon nitride (see image below) . One side of the diaphragm is sealed to provide a reference pressure. The other side is open to the environment and subject to air pressure variation. As the diaphragm moves due to pressure changes, the membrane expands and stretches. The bridge resistors mounted on the membrane also expand and stretch. This expansion of the bridge translates to a change of resistance in the conductive material of the bridge. As the conductive material stretches, its resistance increases.

Pressure Sensor illustrating the

Wheatstone bridge and the Silicon

Nitride Membrane (Diaphragm)

[Image of a pressure sensor built at the

Manufacturing Technology Training

Center (MTTC) at the University of New

Mexico (UNM)]

All materials have electrical resistance. The resistance to electrical current flow of an object

(resistor) is related to a material property called resistivity (

ρ

), and its geometry - length, width, and thickness. It is the combination of the geometry (shape) and material property (resistivity) which determines the overall electrical characteristic (resistance). To calculate the resistance (R) of a material, one can use the following formula:

𝑅 = 𝜌

𝐿

𝐴 where L, and A are the length and cross-sectional area of the resistor, respectively . In the case of a rectangular cross section, the area can be written as

𝐴 = 𝑡 × 𝑤 where t and w are the thickness and width of the structure, respectively.

In the Wheatstone bridge application presented in this activity, the resistivity,

ρ

, is a physical property of the material. Resistivity remains constant under constant temperature and stress

(e.g., pressure). It should be pointed out that the resistivity of a material, ρ, is inversely proportional to its conductivity, σ: 𝜎 =

1 𝜌

As the conductive (resistive) material stretches, the length increases while the area decreases.

This increase in length and decrease in area results in an increase in overall resistance.



Page 4 of 18


You may ask, “ I understand why the resistor gets longer when the membrane it is adhered to stretches, but why does the cross sectional area decrease?” If you consider that the overall mass of the resistor (the total amount of the material) does not change due to the conservation of mass principal, and that the density of the material doesn’t change either, you can therefore assume that the total volume of the resistor has to stay constant. Since volume, V, can be written as a product of length (L) and area (A),

𝑉 = 𝐿 × 𝐴 then as L gets longer, A must get smaller in order for the volume to remain constant.

NOTE: We have assumed the density of the material does not change; however, it could, if the temperature of the material changes. Therefore it is critical for the bridge circuit design to automatically compensate for temperature fluctuations (which could occur in a wide variety of applications).

To re-cap, one can now see from the resistance equation,

𝑅 = 𝜌

𝐿

𝐴

, that as a conductor stretches, the length increases as the cross-sectional area simultaneously decreases resulting in the L/A ratio in the equation to increase.

What is Graphene?

In this activity you will be using graphite to construct the electronic circuit. Graphite consists of stacks of graphene sheets. So what is graphene? Graphene is a material formed when carbon atoms arrange in sheets. Graphene is a one-atom-thick planar sheet of carbon atoms densely packed in a honeycomb crystal lattice (as shown in the graphic below) . Graphene is also used as the structural element for fullerenes such as carbon nanotubes and buckyballs. In this activity, the mixture of graphite (pencil lead) and rubber cement used to construct the Wheatstone bridge contains sheets of graphene. These sheets are thought to slide on top of each other as the material stretches while still maintaining contact. You should see the effect of this when you apply pressure to your pressure sensor model diaphragm.



Graphene Sheet

Graphite is composed of several stacked sheets of graphene

Page 5 of 18


Activity Objectives and Outcomes

Activity Objectives



Explain how a change in length and cross-sectional area affects a material's resistance.



Using your pressure sensor model, demonstrate and explain how pressure affects the resistance and output voltage of a Wheatstone bridge sensing circuit.

Activity Outcomes

In this activity you construct a macro-size pressure sensor with a Wheatstone bridge sensing circuit on a flexible diaphragm. You also discuss microsystems applications. Upon completion of this activity, you should be able to answer the following questions:



How does the length of a conductive material affect its resistance?



What is meant when a Wheatstone bridge is balanced?



What are some applications pressure sensors in microsystems technology?



What are the advantages and disadvantages of using a Wheatstone bridge sensing circuit in the micro and nano-scales?

Resources

SCME Wheatstone Bridge Learning Module

Teamwork

Working with one to two other participants will promote a better understanding of this activity.

Facilities / Workspace / Safety Precautions

You will need a flat table as a workspace.

For safety, it is recommended that you wear safety glasses and latex or nitrile gloves when working with the graphite and rubber cement.



Page 6 of 18


Supplies / Equipment

Supplies provided by Instructor



Safety glasses and gloves



Wipes or paper towels



Metric Ruler



1 bottle of Rubber cement



Scissors

 Blue painter’s tape 1” (or electrical tape)



6 large paperclips



Small brush (to brush out mortar)



Multimeter with clip-on leads

 Marker (e.g., “Sharpie”)



1 small sheet of cardstock (thick paper)



Two sheet of paper or cone shaped coffee filters (No. 2 work great)



Ice pick or large nail

Supplies included in SCME Kit*



2 quart paint cans (empty and unused)



6 Balloons (12 “) (shown)



Pencil Lead (0.9 mm thick HB hardness) – 2 packs 15 leads each (shown)



Mortar and pestle (shown)

 Copper foil tape ¼” wide – conductive on both sides (3M) (shown)



Four 3 cc (3 mL) Plastic Syringes with tip (shown)



Two (2) leads with alligator clip at each end (Leads should be the same length)



Two glass vials with cap size 20-25ml



3 volt source, AAA battery holder with leads and alligator clips



2 AAA batteries or 2 AA batteries



One Wheatstone Bridge Overview Learning Module - Instructor Guide



One Wheatstone Bridge Overview Learning Module - Participant Guide

Documentation

Write a report to include the following:



Hypothesis and predictions



Your procedure



Any problems that occurred and how these problems affected the outcome



All of your measurements



An analysis of the results (Did the outcome agree with your hypothesis and predictions?)



Answers to the Post-Activity questions.



Page 7 of 18


Expectations

This activity allows you to build and explore the operation of a Wheatstone bridge strain-based transducer. Hypothesis: Write a statement that describes what you expect as an outcome.

Make predictions:



What factors will affect the outcome?



What effect will a change in applied pressure have on the circuit's resistance? Why?



What effect will a change in applied pressure have on the circuit's voltage? Why?

Preparation / Setup

Gather all of the supplies for this activity. Set up a workspace on a flat table top large enough for all of the materials and for at least two students to work together to build this device.

Activity: Pressure Sensor Model

Description: Using an empty paint can, balloon and ground mechanical pencil lead (graphene) mixed with rubber cement, you will build a macro-size pressure sensor using a Wheatstone bridge sensing circuit.

Safety a.

From the Internet, download a Material Safety Data Sheet (MSDS) for rubber cement. b.

Answer the following questions relative to rubber cement. a.

What are two hazards of rubber cement that you need to be constantly aware of? b.

What type of personal protective equipment should you wear when handling rubber cement? c.

What conditions should be avoided when working with rubber cement?



Page 8 of 18


Building the Pressure Sensor Model

Constructing the Diaphragm

Remove the lid from the paint can (if applicable).

1.

Using the stencil provided (see attached at the end of this document), cut the bridge pattern from a piece of the cardboard or cardstock. (Figure 1)

2.

Cut the neck off the balloon to about 4 cm from top opening or at least 1 cm below the curvature of neck (Figure 2)

3.

Stretch the balloon tightly over the open end of the paint can.

(Figure 3). You want an “even” stretch.

4.

Secure the edges of the balloon to the can with painter’s tape. (Figure 4)

Figure 2 Figure 3 Figure 4

Figure 1.



Page 9 of 18


Creating the leads and bridge pattern

1.

Center the template over the balloon diaphragm as shown in Figure 1.

2.

Outline the pattern with a marker onto the top of the diaphragm. Remove template from diaphragm. (Figure 5)

3.

Cut four – 8 – 10 cm strips of conductive copper tape.

4.

Remove the backing off one strip of conductive tape. Place one end of the tape on the membrane (balloon) in line and on top of part of the “circuit” as shown in Figure 6.

5.

Pinch the middle of the strip of tape to create a tab and attach the other end of the conductive tape to the side of can (as shown in Figure 6). The tab will be used to connect the meter leads for measuring resistance and voltage.

6.

Repeat steps 5 and 6 with the other three leads (strips of conductive tape). (See Figure 7 for placement of all four pieces of conductive tape)

Figure 5

(Template outline)

Figure 6

(Creating the connection)

Figure 7

(Conductive tape placement)

Making the conductive material (carbon paste)

1.

Put on gloves and safety glasses.

2.

Carefully break one pack of the graphite leads (15 pieces) into small pieces and place in the mortar.

3.

Grind the graphite into as fine of a carbon powder as possible. Grind until you see no

“grain pieces” and the graphite is a powder. The finer the better. You will be mixing this powder with rubber cement and then forcing the mixture through a syringe tip. A small graphite chunk could clog the syringe.

4.

Pour the carbon powder onto sheet of paper or into the coffee filter. Use a small brush to get all of the carbon out of the mortar.

5.

Fold the paper/filter and carefully pour all of the powder into a glass vial.

6.

Using the syringe with tip attached, extract approximately 3 ml of rubber cement.

7.

Transfer the rubber cement to the vial containing the graphite powder.



Page 10 of 18


8.

Unfold a large paperclip, but leave the smaller looped end intact. (This will be your stirring mechanism.)

9.

Using the paperclip, stir the powder and rubber cement mixture in the vial. The color of the mixture should be black, and the viscosity (thickness) should be close to the original cement. If it is too thick, add a little more rubber cement. If too thin, add more carbon powder. (A comment – You will be applying this graphite/rubber cement mixture onto the diaphragm in the same manner as decorating a cake; therefore, the viscosity of the mixture should similar to that of toothpaste.

Your conductive material is now made and ready for use.

Making a conductive bridge

1.

Pull liquid from the vial with the syringe. Fill the syringe with the mixture.

2.

To eliminate the air from the syringe, insert the paperclip into the tip of the needle, through the liquid and into the air gap at the top of the syringe.

3.

Burp the air from the syringe, by gently compressing the liquid in the syringe until a little comes out of the needle. *Note: It is important when filling the syringe that there are no air bubbles because when applying the conductive material it is essential that there are no gaps in the lines.

4.

If the syringe does not have at least 2 ml of liquid, place the syringe tip back into the vial and continue to fill the syringe to the 2 ml mark.

5.

Using a wipe or paper towel, wipe the tip clean.

6.

Using the syringe, carefully apply about a 1 to 2 mm line (width) of your conductive material (rubber cement and graphite mixture) following the pattern transferred from the template. Try to keep the width and height of the carbon/cement line consistent. Be sure to flow ON TOP of and over the copper wire at the bridge corners. You need to make good electrical contact. (Figure 8)

7.

Check for any “opens” in your circuit. Close them with the graphene solution.

Figure 8

(Conductive material placed on pattern and on top of conductive tape)

You have now created a pressure sensor with a Wheatstone bridge.

8.

Before testing your bridge circuit, you should let it set for 15 to 30 minutes.

9.

Squeeze any unused graphite/cement mixture from the syringe, back into the vial.

10.

Cap the vial. The remaining mixture should stay fluid for several weeks.

11.

Clean or properly dispose of the syringe.



Page 11 of 18


Testing your Pressure Sensor (Measuring Resistance)

The above diagrams are of the pressure sensor Wheatstone bridge in a circular configuration.

This is the circuit you constructed in the previous steps of this activity. When comparing the actual circuit components to the Wheatstone bridge circuit, resistors R

2

and R

3

are configured parallel to the edge of the can, and hence, will not stretch as much when the membrane expands.

Resistors R

1

and R

4

are configured over the open part of the membrane or can, parallel to the radius, and will be subject to the highest tension (stretching), experiencing the greatest piezoresistive effect.

To help you better relate to the specific resistors in your circuit, label your circuit with specific resistor notation (R1, R2, R3, R4).

So let’s see how your circuit works.



Page 12 of 18


1.

Clip one of the leads from the multimeter to one of the connecting leads (copper tabs).

2.

Clip the other multimeter lead to the "opposite" connecting lead as shown below in

Figure 9 . Do not hook the battery up yet, you will only be measuring resistance of the circuit.

Figure 9

3.

Gently press down a couple of times on the diaphragm to pre-stretch it.

4.

Set your multimeter to read resistance.

5.

Record your reference circuit's total resistance. R

R

= _________________

( NOTE: The multimeter may indicate a continual drop in pressure as the diaphragm comes to rest at its reference position.)

6.

Gently push down on middle of the balloon. You should see the resistance change.

NOTE: Be creative. Develop a systematic approach to “applying pressure”. For example, you could use coins, small weights, marbles, or any of the same object that is heavy enough to “flex” the diaphragm. Of course if the object is conductive (e.g., coins), a balloon should be used as an insulator between the weights and the circuit.

7.

Record the resistance for three different applied pressures, increasing the pressure before each recording. a.

R

1

= __________________ b.

R

2

= __________________ c.

R

3

= __________________

(NOTE: Because of the elasticity characteristics of the balloon, your resistance reading may not return to the original reference resistance once the applied pressure is removed.

The balloon may lose some of its original rigidity as different pressures are applied.)

8.

How did the applied pressure affect the resistance of the bridge?

__________________________________________________________________



Page 13 of 18


9.

Explain how the following formula relates to your Wheatstone bridge circuit.

𝐿

𝑅 = 𝜌

𝐴

10.

Draw the equivalent circuit with the resistance meter hookup in the space below.

Now let's apply some voltage to your circuit.



Page 14 of 18


Testing your Pressure Sensor (Measuring Voltage)

11.

Using the other two leads with alligator clips, attached a voltage source (2AAA batteries) across the bridge circuit. Follow the setup shown in the photograph below (Figure 10.)

(NOTE: When hooking up a voltage source, always connect the ground lead (- lead) first.)

Figure 10 (Hookup for Voltage Measurements)

12.

Switch meter to measure voltage.

13.

Record initial voltage. V

R

= _______________________

NOTE: A balanced bridge should have a zero voltage as V

R.

Why does your bridge not measure zero?

14.

Press down on the middle of the diaphragm.

15.

Record the voltage for three different pressures, increasing the pressure before each recording. a.

V

1

= __________________ b.

V

2

= __________________ c.

V

3

= __________________

16.

How did the applied pressure affect the voltage across the bridge?



Page 15 of 18


_________________________________________________________________

The following steps allows you to further explore this device and the effects that pressure has on the resistance and voltage of a Wheatstone bridge sensing circuit.

17.

Using the ice pick or nail, punch a hole in the side of the paint can. The hole should be big enough to insert the TT tip of a syringe.

18.

Pull an empty syringe to about 1.5 ml of air.

19.

Place the tip of the syringe in the hole. Make it snug and as airtight as possible.

20.

You can now simulate increases in pressure (pushing on the syringe) and decreases in pressure (pulling on the syringe).

21.

Test your pressure sensor model using various changes in pressure.

22.

This model could also be used to show how a MEMS pressure sensor is affected by temperature. Find ways to increase or decrease the ambient temperature or the temperature of the air trapped inside the can. Study the effects on the circuit’s output.



Page 16 of 18


Post-Activity Questions

1.

In the above procedure, what factors could have an effect on the outcome (the resistivity of the bridge circuit)?

2.

What is meant by the “reference” voltage or reference resistance of the Wheatstone bridge? Does this stay consistent? Why or why not?

3.

What determines the reference voltage / resistance?

4.

What causes a change in resistance or voltage?

5.

Describe three (3) MEMS that use a diaphragm pressure sensor.

6.

How could this pressure sensor model be improved upon?

Summary

A common MEMS pressure sensor uses a Wheatstone bridge sensing circuit on a flexible diaphragm. A change in pressure creates a deflection of the diaphragm. This deflection causes the variable resistors of the bridge to expand, increasing circuit resistance indicating a change in pressure. The amount of change in resistance is proportional to the change in pressure from reference pressure to applied pressure.



Page 17 of 18


Related SCME Units



Wheatstone Bridge Overview unit



Wheatstone Bridge Derivation Activity



MTTC Pressure Sensor Learning Module

If using a one-quart paint can, this template should print out to approximately 3 3/8" (8.57 cm) in diameter and can be used as a template to trace out the piezoresistive Wheatstone bridge structure.

Disclaimer

The information contained herein is considered to be true and accurate; however the Southwest

Center for Microsystems Education (SCME) makes no guarantees concerning the authenticity of any statement. SCME accepts no liability for the content of this unit, or for the consequences of any actions taken on the basis of the information provided.

Support for this work was provided by the National Science Foundation's Advanced

Technological Education (ATE) Program through Grants #0830384 and 0902411.



Page 18 of 18





Wheatstone Bridge Derivation Activity













Phone: 505-272-7150



Wheatstone Bridge Derivation Activity


Description and Estimated Time to Complete

This activity will involve using your knowledge of the Wheatstone bridge to derive the relationship between V in

(Input Voltage) and V g

(Gauge Voltage) for a given circuit. You will also design a

Wheatstone bridge layout to get the maximum effect on the gauge voltage, V g

.

It is recommended that you review the unit Wheatstone Bridge Overview if you haven't already. It will enhance your understanding of the Wheatstone bridge circuitry as you complete this activity.


Allow approximately two hours to complete this activity.

Introduction

The Wheatstone bridge is one of the most sensitive and precise methods of measuring small changes in resistance. This is possible through its use of transducers (devices which change one form of energy into another, such as mechanical to electrical or electrical to mechanical). The

Wheatstone bridge incorporates one or more electrical transducers that change resistance as a result of an environmental change or input (e.g. temperature, pressure, stress). This change is sensed by the circuitry of the Wheatstone bridge which provides a useable electrical output (voltage) representative of the input. The Wheatstone bridge is widely used today in macro-sized and microsized sensors.

Basic Wheatstone Bridge Configuration



Page 2 of 6

WB Derivation Activity

Activity Objectives

Objectives



Derive the mathematical relationship between output voltage (Vg, also referred to as gauge voltage) and resistance in a Wheatstone bridge circuit.



Design the orientation of the resistors on a pressure sensor membrane to maximize the effect on the gauge voltage.

Procedure I: Derivation Activity

1.

Using basic laws of electronics (e.g. Ohm's and Kirchhoff's), derive the mathematical relationship between input voltage, V in, vs. gauge voltage, V g

in terms of input voltage, V in and resistance for the circuit given below.

V g

=V in

{f(R

1,

R

2

,R

3

,R

4

)}

Hint: Starting point would be V g

= V

D

– V

B

.

2.

Using your results from 1), above, show that the Wheatstone bridge is balanced when

R

3

/R

4

= R

1

/R

2

. a.

What values of R

1

, R

2

, R

3

, and R

4

would yield a balanced bridge circuit? b.

Verify your mathematical derivation using these values of resistors. c.

Did your derivation yield a V g

= 0 V? If not, then find and correct the problem and repeat 2b.

3.

Given a Wheatstone bridge with the following V in

and R values, what is V g

? ________



V in

= 10 volts



R

1

= 75 Ω



R

2

= 100 Ω



R

3

= 100 Ω



R

4

= 75 Ω

4.

If R

2

and R

3

are both variable resistors (transducer elements) and continue to increase above

100 Ω, what effect would it have on V g

?



Page 3 of 6


Procedure II: Design a Wheatstone Bridge for a Pressure Sensor

In the case of a pressure sensor, all resistances are designed with the same geometries, therefore, all the resistors have the same resistance values and the circuit is initially balanced and V g

(gauge voltage) is zero.

Variable resisters in the bridge change due to stress on the resistor's material. This is due to the fact that resistance is a function of the resistor's material (resistivity or

ρ

), length ( L ) and cross sectional area ( A ):

R=

ρ

(L/A)

When metal is stressed, it stretches (for instance, a gold resistor on a pressure sensor membrane).

The length, L, increases, which results in an increase in resistance, R. The cross-sectional area, A, decreases; however, ρ does not change as it is a property of the material.

In a pressure sensor, the Wheatstone bridge can be fabricated so that two of the four resistors are effectively stressed when the membrane is stretched. The stress on the other two resistors is ineffective or negligible. Such fabrication will result in a response from the Wheatstone bridge that is sensitive to small changes in pressure. All four resistors on fabricated on the membrane.

Why? Because there is also a temperature dependence of resistance and you want all of the resistors exposed to the exact same temperature environment. All four resistors should be of the same length, width and thickness so they are balanced under no stress. Most pressure sensor systems have an offset circuit to make up for slight variations in the fabrication process.

Questions

1.

For maximum effect on the gauge voltage, V g, which two resistors in the schematic (left) could be variable and which two resistors could be fixed?

2.

Using the image to on the right, how would you orient the resistors (narrow gray lines) on a membrane (green in the right image)? a.

On the schematic, indicate the variable resistors with an arrow. b.

On the pressure sensor diagram, label the four resistors on the diaphgragm and the electrical nodes (A, B, C, and D), indicating V in

and V g

connections.



Page 4 of 6


Post-Activity Questions

Here is an example of a pressure sensor Wheatstone bridge in a circular configuration. This is the circuit you will build if you complete the "Pressure Sensor Model” Activity. This bridge is created by stretching a balloon membrane across an open can and applying a graphite circuit to the membrane. Note, resistors R

2

and R

3

are configured parallel to the edge of the can, and hence, will not stretch as the membrane expands. R

1

and R

4

resistors are configured over the open part of the membrane or can, parallel to the radius, and will be subject to the highest tension (stretching) and experiencing the greatest piezoresistive effect.

1.

Based on the schematic given above, write the equation for V ab

in terms of resistance and V in

.

2.

Sketch a graph that shows the relationship between V ab

and Variable Resistance (R v

).

3.

How would the graph change if R

2

and R

3

were variable and R

1

and R

4

were fixed? (Justify your answer with formulas and/or a graph.)



Page 5 of 6


Disclaimer

The information contained herein is considered to be true and accurate; however the Southwest

Center for Microsystems Education (SCME) makes no guarantees concerning the authenticity of any statement. SCME accepts no liability for the content of this unit, or for the consequences of any actions taken on the basis of the information provided.

Support for this work was provided by the National Science Foundation's Advanced Technological

Education (ATE) Program.



Page 6 of 6



Learning Modules available for download @

scme-nm.org

MEMS Introductory Topics

MEMS History

MEMS: Making Micro Machines DVD and LM (Kit available)

Units of Weights and Measures

A Comparison of Scale: Macro, Micro, and Nano

Introduction to Transducers, Sensors and Actuators

Wheatstone Bridge (Pressure Sensor Model Kit available)

MEMS Applications

MEMS Applications Overview

Microcantilevers (Dynamic Cantilever Kit available)

Micropumps Overview

BioMEMS

BioMEMS Overview

BioMEMS Applications Overview

DNA Overview

DNA to Protein Overview

Cells – The Building Blocks of Life

Biomolecular Applications for bioMEMS

BioMEMS Therapeutics Overview

BioMEMS Diagnostics Overview

Clinical Laboratory Techniques and MEMS

MEMS for Environmental and Bioterrorism

Applications

Regulations of bioMEMS

DNA Microarrays (GeneChip

®

Model Kit available)

MEMS Fabrication

Crystallography for Microsystems (Breaking Wafers and Origami Crystal Kits available)

Oxidation Overview for Microsystems (Rainbow

Wafer Kit available)

Deposition Overview Microsystems

Photolithography Overview for Microsystems

Etch Overview for Microsystems (Rainbow Wafer and Anisotropic Etch Kits available)

MEMS Micromachining Overview

LIGA Micromachining Simulation Activities (LIGA

Simulation Kit available)

Manufacturing Technology Training Center Pressure

Sensor Process (Three Activity Kits available)

MEMS Innovators Activity (Activity Kit available)

Safety

Hazardous Materials

Material Safety Data Sheets

Interpreting Chemical Labels / NFPA

Chemical Lab Safety

Personal Protective Equipment (PPE)

Check our website regularly for the most recent versions of our Learning Modules.

For more information about SCME and its Learning Modules and kits, visit our website scme-nm.org

or contact

Dr. Matthias Pleil at mpleil@unm.edu

Revision: 5/20/11 www.scme-nm.org

Wheatstone Bridge Learning Module

Wheatstone Bridge Learning

Module

Wheatstone Bridge (WB) Unit

Pressure Sensor Model Activity

WB Derivation Activity

Participant Guide www.scme

nm.org

Wheatstone Bridge Overview

Primary Knowledge (PK)

Wheatstone Bridge Overview

10 v (V

) = 5 v + 5v

Pressure Sensor Model Activity

Pressure Sensor Model Activity

Activity: Pressure Sensor Model

Wheatstone Bridge Derivation Activity

Wheatstone Bridge Derivation Activity

scme-nm.org

For more information about SCME and its Learning Modules and kits, visit our website scme-nm.org

or contact

Dr. Matthias Pleil at mpleil@unm.edu

Related documents

Products

Support

Wheatstone Bridge Learning Module

Wheatstone Bridge Learning

Module

Wheatstone Bridge (WB) Unit

Pressure Sensor Model Activity

WB Derivation Activity

Participant Guide www.scme

nm.org

Wheatstone Bridge Overview

Primary Knowledge (PK)

Wheatstone Bridge Overview

10 v (V

) = 5 v + 5v

Pressure Sensor Model Activity

Pressure Sensor Model Activity

Activity: Pressure Sensor Model

Wheatstone Bridge Derivation Activity

Wheatstone Bridge Derivation Activity

scme-nm.org

For more information about SCME and its Learning Modules and kits, visit our website scme-nm.org

or contact

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