Electronics Resistive Sensors and Bridge Circuits Terry Sturtevant September 27, 2012

Switches in voltage dividers

Resistive sensors in voltage dividers

Wheatstone bridges

Electronics

Resistive Sensors and Bridge Circuits

Terry Sturtevant

Wilfrid Laurier University

September 27, 2012

Terry Sturtevant

Electronics Resistive Sensors and Bridge Circuits



Wheatstone bridges


Terry Sturtevant


One of the simplest forms of voltage divider is where one of the elements is a switch .

A switch can be thought of as a resistor which can have a value of either zero or infinity.

Following is an illustration of a voltage divider where one element is a switch.



Wheatstone bridges



Terry Sturtevant






Wheatstone bridges




Terry Sturtevant





Wheatstone bridges





Terry Sturtevant




Wheatstone bridges

V in

R

1

R

2

I

V out

= V in

R

1

R

2

+ R

2

I

True if I out

≡ 0

Terry Sturtevant




Wheatstone bridges

V in

R

1

R

2

I

R

1

= ∞ ⇒ I = 0

V

2

= V out

= 0

Terry Sturtevant




Wheatstone bridges

V in

R

1

R

2

I

R

1

= ∞ ⇒ I = 0

V

2

= V out

= 0

Terry Sturtevant




Wheatstone bridges

V in

R

1

R

2

I

R

1

= 0 ⇒ V

1

= 0

V

2

= V out

= V in

Terry Sturtevant




Wheatstone bridges

V in

R

1

R

2

I

R

1

= 0 ⇒ V

1

= 0

V

2

= V out

= V in

Terry Sturtevant




Wheatstone bridges

So if one of the elements is a switch , the output varies between 0 and V in

.

Terry Sturtevant


If either resistor in a voltage divider is variable , then a range of output voltages is possible.



Wheatstone bridges

So if one of the elements is a switch , the output varies between 0 and V in

.

If either resistor in a voltage divider is variable , then a range of output voltages is possible.

Terry Sturtevant




Wheatstone bridges

V in

R

1

R

2

I

V out

= V in

R

1

R

2

+ R

2

I

True if I out

≡ 0

Terry Sturtevant




Wheatstone bridges

Resistive sensors

Resistive sensors

Terry Sturtevant


A resistive sensor is a resistor which changes according to some physical change in its environment. Some examples would be:

Potentiometer; the resistance varies with physical movement

Photoresistor; the resistance varies with light

Thermistor; the resistance varies with heat

Strain gauge (or gage); the resistance varies with stress or compression

Force-dependent resistor; the resistance varies with applied pressure



Wheatstone bridges

Resistive sensors

Resistive sensors

A resistive sensor is a resistor which changes according to some physical change in its environment.

Terry Sturtevant


Some examples would be:








Wheatstone bridges

Resistive sensors

Resistive sensors


Terry Sturtevant









Wheatstone bridges

Resistive sensors

Resistive sensors


Potentiometer;

Terry Sturtevant


the resistance varies with physical movement







Wheatstone bridges

Resistive sensors

Resistive sensors



Terry Sturtevant








Wheatstone bridges

Resistive sensors

Resistive sensors



Photoresistor;

Terry Sturtevant


the resistance varies with light






Wheatstone bridges

Resistive sensors

Resistive sensors




Terry Sturtevant







Wheatstone bridges

Resistive sensors

Resistive sensors




Thermistor;

Terry Sturtevant


the resistance varies with heat





Wheatstone bridges

Resistive sensors

Resistive sensors





Terry Sturtevant






Wheatstone bridges

Resistive sensors

Resistive sensors





Strain gauge (or gage);

Terry Sturtevant


the resistance varies with stress or compression




Wheatstone bridges

Resistive sensors

Resistive sensors






Terry Sturtevant





Wheatstone bridges

Resistive sensors

Resistive sensors






Force-dependent resistor;

Terry Sturtevant


pressure the resistance varies with applied



Wheatstone bridges

Resistive sensors

Resistive sensors







Terry Sturtevant




Wheatstone bridges

Resistive sensors

Here’s an example of how a strain gauge works.

Terry Sturtevant




Wheatstone bridges

Resistive sensors

R = ρ

L

A

Resistance

Terry Sturtevant




Wheatstone bridges

Resistive sensors

Resistance

6

?

Terry Sturtevant




Wheatstone bridges

Resistive sensors

Resistance

6

?

R

0

= ρ

( L − ∆ L )

( A +∆ A )

< R

Terry Sturtevant




Wheatstone bridges

Resistive sensors

R = ρ

L

A

Resistance

Terry Sturtevant




Wheatstone bridges

Resistive sensors

Resistance

?

6

-

Terry Sturtevant




Wheatstone bridges

Resistive sensors

Resistance

?

6

R

0

= ρ

( L +∆ L )

( A − ∆ A )

> R

-

Terry Sturtevant




Wheatstone bridges

Resistive sensors

Resistance

( Ω )

Temperature (

◦

C)

This is the resistance/temperature curve for a thermistor.

Terry Sturtevant




Wheatstone bridges

Resistive sensors

Resistance

( Ω )

(High temperature;

Temperature (

◦

C)


R min

)

Terry Sturtevant




Wheatstone bridges

Resistive sensors

(Low temperature; R max

)

Resistance

( Ω )

(High temperature;

Temperature (

◦

C)


R min

)

Terry Sturtevant




Wheatstone bridges

Resistive sensors

If we want to put this variable resistor in a voltage divider, then we need to choose the other resistor.

Terry Sturtevant


To make the output vary over as large a range as possible as the variable resistor goes from R min to R max

, it turns out we want to choose the other resistor, R so that

√

R = R min

× R max



Wheatstone bridges

Resistive sensors




Terry Sturtevant


R =

√

R min

× R max



Wheatstone bridges

Resistive sensors




√

R = R min

× R max

Terry Sturtevant




Wheatstone bridges

Wheatstone bridges

Balancing a Wheatstone Bridge

Terry Sturtevant


A common type of circuit is a Wheatstone bridge .

It is really a pair of voltage dividers using a common voltage source.

It’s usually operated with the output voltage at or close to zero.



Wheatstone bridges

Wheatstone bridges



Terry Sturtevant






Wheatstone bridges

Wheatstone bridges




Terry Sturtevant





Wheatstone bridges

Wheatstone bridges





Terry Sturtevant




Wheatstone bridges


Terry Sturtevant




Wheatstone bridges


R

1

R

2

R

3

R

4

Terry Sturtevant




Wheatstone bridges


V in

R

1

R

2

R

3

R

4

Terry Sturtevant




Wheatstone bridges


V in

R

1

R

2

V out

R

3

R

4

Terry Sturtevant




Wheatstone bridges


V in

R

1

R

2

V out

R

3

R

4

This is a Wheatstone bridge.

Terry Sturtevant




Wheatstone bridges


V in

R

1

V out

R

3

R

2

R

4

Here it’s redrawn to show the two voltage dividers.

Terry Sturtevant




Wheatstone bridges


V in

R

1

V out

R

3

R

2

R

4

Here’s one voltage divider.

Terry Sturtevant




Wheatstone bridges


V in

R

1

V out

R

3

R

2

R

4

Here’s the other voltage divider.

Terry Sturtevant




Wheatstone bridges


Often a Wheatstone bridge is used with one resistor variable, such as a resistive sensor.

Terry Sturtevant


Knowing the other resistors allows the variable one to be easily determined.

The circuit is very sensitive to small changes in the variable resistor.



Wheatstone bridges




Terry Sturtevant





Wheatstone bridges





Terry Sturtevant




Wheatstone bridges


V in

R

1

V

A

V out

V

B

R v

R

2

R

4

The variable resistor could be in any of the four positions; this is one example.

Terry Sturtevant




Wheatstone bridges



Terry Sturtevant


When the bridge is “balanced”, V o

= 0 or V

A

(This will happen when

R

1

R

2

=

R v

R

4

.)

= V

B

.

For our diagram R

1

→ R

2 is the reference

R v

→ R

4 is the evaluation branch.

branch, and

If R v increases, V

B will decrease, and vice versa.

For optimum performance, all resistors should be of the same order of magnitude.

If using a resistive sensor, use a meter to measure resistance of sensor to get a correct order of magnitude.



Wheatstone bridges




= 0 or V

A

= V

B

.

Terry Sturtevant



R

1

R

2

=

R v

R

4

.)

For our diagram R

1

→ R


R v

→ R


branch, and







Wheatstone bridges




= 0 or V

A


R

1

R

2

=

R v

R

4

.)

= V

B

.

Terry Sturtevant


For our diagram R

1

→ R


R v

→ R


branch, and







Wheatstone bridges




= 0 or V

A


R

1

R

2

=

R v

R

4

.)

= V

B

.

For our diagram R

1

→ R

2 is the reference branch, and

R v

→ R


Terry Sturtevant








Wheatstone bridges




= 0 or V

A


R

1

R

2

=

R v

R

4

.)

= V

B

.

For our diagram R

1

→ R


R v

→ R




Terry Sturtevant






Wheatstone bridges




= 0 or V

A


R

1

R

2

=

R v

R

4

.)

= V

B

.

For our diagram R

1

→ R


R v

→ R





Terry Sturtevant





Wheatstone bridges




= 0 or V

A


R

1

R

2

=

R v

R

4

.)

= V

B

.

For our diagram R

1

→ R


R v

→ R






Terry Sturtevant




Wheatstone bridges


V in

R

V

A

V out

V

B

R R

R v

= R + ∆ R

If resistors are chosen to be equal, except for R v

, then the output voltage will vary with changes in R v

.

Terry Sturtevant


Specifically,



Wheatstone bridges


Terry Sturtevant


V

A

= V

R

2 R

= V / 2

V

B

= V

V / 2 − V

R

2 R +∆ R

∆ R / 2

2 R

= V

R +∆ R / 2 − ∆ R / 2

2 R +∆ R

= V /

If no current flows between A and B then

2 − V

∆ R / 2

2 R +∆ R

≈

V

A

− V

B

≈ V

∆ R

4 R which can be rearranged to give

∆ R ≈

( V

A

− V

B

V

)

4 R

So we can determine ∆ R .

(This approximation is true as long as ∆ R << R)



Wheatstone bridges


Specifically,

V

A

= V

R

2 R

= V / 2

Terry Sturtevant


V

B

= V

V / 2 − V

R

2 R +∆ R

∆ R / 2

2 R

= V

R +∆ R / 2 − ∆ R / 2

2 R +∆ R

= V /


2 − V

∆ R / 2

2 R +∆ R

≈

V

A

− V

B

≈ V

∆ R


∆ R ≈

( V

A

− V

B

V

)

4 R





Wheatstone bridges


Specifically,

V

A

= V

R

2 R

=

V

B

= V

V / 2 − V

R

2 R +∆ R

∆ R / 2

2 R

V /

=

2

V

R +∆ R / 2 − ∆ R / 2

2 R +∆ R

= V / 2 − V

∆ R / 2

2 R +∆ R

≈

Terry Sturtevant



V

A

− V

B

≈ V

∆ R


∆ R ≈

( V

A

− V

B

V

)

4 R





Wheatstone bridges


Specifically,

V

A

= V

R

2 R

= V / 2

V

B

= V

V / 2 − V

R

2 R +∆ R

∆ R / 2

2 R

= V

R +∆ R / 2 − ∆ R / 2

2 R +∆ R

= V /


2 − V

∆ R / 2

2 R +∆ R

≈

Terry Sturtevant


V

A

− V

B

≈ V

∆ R


∆ R ≈

( V

A

− V

B

V

)

4 R





Wheatstone bridges


Specifically,

V

A

= V

R

2 R

= V / 2

V

B

= V

V / 2 − V

R

2 R +∆ R

∆ R / 2

2 R

= V

R +∆ R / 2 − ∆ R / 2

2 R +∆ R

= V /


2 − V

∆ R / 2

2 R +∆ R

≈

V

A

− V

B

≈ V

∆ R

4 R

Terry Sturtevant


which can be rearranged to give

∆ R ≈

( V

A

− V

B

V

)

4 R





Wheatstone bridges


Specifically,

V

A

= V

R

2 R

= V / 2

V

B

= V

V / 2 − V

R

2 R +∆ R

∆ R / 2

2 R

= V

R +∆ R / 2 − ∆ R / 2

2 R +∆ R

= V /


2 − V

∆ R / 2

2 R +∆ R

V

A

− V

B

≈ V

∆ R


≈

Terry Sturtevant


∆ R ≈

( V

A

− V

B

V

)

4 R





Wheatstone bridges


Specifically,

V

A

= V

R

2 R

= V / 2

V

B

= V

V / 2 − V

R

2 R +∆ R

∆ R / 2

2 R

= V

R +∆ R / 2 − ∆ R / 2

2 R +∆ R

= V /


2 − V

∆ R / 2

2 R +∆ R

V

A

− V

B

≈ V

∆ R


∆ R ≈

( V

A

− V

B

V

)

4 R

≈

Terry Sturtevant






Wheatstone bridges


Specifically,

V

A

= V

R

2 R

= V / 2

V

B

= V

V / 2 − V

R

2 R +∆ R

∆ R / 2

2 R

= V

R +∆ R / 2 − ∆ R / 2

2 R +∆ R

= V /


2 − V

∆ R / 2

2 R +∆ R

V

A

− V

B

≈ V

∆ R


∆ R ≈

( V

A

− V

B

V

)

4 R


≈

Terry Sturtevant





Wheatstone bridges


Specifically,

V

A

= V

R

2 R

= V / 2

V

B

= V

V / 2 − V

R

2 R +∆ R

∆ R / 2

2 R

= V

R +∆ R / 2 − ∆ R / 2

2 R +∆ R

= V /


2 − V

∆ R / 2

2 R +∆ R

V

A

− V

B

≈ V

∆ R


∆ R ≈

( V

A

− V

B

V

)

4 R


≈


Terry Sturtevant


Electronics Resistive Sensors and Bridge Circuits Terry Sturtevant September 27, 2012

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