This course explains how to analyze circuits that have direct current (DC) current or voltage sources. A DC source is one that is constant. Circuits with resistors, capacitors, and inductors are covered, both analytically and experimentally. Some practical applications in sensors are demonstrated.
4.5 Wheatstone Bridge.
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Del curso dictado por Georgia Institute of Technology
Linear Circuits 1: DC Analysis
125 calificaciones
De la lección
Module 4
This module introduces additional methods for analyzing circuit problems and how resistors are used in sensors.
Conoce a los instructores
Dr. Bonnie H. FerriProfessor
Electrical and Computer Engineering
Dr. Joyelle HarrisDirector of the Engineering for Social Innovation Center
School of Electrical and Computer Engineering
Dr Mary Ann Weitnauer
[MUSIC]
Welcome back to Linear Circuits, this is Dr. Ferri.
In this lesson, we will go over an application of resistors,
that is Wheatstone bridge.
Wheatstone bridge, is used very commonly when we're doing sensor measurements.
It's to improve our measurements.
So, we'll define the Wheatstone bridge configuration, actually looks like this.
And we'll show an example very commonly used in structural measurements.
Measurements of bridges and other structural devices.
This lesson builds upon some previous lessons that we've covered.
We've looked at variable resistors, in particular strain gauge.
And we will also be using the voltage divider law.
Now let's take a look at the Wheatstone bridge circuit.
If I look at this circuit, right here, I notice that I've got two sets of
resistors that are in series with one another.
This set and then this set.
I'm going to be interested in the voltage between a and b.
So I'll go from b to a.
And that is V sub ab.
If these two node voltages, that means from a, let's say this is ground.
So, the node voltage at a,
is equal to node voltage at b, then we've got this equal.
So looking at a voltage divider law, so
I'm going to be looking at this loop right here.
And if I'm interested in V sub a right here.
So this is V sub a.
And this will be V sub b.
V sub a, is using voltage V sub s.
And then V sub b, I do the same thing over on this side here.
Similarly, I can do the voltage divider law over
looking at the voltage drop across R1 and R2.
And I get this relationship right here.
If I divide this equation, actually I can cancel out these, right here.
If I divide this equation by this equation, I will get this relationship.
And this is what we say is the, balanced Wheatstone bridge configuration.
This holds when the voltage drop here is zero.
Let's look at a very common application of a Wheatstone bridge as a sensor.
This is a flexible beam.
It's kind of thin and long.
So, it can be bent.
See how long it is?
Very thin, and it can be bent.
It's a flexible beam.
I've mounted two strain gauges on each side, two on the top,
and two on the bottom.
String gauges are variable resistors.
They vary based on the length of the strain gauge.
As a strain gauge elongates, then the resistance goes up, and
if it shortens, the resistance goes down.
So this is mounted.
You see these wires here?
This is mounted, and
wired, as a Wheatstone bridge, with R1 and R4 on the top.
Now let's look at the schematic of this.
It's just a sketch, of a cutout of the bead,
with R1 and R4 strain gauges on the top.
R2 and R3 on the bottom.
You can see, that some of these wires are connected to ground, and
some of them to a power supply.
This is a 5 volt power supply.
And the other two, are connected back and forth, so
the leads from the strain gauges are connected together.
With pick-off points a and b.
That's back into the standard configuration of a Wheatstone bridge.
I've got R1 and R2 mounted on the top.
Or rather, R1 and R4 mounted on the top.
R2 and R3 on the bottom, and I've got these pick-off points.
So, I'm going to be measuring the potential point a,
and the potential point b.
Now, if this bends backwards so, R1 and R4 elongate.
And R2 and R3 shorten, so R1 and R4 elongate, R2 and R3 shorten.
Then R1 goes up, R4 goes up, and the other two go down.
So remembering how Wheatstone bridge works,
it's based on a voltage divider law.
So if this decreases, and this increases, the potential a will go down.
Similarly, if this increases, and R2 decreases, the potential of b goes up.
That means the voltage difference v sub a minus v sub b becomes negative.
So if I bend this backward, the potential v sub a minus v sub b becomes negative.
Now if I bend this up, and these two, R2 and R3 elongate.
So they become larger, larger resistors.
These two become larger resistors, while R1 and R4 decrease in resistance.
That means a potential of a goes up, and the potential of b goes down.
So that v sub b minus v sub a becomes more positive.
So bending it back, so these elongate, means that the potential becomes negative.
The difference between va and vb becomes negative.
And if I bend it the other direction, so
that these elongate, then that voltage difference becomes positive.
Let's look back at our physical device here.
So there's R1, R4 and you can see the little wires back and
forth, connecting the Wheatstone bridge.
Let me show how this bends.
So, right now, I'll be bending it so that R1 and R4 elongate.
If you look at the resistance, or the voltage on the digital multimeter,
you can see it becomes negative like we predicted.
And the more I bend it, the more it becomes negative.
And that reading is in millivolts.
Now let me, bend it, in the other direction, and
notice as we predicted, it becomes positive.
So bending in this direction I get positive voltage.
The more I bend it, the higher the voltage.
And if I go back to the balance condition,
it's close to zero, millivots.
You may ask, why do we bother with four strain gauges?
We've looked at a Wheatstone bridge before.
We analyzed it with one flexible, then variable resistor.
Why do we now use four?
Well, the reason isn't anything to do with electrical properties.
The reason that we use four variable resistors here, we mount two
strain gages on the top, and two on the bottom, is because of thermal properties.
We want to negate the thermal expansion of this beam.
As it gets warm, the beam will elongate.
Well, if the beam elongates, so will those strain gages.
And that will change the resistance.
The things is, if these resistors, the top and bottom,
both elongate at the same amount, their ratios don't change, so
it still stays in a balanced Wheatstone configuration.
And that way, we negate all effects of thermal expansion.
And the only effects,
that we will be measuring with this, is the bending effects.
And that's what we were trying to measure.
Looking again, as I bend it this direction, it becomes positive voltage.
Bending it this direction becomes negative voltage.
It's a very common application of a Wheatstone bridge.
And Wheatstone bridges with string gauges, are oftentimes used in not only flexible
beams, but also in bridges looking at loads on bridges.
To summarize,
we've shown how to use Wheatstone bridge to detect small changes in resistance.
And what we've found is that, we can get a lot more resolution in our measurements
if we use a Wheatstone bridge.
The other thing we looked at was the specific application of a string gauge.
And we put the four strain gauges in the Wheatstone bridge to eliminate
thermal effects in structural, structures.
So when the entire structure expands due to thermal expansion,
we can remove that affect.
And only measure the changes due to a flexure in the structure.
All right, thank you very much.
[MUSIC]
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