wheat stone talk 1

8/3/2019 Wheat Stone Talk 1

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S A D A R S Stevenage And District Amateur Radio Society

The Wheatstone Bridge


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We are all familiar with modern

electrical measuring instruments.

These instruments accuratelymeasure ac and dc volts, ac and dccurrents, resistance and otherelectrical quantities to a highaccuracy.

But, have you ever thought abouthow these instruments arecalibrated?

How do we know, for example, thatwhen the instrument indicates1.00V, there is actually 1.00Vpresent?

http://upload.wikimedia.org/wikipedia/commons/a/a6/Digital_Multimeter_Aka.jpg


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Before the arrival of the Digital

Multimeter (DMM), galvanometers suchas the moving coil meter, were the mainway of measuring electrical quantities.

Here, a coil is suspended in a permanentmagnet field and when a current is

passed through that coil it generates itsown magnetic field. These fields thenreact with each other so causing amechanical force to exist between them.

With the aid of a spring and pivots, the

coil rotates with respect to thepermanent magnet and a pointerattached to the coil also moves.

Galvanometer

a device thatresponds to the application ofan electrical current


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Early galvanometers often included lensand mirror assemblies to shine a spot orvertical beam of light onto a scale, tomagnify the mirror movement.
http://upload.wikimedia.org/wikipedia/commons/a/a0/Thompson_mirror_galvanometer_use.png


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The galvanometer by itself is only a device that provides a response to a

small applied current.

How do we change its sensitivity so that it can respond to a larger current?

How can we change its arrangement so that it can indicate a voltage level,rather than a current level?

How can we change its arrangement such that it can be used to measureother electrical quantities such as resistance?

The fundamental method of adapting the galvanometer to do these jobs isto use resistors as either shunts or multipliers (or a combination of both).


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Resistorsthe main devices used to modify the galavanometersfundamental function into a more usable format. But then, how to know

what resistance your resistor presents?

Remember, in the early days of electrical engineering people did nothave accurate instruments to check the accuracy of other instrumentsaccurate measurements had to start somewhere.

What was needed was a method to measure (or compare) resistorvalues without the need for a calibrated indicator such as agalvanometer.

A galvanometer responds to the application of an electrical current, so ifthe galvanometer indicates no response, there must be no electricalcurrent applied to it (assuming no losses within the mechanics of the

galvanometer). This is where the Wheatstone Bridge comes into playbecause it relies on measuring resistance under the condition of zerocurrent through the galvanometer so the galvanometer does not haveto be calibrated, it just needs to be an indicator.


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The potential divider R1 & R2

The voltage Vx with respect to0V common depends uponthe battery voltage and therelative resistance values of

R1 and R2.

Vx = V+ x R2(R1 + R2)

Notice that it is the ratio of the

resistances R1 to R2 thatprovides the result, not theirabsolute values.


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The potential divider, calculation and demonstration

Each resistor R1 to R10 is 1kW

Take the 7V output tap, for example;

Vx = V+ x R2 from previous slide

(R1 + R2)

V+ = 10V

`R1` = R1 + R2 + R3 = 3kW

`R2` = R4 + R5 + R6 + R7 + R8 + R9 + R10 = 7kW

So Vx = 10V x 7kW = 70VkW = 7V3kW + 7kW 10kW

Try the calculations yourself at different tappings.


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If we now add a secondpotential divider, R3 & R4 andmake the ratio of R3 to R4 thesame as R1 to R2, then

Vx = V+ x R2(R1 + R2)

Vy = V+ x R4(R3 + R4)


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But Vx must be the same as

Vy because the resistorratios are the same, thus

V+ x R2 = V+ x R4(R1 + R2) (R3 + R4)

The same battery supply isbeing used, so the V+ termcancels out leaving us with

R2 = R4 _(R1 + R2) (R3 + R4)

So, if we know theresistance values of R1, R2and R3, we can calculatethe resistance of R4


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Now the mathematics bit, from the previous slide ,

R2 = R4 .(R1 + R2) (R3 + R4)

and remembering that whatever is done to one side of the equation has to bedone to the other side of that equation

So, R2 x (R3 + R4) = R4 x (R1 + R2) (above equation cross multiplied)

R2 x R3 + R2 x R4 = R4 x R1 + R4 x R2 (bracket terms expanded)

But R2 x R4 appears on both sides of the equation and so cancels out

Thus, R2 x R3 = R4 x R1

Or R4 = R2/R1 x R3 and R2/R1 is the ratio between these 2 resistors

But if R1 = R2, then R4 = R3 (which is a special case)


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Demonstration equal taps on the chain

If we now add a second potential divider to theone shown earlier, connected to the samepower supply;

we can firstly show that each tapping on thesecond chain again provides 1V steps

and secondly show that if we connect a meteracross the same tap point on each chain (forexample the 6V tap on the left hand chain tothe 6V tap on the right hand chain), the meterindicates zero

(any small errors are due to the tolerances ofthe components used in this demonstration)


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We now have the familiarWheatstone Bridge circuit,which is exactly the samecircuit as the one shown bythe previous slide.

The unknown resistance isconnected in one arm andthe variable resistancechanged until the

galvanometer indicateszero.


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Early Wheatstone

bridge designs hadslider contacts onresistive conductors sothe ratio (of R1 and R2)could be determined byusing a ruler.


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Another arrangement tosliders on a bar was tocalibrate the resistive

wire along its length


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Later Wheatstone bridge designs

used the earlier models to calibrateindividual resistors, which could thenbe connected into the bridge circuit tosuit the measurements and ratios asdesired, expanding the availableranges.

Here, you can now begin to see the

process of measuring and calibratingnewer designs by using previousmodels which eventually leads usto the measuring devices that weuse today.


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Demonstration the Wheatstone Bridge

From the earlier slides

R4 = R2/R1 x R3

If R1 = R2, then R4 = R3

For R1 and R2 we use the 10 resistor chain

For R3 we use a 10 turn 10kW potentiometerwhere the 10 turn dial indicates its resistancesetting.

We connect an unknown resistor into the R4position, switch on the power supply andthen adjust the potentiometer until the meterindicates zero.

The potentiometer setting lets us work out R4


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So far, we have been energising the bridge from dc supply, which is howthe early engineers used this instrument, but will it work with an ac supply?

Why should we consider an ac supply anyway?

The answer to this question relates to the other passive components thatwe use, capacitors and inductors, since these components respond to ac,rather than dc, signals.

The most significant problem associated with a Wheatstone Bridge and acsupplies is the detecting device, where a dc galvanometer will not respondto ac signals.

There were meter movements available like the moving iron type which do

respond to ac, but these tend to be insensitive devices.

These days it is quite easy to rectify an ac signal, so as to produce a dcsignal that will activate a galvanometer, but remember that in the earlydays, before thermionic diodes and valves were invented, such rectificationwas not an easy task.


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This is the galvanometer circuit

that is used in the demonstrationunit for dc indications.

The added resistor and diodesare present to prevent damageto the meter when the bridge is

way off balance.

The resistor limits the meter current and the silicon diodes conduct when thevoltage applied to the inputs exceeds about 0.7V in either polarity.

When the bridge is in balance the voltage across the inputs is zero, so thediodes have no effect. The resistor reduces the meters sensitivity and so

could be shorted out near balance to improve circuit sensitivity. CommercialWheatstone bridges sometimes included such a switch.


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This is the entire meter circuit of

the demonstration unit.

The 4 added germanium diodesare switched into circuit when ac

is selected and convert the acinput signal to dc.

The forward voltage drop ofthese germanium diodes reducesthe sensitivity of the meter,especially near zero input.

Bridge sensitivity, and thus the accuracy of the balance obtained, would beimproved by either increasing the input signal to the bridge (which has theadverse effect of increasing dissipation in the bridge components) or byadding an ac amplifier between the bridge output and the meter circuit.


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This is a schematic of a practical capacitor measuring bridge.

The ac signal source frequency is adjusted to suit the capacitor beingmeasured (higher frequency for lower value capacitors).

The potentiometer is used for one complete arm of the bridge (ratherthan just one element of the bridge) and is calibrated accordingly. Seethe capacitor measurement box being passed around.


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This talk has shown us some of the history of the WheatstoneBridge and how its use has led up to the measuring devices thatwe use today.

Are there any questions or further explanations needed byanyone?

Now is the time for you to come up to the demonstration unit andto make some measurements yourselves.

wheat stone talk 1

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