Transcript The Wheatstone Bridge

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Stevenage And District Amateur Radio Society
The Wheatstone Bridge
SADARS
Stevenage And District Amateur Radio Society
We are all familiar with modern
electrical measuring instruments.
These instruments accurately
measure ac and dc volts, ac and dc
currents, resistance and other
electrical quantities to a high
accuracy.
But, have you ever thought about
how these instruments are
calibrated?
How do we know, for example, that
when the instrument indicates
1.00V, there is actually 1.00V
present?
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Before the arrival of the Digital
Multimeter (DMM), galvanometers such
as the moving coil meter, were the main
way of measuring electrical quantities.
Here, a coil is suspended in a permanent
magnet field and when a current is
passed through that coil it generates its
own magnetic field. These fields then
react with each other so causing a
mechanical force to exist between them.
Galvanometer – a device that
responds to the application of
an electrical current
With the aid of a spring and pivots, the
coil rotates with respect to the
permanent magnet and a pointer
attached to the coil also moves.
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Early galvanometers often included lens
and mirror assemblies to shine a spot or
vertical beam of light onto a scale, to
magnify the mirror movement.
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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 measure
other electrical quantities such as resistance?
The fundamental method of adapting the galvanometer to do these jobs is
to use resistors as either shunts or multipliers (or a combination of both).
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Resistors – the main devices used to modify the galavanometer’s
fundamental 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 not
have accurate instruments to check the accuracy of other instruments –
accurate measurements had to ‘start somewhere’.
What was needed was a method to measure (or compare) resistor
values without the need for a calibrated indicator such as a
galvanometer.
A galvanometer responds to the application of an electrical current, so if
the galvanometer indicates no response, there must be no electrical
current applied to it (assuming no losses within the ‘mechanics’ of the
galvanometer). This is where the Wheatstone Bridge comes into play
because it relies on measuring resistance under the condition of zero
current through the galvanometer – so the galvanometer does not have
to be calibrated, it just needs to be an indicator.
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The potential divider R1 & R2
The voltage Vx with respect to
0V common depends upon
the battery voltage and the
relative resistance values of
R1 and R2.
Vx =
V+ x R2
(R1 + R2)
Notice that it is the ratio of the
resistances R1 to R2 that
provides the result, not their
absolute 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
(R1 + R2)
from previous slide
V+ = 10V
`R1` = R1 + R2 + R3 = 3kW
`R2` = R4 + R5 + R6 + R7 + R8 + R9 + R10 = 7kW
So Vx = 10V x 7kW
3kW + 7kW
= 70VkW
10kW
= 7V
Try the calculations yourself at different tappings.
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If we now add a second
potential divider, R3 & R4 and
make the ratio of R3 to R4 the
same 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 resistor
ratios are the same, thus
V+ x R2 = V+ x R4
(R1 + R2) (R3 + R4)
The same battery supply is
being used, so the V+ term
cancels out leaving us with
R2
=
R4 _
(R1 + R2) (R3 + R4)
So, if we know the
resistance values of R1, R2
and R3, we can calculate
the 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 be
done 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 the
one shown earlier, connected to the same
power supply;
we can firstly show that each tapping on the
second chain again provides 1V steps
and secondly show that if we connect a meter
across the same tap point on each chain (for
example the 6V tap on the left hand chain to
the 6V tap on the right hand chain), the meter
indicates zero
(any small errors are due to the tolerances of
the components used in this demonstration)
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We now have the familiar
Wheatstone Bridge circuit,
which is exactly the same
circuit as the one shown by
the previous slide.
The unknown resistance is
connected in one arm and
the variable resistance
changed until the
galvanometer indicates
zero.
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Early Wheatstone
bridge designs had
slider contacts on
resistive conductors so
the ratio (of R1 and R2)
could be determined by
using a ruler.
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Another arrangement to
sliders on a bar was to
calibrate the resistive
wire along its length
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Later Wheatstone bridge designs
used the earlier models to calibrate
individual resistors, which could then
be connected into the bridge circuit to
suit the measurements and ratios as
desired, expanding the available
ranges.
Here, you can now begin to see the
process of measuring and calibrating
newer designs by using previous
models – which eventually leads us
to the measuring devices that we
use 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 potentiometer
where the 10 turn dial indicates its resistance
setting.
We connect an unknown resistor into the R4
position, switch on the power supply and
then adjust the potentiometer until the meter
indicates 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 how
the 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 that
we use, capacitors and inductors, since these components respond to ac,
rather than dc, signals.
The most significant problem associated with a Wheatstone Bridge and ac
supplies is the detecting device, where a dc galvanometer will not respond
to 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 dc
signal that will activate a galvanometer, but remember that in the early
days, before thermionic diodes and valves were invented, such rectification
was not an easy task.
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This is the galvanometer circuit
that is used in the demonstration
unit for dc indications.
The added resistor and diodes
are present to prevent damage
to the meter when the bridge is
‘way off’ balance.
The resistor limits the meter current and the silicon diodes conduct when the
voltage 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 the
diodes have no effect. The resistor reduces the meter’s sensitivity and so
could be shorted out near balance to improve circuit sensitivity. Commercial
Wheatstone bridges sometimes included such a switch.
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This is the entire meter circuit of
the demonstration unit.
The 4 added germanium diodes
are switched into circuit when ‘ac’
is selected and convert the ac
input signal to dc.
The forward voltage drop of
these germanium diodes reduces
the sensitivity of the meter,
especially near zero input.
Bridge sensitivity, and thus the accuracy of the balance obtained, would be
improved by either increasing the input signal to the bridge (which has the
adverse effect of increasing dissipation in the bridge components) or by
adding 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 being
measured (higher frequency for lower value capacitors).
The potentiometer is used for one complete arm of the bridge (rather
than just one element of the bridge) and is calibrated accordingly. See
the capacitor measurement box being passed around.
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This talk has shown us some of the history of the Wheatstone
Bridge and how its use has led up to the measuring devices that
we use today.
Are there any questions or further explanations needed by
anyone?
Now is the time for you to come up to the demonstration unit and
to make some measurements yourselves.