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In the previous class, we are discussing about high resistance measurements, because we had
started at how to make resistance measurement. In that connection, we discussed about how
to make high resistance measurement, like 100 ohm, 100 megohm, 10 megohm resistances
are there, then, how to make measurements, that is what we are discussing.
Now, in that connection, we are using Ratio Transformer Bridge. So, using ratio transformer,
how to make high resistance measurement. So, basically, we are use ratio transformer, that
is primary will energies with the AC source; then, you have center tapped transformer with
both sides we connect the resistance, and then, we connect a, say basically AC volt
meter, and then, connect this, and then, this center tap that variable tap is connected
to ground. So, this is high resistance under test. This also high resistance, but it is
a fixed standard resistance. So, essentially, the basic working is like
this, if this is taken as 0, then if this taken as V 1 and it is taken as V 2, then
this current that is coming here, actually goes through this and then, this V 1 and V
2 are 180 degree out of phase. So, V 1 and V 2 are 180 degree out of phase.
So, that makes this current and this current are opposite; so, this current is flowing
like this. So, if you take this current is flowing like this, then this current is flowing
like this. So, essentially this current comes like this, and then, this current comes like
this. So, we have two opposite currents, such a line in this; one is given by this. So,
this current is given by V 1 by R measurement, say R m and this is R s; so, V 1 by R s R
m is the current flowing here, in this form, and then, V 2 by R s is the current flowing
in the opposite direction. So, at balance both are equal. So, this current, actually
fixed resistance current, is actually V 2 by R s.
So, at balance these two currents are equal, that is, this current is equal to this current;
so, I can equate these two. So, essentially it becomes V 1 by R m actually equal to V
2 by R s. So, one can, if I have provision to vary the center tap, the midpoint winding,
then this voltage and this voltage will be varying and V 1 by V 2 will give you R m by
R s actually; so, that will make V 1 by V 2 would be equal to R m by R s actually.
So, essentially one knows V 1 and V 2, we can find out the R m the unknown value because
R s is known. Since R s is known, R s is known, if V 1 and V 2 ratio is known, ratio is known,
ratio is known, that is a V 1 by V 2 is known, then unknown resistance can be calculated.
Now, that is how it is working, but then the question is why it is very popular, and why
it is specially good for measuring high resistance values. Now, the beauty of the bridge is that
leakage resistances, because when you are dealing with high resistance, there will be
a leakage. For example, if I take the circuit again carefully, look at it, we have the resistance
connect it here, voltage source connect it here, and then, you have the two, you have
the center tap, and then, we have the two resistance here connected, and then, this
point is grounded and the volt meter is connect at here.
Now, it is possible that you will have leakage of this resistance, from this point to this
point to ground. Similarly, there will be a leakage from this point to ground to this
point; similarly, there will be a leakage from here to this point and then leakage from
here to here. Now, these are the four leakage resistance
that is possible; that is I will call R 1, R 2, R 3, R 4. So, basically R 1, R 2, R 3,
R 4 are leakage resistances. A normal case, normal case R 1, R 2, R 3, R 4, all will affect
the measurement. In this bridge, these leakage resistances will not play any role in balance
in a bridge and net result is that is leakage resistance is no effect on the resistance
measurement. That is why this bridge is popular and one can measure 100 megohm or even 1000
megohm using this bridge, because these resistors - R 1, R 2, R 3, R 4 - are not contributing
for the balance. So, these resistances are not contributing for the balance. So, these
resistances are not contributing for the balance.
Now, the question is - why they are not contributing for the balance. Now, if you look at the circuit
carefully that the at balance, this point, say this point, as say take is ground point
is G and this midpoint as M. Now, at balance, voltage across G M is 0, because you know,
we are adjusting the center point and balancing the bridge to find the value of unknown resistance.
This is unknown resistances R m and then this is the center resistance R s. So, we are balancing
the center tap and finding out the R m and R s.
Now, at balance, essentially, M is at 0 potential that is M as 0 because there is no voltage
across this. That makes across R 2 also, across R 2 also 0 volt; across R 4 also you get a
0 volt, that means no current is flowing through R 4 and R 2 that means these resistances are
not contributing for bridge balance that is bridge balance is not affected by these resisters,
resistance values. So, the, that means, the balancing point is
not affected by this resistance. Now, if we look at R 1 and R 3, now, the, this is a transformer
and the impedance of these transformer is very low, the, if we take as voltage source,
the output implement of the voltage source is this transformer is very low. So, if we
take this leakage is R 1 and R 3, the merely loading the transformers. This currents are
not actually flowing through this; so, this, the merely loading the transformer secondary’s.
Since the impedance of this the voltage source impedance equal to voltage source impedance
of the transformer is very low and the current actually flowing through this is creating
no effect on the voltage at this point, because the impedance is very low. So, whatever the
current that is flowing it is deliver by the winding and that is no effect at the voltage
at this point and this point. So, essentially, voltage at this point say
A and B are unaffected by the resistance R 1 and R 3 that means, the balance not going
to get affected by the R 1 R 3. So, essentially, all these four resistors - R 1, R 2, R 3,
R 4 - are not contributing in anyway balance of the bridge. The net result is you will
get the resistance value R m accurately. That is why this resistance can be even 100 megohm
or 200 megohm, you will get accurate result which is not possible in other circuits.
So, this is the celebrated circuit originally used for capacitance measurements. This can
be used for resistance measurement. So, these effectively these resistors are not contributing
for the balance of the bridge, why? Because, if look at it, this resistance R 2 R 4, see,
why, voltage across, voltage across R 3, R 4 is equal to 0 at balance.
So, no current is, so, no current is flowing, flowing through R 3, R 4 at balance. So, it
is not affecting the bridge balance. Similarly, if I look at R 1 and R 2, R 1 and R 3, so,
these R 2 and R 4, voltage across R 2 and R 4 equal to 0 at balance. So, R 2, the, so,
no current is flowing through R 2 and R 4.
Similarly, if you take R 1 and R 3, R 1, R 3 are just loading the secondary of the transformer, but the output
impedance of the, output, output, output impedance of the, of the transformer is very low. So, this loading is not affecting
the, so, this loading is not affecting low, so, the loading of R 2, R 4, the loading of
R 2, R 4, I think the loading of R 1 and R 3, sorry, loading of R 1, R 3, loading of
R 1, R 3 will not, will not change V 1, V 2.
So, the secondary voltage are not getting affected by the loading, so, no effect on
the balance of the bridge. So, because of this, since these leakage resistance is no
effect on balancing of the bridge, this method of measurement is very accurate; that is why
it is the very popular circuit, and it is essentially used, essentially used for high
resistance measurement, and it was originally developed for capacitance measurement. We
will discuss about this later - how the capacitance measurement can be done using this bridge
accurately.
Now, only problem this is that how to balance the bridge, because if it has to work well,
then somebody have to manually balance this, then only it is it possible to find what is
the ratio of V 1 and V 2. Essentially means that we have to balance this and measure the
voltage V 1 here and V 2 here, V 1 by V 2 will give you R m by R s, but when, of course,
one can manually balance and then one have to measure this voltage and this voltage.
Now, let us see how this measurement of voltage can be easily avoided by modifying the transformer
slightly. So, that one need not worry about measuring this voltage, because once you start
measuring, then the error in V 1, V 2 will get in and that will make the bridge not accurate.
So, how to avoid making the measurements? So, essentially, now, if look at the measurement,
so, V 1 by V 2, that comes as R m by R s, how to avoid measuring V 1 and V 2? That is
other way around, if V 1 and V 2 are measured, if V 1 and V 2 are measured using a meter,
then, the, these errors, the error, the error involved, involved in this measurement, in
this measurement also to be consider, also to be consider.
So, the measurement of V 1 and V 2 can be avoided were modifying the transformer. So,
the measurement of, so, next is how to avoid the measurement of V 1 and V 2, how to avoid
V 1, V 2 measurement. This can be achieve by modifying the bridge, that is, what can
be done is that we can modify the ratio transformer slightly; what is done is you keep the primary
of the transformer same, you energized with the AC source, - low frequency AC source - then
wind the first primary, assume you have 10 turns here, that is, you have 1, 2, 3, 4,
5, 6, 7, 8, 9, 10 turns. So, we have 1, 2, 3, 4, 5, so, we have 1, 2, 3, 4, 5, 6 7, 8,
9, 10 turns, so, we have turns from, this is 0 turn and this the 10th turn, so, 10 turns
I put that means whatever voltage at given here, assume that this also having at 10 turns.
Assume, I have put 1 volt here, this is 10 turn and I also have 10 turns here. For at
each turn, I taken 1 tap, so, I have taken this, so, that means, this voltage across
this will be 1 volt. If I give 1 volt here, then total voltage across 10 turns will be
1 volt, then each 1 will be 0.1 volt, each 10 will have 0.1 volt, so, 0.1 volt 0.2 volt
and so on. Each 10 will representing 0.1 volt. So, if we write it, that is, voltage at there
are 10 turns in the secondary one, 10 turns in the primary as well as in the secondary,
in the primary and secondary. So, for 1 volt primary, then voltage across each turn of
secondary is equal to 0.1 volt. So, each turn will have 0.1 volt, we, across each turn of
the secondary, you will have 0.1 volt. Now what we can do is that we can use center
tap which is actually movable from one point to another. So, we can select here. This center
tap can take, if it is making contact, if this movable tap makes conduct here, then
you will get 0.1 volt; if it makes it here, at this point, then you will get 0 volts.
So, 0, 0.1, 0.2, 0.3, and then, when it makes contact here, you will get 1 volt.
So, voltage across this, whatever we are getting, voltage across this depends on to which terminal
it is making contact. Now, to make it more accurate what is done is, you had one more
turn here, what you do is, normally what is done is, you take this rewind in just 1 turn,
this is 1 turn. So, voltage across this also will be 0.1 volt.
Now, this can be taken, this can be taken, and then, this can be connect at this, so,
what, another 10 turn is own, you wind one more 10 turns here, so, you have 10 turns.
So, 3 4 5 6 7 8 9 and 10, so, you can have a 10 turns and this 10 turns can be connect
to energies this 0.1 volt. So, now, we have the one more secondary winding,
that is, we have one secondary winding we call this one as S 1 and the another one secondary
winding is S 2. So, S 1 is having totally, S 1 is having totally 10 turns and voltage
across this each one is 0.1 volt, and there is a another secondary added to this, this
is only 1 turn, so, voltage across this also 0.1 volt. So, that will applied to this to
the second secondary S 2, and the total voltage across this is 0.1 volt, and you have a 10,
10 turns in this, that means voltage across each one will be 0.01 volt, because the total
voltage is 0.1 volt and divided by 10 that gives you 0.01 volt. So, voltage across this
is 0.01 volt, and what is done is that this point is connected to, this center point is
connected to this, and this has its own secondary point center tap.
Now, if I take this point and this point, if I look at the voltage across this, so,
if this is, for example, if it is at the midpoint 0.5, then the voltage at this point is 0.5
volt, because it is at the midpoint, this is 0, this is 5th winding, so, that means
the voltage at this point is 0.5, and then, this is 0.5, and if this is sitting at 5th
winding, then assume that this is the also at 5th, then this voltage is 0.05.
The each one is 0.01, so, it is at the 5th terminal. So, voltage across this consume
0.05 that means, if I take this as 0, then this is sitting at 0.5, this is 0.05, so,
that means this would be 0.55 volt. Voltage at this point becomes 0.55 with respect to
this point. Now, for example, I can now, I can move, suppose
if I keep it at point 4th terminal, then I will get 0.45; if this is at the 5 and if
this is 4, then I get 0.45; if it is, the, this one at first one 0.1 and if this is at
5th one, then I will get 0.15 volt, like this I can, if I want, I can even add one more
winding to get it more accurate; all that I need to do is that I had one more, for this
I output one more 1 turn. So, voltage across this, you know, voltage,
this is actually 10 turns are there, and voltage across the full 10 turn is 0.1 volt. So, voltage
across this became 0.01 volt, so, that is 0.01 volt what you get across this, because
this is 10 turns, this is 10 turns here and there only 1 turn here, so, voltage across
this will be 1 10th of this. Since this is 0.1 volt and you get 0.01 volt, if you want
add one more, I can energies this. Same thing I can do this; I can connect this to this;
I connect to this. So, you can use this one as third winding S 3.
So, in S 3, you also you have 10 turns, and only thing is each one is 1 millivolt, each
one is 1 millivolt. So, for example, if it is at midpoint, it will be 0.5, and this is
at midpoint will be another 0.05, so, it will be 0.55, and if it is also midpoint, you will
get 0.555 volt with respect to this point. So, by this arrangement, by varying these,
the, by varying the tapping, one can vary the voltage accurately, and one, there is
no need to measure the voltage using a volt meter to avoid the measurement error. So,
if you look at this, this is a commercial ratio transformer made, and then, these have
the commercial transformer is made. If it is 3 decade ratio transformer, and one can
connect the, for example, in these case, if you want connect the resistance, one can connect
from the top and bottom.
So, we will, I will put it in order now. So, to measure this, so, what is done is that,
for 3 decades, for 3 digit accuracy use 3 secondaries in the ratio transformer: first
one, that is, first transformer, first secondary, first secondary voltage is 1 volt, this is
because you have 1 volt in the primary, and then, you have 10 turns, that is, S 1. First
secondary voltage is the 1 volt; the step size here is 0.1 volt, so, each turn is having
0.1 volt. Then, another one 0.1 volt is added step size is 0.1 volt, the auxiliary winding,
is having, is having 0.1 volt.
This 0.1 volt energizes the second winding. So, what is done is that this 0.1 volt, what
we have from the first coil? So, first coil is here and that primary is here. This energies
the second coil, so, this is S 2, this is S 1, so, this is 0.1 volt. So, voltage across
S 2 is 0.1 volt step size, there are 10 turns here, step size, step size in S 2 is 0.01
volt step size, this thing is 0.0, step size in S 2 is 0.01 volt
Then, this S 2 also having its shown auxiliary winding. So, the here the voltage is 0.01
volt. The, the auxiliary winding of S 2, S 2 is having, is having voltage of, voltage
of 1 millivolt, sorry, 10 millivolt. This, this is, this winding of 10 millivolt is connected
to the third winding S 3, connected to the third winding, third winding S 3 .
So, essentially, if you look at this, we got, third, three winding, so, we start from other
primary, then we had a first S 1, and it has its own auxiliary winding, then this energizes
this S 2, so, that is S 1, and then S 2; then S 2 has its own auxiliary winding which energizes
S 3. So, this is 10 millivolt and this is 100 millivolt because, the, this is having
only this is 10 turns and this is having only 1 turn. So, 1 tenth of this voltage is coming
here, so, 100 millivolt is across this, so, you will get a 10 millivolt, and now, this
is each there 10 turns, so, each one is having 1 millivolt. So, S 3, so, voltage across S
3, step size in S 3 is, step size S3 equal to 1 millivolt.
So, now we can connect the entire transformer together that actually looks like this. So,
that means, if I can use the center tap, this can be connected to this and this will be
coming as output. Then, and this as its own secondary tap, that can be connected to this
and the final one is coming like this. Now, for example, for high resistance measurement,
one to standard resistance is connect at here, and then the other resistance is actually
taken from here, and then, connected to this, and then connect the measuring meter here,
voltmeter error. The volt meter is connected at this point.
So, this is standard resistance and this resistance under measurement. By this, by this ratio
transformer method, one can measure the unknown resistance accurately without need to have
any voltage measurement. Even this is need not to be accurate because we are only making
a null method, that is, the, this one, we are looking for a 0 here, so, accuracy of
this meter makes no, no contribution for the error, that is, the resistance can be measure
accurately even if this meter is not accurate because we are looking at only the 0 point,
and then, this supposed to be grounded, otherwise, the leakage resistance what we are discussed
R 1, and R 2, R 3, R 4, you know, there all here, there leakage resistance are here. So,
they have no effect on the measurement. Now, that, I will remove this avoid the confusion.
Now, for example, if I keep this one at 0.5, the midpoint set 5, and if this is at 5 and
this is at 5, then if I take, you know, the, your, if I look at this voltage across this,
this will be 0.5, 0.55, 0.5 because voltage at this point will be 0.555.
Then, if I look at the voltage at this point, that will be 0.5, because, you know, you have,
this is 0, if I take this as 0, this is midpoint 0.5, this is 1 volt, so, you have voltage
at this point coming as 0.5, this is coming as 1 volt.
So, essentially speaking that, you know, if I take this as 0, this as 0 point, if I take
this as 0 point, so, this is taken as, this is taken as 0 point, so this is taken as,
then automatically this becomes 0.5 because we know that this is at 1 volt, and if I take
this as 0 point, so, the question is what is the voltage difference between this and
this, because our interest is what is the voltage difference between this and this?
What is the voltage difference between this and this?
So, this voltage is 0.555, and then, with respect to this point, this is 1 volt; so,
with respect to this, it is 0.5 volt, that is, with respect to this point 0.55, and if
I take this one, this will be 0.45. So, this will be 1 minus 0.55, that will be, I will
put it like this, so, this will be 1 minus 0.555. That is because this is sitting at
0.5, this is 0.55, then automatically this becomes 0.45 and this 0.05 and that makes
1 minus 0.555. So, the voltage at this point is this much; the voltage at this point is
known, and then, the ratio of these gives you the ratio of these two resistances, the
ratio of these gives you the ratio of these two resistances. Ratio of these voltages nothing
but the contact points what is used in the ratio transformer.
So, since we are only worried about at what turns, you know, each ones only at turns the
integral number of turns, so, there is no question of any measurement error here and
the reading will be is so accurate. Suppose, even if the voltage changes, suppose if the,
we are given here 1 volt, and if this voltage changes, then all the voltages are equally
changing, you know, the proportionally this voltage and this voltage proportionally changing,
and this voltage and this voltage also will be proportionally changing, and that has no
effect on the balance of the bridge. So, even if the excitation voltage changes that has
no effect on the balance.
So, the excitation voltage change, voltage, that is, voltage applied, applied to the primary,
primary changes, voltage applied to the primary changes, changes, changes, then also the measurement
is, the measurement is accurate. This is because, because the primary voltage change in the
primary, change in the primary affects proportionally all the secondary’s.
So, the ratio V 1 by V 2 is not changing, so, the, there is no, because of this there
is no measurement error even if the excitation voltage changes, and, the, and the volt meter
used to balance also has no effect.
The second one is the volt meter used, the voltmeter used for balancing, is, will not
affect the measurement even, even if it is not calibrated, even if it is not calibrated.
This is because it is a null method, this is because it is a null method.
So, one can measure the resistance accurately, and then, the leakage resistance is no effect
that we are already discussed. So, the leakage resistance has no effect and voltmeter what
we are using here, for balancing, even if you, it has error, that will not produce any
error in measurement. Even if the excitation voltage changes, that also has no effect on
the measurement. So, this method is very accurate - one can go parts per million level of accuracy
in resistance measurement particularly high resistance measurement.
Of course, this bridge can be used for median level resistance. For example, 1 k, 10 k,
level of resistance if I want compare, I can compare and get it accurately, but if the
resistance is too low, for example, if it is 1 ohm, 10 ohm like that, value to be measured.
This method is not suitable, because in that case, there will large current flowing here
and that will drop a voltage drop across the winding of this resistance, and then, large
current flowing here will also to make it consider, the wire inductance involved in
this; they will create error. So, this method is not suitable for very low resistance measurements,
this method is suitable for high resistance measurement and median level resistance measurement.
So, one had to be careful using this bridge. So, essentially, this method, this method
of measurement, method is good for high resistance measurement, say probably greater than 10
k up to several 100 megohms. This is not good for low resistance measurement, not good for
low resistance measurement, because low resistance measurement, because, the current drawn from
the transformer secondary, the current drawn from the transformer secondary, so, they will
produce, will produce voltage error. So, they, this is not good for low resistance measurement.
Of course, the main disadvantage with this method is that one have took manually balance
this, that is, major disadvantage with this method is, major disadvantage with this, manual
balance is required. Of course, electronic version of these also can be done without
needing to balance the bridge manually, so, that we can do simulating the ratio transformer
electronically. So, all that needed is we had to produce; if you carefully look at the
ratio transformer, all that required is that we have to produce 2 voltage is V 1 and V
2 accurate. So, if I go to our original transformer and see, all that required is we at have 2
voltage is here, that is V 1 and this is V 2, you know, this voltage and this voltage,
V 1, V 2 to be generated; there 180 degree out of phase, and then, I should able to this
V 1 and V 2, such that, the balancing is a done.
So, that we can achieve using operation amplifier, for example, I can show you how to make this
measurement. This using operational amplifier, the same bridge can be obtained, but they
are no need, it has the balancing. So, what can be done is that we can have a voltage
source, - AC voltage source - then op amp the oscillator we can obtain a AC voltage
source. Then, this voltage can be applied to the operational amplifier so that I can
put a follower and get the voltage. Since the output of the op amp is, impedance
of the output of the, output impedance of the op amp is very low, so, this qualifies,
you know, like our transformer output, this gives you low voltage, low impedance source
that is the output impedance is low, and then, to get 180 degree out of phase, I can give
this one to another op amp and there I can invert it.
So, I put the equal resistance here. So, I get this voltage and this voltage equal and
opposite 180 degree out of phase, like that 2 secondaries of the transformer. Now, if
I want make ratio transformer bridge using this, then I will connect similar to that
the two resistances: one is that R m, another is that R s, then connect this, this is standard
resistance R s, then I put the voltmeter here and connect this one to ground.
This actually we are now similar to it artificially the ratio transformer bridge because our aim
is we want avoid the manual balancing, because the ratio transformer has many advantage,
that is, you know, it is intensive for the leakage resistances, and then, the voltmeter
error is not coming into picture, and even if this voltage changes, the measurement is
accurate, it has no effect on the measurement. So, we want take the goodness of the ratio
transformer bridge, and then, I remove its main drawback, that is, one have to manually
adjust, that is the main drawback of the ratio transformer which we want remove. So, that
is what we are tried to do in this, so, we have done this. Now, what you do is, now we
had to balance the bridge, that is, if the voltage across this should be 0; if it is
not 0, then one have to vary this and this. Now, that we can achieve easily by taking
this voltage, for example, I can do one thing, I can take this voltage, and if I know that
this is a voltage, then I merely amplify this voltage, I just amplify this voltage, then
I can connect this one to add this voltage to this.
For example, if this voltage is not 0, say it is not a balance, that will happening these
two resistance ratio and these two voltages, I will put it as V 1 and V 2, this is V 1
and V 2, if V 1 V 2 ratio is not same as R m by R s ratio, then the bridge will not be
balanced. Assume that this is plus, this voltage is a plus, then this plus voltage will be
amplify, and then, it will be subtract. Assume that I put here, or so, this voltage, whatever
is there, if it is plus, then it will make this voltage more, it will make the V 2 increase.
We again we are inverting and giving, so, it is equivalently V 2 is increasing and V
2 is minus, so, the, it will, output will come down. So, as long as the gain is higher
here, the gain of this is of higher, then the bridge is, you know, whatever small voltage
is there, that will make this voltage is higher, and then, balance the bridge. Of course, still
you have a problem of making V 1 and V 2 measurement, which was not there in the case of ratio transformer,
because if I put it like this and if I have a large gain, the bridge will be automatically
balanced, one need not go and balance it, because if it error is plus, then automatically
it puts more minus. In case, if the error is minus, then automatically it puts, it reduces
this voltage. Of course, this voltage remains same and that makes the bridge to balance
automatically. So, how close it get balance, it depends upon
how much gain that we at given in this. Higher the gain and more accurately it will be balanced.
All that one need it do is that I had to measure V 1 and V 2 now with the volt meter, or I
can convert V 1 and V 2 into DC and make accurate measurements.
In that case, it will give correct reading, but that is no way that we can avoid voltage
measurement similar to what we are done in the ratio transformer bridge. So, essentially,
this bridge automatically balances. So, if we look at it is this, the gain is, I will
call as amplifier A, if the gain of the amplifier A is high, A is high, then bridge will get
balanced automatically, because bridge manual balancing is a problem and this automatic
balancing that way helps us.
So, need not balance the bridge, so, bridge balance taking place is automatically. This
is achieved by varing V 1 and V 2. This is achieved, this is because, this is because
V 2 is changing, it is changing, opposite, in opposite way, in opposite way to the error
voltage, that is, this is consider as error voltage, this is consider as error voltage.
So, the error voltage is more, V 2 decreases - if this is decreases, this is increases.
So, this error voltage, we call this is error voltage at this point. So, error voltage changes
the V 2 and opposite way, that, that is why the bridge is balancing, so, the error voltage,
opposite way to the error voltage. So, V 1 and V 2 ratio is adjusted automatically to balance the bridge. So, automatic balancing
is achieved and V 1 and V 2 ratio that automatically adjusted. Then one can find V 1 by V 2 is
equal to R m by R s, but V 1 V 2 add to be measured, but V 1 and V 2 must be measured,
which was not there in the case of ratio transformer. The error introduce V 1, V 2 will be added
to the measurement error. So, the error, the erorr in, error in, error in the measurement
of V 1 and V 2 affects the resistance measurement.
So, it is
not as accurate as ratio transformer bridge, so, it is not, it is not as accurate, accurate
as ratio transformer bridge. In addition to this, it has another drawback, that is, the
drawback is, the main drawback, if the, if the op amps, if the op amps introduce, introduce
phase shift error, then measurement will not be accurate, that means we have to see that
phase shift introduced by the op amps are very small.
So, for this two work make sure the phase shift introduce by the op amp, the phase shift
introduce by the op amp will be very small, op amps must be very small. This can be achieved
by weight band width op amp. So, it is required, so, high band width of op amps required, stage
is required, op amp stage is required.
Alternatively, use op amp with load gain, you use or use several op amps, each one is
with low gain from each stage, low gain from each stage, each stage. So, we will be discussing
about this little latter how to reduce the phase shift the op amp. One way is that the
frequency of the measurement is low; this is not a series problems. So, if one uses
low frequency measurement, for low frequency measurement, this not a series problem. Frequency
measurement, measurement, says few hertz, few hertz, then phase shift is not a problem,
phase shift is not a problem. So, one can use the op amp for automatic balancing,
and of course, you had to measure V 1, V 2 to make the measurement accurate, and keep
the frequency of the measurement low so that the error is small. So, this is have the high
resistance measurement can be made which is not sustainable for leakage resistance and
so on, and this method is very popular and is essentially used as a ratio transformer
technique. Next class we will see the other issues of the bridge method.