I am going throw the below circuit.

I have few questions
1)May I know h*ow the Vout Equation is derived
2)May I know the use of M1 and M2
3)May I know the use of REF and D1
LTC2063
Recommended for New Designs
The LTC2063/LTC2064/LTC2065 are single, dual, and quad low power, zero-drift, 20kHz amplifiers. The LTC2063/LTC2064/LTC2065 enable high resolution measurement...
Datasheet
LTC2063 on Analog.com
I am going throw the below circuit.

I have few questions
1)May I know h*ow the Vout Equation is derived
2)May I know the use of M1 and M2
3)May I know the use of REF and D1
Potential answers:
1) As you would expect from an op-amp,
the output of the LTC2063 does whatever
it has to do in order to make the voltages
on its (+) and (-) inputs be identical.
Assume the (+) and (-) currents into
the op-amp are zero. In this case,
the (+) input to the op-amp is Vload,
the voltage that appears across the
box labelled "load" (why? since
the (+) input is zero current,
there is no voltage drop across R1).
And so, the LTC2063 does whatever it
has to do to make the voltage on its
(-) input also be Vload. And so,
the V=IR equation applied to Rin
implies the current Iin going through
Rin must be Iin = (Vin - Vload)/Rin.
Where does this current go? It can't
go into the (-), and so it must go
through transistor M1. And so, the
LTC2063 sets its output voltage to
be the value that makes M1 pass
the current Iin. This Iin current
then passes through Rdrive, yielding
Vout = Iin*Rdrive = (Rdrive/Rin)*(Vin-Vload).
However, applying V=IR to Rsense yields:
Vin-Vload = Isense*Rsense.
and if we plug that into the previous
equation we get:
Vout = Iin*Rdrive = ((Rsense*Rdrive)/Rin)*Isense.
Plugging in the resistor values yield Vout = 10.2*Isense.
To answer 2) and 3):
Vin can be up to 90V, but the LTC2063 can only handle
5.5V max across its power rails. M2, REF, D1, and
associated passives form a circuit to "float" the
minus voltage rail of the LTC2063 to keep the difference
across the power rails to be under 5.5V.
Thank you for the nice explanation.I clearly understood the answer.
If you don't mind could you please elaborate your statement "
Vin can be up to 90V, but the LTC2063 can only handle
5.5V max across its power rails. M2, REF, D1, and
associated passives form a circuit to "float" the
minus voltage rail of the LTC2063 to keep the difference
across the power rails to be under 5.5V."
How this circuitry always maintains 5.5V across OPAMP
The two diodes connect the positive rail
and the negative rail of the LTC2063.
The REF diode is a zener diode: the
voltage across this diode won't exceed
4.096V (thus its name). The other
diode is a normal diode, let's say
it's forward voltage is 0.7V.
So, 4.096V + 0.7V = 4.796 volts. So,
the voltage across the rails of the
LTC2063 can never be more than 4.796V,
which is below the 5.5V absolute maximum.
The other parts (C1, R2, M2, and the
10uF capacitor) act to coordinate the
"floating" of the negative LTC2063
rail to Vin - 4.796V when the power
to the circuit is turned on, and
"de-floating" the negative rail
back to ground when the power turns
off. The 10uF capacitor charges via
the two diodes, and discharges via
M2.
There are more modern op-amps in
the "Power by Linear" catalog that
can handle voltage rails of 100V
or more, which makes this floating
scheme unnecessary. I'll leave it
to one of the Analog Devices employees
to recommend which one to use.
Hi John,
Thank you
Sorry for the delay in my response.
From the schematic it is clear that Vin is directly coming in contact with opamps V+.
During turn on will this damage the Opamp.
Reagrads
HAri
The absolute rating is for the difference between the positive rail
and the negative rail. The floating circuitry ensures that as
Vin ramps up from ground, the negative op-amp rail also ramps up from
ground, to ensure the differential voltage between the rails does
not exceed the absolute rating. So, if Vin ramps from 0 to 90V,
when Vin hits 10V the minus rail is (10V - 4.796V), when Vin hits
20V the minus rail is (20V - 4.796V), and when Vin finally gets
to 90V, the minus rail is (90V - 4.796V). And in this way the
absolute rating is never exceeded during the ramp-up.