AN3222

Theoretical and practical measurements

Doc ID 17551 Rev 1

7/18

5

Theoretical and practical measurements

5.1

Theoretical results

Cf helps to stabilize the operational amplifier and can be ignored for the DC analysis.

Using Figure 2 as reference for the components:

Equation 1

Equation 2

This equation can be simplified assuming Rf2 = Rf1 = Rf, and Rg2 = Rg1 = Rg.

Only errors due to Vio and Iio remain.

If we also consider the errors due to inaccuracies of the resistors, we obtain with a first-order

limited development and with:

Equation 3

As you can see, with correct resistor matching (Rf and Rg) on the inputs, Iib does not have

any influence on Vout.

is the resistance tolerance.

For example: 0.1% in our case for Rg and Rf, and 1% for Rshunt.

If the accuracy of the resistors Rf1, Rf2, Rg1 and Rg2 =

these inaccuracies create a maximum deviation of (2.

Equation 4

Equation 3 can be simplified to become:

Equation 5

Figure 5 on page 8 depicts the theoretical behavior of the above-defined application.

Vout_th, Vout_min and Vout_max are represented from the left Y-axis.

Vout

Rs

I 1

Rg2

Rg2

Rf2

+

----------------------------

–

⎝⎠

⎛⎞

1

Rf1

Rg1

-----------

+

⎝⎠

⎛⎞ Ip

+

Rg2

Rf2

⋅

Rg2

Rf2

+

-----------------------------

⎝⎠

⎛⎞

1

Rf1

Rg1

-----------

+

⎝⎠

⎛⎞ In Rf1 Vio 1 Rf1

Rg1

-----------

+

⎝⎠

⎛⎞

–

⋅

–

⋅

⋅

⋅

=

Vout

Rs

I

Rf

Rg

--------

Vio

1

Rf

Rg

--------

+

⎝⎠

⎛⎞ Rf Iio

⋅

+

⋅

–

⋅

=

Vth

Rs

I

Rf

Rg

--------

⋅⋅

=

Vout

Vth 1

ΔRs

Rs

-----------

Rf

Rf

Rg

+

-------------------- ΔRf1

Rf1

--------------

ΔRg1

Rg1

---------------

–

⎝⎠

⎛⎞

Rg

Rf

Rg

+

-------------------- ΔRf2

Rf2

--------------

ΔRg2

Rg2

---------------

–

⎝⎠

⎛⎞

++

+

⎝⎠

⎛⎞ Rf Iio Vio 1 Rf

Rg

--------

+

⎝⎠

⎛⎞

–

⋅

+

=

ΔR

R

--------

Vth Δ

Rs

Rs

-----------

Rf

Rf

Rg

+

-------------------- ΔRf1

Rf1

--------------

ΔRg1

Rg1

----------------

+

⎝⎠

⎛⎞

Rg

Rf

Rg

+

-------------------- ΔRf2

Rf2

--------------

ΔRg2

Rg2

----------------

+

⎝⎠

⎛⎞

++

⎝⎠

⎛⎞ Vth ε2

Rf

Rf

Rg

+

-------------------- 2

ε 1

Rg

Rf

Rg

+

-------------------- 2

ε 1

⋅

+

⋅

+

⎝⎠

⎛⎞

Vth

ε 22 ε 1

⋅

+

()

=

=

Vout

Vth

ε % Vth Rf Iio Vio 1 Rf

Rg

--------

+

⎝⎠

⎛⎞

–

⋅

+

⋅

+

=