Circuit Note

CN-0335

Rev. A | Page 3 of 8

The transfer function is obtained from the superposition principle:

OFFSET

GAIN

V

k

R0

R5

R0

V

k

R

R4

R

V

R1

R2

R6

R4

R5

R6

R4

V

R1

R2

R6

R5

R4

R6

R5

V

V

IN

REF

IN

REF

IN

OUT

+

=

+

+

+

=

=













+

+

+













+

+

=

1

1

(1)

where:

R6

R5

R5R6

R6

R5

R

+

=

=

,

R6

R4

R4R6

R6

R4

R0

+

=

=

(2)

and













+

=

R1

R2

k

1

(3)

Calculation of the Gain, Output Offset, and the Resistor

Values

For input voltage range ±10 V, the calculations are as follows.

The gain of the circuit is:

115

.

0

V

20

V

2.3

V)

10

(

V

10

V

0.1

V

4

.

2

=

=

−

−

+

−

=

∆

∆

=

IN

OUT

V

V

GAIN

(4)

and according to the transfer function:

k

R

R4

R

R1

R2

R6

R5

R4

R6

R5

GAIN

+

=













+

+

=

1

(5)

The output offset of the circuit is:

V

1.25

2

V

0.1

V

2.4

V

1

.

0

V)

0

(

=

−

+

=

=

=

IN

OUT

V

V

OFFSET

(6)

and according to the transfer function:

k

R0

R5

R0

V

R1

R2

R6

R4

R5

R6

R4

V

OFFSET

REF

REF

+

=













+

+

=

1

(7)

From Equation 4, for k =1.23 (this value can vary, depending on

the value of the standard value resistors R1 and R2), the ratio

R4/R can be calculated:

R

R4

696

.

9

=

(8)

From Equation 7, for VREF = 2.5V and k =1.23 the ratio R5/R0

can be calculated:

R0

R5

46

.

1

=

(9)

Using Equation 2 for the resistors R and R0, and the ratios in

Equation 8 and Equation 9, the ratio R4/R6 can be calculated:

R6

R4

346

.

5

=

(10)

From Equation 8, Equation 9, and Equation 10, the resistors R4,

R5,and R6 can be calculated. For example choosing R6 = 10 kΩ

leads to R4 = 53.46 kΩ, and R5 =12.3 kΩ.

In the actual circuit the nearest available standard resistor

values were chosen for R4 and R5. The values selected were R4

= 52.3 kΩ and R5 = 12 kΩ. Note that R1 = R4 and R2 = R5.

If these values are chosen carefully, the overall error due to

substituting standard value resistors can be made less than a few

percent. However, use Equation 1 to recalculate the U1A op

amp output for ±10 V inputs to ensure that the required

headroom is preserved.

The absolute accuracy in this type of circuit is primarily

determined by the resistors, and therefore gain and offset

calibration is required to remove the error due to standard value

substitution and resistor tolerances.

Calculation of Resistor Values for Different Input Ranges

For input ranges other than ±10 V complete the following

calculation steps.

Define the input span, the output span, and the offset:

MIN

IN

MAX

IN

IN

V

V

V

_

_

−

=

∆

(11)

MIN

OUT

MAX

IOUT

OUT

V

V

V

_

_

−

=

∆

(12)

MIN

OUT

OUT

V

V

Offset

_

2

+

∆

=

(13)

Calculate the gain:

IN

OUT

V

V

GAIN

∆

∆

=

(14)

Calculate the offset:

MIN

OUT

OUT

V

V

Offset

_

2

+

∆

=

(15)

Choose the value for the parameter k:













+

=

R1

R2

k

1

(16)

Calculate the ratio R4/R, using:

k

R

R4

R

GAIN

+

=

(17)

Calculate the ratio R5/R0, using:

k

R0

R5

R0

V

Offset

REF

+

=

(18)

Replace R and R0 in Equation 17 and Equation 18 with the

values defined in Equation 2, and solve both equations find the

ratio R4/R6.

Choose a value for the resistor R6. Calculate R4 using the ratio of

R4/R6. Knowing the values for R4 and R6, calculate R5 using

Equation 2 and the R4/R6 ratio. Calculate R2 and R1 using

Equation 16. It is reasonable to choose R1 = R4 and calculate R2.