CN0336 Datasheet, PDF (3/7 Pages) Analog Devices – Devices Connected

Circuit Note
CN-0336
The transfer function is obtained from the superposition principle.
V _OUT
=
I
IN
R3


1
+
R5
R4||R6


− V _REF
R5 ₌
R4
I * _IN
R3


1
+
R5
R4||R6


+
4
mA ×
R3


1
+
R5
R4||R6


−
V
REF

R5
R4
(1)
where:
I _IN
=
I
*
IN
+ 4 mA
(2)
I
*
IN
= 0 mA to 16 mA
(3)
and _{R4 R6 =} ^R4R6
(4)
R4 + R6
Calculation of the Gain and the Resistor Values
The gain of the circuit is:
GAIN = ^∆VOUT
( 2.4 − 0.1) V
=
=
2.3 V

= 143.75 _
V


∆I _IN
(
I
*
IN
) _MAX
16 mA
 mA  ⁽⁵⁾
=
R3


1+
R5
R4||R6


In case of an input range from 0 mA to 20 mA, the circuit does
not need level shifting, and the op amp operates as follower. Then,
the voltage drop on R3 must not exceed the upper limit (2.4 V)
of the output range, and can be calculated from the equation:
R3 × ( I _IN ) _MAX = R3 × 20 mA ≤ 2.4 V
(6)
If R3 = 120 Ω, the ratio R5/(R4||R6) can be calculated from
Equation 5:
R5 ₌ GAIN _{− 1 =} 143.75 _{− 1 = 0.198}
(7)
R4 R6 R3
120
The output offset of the circuit can be derived from Equation 1
for IIN = 4 mA:
OFFSET =
(8)
V _OUT ( I _IN = 4 mA) = 0.1 V
=
4
mA ×
R3


1
+

R5
R4 R6



− V _REF
R5
R4
Substituting Equation 7 into Equation 8 and solving for R5/R4:
R5
R4
=¹
V _REF




4
mA
×
R3 _{}

1+
R5
R4 R6


−
0.1
V



=
0.19


(9)
Resistors R4, R5, and R6 can now be calculated from Equations
7 and 9, if a value to one of them is given. For example if R5 =
1000 Ω, then R4 = 5,263 Ω, and R6 = 125,310 Ω.
In the actual circuit the nearest available standard resistor
values were chosen for R4 and R6. The values selected were R4
= 5.11kΩ and R6 = 124 kΩ.
If these values are chosen carefully, the overall error due to
substituting standard value resistors can be made less than a few
percent. However, Equation 1 should be used to re-calculate the
U1A op amp output for 4 mA and 20 mA input currents 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.
Effect of Resistor Temperature Coefficients on Overall Error
Equation 1 shows that the output voltage is a function of four
resistors: R3, R4, R5, and R6. The sensitivity of the full-scale
output voltage at TP1 to small changes in each of the four
resistors was calculated using a simulation program. The input
current to the circuit was 20 mA. The individual sensitivities
calculated were SR3 = 1.2, SR4 = 0.01, SR5 = 0.00, SR6 = 0.01.
Assuming the individual temperature coefficients combine in a
root-sum-square (rss) manner, then the overall full-scale drift
using a 25 ppm/°C resistor for R3 and 100 ppm/°C resistors for
R4, R5, and R6 is approximately:
Full scale drift
= 100 ppm/°C√[(0.25 × SR3)² + SR4² + SR5² + SR6²)]
= 100 ppm/°C√[(0.25 × 1.2)² + 0.01² + 0.00² + 0.01²)]
= 30 ppm/°C
The full-scale drift of 30 ppm/°C corresponds to 0.003%FSR/°C.
Effect of Active Component Temperature Coefficients on
Overall Error
The dc offsets of the AD8606 op amps and the AD7091R ADC
are eliminated by the calibration procedure.
The offset drift of the ADC AD7091R internal reference is
4.5 ppm/°C typical and 25 ppm/°C maximum.
The offset drift of the AD8606 op amp is 1 μV/°C typical and
4.5 μV/°C maximum.
The error due to the input offset of the U1A AD8606 is
referenced to the input voltage range of 2.4 V – 0.48 V = 1.92 V,
and is therefore 2.3 ppm/°C. The error due to the U1B reference
buffer is referenced to 2.5 V and is also approximately 2 ppm/°C.
The total drift error is summarized in Table 1. These errors do
not include the ±1 LSB integral nonlinearity error of the AD7091R.
Table 1. Error Due to Temperature Drift
Error Source
Resistors (1%, 100 ppm/°C)
AD7091R (∆VVREF/∆T = 25 ppm/°C)
AD8606, U1A (∆VOS/∆T = 4.5 μV/°C), 2 ppm/°C,
Referenced to 1.92 V
AD8606, U1B (∆VOS/∆T = 4.5 μV/°C), 2 ppm/°C,
Referenced to 2.5 V
Total FSR Error Temperature Coefficient
Total %FSR Error for ∆T = ±10°C
Total Error
±0.0030 %FSR/°C
±0.0025 %FSR/°C
±0.0002 %FSR/°C
±0.0002 %FSR/°C
±0.0059 %FSR/°C
±0.059 %FSR
Rev. A | Page 3 of 7