DETAILED ERROR ANALYSIS
The ideal output current is
A. AT THE LOWER RANGE VALUE (T = +25°C).
σO = IOS RTO = ±6µA
iO IDEAL = 4mA + K eIN
∆VCC
σI = VOSI + (IB1 ∆R + IOS1 R4) +
PSRR
K is the span (gain) term, (0.016Ω + (40/RS))
(3)
(e1 + e2)/2 – 5V
In the XTR101 there are three major components of error:
+
CMRR
1. σO = errors associated with the output stage.
2. σS = errors associated with span adjustment.
3. σI = errors associated with the input stage.
∆R = RT 25°C – R4 = 109.4 – 109 ≈ 0
∆VCC = (24 X 0.005) + 4mA (250Ω + 100Ω) + 0.6V
= 120mV + 1400mV + 600mV
= 2120mV
The transfer function including these errors is
iO ACTUAL = (4mA + σO) + K (1 + σS)(eIN + σI)
(4)
When this expression is expanded, second order terms
(σS σ1) dropped, and terms collected, the result is
e1 = (2mA X 2.5kΩ) + (1mA X 109Ω) = 5.109V
e2 = (2mA X 2.5kΩ) + (1mA X 109.4Ω)
= 5.1094V
iO ACTUAL = (4mA + σO) + K eIN + KσI + KσS eIN
(5)
(e1 + e2)/2 – 5 = 0.1092V
PSRR= 3.16 X 105 for 110dB
CMRR = 31.6 X 103 for 90dB
The error in the output current is iO ACTUAL – iO IDEAL and
can be found by subtracting equations (5) and (3).
iO ERROR = σO + Kσ1 + KσS eIN
(6)
σ1 = 30µV + (150nA X 0 + 20nA X 109Ω)
This is a general error expression. The composition of each
component of error depends on the circuitry inside the
XTR101 and the particular circuit in which it is applied. The
circuit of Figure 9 will be used to illustrate the principles.
2120mV
3.16 X 105
0.1092V
3.16 X 103
+
+
(10)
= 30µV + 2.18µV + 6.7µV + 3.46µV
= 42.34µV
1. σO = IOS RTO
2. σS = εNONLINEARITY + εSPAN
(7)
(8)
(9)
σS = εNONLIN + εSPAN
∆VCC
= 0.0001 + 0 (assumes trim of RS)
IO error = σO + K σI + K σS eIN
3. σI = VOSI + (IB1 + R4 – IB2 RT) +
PSRR
(e1 + e2)/2 – 5V
+
40
RS
40
Ω
K = 0.016 +
= 0.016 +
= 0.340
CMRR
123.3Ω
The term in parentheses may be written in terms of offset
current and resistor mismatches as IB1 ∆R + IOS' R4.
eIN = e2 – V4 = IREF1 RT 25°C – IREF2 R4
since RT 25°C = R4,
VOSI* = input offset voltage
IB1*, IB2* = input bias current
IOSI* = input offset current
eIN = (IREF1 – IREF2) R4 = 0.4µA X 109Ω
= 43.6µV
I
OS RTO* = output offset current error
∆R = RT – R4 = mismatch in resistor
∆VCC = change supply voltage between
pins 7 and 8 away from 24V nominal
PSRR* = power supply rejection ratio
Since the maximum mismatch of the current references is
0.04% of 1mA = 0.4µA,
Ω
Ω
IO error = 6µA + (0.34 X 42.34µV) + (0.34
X
0.0001 X 43.6µV) = 6µA + 14.40µA + 0.0015µA
= 20.40µA
CMRR* = common-mode rejection ratio
εNONLIN* = span nonlinearity
20.40µA
εSPAN* = span equation error. Untrimmed error
= 5% max. May be trimmed to zero.
% error =
X 100%
16mA
Items marked with an asterisk (*) can be found in the
Electrical Specifications.
0.13% of span at lower range value.
B. AT THE UPPER RANGE VALUE (T = +150°C).
∆R = RT 150°C – R4 = 156.4 – 109.4 = 47Ω
∆VCC = (24 X 0.005) + 20mA (250Ω + 100Ω) +
0.6V = 7720mV
EXAMPLE 3
The circuit in Figure 9 with the XTR101BG specifications
and the following conditions: RT = 109.4Ω at 25°C, RT =
156.4Ω at 150°C, IO = 4mA at 25°C, IO = 20mA at 150°C,
RS = 123.3Ω, R4 = 109Ω, RL = 250Ω, RLINE = 100Ω, VDI
=
e1 = 5.109V
0.6V, VPS = 24V ±0.5%. Determine the % error at the upper
and lower range values.
e2 = (2mA X 2.5kΩ) + (1mA X 156.4Ω) = 5.156V
(e1 + e2)/2 – 5V = 0.1325V
®
XTR101
14
BB [ BURR-BROWN CORPORATION ]
