. Measurement of low currents
AE1B38EMA
4. MEASUREMENT OF LOW CURRENTS
4.1. Tasks of the measurement
4.1.1. Measure the forward current of the germanium diode in the low voltage region (20 mV
to 100 mV) in five points of the characteristics (see Fig. 4.1):
a) using analog micro-ammeter,
b) using digital micro-ammeter on more measurement ranges,
c) using current-to-voltage converter with an operational amplifier; find the value of
the feedback resistor R of the I/U converter to achieve the current-to-voltage
conversion factor 105 V/A.
Plot the measured curves into a common graph.
4.1.2. Evaluate the methodical error caused by non-zero input ammeter resistance in cases
4.1.1a and 4.1.1b.
4.1.3. Evaluate the standard uncertainty of the micro-ammeter reading for cases a and b. For
the case c evaluate the expanded uncertainty of current measurement (coverage factor
k = 2); consider also input bias current of the op amp.
4.1.4. Evaluate the input resistance of the used micro-ammeters.
4.2. Schematic diagrams
90 
I
+
I
A'
A
U1
0 to 1 V
V1
10 
A
U1'
-
B'
B
a), b)
R
I
A''
-
+
V2
B''
c)
Fig. 4.1 Connection diagram for measurement of low currents
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. Measurement of low currents
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4.3. List of the equipment used
V2
- digital voltmeter, type ..., accuracy ± ... % of range ± ... % of reading
A 1
- PMMC micro-ammeter, accuracy class ... , range ...
A 2
R
OA
U1
- digital micro-ammeter, type ..., accuracy ± ... % of range ± ... % of reading
- accurate resistor or decade resistor, accuracy 0.1 % (or 0.2 %)
- operational amplifier in a box
- variable voltage source with digitally adjustable output value
4.4. Theoretical background
The diode is supplied from voltage source using the resistive divider 10:1 (resistors 90  and
10 ) according to the Fig. 4.1. If the micro-ammeter (analogue or digital, both have rather
high input resistance - in the order of k) is connected in series with the diode, the voltage
drop on the micro-ammeter is comparable to that of the diode. In other words, the voltage
drop on the 10  resistor will not be on the diode only, but splits between diode and microammeter. The current passing through the series of diode and ammeter resistance will
therefore be (for the same voltage drop on the 10  resistor) smaller than in case of the shortcircuit between A and B points. Thus, the non-zero resistance of micro-ammeter causes rather
important methodical error that cannot be estimated in advance. If we use (contrary to basic
rules of measuring range selection) higher measurement range of the digital ammeter, the
input resistance will be smaller and, consequently, the methodical error will be smaller as
well. On the other hand, the measurement uncertainty will be higher – the portion of
uncertainty given by error of measuring range will increase. It means, the following dilemma
is to be solved: to measure with small uncertainty the value that is affected by high
methodical error or to measure with higher uncertainty the value affected by smaller
methodical error.
The explanation of the above problem is the main goal of the whole task. The measurement
cannot be regarded as diode volt-ampere characteristic in forward direction evaluation since
in this case the voltage would be acquired directly on the diode. Considering the input
resistance of contemporary digital voltmeters (107 to 109  or even more), the methodical
error would be negligible.
Note: The application of resistive divider has two reasons. It is difficult to set and measure
voltage of tens of mV. In case of resistive divider incorporation we set the voltage 10
times higher. The second function of the divider is a protection. The diode may be
easily destroyed in case of direct connection to higher voltage.
In connection according to Fig. 4.1c (current-voltage converter with operational amplifier),
the voltage on the diode is really equal to that of U 1/ , since no voltage difference (virtual zero)
appears between inputs of the OA (neglecting its voltage offset). The diode current is given
by the expression (U 2 being I/U converter output voltage)
I
U2
R
(4.1)
Input current bias I 0 of the OA can cause additional measurement error (for OP07 type
I 0max = 7 nA); the resulting standard uncertainty of the current measurement is given by
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. Measurement of low currents
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2
uI 
2
2

 I0 
 1
  U 2


uU 2  
uR
 


3
 R
  R 2



(4.2)
Note: In our circuit, the input bias current can be estimated by OA output voltage
measurement with connected points “A” and “B”. For this measurement, the feedback
resistor R=10 M should be used to achieve higher value of the output voltage
(proportional to I 0 : I 0 = U 2 /107).
The absolute methodical error for analogue or digital micro-ammeter measurement is given
as measured value – true value
 met  X M  X T
(mA)
(4.3)
Relative methodical error is given by
 met 
 met
XM  XT
 100 % 
 100 %
S
XT
(4.4)
where measured value X M is the current measured by the micro-ammeter and the true value
X T is the value calculated according (4.1) for the corresponding voltage.
4.5. Result presentation
Write the measured and calculated values in the table and draw the dependencies I  f (U 1/ )
to one common graph. The input resistance of both analogue and digital micro-ammeters
(causing the methodical error) can be estimated from such a graph – see Fig. 4.2.
I

A1
OA
A 2
I
UA1
UA2
U 1 / (V)
Fig. 4.2 Figure allowing to determine resistances of micro-ammeters
Note: It is necessary to use graphical solution (the circuit is non-linear). The values of
resistance of A 1 , A 2 micro-ammeters are (for chosen value of I ):
RA1 
U A1
U
, RA 2  A2
I
I
(4.5)
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