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DC System Riddle No.3 - Measuring the DC current
How do we measure the DC current if the ammeters are not working?
Author : Siaga TC - From: south africa
Thu, March 31st, 2011 - 16:44
As I understand your question, you want to know different ways of current measurement. I hope following description will be useful.
One of the simplest measurement methods is the direct comparison of measured value with the standard one. An example of the direct measurement method is presented in Figure below. In this method the idea of weighting it is applied (this method is sometimes called the current weight).
One coil of the electromagnet is supplied by the measured current Ix , which causes that the ferromagnetic element on one arm of the balance is attracted. (It is possible to use also other electric mechanism, for example attracting of the magnet or attracting other coil – this last mechanism is very close to the definition of the ampere.)
On the second arm of the balance similar mechanism is placed – this time the coil is supplied by the standard reference current Is. Changing the value of the standard current we can balance the weight – the equilibrium state is when the pointer is at the zero position. We can also determine the state of equilibrium using the electrical method – for example by the measurement of the resistance Rx of the resistor with moving slider causing the change of the resistance (the potentiometer). This idea is presented in Fig.b. Figure b presents the indirect method of measurement of the value of electric current. This time, the measured current causes the change of the resistance Rx. In this circuit there is a lack of the standard of current, but this does not mean that this standard does not exist. It exists as the scale of resistance and it could be introduced to this method by the earlier supplying the coil by the reference standard current (in such way we introduced the dependence Rx=f(I) to this method).

Figure b presents the weight that is weighted automatically. It is because in this method we applied the idea of feedback. The resistor Rx (sensor of the position or displacement) is connected into the bridge circuit consisting of four resistors and supply voltage. When all resistors are the same then the output signal (connected to the amplifier) is equal to zero.
When one of the resistances is changed then the equilibrium is disrupted and the signal of unbalance appears at the output of the amplifier.
The process of current measurement is as follows. If current Ix = 0 then the bridge circuit is in equilibrium state and the weight is balanced. If the current Ix changes, then the electromagnet (the coil) attracts the ferromagnetic element on the arm and the resistance Rx changes. This causes signal voltage to appear at the output of the bridge circuit. This signal after amplification supplies the second coil as the current Iout, which causes the movement of the second arm and balancing of the weight (similarly as it was performed manually in the example presented in Fig. a). After short period of time (the transient state) the balance returns to the equilibrium state, which is detected as zero voltage on the output of the bridge circuit.
Thus by means of feedback we realize the automatic balancing of the weight and the output current Iout can be the measure of the tested current Ix.
The measurement of the current can be performed by the null measurement method – we balance the circuit and the balance state is indicated by the pointer or electrically by the zero output voltage of the bridge circuit. The same measurement can be performed by differential measurement method. In this case it is not necessary to balance the circuit –the deflection of the pointer or the output voltage of the bridge circuit can be used as the measure of the current value. It is also possible to use the null differential measurement method. In this method we roughly balance the weight by the current I0 and the deflection of the pointer (or change of the output voltage of the bridge circuit) is caused by the difference between equilibrium state and state after the change of the current dI=Ix-I0. Using the null-differential method we can obtain improvement of the sensitivity of the measurement – the movement of the pointer can be realized by the smaller current dI instead of current equal to Ix.
The measurement method is characterized by the sensitivity of the method (and related to this parameter the resolution of the method) and by the range of the measuring device. The sensitivity of the method informs us what value of the measured quantity is necessary to obtain output signal – the smaller this value, the larger the sensitivity. Suppose that in the example presented in
Fig. a,b both coils are the same. Then to balance the weight it is necessary to use the same current Is as the measured current Ix and the sensitivity S = Ix /IS is equal to 1. We can improve the sensitivity by increasing the number of turns of the second coil. For example, if the number of turns is n2 = 2n1 then to obtain the equilibrium the reference current Is can be 50% of the measured current Ix. Thus the sensitivity S = Ix /0.5 Is is two times larger.
The resolution informs us about the smallest value of the measured quantity, which could be possibly detected. For instance, if we can detect the deflection of the pointer equal to 5° (represented for example by one graduation on the scale), then after improving the sensitivity by factor of two we can detect two times smaller change in the measured current. The measurement range of the measuring device is the maximal value of the quantity, which we can measure. In the null method described above the range is equal to Ixmax, while for the null-differential method it is Ixmax-I0 (and generally Ixmax - Ixmin when the beginning of the scale is not equal to zero).
Figure below presents another idea of the indirect measurement of the current by applying the weight. In this case the movement α of the pointer (caused by attracting of the arm by the force depending on the measured current Ix) is balanced by the force of gravity F of the weight G. The standard of the current is not presented in the Figure below, but it does not mean that it does not exist. It could be introduced to this method by the earlier scaling of the measuring device. The scaling process could be realized by supplying the coil with the standard values of the current and determination of the pointer deflection. In this way we can determine the dependence α = f(Ix).
For scaling of the device we can used the source of standard values called the calibrator.
In the example presented in Figure for scaling purposes standard of the weight G could be used instead of the current source. Before we perform the measurement, we could determine the dependence between the current Ix and the weight G as G = K Ix. This time we de facto measure the force (or rather the mass G) and we determine the investigated current knowing the constant K.
The indirect measurement methods are employed in almost all indicating instruments. In these instruments the measured value is expressed by the deflection of the pointer (in analogue instruments). This pointer indicates themeasured value at the point on the scale – thus we compare the measured value and the deflection of the pointer. But also in such instrument the standard of the measured quantity exists in the background, because the points on the scale were marked by the scaling process earlier.

The important method of comparison of the measured value and the standard one is the compensation measurement method illustrated in Figure below.
In the compensation method we determine the difference between two values (measured and standard) and we can precisely determine the state when this difference is equal to zero. Thus the compensation state (the equilibrium state) means that both values are the same and cancel each other. As the results, in the state of equilibrium the signal at the output of the circuit is zero.
In the example presented in Figure the measured voltage Ux is compensated by the voltage drop Us on the resistor Rs. The state of equilibrium is indicated as the zero of the output signal by the null indicator
NI (for this purpose a very sensitive voltmeter called galvanometer can be used).
The measuring procedure consists of two steps. In the first step, the standard value of the current Is is established (for example by comparing it with the standard value). In the second step, the resistance Rs is being changed until the null indicator NI indicates the state of equilibrium. For known value of the current Is the resistor Rs can be scaled directly in the voltage units.

The compensation methods enable the measurements of voltage with excellent accuracy, because we are capable of manufacturing the resistors very precisely (with very small uncertainty). Therefore the devices called potentiometers were one of the most accurate measuring instruments – nowadays the potentiometers are substituted by accurate digital voltmeters often using the idea of compensation.
The compensation method exhibits very important advantage. In the state of equilibrium the measuring device does not take the energy from the tested source – the measurement is performed in truly non-invasive way with the infinite input resistance of the measuring instrument.
Figure b above presents the realization of the compensation idea performed automatically by applying the feedback technique. The amplifier works as the null indicator amplifying the difference between the measured voltage Ux and the drop voltage Us. This difference causes the output current Iout, which is increased until the input voltage of the amplifier again returns to the zero.
Apart from the compensation method there is also used the comparative measurement method. The magnetic direct current comparator (DCC) is currently used for the most precise reconstruction of the resistance standard (NIST 1458 – 2003). The term comparator is not always correctly interpreted, because comparison is in the definition of the measurements and practically all measuring instruments compare the measured value with the standard one. The comparative method is defined in narrower sense – as the compensation method uses the difference between two values the comparative method uses the ratio of two values2.

An example of the comparator is presented in Figure below. In the circuit presented in Figure we can obtain the equilibrium by the compensation of the currents Ix and Is.

This state of equilibrium can be realized by the change of the voltage U1 or U2 . The condition of the equilibrium is

Thus we can use this circuit for resistance measurement. The current compensation circuit was used as the resistance comparator.
Author : Hamid - From: Iran
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