Basics of electronic ...

When working with electronic systems, one usually proceeds in such a way that first the constant-current conditions of their operation are checked, and then the behavior of these systems when exposed to signals (alternating currents). Hence the use of various measuring instruments. Analog and digital multimeters are used to measure DC voltages and currents, each of them has its own advantages and disadvantages. On the other hand, checking the operation of electronic systems with signals requires the use of, most often, but not only, devices such as generators and oscilloscopes, and then analyzers of various types. Here, in the elementary approach, only multimeters will be presented, i.e. universal devices allowing to measure mainly direct currents (DC) and alternating currents (AC), voltages and currents (often limited to only small frequencies, like 50-60 Hz), but also other physical quantities, while the discussion of the operation of other devices (including oscilloscopes) is postponed for further presentation.

Analysis of the influence of measuring instruments on the operation of the circuit

1. Influence of the voltmeter on the voltage at the load

Assumptions: the analog voltmeter has a characteristic resistance of 10 \( k\Omega/V \) and it is set to the range of 1 V, hence it then has a resistance R_V = 10 \( k\Omega \).

Circuit without instruments (actual voltages) :

\( U_{L} = E \frac{R_{L}}{R_{S}+R_{L}} = 1 V \frac{9 k\Omega}{1k\Omega + 9k\Omega} = 0.9 V \)

Circuit with instruments (voltages in this state):

Absolute error of voltage measurement on the load: \( \Delta U_L = U'_L - U_L = 0.826V - 0.900 V = -0.074 V \)

Relative error of voltage measurement on the load:  \( \delta U_L = \frac{\Delta U_L}{U_L} = \frac{-0.074 V}{0.900 V} = -0.083 = -8.3 \)%

Where did the assumptions come from?

Analog voltmeters (electric, passive) are built as a series connection of a magnetoelectric meter and precise resistor (series resistor) with resistance depending on the set measuring sub-range. Such voltmeters are characterized by the characteristic resistance expressed in \( k \Omega / V \) (here the value of 10 \( k \Omega / V \) was adopted). It was also assumed that the multi-range voltmeter has the sub-ranges of 0.3V, 1V, 3V, 10V, 30V, 100V, 300V. Due to the obvious requirement of obtaining the highest possible accuracy, the range of 1.0V was selected, as according to Fig. 4.1.1, the voltage on the load is 0.9 V (in laboratory practice, the approximate value will be obtained from preliminary measurements!). Thus, the resistance of the voltmeter in this range is: RV = 10 \( k \Omega / V \) * 1 V = 10 \( k \Omega \), Note: Digital voltmeters have an input resistance (internal) independent of the range and typically equal to 10 \( M \Omega \).

2. Influence of the ammeter on the current in the load

Assumption: the ammeter has an internal resistance R_A = 2 \( k\Omega \).

Circuit without instruments (actual currents):

\( I = \frac{E}{R_S + R_L} = \frac{1 V}{1 k\Omega + 9k\Omega} = 0.1 mA = 100 \mu A \)

Circuit with instruments (currents in this state):

\( I' = \frac{E}{R_S + R_L + R_A} = \frac{1 V}{1 k\Omega + 9 k\Omega + 2 k\Omega} = 83.3 \mu A \)

Where did the assumptions come from?

The ammeters are built as a combination of a magnetoelectric meter and shunt resistor (parallel resistor) with a resistance depending on the set measuring range. In the commonly used Ayrton shunt system, multi-range ammeters have the property that their shunt resistances are selected in such a way that the voltage across the ammeter is always the same at different ranges (often 0.2V); hence the resistance of the ammeter in the different ranges can be easily calculated. In the given example, assuming that the ammeter works in the sub-range 100 uA, its resistance is therefore RA = 200 mV / 100 \( \mu A \) = 2 \( k \Omega \). This principle also applies to digital ammeters.

Absolute error of the load current measurement: \( \Delta I = I' - I = 83.3 \mu A - 100 \mu A \)

Relative error of load current measurement: \( \delta I = \frac{\Delta I}{I} = \frac{-16.7 \mu A}{100 \mu A} = 0.167 = -16.7 \)%

After analyzing the influence of the measuring instruments on the operation of the circuit, the accuracy of the measurements should be assessed using the metric of the instrument used, provided by the manufacturer. It is different for analog devices than for digital devices.

The accuracy of measurements with analogue instruments is determined on the basis of the specified instrument class k, defined as the ratio of the absolute error Dx expressed as a percentage to the value corresponding to the maximum pointer deflection xmax. Knowing the meter class k [%] and xmax, first the absolute error (constant for a given range) is calculated Dx = xmax * 0.01* k, and then having the absolute error \( \Delta x \) and the indicated measured value x, the relative measurement error \( \delta x = \frac{\Delta x}{x} \) is determined.

The accuracy of measurements with digital instruments is determined as follows: The accuracy for the range used, given in percent, should be multiplied by the read voltage or read current value and the value indicated in the manual shall be added corresponding to the change in the last digits of the indicator (usually by one, two or more, usually marked as digit value).

Another characteristic parameter of a measuring instrument is its resolution, defined as the smallest change recorded by the instrument. In the case of analog devices, the resolution is usually the value of the measured quantity that corresponds to the change of the pointer position by half of the smallest division. In the case of digital instruments, the measurement resolution means a change in the value of the measured quantity by 1 of the least significant digit, e.g. for a 3.5-digit meter in the 2 V range, the highest indication is 1.999 V, and the resolution is 0.001 V. accuracy and resolution in the case of digital instruments (wrongly stating that the accuracy of measurements with a meter 3.5 digit with a nominal range of 2.000 V is 0.001 V - = 1 mV).

Comparison of the properties of various multimeters (multimeters) as an example DC voltmeters

Properties	Electric meter UM-112B type by ERA	Electric meter V-640 type by ELPO	Digital meter type M-3610 by METEX
Reset	Manual mechanical	Manual mechanical and electric	Automatic electric
Need for power supply	No	Yes	Yes
The position of the meter during operation	horizontal	horizontal	any
Change of polarity	manual	manual	automatic
RWE on various range	variable: 20 k\Omega/V	constant: 100 M\Omega	constant: 10 M\Omega
Input	"Floating"	“Single-ended” [correct ground connection necessary]	"Floating"
Accuracy	class 1 + reading error	Class 1.5% (± 1.5% of the span value)	±0,3% rdg + 1 dgt
Resolution	0.5 div	0.5 div	1/2000 range (3½ digital instrument)
Voltage drop with current measurement	30..480 mV depending on the scope	5 or 50 mV depending on the sub-range	200mV