# Laboratory Exercise 1 Multimeter

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```					MIT-1016                               Laboratory Exercises                                         1       MIT-1016                                Laboratory Exercises                                         2
leads. Many multimeters can also measure frequency. Many meters select the measurement
Laboratory Exercise 1: Multimeter                                                         range automatically, after the user has selected the measurand he wants.
Ana-digi-meters are digital multimeters, which have both normal e.g. 3½-digit numerical liquid
The purpose of this exercise is to introduce to you some of the most common measurement de-                  crystal display and an analog bar display.
vices of voltage, current and resistance and to help you understand the operational principle of             Numerical (digital) display does not make a digital meter more accurate than an analog meter.
the oscilloscope. The theory section supplements the information in the course material.                     Input impedance of a digital multimeter is typically 10 M , and it is usually larger than the input
impedance of an analog multimeter. Sometimes also a digital multimeter loads the measured ob-
1.1 Multimeters                                                                                                   ject too much, which causes the value of the measurand to change and the measurement result
Multimeter is a device used for the measurement of AC or DC voltages, currents and also resis-               will be wrong. Due to the finite word length of an A/D-converter, the result may contain some
tances. Some meters are also capable of measuring temperatures, conductivities and frequen-                  quantization noise. In addition to this, warming-up of the meter during its use changes the prop-
cies. Multimeters can be analog or digital, or combination of these (the most modern meters).                erties of the meter a bit.
For the most accurate meters a warm-up time, after which certain accuracy level is achieved, is
Analog multimeter
specified. For digital multimeters the inaccuracy is usually given in a bipartite way: ± (inaccuracy
Analog multimeter has a pointer, which moves continuously along the scale, and the measurer                  of the reading (or range) as percent + number of counts of the least significant digit). Example:
reads the position of the indicator on the scale. Alternatively, there are also device structures in         Reading of the meter is 0,71549 V and the inaccuracy of the meter is given as (0,25% rdg + 70
which the scale moves behind a fixed indicator line.                                                         digits; rdg stands for reading). Thus the inaccuracy of the measurement result is ± (2,5 10-3
Moving-coil instrument is the most commonly used electromechanical analog meter because                      715 mV + 70 10-5 V) = ± 2,5 mV
of its high sensitivity. Passive meter does not need supply voltage for measurements of voltage
and current, since the energy needed for indication is driven from the measurand. In direct cur-
rent (DC) measurements the voltage or the current to be measured is brought into the mecha-            1.2   Measurements carried out with multimeters
nism through a suitable shunt or series resistance. In alternating current (AC) measurements,
full-wave rectification is performed first. In resistance measurements the internal battery of the           Voltage measurements
meter is connected in series with the movement and the resistance is determined by the current               The smallest DC voltages to be measured with both analog and digital multimeters are in order
flowing through the resistor.                                                                                of mV. With the most accurate digital multimeters the smallest measurable voltage is in order of
When constant current (nominal current) flows through a moving-coil mechanism, it will result in             microvolts. On AC range digital multimeters are able to measure millivolts, but with passive ana-
a full-scale reading. In voltage measurements the sensitivity of the meter is specified as recipro-          log multimeters operating range ends in the order of volt. The highest voltage ranges are for
cal of the nominal current /V, independent on the measurement range. For this reason the in-                 both DC and AC voltages typically 500 - 1000 V.
put resistance of the meter depends on the he measurement range. The value of this resistance                A multimeter may be damaged if high voltages are measured with too sensitive measurement
can be determined by multiplying the sensitivity of the meter by the full-scale voltage reading of           range. Many meters have different terminals for measuring high or low voltages. Some digital
the given measurement range.                                                                                 multimeters tolerate supply voltage on all voltage ranges
Inaccuracy of an analog multimeter is specified as an accuracy class. It tells the value of the in-          In AC measurements, the indication of an analog moving-coil mechanism is based on the full-
accuracy of the meter as percent of the full-scale reading of the measurement range. The                     wave rectified mean. The result will be equal to the root-mean-square (RMS) value of a sinusoi-
measurer should choose the measurement range so that the indication of the meter is as high                  dal signal corresponding to this mean. Thus, for other waveforms than sinusoidal, the analog
as possible. Inaccuracy is higher in AC measurements than in DC measurements.                                multimeter will not give correct results.
Analogic indication is more practical than a digital one when one has to be able to observe the              The properties of digital multimeters vary quite a lot in AC measurements. Like analog meters,
rate and direction of change of the measurand. Disadvantages of an analog multimeter are its                 most digital multimeters measure the rectified mean of the signal and indicate the RMS value of
relatively small input resistance (loads the measured object relatively much) and inaccuracy of              corresponding sinusoid. Usually these meters are most accurate in the frequency range of 50 -
the indication. Analog multimeters are usually inexpensive. In the most modern analog multime-               500 Hz. True RMS-meters can be used to measure RMS values of other than sinusoidal wave-
ters a liquid crystal bar replaces the easily damaged indicator.                                             forms. For these meters, the highest waveform crest factor (CF), with which they will still oper-
Digital multimeter                                                                                           ate with high enough accuracy, is given. CF is the ratio of the peak value to the RMS value of an
In digital multimeters the measurement result is given in numerical form. The most important                 AC signal. The highest CF-value of True RMS -meters is in order of 3...5. Together the crest fac-
component in it is an analog-to-digital (A/D) converter, which converts the measured (or from it             tor, frequency sensitivity, accuracy and bandwidth of a multimeter give a general idea of how
electronically formed) DC voltage into numerical presentation.                                               accurately different waveforms can be measured with it. In AC measurements it is good to use
In addition to the usual multimeter functions, microprocessor technology has enabled some new                an oscilloscope to help observing the waveform, especially if the properties of either the signal
features in digital multimeters. Readout holding 'freezes' the displayed value instantly after the           or the meter are not exactly known. Among the analog meters there is the iron-vane-meter,
probe touches the measurement point; thus the user may concentrate on aligning the testing                   which also shows the RMS value of an AC voltage independent on the waveform.
wires to the measured object. Short-circuit testing beeps when the resistance is below a certain             If the meter is AC coupled, the result of an AC measurement will show only the RMS value of the
limit. A multimeter with recording of minimum and maximum values can be left to record mini-                 AC component. In order to determine the true RMS value of mixed voltage, its DC component
mum-maximum values on its own, no matter whether they are voltages, currents, resistances or                 has to be measured separately. RMS value of mixed voltage is determined by equation:
temperatures. Peak value holding is useful, when the measured circuit has voltage transients or
2      2
impulse currents of less than one period’s length. The use of offset makes it possible to record a           U      U DC   U AC
signal value into the meter’s memory and adding this value to or subtracting it from the following
values; in this way two different voltages can be compared quickly. When offset is used together             where UAC is the RMS value of the AC component. Depending on the meter, a DC-coupled
with dB-function, the dB-values can be read directly on the meter. Offset can also be used for               RMS meter displays either only the DC component or the combined RMS value of both the AC
the compensation of the measurement error caused by the resistance of the measurement                        and DC component.
MIT-1016                              Laboratory Exercises                                        3       MIT-1016                               Laboratory Exercises                                   4

Current measurements
1.3 Function generators
The lowest current ranges in both analog and digital multimeters are in the order of mA. Highest
ranges are usually 2 - 10 A. There will always be a small voltage loss over an ammeter, whose             Function generator is a signal source, which generates both sinusoidal and several other wave-
effect on the measured circuit must be taken into account when judging the correctness of the             forms, e.g. triangular, sawtooth, square, pulse and DC voltage waveforms. Frequency range
measurement result. In current measurements the input resistance of the multimeter is very                may be as wide as from 1 Hz to 50 MHz. In addition to the selection of waveform, amplitude
small. If the meter is connected wrongly, both the measured object and the meter may be dam-              and frequency there may be several other function in a function generator, e.g. setting of im-
aged. In many meters there is a special connector used only for current measurements in order             pulse ratio. The front panel of a function generator is shown in next figure.
to prevent this.
If the measured currents are too high for the meter, a separate measurement resistor (shunt)
or a clamp-on current probe must be used. Shunt is a resistor, which is connected to a circuit
under inspection. It has a small resistance and it can withdraw high power loss. The voltage over
the shunt is measured and the magnitude of the current is determined mathematically. Clamp-on
current probe must be used if the measured circuit can’t be broken for the measurement.
Most clamp-on current probes are current transformers, which can be used only for measuring
AC currents. For DC current measurements one must use probes based on Hall effect, which
give the voltage proportional to the current.

Resistance measurements
With a typical digital multimeter, resistances between 0,1     - 20 M can be measured. Some
digital multimeters have conductance modes (conductance = 1/resistance), with which resis-                                                                                                 2
tances up to 10 G can be measured. The scale of an analog multimeter is non-linear in the
ohm range. The smallest measurable resistance is 0        and the highest is infinite, but reading                          3
accuracy is bad on high values.
Analog multimeter must be set to zero by short-circuiting the measurement leads and adjusting
the meter’s indication to zero ohm always before resistance measurements or when measure-            1.4 Power supply
ment range is changed. The resistances of the measurement leads and contacts must be taken                A power supply produces DC voltage (or current). The available voltage
into account while measuring small resistances. In some digital multimeters the resistance of the         and current ranges vary between the supplies. The output current is de-
measurement leads can be compensated by short-circuiting the leads and pressing the zeroing               termined by the ratio of the output voltage and the resistance load, and it
switch, which sets the meter’s indication to zero. Otherwise the resistance of the leads must be          can usually be limited to a certain value. There are separate controls for
subtracted from the measurement result. The most accurate results are achieved using instru-              voltage control and current regulation. Sometimes the power supply has
ments with four-wire measurement of resistance. In four-wire measurement one wire couple is               separate switches for operating voltage and output voltage. The supplies
used for feeding constant electric current through measured object and the other couple is used           have displays for both the output voltage and output current, but those
for measuring the resulting voltage over the object. Measurement instrument calculates the re-            values can also be measured with a multimeter before connecting the
sistance from the proportion of measured voltage and current. Almost no current flows through             supply to the circuit under investigation.
the voltage measurement wires, so there will be hardly any voltage loss. Thus the resistances of
the measurement wires and contacts will not affect the result.
Semiconductor junctions make it more difficult to analyse the results when resistances between
different points on a circuit board are measured. The resistance of a semiconductor junction de-
pends highly on forward voltage affecting the junction. In digital multimeters, those resistance     1.5 Pre-report
ranges that feed high enough voltage to make the pn-junction conductive are often marked with
diode symbol. With these meters the pn-junction should not be conductive when other meas-                                Answer the following questions before coming to the laboratory.
urement ranges are used. In a specific diode testing mode the meter feeds small current into di-
ode and the threshold voltage over the pn-junction is displayed. Many digital multimeters have a
continuity summer which beeps when the resistance between the leads is small (typically less
than 100 ). When analog multimeter is used for measuring semiconductors one must remem-                1. Explain how and with what kind of multimeter you can measure
ber that the meter gives a voltage whose polarity is reversed compared with the indication of the             a) RMS value of the mains voltage?
connection terminals.                                                                                         b) voltage output of a thermocouple, when the temperature difference is 100 K (about 5
mV)?
c) RMS value of a positive square wave?

2. Moving-coil mechanism of the analog multimeter used in the laboratory has a nominal current of
50 A in DC ranges. a) What is the input resistance of the meter, when the voltage range is 2,5
V, 10 V, 25 V? b) This meter is used for measuring DC voltage of 5 V. Source impedance of the
MIT-1016                               Laboratory Exercises                                       5       MIT-1016                               Laboratory Exercises                                         6

power supply is 1 M . What is the meter reading when 10 V measurement range is used? What           1.6.3 Getting acquainted to the oscilloscope
is the reading if a digital multimeter with input impedance of 10 M is used?                             Switch the oscilloscope on. Set trigger signal to be taken from the channel 1 and set triggering
mode switch to AT-position (automatic triggering). Adjust the display’s brightness and contrast
correctly. Connect 1 kHz sinusoidal signal from the function generator to the oscilloscope input.
3. For a positive square wave (voltage levels 0 and A, impulse ra-                                           Test the effects of the different controls of the oscilloscope on the signal displayed on the
tio D = d/T, look at the figure beside), calculate                                                        screen.
a) DC component value (time average)
b) RMS value for AC component (you get the AC compo-
nent by subtracting the DC component from the original                                       1.6.4 Measurement of RMS value of a sinusoidal AC voltage
signal)                                                                                           Exercise 3
c) total RMS value                                                                                    In this exercise, accuracy properties of different meters are examined. Find the given inaccura-
as a function of the impulse ratio?                                                                       cies for each meter from their specifications and write them down in table below. Note! The in-
d) What is the crest factor of this signal?                                                               accuracy of the analog multimeter is given as percent of the full-scale reading of the measure-
ment range and it can be found below the measurement scale. Use the oscilloscope to set the
amplitude of the function generator signal to 10 V. Set its frequency to 127 Hz and its waveform
to sinusoidal wave. Calculate the theoretical RMS value of this signal. Measure the voltage with
1.6   Measurements in laboratory                                                                               meters mentioned in table below in such a way that all meters are connected simultaneously.
Calculate the inaccuracies for the measurement results.

1.6.1 Resistance measurements                                                                                            Meter           Measurement         Given inaccuracy                  Inaccuracy of the
Exercise 1                                                                                                                          result [V]                                               result [V]
Measure the resistance of the given resistors with the meters mentioned in table below.                         Analog meter
IMPORTANT: compensate the measurement lead resistances, if it is possible with the meter                         Digital meter
used. Use either zero-setting or four-wire measurement according to the meter properties. Write                Theoretical RMS
the measurement results down in table below. Determine also the nominal values for the resis-                       value
tances.
a) Does connecting/disconnecting of meters cause any changes in the indications of the other
Meter                 R1                      R2                        R3                          meter?
Analog meter
Digital meter                                                                                       b) What causes the observed phenomenon and what kind of consequences does it have on
Nominal value                                                                                          measurement results?

How can you eliminate the effect of the measurement leads if there is no compensation in the             c) Are the results given by different meters alike (measurement uncertainty taken into account)?
meter?                                                                                                   Why?

1.6.2 DC voltage measurements                                                                             1.6.5 Pulse wave measurements
Exercise 2                                                                                               Exercise 4
Supply U = 10 V DC voltage to the given test circuit from the DC power supply. Check the value           In this exercise, measurement of the RMS value of a waveform different from sinusoid is stud-
of the voltage before connecting the supply. The structure of the circuit is presented on the box        ied. Change the waveform of the voltage set in the previous exercise into a positive square
containing the circuit. 10 V voltage is the input for a voltage regulator, which gives a constant        wave (pulse wave) with frequency of 100 Hz and impulse ratio of 1/5. Set its amplitude to 10 V
output voltage. This unknown output voltage is measured in this exercise.                                again. Calculate the theoretical RMS value of this signal (see pre-report). Write the measure-
ment results down in table below.
Measure the voltages from the connectors Ua … Ud with both of the meters. Write down both the
measurement results and the input impedances Rm of the meters on the measurement ranges                                      Meter                      AC                     DC
you used. Based on the measurement results and structure of the test circuit, determine the                              Analog meter
regulator voltage E when using meters mentioned in the table. (See pre-report.)                                          Digital meter
Theoretical RMS value
Meter           Rm        Ua       Ub        Uc       Ud        E
Analog meter                                                                                    Compare the results with the theoretical value you calculated. Explain the differences between
Digital meter                                                                                   the results.

What causes the differences between the results given by analog multimeter? How about the                 Set the function generator to sinusoidal waveform, frequency 1 kHz, adjust the horizontal and
differences between analog and digital multimeter?                                                        vertical deflections on the oscilloscope properly for the sine wave and switch off the instruments.

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