notes on multi meters

8/13/2019 Notes on Multi Meters

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VOLTAGE, CURRENT AND RESISTANCE MEASURING INSTRUMENTS

To measure voltage (ac,dc), current (ac, dc) and resistance, two types of instruments,

analog and digital meters, are utilized. The measurements of these fundamental electrical

quantities are based on either one of the following:

i) Current sensing. The instruments are mostly of the electromagnetic meter movement

type, such as an analog multimeter.

ii) Voltage sensing. The instruments are mostly electronic in nature, using amplifiers

and semiconductor devices, such as a digital multimeter.

1) ANALOG MULTIMETER

The main part of an analog multimeter is the D’Arsonval meter movement also known

as the permanent-magnet moving-coil (PMMC) movement. This common type of movement

is used for dc measurements. The basic construction of a such meter movement is shown in

Figure 1.

Figure 1.

When the meter current Im flows in the wire coil in the direction indicated in Figure 1,

a magnetic field is produced in the coil. This electrically induced magnetic field interacts with

the magnetic field of the horseshoe-type permanent magnet. The result of such an interaction

is a force causing a mechanical torque to be exerted on the coil. Since the coil is wound and

permanently fixed on a rotating cylindrical drum as shown, the torque produced will cause the

rotation of the drum around its pivoted shaft.



When the drum rotates, two restraining springs, one mounted in the front onto the shaft

and the other mounted onto the back part of the shaft, will exhibit a countertorque opposing

the rotation and restraining the motion of the drum. This spring-produced countertorque

depends on the angle of deflection of the drum,θ , or the pointer. At a certain position (or

deflection angle), the two torques are in equilibrium.

Each meter movement is characterized by two electrical quantites:

1. Rm: the meter resistance which is due to the wire used to construct the coil.

2. IFS: the meter current which causes the pointer to deflect all the way up to the full-scale

position on the fixed scale (this is marked FS in Figure 1). This value of the meter current

is always referred to as the fullscale current of the meter movement.

Figure 2 indicates the electrical circuit symbol of the meter movement that will be used.

Rm Im

Figure 2.

The meter sensitivity S, also referred as the ohm/volt rating of the meter movement, is

the reverse of the full-scale current.

VI

1S

FS

Ω= (1)

IFS or S (fixed value) is defined for a given meter movement and is usually noted on its

casing or in the manufacturer's data sheets. The meter becomes more sensitive as its full-scale

current decreases. Typically the minimum value of IFS is 50 µ A and hence the maximum

value of S is 20 KΩ /V.

i

The PMMC movement cannot be used directly for ac measurements since the inertia of

PMMC acts as an averager. Because ac current has zero average value and it produces a

torque that has also zero average value, the pointer just vibrates around zero on the scale. In

order to make ac measurements, a bridge rectifier circuit is combined with PMMC as shown

in Figure 3.



i1(t)

Bridge rectifier

i(t)

T/2 T-I

I

i (t)

T/2 T0

I

i1(t)

Figure 3.

In Figure 3 the bridge rectifier rectifies the ac current i and produces the current i 1=|i|

which has a mean value (average or dc value).

∫ ∫

π=ω==

2 / T

0

2 / T

0

1mean,1

I2dt)tsin(I

2 / T

1dt)t(i

2 / T

1i (2)

The rms (root-mean-square) value of a periodic waveform i(t) of period T is defined as

∫

=

T

0

2

rms dt)t(iT

1i (3)

The form factor of the same waveform is the rms value divided by the mean value of the

full-wave rectified waveform or equivalently

mean,1

rms

i

i)FF(FactorForm = (4)

On the ac scale, an analog multimeter is calibrated to read the rms value of a sine wave.

Since the rms value and the form factor of a sine wave of peak value I are 2 / I and 1.11,

respectively, the meter indication corresponds to the value )2 / I(i11.1 mean,1 =×

.



When measuring the rms values of other waveforms, the analog multimeter measures

the mean value of the rectified signal and multiplies with 1.11 as if it is a sine wave. Thus, the

analog multimeter gives wrong results for rms values of other waveforms. In order to

calculate true rms values of other waveforms, their form factors should be taken into account,

e.g., the factor of a triangular wave is 1.155 and the form factor of a square wave is 1.0. Then

for a triangular wave the analog multimeter indication corresponds to 1.11/1.155 times the

true rms value and it corresponds to 1.11/1.0 times the true rms value for a square wave.

A) AMMETER

As pointed out above, the deflection of the pointer in the D’Arsonval meter movement isproportional to the meter current I. Therefore, this instrument can be used to measure current.

However, the meter movement by itself is of limited use and capability, since its full-scale

current value IFS is practically too small (at most in the order of milliamperes). If the current

allowed to flow in the movement, Im, exceeds IFS, permanent damage can result, in particular

to the restraining springs.

To be able to measure currents higher in value than IFS of a given meter movement, the

division principle is applied. Figure 4 shows the construction of an ammeter.

A Rm

IIm

Rsh

Ish Ammeter

Actual circuit

I

Symbol

Figure 4.

Hereshm

shm

RR

RII

+= (5)

where Im is the movement current, I the circuit current being measured, Rm the

resistance of the movement, and Rsh the "shunt" resistance connected in parallel with the

movement to provide a path for the portian of the circuit's current not allowed to flow thoughthe meter movement.



resistance, RA, which could disturb the circuit conditions and change the current distribution

in the circuit. This is what is called the meter's loading effect.

B) VOLTMETER

The meter movement is modelled as a resistance of value Rm, as shown in Figure 7.

Therefore, Ohm's law applied to this movement provides (8)

mmm IRV = (7)

where Vm is the voltage across the meter movement when the current flowing in it is I m.

When the current in the movement is IFS,

FSmFS IRV =

(8)

To increase the full-scale voltage range of the movement when functioning as a

voltmeter, the meter movement current Im has to be lowered. This can easily be achieved by

inserting a large resistance, called the multiplier resistance, Rmult, in series with the meter

movement, as shown in Figure 7.

V

Rm V

Rmult

Voltmeter

Symbol

Im

Actual circuit

V

Figure 7.

The resistance of the voltmeter, Rv, is the series combination of Rm and Rmult as can be

seen from Figure 7.

Svoltmeterof rangeI

1V

I

VRRR

FS

max

FS

maxmmultv ×=×==+= (9)

Eq. (9) is quite important. It indicates that the higher the range of the voltmeter, the

larger would be internal resistance of the voltmeter, Rv. This is a clear since a higher voltage

range requires a larger multiplier resistance. Also, Eq. (9) indicates that a more sensitive

meter movement (higher S or lower IFS) also results using a larger voltmeter resistance.



Using the same meter movement, a multirange voltmeter can be designed. A three-range

voltmeter is shown schematically in Figure 8.

Rm

Multi-position switch Rmult1

Rmult2

Rmult3

Figure 8.

The voltmeter must be connected in parallel with a terminal pair across which the

potential difference is to be measured. For example, to measure the voltage V’ across the

terminals A and B in Figure 9(a) the voltmeter is connected as shown in Figure 9(b).

EV’

A

B

(a)

E

A

B(b)

V

Figure 9.

In order for this measurement process not to disturb the value of the potential difference

being measured, the resistance of the voltmeter (which is parallel connected) should ideally be

infinity so that the circuit remains unchanged. However, a practical voltmeter has a finite but

large resistance, Rv, which could disturb the circuit conditions and result in reading errors

called loading effect errors. To reduce the loading effect, Im must be very small or Rv must be

made as large as possible. Examining Eq. (10) reveals that Rv is increased by using a higher

sensitivity meter movement or 'by using a higher range to read the voltage which may not

always be acceptable because of the reading errors near the lower end of the scale.

C) OHMMETER

If the meter movement current Im is somehow made to be proportional to the value of an

unknown resistance to be measured, the meter's scale can be calibrated to read resistance

directly. Here, however, a voltage source (e.g., a battery) must be added to the meter’s circuitto drive the current necessary for the deflection of the pointer. A typical ohmmeter circuit is



2

I

RR

R

R2

EI FS

m1

1

MS

m =+

×= (14)

This indicates that the meter movement current will be half its full-scale value when the

value of the unknown resistance is RMS.

Figure 11.

Referring to Figure 10, one should note that

1. The battery is connected so that it drives the meter movement current Im into the

positive (red) terminal of the movement, in order to cause an upscale deflection of the pointer.

Therefore, the current in the external resistance flows from the negative (black) terminal

toward the positive (red) terminal, as shown, due to the battery polarity connections.

2. R2 is a series connection of two resistors: one of them fixed and the other one (about

20% of Rı) variable. The variable resistor is called the "zero-adjust resistor". When R is zero

(i.e., a short circuit is connected across the ohmmeter terminals), the pointer should deflect all

the way up to the full-scale position [see Eq. (13)]. Because the battery voltage E does decay

(change) with time, readjustment of the value of R2, through the zero-adjust resistor, is

necessary to compensate for this battery voltage change. This is usually an initial checking

procedure to ensure that the ohmmeter would function properly; otherwise, the source should

be replaced by a new battery.



E) VOLTAGE MEASUREMENT

To measure voltage, the instrument should be set to a suitable A.C. or D.C. range, and

then connected parallel across the source of voltage to be measured. The range should be set

from upper-right part. If the expected magnitude of the voltage is within the range of themeter, but its actual value is unknown, the instrument should be set to its highest range,

connected up and if below 1000 V the appropriate selector knob should be rotated decreasing

the ranges step by step, until the most suitable range has been selected.

On D.C. ranges, the meter consumes only 50µ

A at full scale deflection, this sensitivity

corresponding to 20,000 ohms/volt. In the case of A.C. ranges from 10 V upwards, full-scale

deflection is obtained with a consumption of 1 mA (1000 ohms/volt). The 2.5 V A.C. range

consumes 10 mA at full scale deflection.

F) RESISTANCE MEASUREMENT

On resistance ranges, the meter must not merely start from its instrument zero, but must

have, in addition a resistance zero corresponding to the full scale deflection of the meter.

Before carrying out tests for resistance a check and, if necessary, adjustment should be carried

out to ensure that when the leads are joined, together the meter actually indicates zero ohms,

irrespective of the condition of the battery (within the limits of adjustment). The method of

adjustment is given below.

1. Set left-hand knob at “Ω

-OHMS”.

2. Join probes together.

3. Set right-hand knob to “x 1 k Ω

” or “x 100Ω

” from the middle-right part (green part).

4. The drum should be steady at zero on the green scale. If it is not, arrange knob on the

upper-left part until the drum is steady at zero.

If it is not possible to obtain zero ohms setting, or furthermore the pointer position does

not remain constant, falls steadily, the internal battery (or batteries) should replaced. To test a

resistance, the right-hand knob should be at the range required, the leads being connected

across unknown component. However, the value, where the drum is steady, should be

multiplied by the selected ohm range. For example, if “x 1 k Ω ” is selected and the drum is on

10 on the green scale, the value of the resistance is 10 k Ω

.

It should be noted that a positive potential appears at the negative terminal of the



instrument when set for resistance tests. A resistance of component should be measured when

it is not connected to any circuit that resistance test should never be carried out on

components which are already carrying current on or when it is connected to a circuit.

2) DIGITAL MULTIMETER

While most analog meters require no power supply, give a better visual indication of

trends and changes, suffer less from electric noise and isolation problems, and, are simple and

inexpensive, digital meters offer higher accuracy and input impedance, unambiguous readings

at greater viewing distances, smaller size, and a digital electrical output (for interfacing with

external equipment) in addition to visual readout.

The main part of most of the digital multimeter (DMMs) is the analog to digital

converter (A/D) which converts an analog input signal to a digital output. While

specifications may vary, virtually such multimeters are developed around the same block

diagram of Figure 13.

Figure 13.

Since the DMM is a voltage sensing meter; current is converted to volts by passing it

through a precision low resistance shunt while ac is converted to dc at the AC converter by

employing rectifiers and filters. Most of the AC converters detect the peak value of the signal

and are calibrated to give the rms value of a sine wave. However, some measures the mean of

the rectified signal such as the digital multimeter Agilent 34401A. Finally, this dc level isapplied to the A/D converter to obtain the digital information.



For resistance measurement, the meter includes a precision low current source that is

applied across the unknown resistor. Then the dc voltage drop across the resistor, which is

proportional to the value of the unknown resistor, is measured.

For AC measurements, the digital multimeter is a true rms instrument that it measurestrue rms value of any periodic signal.

Figure 14. The digital multimeter used in this laboratory.

A) VOLTAGE MEASUREMENT

To measure voltage, the instrument should be set to a A.C. or D.C. range (the buttons of

“DC V” and “AC V”). The red probe should be connected to upper-right socket and black one

to middle-right socket as indicated in Figure 14. The digital multimeter is an auto-range

device that it is not needed to arrange the range of voltage.

B) CURRENT MEASUREMENT

To measure current, the instrument should be set to a suitable A.C. or D.C. range. Forthis purpose, firstly, blue “Shift” button is depressed then “DC V” or “AC V” button is

depressed. The red probe should be connected to lower-right socket and black one to

middle-right socket.

C) RESISTANCE MEASUREMENT

To measure resistance, the “Ω

2W” button should be depressed without selecting blue

“Shift” button. The red probe should be connected to upper-right socket and black one to

middle-right socket as in voltage measurement.

notes on multi meters

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