MODULE- 4 DEPT OF ECE, MITK SENSORS AND INSTRUMENTATION

‘Syllabus:
Digital Multimeter: Digital Frequency Meter and Digital Measurement of Time, Function Generator. Bridges:
Measurement of resistance: Wheatstone's Bridge, AC Bridges - Capacitance and Inductance Comparison bridge,
Wien's bridge. (Text2:refer 6.2,6.3 up to 6.3.2, 6.4 up to 6.4.2, 8.8, 11.2, 11.8 -11.10, 11.14)

Digital Multimeter:

Working Principle : Digital Multimeter employ some kind of analog to digital (A/D) and have a visible readout display
at the converter output.
The basic circuit shown in fugure above.
As seen from diagram, multimeters can read ac and dc – voltage, currents and resistances over several ranges.
Resistance measurement: Resistance is measured by passing a known current, from a constant current source, through an
unknown resistance. The voltage drop across the resistor is applied to the A/D converter, thereby producing an indication of
the value of the unknown resistance.
Current Measurement:
Alternating Current is converted to voltage.Then; alternating current is converted into dc by employing rectifiers and filters
and given to ADC circuit.
Direct current is converted into voltage –then given to ADC circuit
Voltage Measurement:
Alternating Voltage is passed through attenuator (to prevent damage of circuit if any high value), alternating voltage is
converted into direct voltage by employing rectifiers and filters and given to ADC circuit.
DC voltage is passed through attenuator then given to ADC circuit.

Current to voltage conversion: The current to be measured is applied to the summing junction (Σi) at the input of the
opamp. Since the current at the input of the amplifier is close to zero because of the very high input impedance of the
amplifier, the current IR is very nearly equal to Ii, the current IR causes a voltage drop which is proportional to the current, to
be developed across the resistors. This voltage drop is the input to the A/D converter, thereby providing a reading that is
proportional to the unknown current.

Digital Frequency Meter:

Principle of Operation of Digital Frequency Meter – The signal whose frequency is to be measured is converted into a
train of pulses, one pulse for each cycle of the signal. The number of pulses occurring in a definite interval of time(STATE 1
of pulse) is then counted by an electronic counter. Since each pulse represents the cycle of the unknown signal, the number
of counts is a direct indication of the frequency of the signal (unknown).

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Basic Circuit of a Digital Frequency Meter:

The block diagram of a basic circuit of a digital frequency meter is shown in Fig. 6.5.

The signal may be amplified before being applied to the Schmitt trigger. The Schmitt trigger converts the input signal into a
square wave .The output pulses from the Schmitt trigger are fed to a START/STOP gate. When this gate is enabled, the
input pulses pass through this gate and are fed directly to the electronic counter, which counts the number of pulses
which is equivalent to unknown frequency.
When this gate is disabled, the counter stops counting the incoming pulses.
Basic Circuit for Frequency Measurement:
The basic circuit for frequency measurement is as shown in Fig. 6.6. The output of the unknown frequency is applied to a
Schmitt trigger, producing positive pulses at the output. These pulses present at point A of the main gate. Positive pulses
from the time base selector are present at point B of the START gate and at point B of the STOP gate.

Initially the Flip-Flop (F/F-1) is at its logic 1 state. The resulting voltage from output Y is applied to point A of the STOP gate
and enables this gate. The logic 0 stage at the output Y̅ of the F/F-1 is applied to the input A of the START gate and disables
the gate.

As the STOP gate is enabled, the positive pulses from the time base pass through the STOP gate to the Set (S) input of the
F/F-2
So,Y̅=0 of F/F-2 which is applied to terminal B of the main AND gate. Countng is also disabled now.
To start the operation, a positive pulse is applied to (read input) reset input of F/F-1, Now, Y̅ = 1, Y = 0, STOP gate is
disabled and the START gate enabled.
When the next pulse from the time base -passes through the START gate and resets reset F/F-2. Now, Y̅ = 1-is applied at B
input of main gate and is enabled.

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Now the pulses from the unknown frequency source pass through the main gate to the counter and the counter starts
counting. This same pulse from the START gate is applied to the set input of F/F-1, changing its state from 0 to 1. This
disables the START gate and enables the STOP gate. However, till the main gate is enabled, pulses from the
unknown frequency continue to pass through the main gate to the counter.

The counter counts the number of pulses occurring between two successive pulses from the time base selector.

Digital Measurement of Time

Principle of Operation of Digital Measurement of Time – The beginning of the time period is the start pulse originating from
input 1, and the end of the time period is the stop pulse coming from input 2.
The oscillator runs continuously, but the oscillator pulses reach the output only during the period when the control F/F is in
the 1 state. The number of output pulses counted is a measure of the time period.

Time Base Selector:

It is clear that in order to know the value of frequency of the input signal, the time interval between the start and stop of
the gate must be accurately known. This is called time base.
The time base consist of a fixed frequency crystal oscillator, called a clock oscillator. The output of this constant
frequency oscillator is fed to a Schmitt trigger, which converts the input sine wave to an output consisting of a train
of pulses at a rate equal to the frequency of the clock oscillator. The train of pulses then passes through a series of
frequency divider decade assemblies connected in cascade. Each decade divider consists of a decade counter and divides
the frequency by ten. Outputs are taken from each decade frequency divider by means of a selector switch; any output may
be selected.

Measurement of resistance: Wheatstone's Bridge

Wheatstone bridge, also known as the resistance bridge, calculates the unknown resistance by balancing two legs of the bridge circuit. One leg includes
the component of unknown resistanceinvented by Samuel Hunter Christie in 1833 and later later popularized by Sir Charles Wheatstone in 1843.

The Wheatstone Bridge Circuit comprises two known resistors, one unknown resistor and one variable resistor connected in the form of a
bridge. This bridge is very reliable as it gives accurate measurements.
Wheatstone Bridge Diagram:

A Wheatstone bridge circuit consists of four arms, of which two arms consist of known resistances while the other two arms
consist of an unknown resistance and a variable resistance. The circuit also consists of a galvanometer and an electromotive
force source. The emf source is attached between points a and b while the galvanometer is connected between
points c and d. The current that flows through the galvanometer depends on its potential difference The galvanometer is a
sensitive microammeter, with a zero centre scale. When there is no current through the meter, the galvanometer pointer
rests at 0, i.e. mid scale.

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When SW 1 is closed, current flows and divides into the two arms at point A, i.e. I 1 and I2. The bridge is balanced when the
potential difference at points C and D is equal, i.e. the potential across the galvanometer is zero.

To obtain the bridge balance equation, we have from the Fig. 11.1.

For the galvanometer current to be zero, the following conditions should be satisfied.

Substituting in Eq. (11.1)

This is the equation for the bridge to be balanced.

When the bridge is balanced, the unknown resistance normally connected at R4.
Hence

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Unbalanced Wheatstone’s Bridge:

To determine the amount of deflection that would result for a particular degree of unbalance, general circuit analysis can be
applied, but we shall use Thevenin’s theorem.

Now. Thevenin’s equivalent is to be find out. This is done by short circuiting voltage source and open circuiting current
source.

Step1:open-circuit current source and find voltage between terminals a and b.

Applying the voltage divider equation, the voltage at point a can be determined as follows

Therefore, the voltage between a and b is the difference between E a and Eb, which represents Thevenin’s equivalent
voltage.

Therefore

Step 2:Short circuit voltage source and find Thevenin’s equivalent resistance

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The equivalent resistance of the circuit is R1//R3 in series with R2//R4 i.e. R1//R3 + R2//R4.

Therefore, Thevenin’s equivalent circuit is given in Fig. 11.4.

If a galvanometer is connected across the terminals a and b -there will be the same deflection at the output of the bridge.

Slightly Unbalanced Wheatstone’s Bridge:

If three of the four resistor in a bridge are equal to R and the fourth differs by 5% or less, we can develop an approximate but
accurate expression for Thevenin’s equivalent voltage and resistance.

Consider the circuit in Fig. 11.7.

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The voltage at point a is

The voltage at point b is

Thevenin’s equivalent voltage between a and b is the difference between these voltages.

Therefore

If Δ r is 5% of R or less, Δ r in the denominator can be neglected without introducing appreciable error. Therefore,
Thevenin’s voltage is

The equivalent resistance can be calculated by replacing the voltage source with its internal impedance (for all practical
purpose short-circuit). The Thevenin’s equivalent resistance is given by

Again, if Δr is small compared to R, Δ r can be neglected. Therefore,

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Application of Wheatstone’s Bridge:

A Wheatstone bridge may be used to measure the dc resistance of various types of wire, either for the purpose of quality
control of the wire itself, or of some assembly in which it is used. For example, the resistance of motor windings,
transformers, solenoids, and relay coils can be measured. Wheatstone Bridge diagram is also used extensively by telephone
companies and others to locate cable faults. Limitations of Wheatstone’s Bridge:

In the case of high resistance measurements in mega ohms, the Wheatstone’s bridge cannot be used.

AC Wheatstone Bridge:

Impedances at AF or RF are commonly determined by means of an ac Wheatstone bridge. The diagram of an ac bridge is given in
Fig. 11.17.

Comparison Bridge:
There are two types of Comparison Bridge, Namely
1. Capacitance Comparison Bridge 2. Inductance Comparison Bridge
Capacitance Comparison Bridge:

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Condition for balance: 𝐳𝟏 𝐳𝐱 = 𝐳𝟐 𝐳𝟑 ,i.e,𝑅1 (𝑅𝑋 − 𝑗

Ɯ𝐶𝑋
𝑗𝑅
𝑋
𝑗𝑅
) = 𝑅2 (𝑅3 − Ɯ𝐶𝑗 3 ) , 𝑖. 𝑒, 𝑅1 𝑅𝑋 − Ɯ𝐶1 = 𝑅2 𝑅3 − Ɯ𝐶2
3

Two complex quantities are equal when both their real and their imaginary terms are equal. Therefore,
𝑅1 𝑅
i.e., 𝑅1 𝑅𝑋 = 𝑅2 𝑅3 , AND = Ɯ𝐶2
Ɯ𝐶𝑋 3

𝑹𝟐 𝑹𝟑 𝑪𝟑 𝑹𝟏
=>𝑹𝑿 = 𝑪𝑿 =
𝑹𝟏 𝑹𝟐

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2. Inductance Comparison Bridge:

From above diagram, 𝒁𝟏 = 𝑹𝟏 , 𝒁𝟐 = 𝑹𝟐 , 𝒁𝟑 = (𝐑𝟑 + 𝐣Ɯ𝐋𝟑 ), 𝒁𝑿 = (𝐑𝐗 + 𝐣Ɯ𝐋𝐗 )

Condition for balance: 𝐳𝟏 𝐳𝐱 = 𝐳𝟐 𝐳𝟑 , i.e,𝐑𝟏 (𝐑𝐗 + 𝐣Ɯ𝐋 ) = 𝐑𝟐(𝐑𝟑 + 𝐣Ɯ𝐋 ), 𝐢. 𝐞, 𝐑𝟏𝐑𝐗 + 𝐣𝐑𝟏Ɯ𝐋𝐗 = 𝐑𝟐𝐑𝟑 + 𝐣𝐑𝟐Ɯ𝐋𝟑
𝐗 𝟑

Two complex quantities are equal when both their real and their imaginary terms are equal. Therefore,

i.e., 𝑅1 𝑅𝑋 = 𝑅2 𝑅3 , AND R 1 L X = R 2 L3

𝑹𝟐 𝑹𝟑 𝐑 𝟐 𝐋𝟑
=>𝑹𝑿 = 𝐋𝐗 =
𝑹𝟏 𝑹𝟏

Wien Bridge Circuit Diagram:

The Wien Bridge Circuit Diagram shown in Fig. below has a series RC combination in one arm and a parallel combination in the
adjoining arm. Wien’s bridge in its basic form, is designed to measure frequency. It can also be used for the measurement of an
unknown capacitor with great accuracy

The impedance of one arm is

The admittance of the parallel arm is

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Using the bridge balance equation,

we have

Therefore,

Equating the real and imaginary terms we have

Therefore

and

as

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The two conditions for bridge balance, (11.21) and (11.23), result in an expression determining the required resistance ratio
R2/R4 and

another expression determining the frequency of the applied voltage.

If we satisfy Eq. (11.21) and also excite the bridge with the frequency of Eq. (11.23), the bridge will be balanced.

In most Wien Bridge Circuit, R1 = R3 = R and C1 = C3 = C.

Equation (11.21) therefore reduces to R2/R4 = 2

Eq. (11.23) to f = ½πRC, which is the equation for the frequency of the bridge circuit.

Applications:

The bridge is used for measuring frequency in the audio range. The audio range is normally divided into 20 – 200 – 2 k – 20 kHz
ranges. In this case, the resistances can be used for range changing and capacitors C1 and C3 for fine frequency control within the
range.

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