Lecture Notes: EEEC6430312 Measurements And Instrumentation - Instrumentation

EEEC6430312 MEASUREMENTS AND INSTRUMENTATION
FACULTY OF ENGINEERING AND COMPUTER TECHNOLOGY
BENG (HONS) IN ELECTRICALAND ELECTRONIC ENGINEERING
Ravandran Muttiah BEng (Hons) MSc MIET
Instrumentation

Thermistors are non-linear temperature dependent resistors with a high
resistance temperature coefficient. They are advanced ceramics where the
repeatable electrical characteristics of the molecular structure allow them
to be used as solid-state, resistive temperature sensors. This molecular
structure is obtained by mixing metal oxides together in varying
proportions to create a material with the proper resistivity.
Two types of Thermistors are available: Negative Temperature Coefficient
(NTC), resistance decreases with increasing temperature and Positive
Temperature Coefficient (PTC), resistance increases with increasing
temperature. In practice only NTC Thermistors are used for temperature
measurement. PTC Thermistors are primarily used for relative
temperature detection.
In this class we will use an NTC thermistor. The temperature versus
resistance data of our thermistor is shown on the table and figure below.
Thermoelectric Transducer
1

2
Resistance Multiplier 10 K
Temperature
(℃)
Rt/R25
Nominal
0 3.363000
5 2.599000
10 2.024000
15 1.589000
20 1.256000
25 1.000000
30 0.801300
35 0.646100
40 0.524100
45 0.427600
50 0.350700
55 0.289400
60 0.240000
65 0.200100
70 0.167700
75 0.141200
80 0.119400
85 0.101400
90 0.086520
95 0.074090
100 0.063700
Figure 1
NTC Thermistor
Temperature (Celcius)
Resistance
(Ω)

For convenience we would like derive a mathematical expression which
describes the behavior of the device. The Steinhart and Hart equation is an
empirical expression that has been determined to be the best mathematical
expression for resistance temperature relationship of NTC thermistors. The
most common form of this equation is:
1
𝑇
= 𝑎 + 𝑏 ln 𝑅 + 𝑐 ln 𝑅 3
(1)
Where T is in Kelvin and R in Ω. The coefficients a, b and c are constants
which in principle are determined by measuring the thermistor resistance at
three different temperatures T1, T2, and T3 and then solving the resulting three
equations for a, b, and c.
1
𝑇1
= 𝑎 + 𝑏 ln 𝑅1 + 𝑐 ln 𝑅1
3
1
𝑇2
= 𝑎 + 𝑏 ln 𝑅2 + 𝑐 ln 𝑅2
3
1
𝑇3
= 𝑎 + 𝑏 ln 𝑅3 + 𝑐 ln 𝑅3
3
3

The parameters a, b and c for the thermistors provided with the lab kit in the
temperature range between 0 − 50 ℃ are:
𝑎 = 1.1869 × 10−3
𝑏 = 2.2790 × 10−4
𝑐 = 8.7000 × 10−8
The Steinhart and Hart equation may be used in two ways.
(i) If resistance is known, the temperature may be determined from equation 1.
(ii) If temperature is known the resistance is determined from equation 2.
𝑅 = exp 𝛽 −
𝛼
2
1
3
− 𝛽 +
𝛼
2
1
3
(2)
where, 𝛼 =
𝑎−
1
𝑇
𝑐
and 𝛽 =
𝑏
3𝑐
+
𝛼2
4
4

The non-linear resistance versus temperature behavior of the thermistor is
the main disadvantage of these devices. However, with the availability of
low cost microcontroller systems the non-linear behavior can be handled in
software by simply evaluating the Steinhart and Hart equation at the desired
point.
The sensitivity of the thermistor,
d𝑅
d𝑇
, varies with temperature. For our
thermistor the sensitivity as a function of temperature is shown on the
following figure.
Note that the thermistor sensitivity decreases with increasing temperature.
This is the primary reason for the small temperature measuring range of
thermistors. Notice however that in temperature range of interest to
biological and most environmental applications the sensitivity is greater
than 100
Ω
℃
which results in the design of sensitive and robust systems.
5

6
Figure 2
Temperature (Celcius)
NTC Thermistor Sensitivity
d𝑅
d𝑇
(
Ω
℃
)

Electronic Transducer
7
Figure 3
Earth
Ground
AC
Return
240 V
AC Plug Heater
Elements
Toaster Adjustment,
Moves Magnet w.r.t.
Heater Element
Magnet
On Spring
Solenoid

8
The Function Of Electronic Transducer
For a certain design when a toaster is engaged a magnetic material is placed in
contact with an electromagnet. The magnetic contact to the solenoid is made
of a material whose magnetism is a function of temperature. Indeed the
temperature at which the material loses its magnetisation (labeled the Curie
temperature Tc) is in the order to 100 ℃. When the temperature is less than Tc
the magnet maintains its magnetism, however when T > Tc, then the
magnetism is lost and the switch opens. Pushing down on the toaster engages
the switch. The control for browning the toast, simply moves the magnetic
switch closer or further away from the heating elements. Notice that the AC
plug has two grounds. The Earth ground is for user protection and typically is
connected to the chassis of the toaster. The AC return completes the circuit and
allows current to flow. The Earth and AC return should never be connected
together. In two prong AC plugs the Earth ground is missing.

9
𝑉
s
𝐼Total
𝐼2
𝐼1
𝑅4
𝑅3
𝑅2
𝑅1
Figure 4: Wheatstone bridge.
Wheatstone Bridge
The Wheatstone bridge was originally developed by Charles Wheatstone to
measure unknown resistance values and as a means of calibrating measuring
instruments, voltmeters, ammeters, etc, by the use of a long resistive slide wire.
𝑉C − 𝑉D
𝑉out
A
B
D
C
+
−

10
Although today digital multimeters provide the simplest way to measure a
resistance. The Wheatstone bridge can still be used to measure very low
values of resistances down in the milli-Ohms range.
The Wheatstone bridge (or resistance bridge) circuit can be used in a number
of applications and today, with modern operational amplifiers we can use
the Wheatstone bridge circuit to interface various transducers and sensors to
these amplifier circuits.
The Wheatstone bridge circuit is nothing more than two simple series-parallel
arrangements of resistances connected between a voltage supply terminal and
ground producing zero voltage difference between the two parallel branches
when balanced. A Wheatstone bridge circuit has two input terminals and two
output terminals consisting of four resistors configured in a diamond-like
arrangement as shown. This is typical of how the Wheatstone bridge is
drawn.

11
When balanced, the Wheatstone bridge can be analysed simply as two series
strings in parallel. In our tutorial about resistors in series, we can see that
each resistor within the series chain produces an 𝐼𝑅 drop, or voltage drop
across itself as a consequence of the current flowing through it as defined by
Ohms Law. Consider the series circuit in figure 5.
Figure 5
12 V
𝐼 A
B
𝑉𝑅1
𝑉𝑅2
𝑅1
𝑅2
10 Ω
20 Ω
C

12
As the two resistors are in series, the same current, 𝐼 flows through both of
them. Therefore the current flowing through these two resistors in series is
given as, 𝑉 𝑅T.
𝐼 =
𝑉
𝑅
=
12 V
10 Ω + 20 Ω
= 0.4 A
The voltage at point C, which is also the voltage drop across the lower
resistor, 𝑅2 is calculated as,
𝑉𝑅2
= 𝐼 × 𝑅2 = 0.4 A × 20 Ω = 8 V
Then we can see that the source voltage 𝑉S is divided among the two series
resistors in direct proportion to their resistances as 𝑉𝑅1
= 4 V and 𝑉𝑅2
=
8 V. This is the principle of voltage division, producing what is commonly
called a potential divider circuit or voltage divider network.

13
Now if we add another series resistor circuit using the same resistor values in
parallel with the first we would have the circuit as in figure 6.
As the second series circuit has the same resistive values of the first, the
voltage at point D, which is also the voltage drop across resistor, 𝑅4 will be the
same at 8 V, with respect to zero (battery negative), as the voltage is common
and the two resistive networks are the same.
Figure 6
12 V
𝐼 A
B
𝑅1
𝑅2
10 Ω
20 Ω
C D
𝑅4
20 Ω
10 Ω
𝑅3
𝐼2
𝐼1

14
But something else equally as important is that the voltage difference between
point C and point D will be zero volts as both points are at the same value of
8 V as, C = D = 8 V, then the voltage difference is 0 V.
When this happens, both sides of the parallel bridge network are said to
be balanced because the voltage at point C is the same value as the voltage at
point D with their difference being zero.
Now let’s consider what would happen if we reversed the position of the two
resistors, 𝑅3 and 𝑅4 in the second parallel branch with respect to 𝑅1 and 𝑅2.
Figure 7
12 V
𝐼 A
B
𝑅1
𝑅2
10 Ω
20 Ω
C = 8 V
𝑅4
10 Ω
20 Ω
𝑅3
𝐼2
𝐼1
D = 4 V

15
With resistors, 𝑅3 and 𝑅4 reversed, the same current flows through the series
combination and the voltage at point D, which is also the voltage drop across
resistor, 𝑅4 will be,
𝑉𝑅4
= 0.4 A × 10 Ω = 4 V
Now with 𝑉R4 having 4 volts dropped across it, the voltage difference between
points C and D will be 4 volts as: C = 8 V volts and D = 4 V. Then the
difference this time is, 8 − 4 = 4 V.
The result of swapping the two resistors is that both sides or “arms” of the
parallel network are different as they produce different voltage drops. When this
happens the parallel network is said to be unbalanced as the voltage at point C is
at a different value to the voltage at point D.
Then we can see that the resistance ratio of these two parallel
arms, ACB and ADB, results in a voltage difference between 0 V (balanced) and
the maximum supply voltage (unbalanced), and this is the basic principal of
the Wheatstone Bridge Circuit.

16
So we can see that a Wheatstone bridge circuit can be used to compare an
unknown resistance 𝑅X with others of a known value, for
example, 𝑅1 and 𝑅2, have fixed values, and 𝑅3 could be variable. If we
connected a voltmeter, ammeter or classically a galvanometer between
points C and D, and then varied resistor, 𝑅3 until the meters read zero, would
result in the two arms being balanced and the value of 𝑅X, (substituting 𝑅4)
known as shown in figure 8.
Figure 8: Wheatstone bridge circuit.
12 V
𝐼2
𝐼1
𝑅X
𝑅3
𝑅2
𝑅1
𝑉out = 𝑉C − 𝑉D
A
B
D
C
+
−
V

17
By replacing 𝑅4 above with a resistance of known or unknown value in the
sensing arm of the Wheatstone bridge corresponding to 𝑅X and adjusting the
opposing resistor, 𝑅3 to “balance” the bridge network, will result in a zero
voltage output. Then we can see that balance occurs when:
𝑅1
𝑅2
=
𝑅3
𝑅X
= 1 (Balanced)
The Wheatstone bridge equation required to give the value of the unknown
resistance, 𝑅X at balance is given as,
𝑉out = 𝑉C − 𝑉D = 𝑉𝑅2
− 𝑉𝑅4
= 0
𝑅C =
𝑅2
𝑅1 + 𝑅2
and 𝑅D =
𝑅4
𝑅3 + 𝑅4
At Balance, 𝑅C = 𝑅D
∴
𝑅2
𝑅1 + 𝑅2
=
𝑅4
𝑅3 + 𝑅4

18
∴ 𝑅2 𝑅3 + 𝑅4 = 𝑅4 𝑅1 + 𝑅2
𝑅2𝑅3 + 𝑅2𝑅4 = 𝑅1𝑅4 + 𝑅2𝑅4
∴ 𝑅4 =
𝑅2𝑅3
𝑅1
= 𝑅X
Where resistors, 𝑅1 and 𝑅2 are known or preset values.

19
Example 1:
The following unbalanced Wheatstone bridge is constructed. Calculate the
output voltage across points C and D and the value of resistor 𝑅4 required
to balance the bridge circuit.
Figure 9
100 V
𝑅1
80 Ω
𝑉out
A
B
D
C
𝑅3
480 Ω
𝑅2
120 Ω
𝑅4
160 Ω

20
For the first series arm, ACB
𝑉C =
𝑅2
𝑅1 + 𝑅2
× 𝑉S
𝑉C =
120 Ω
80 Ω + 120 Ω
× 100 = 60 V
For the second series arm, ADB
𝑉D =
𝑅4
𝑅3 + 𝑅4
× 𝑉S
𝑉D =
160 Ω
480 Ω + 160 Ω
× 100 = 25 V
The voltage across points C-D is given as,
𝑉out = 𝑉C − 𝑉D
∴ 𝑉out= 60 − 25 = 35 V

21
The value of resistor, R4 required to balance the bridge is given as,
𝑅4 =
𝑅2𝑅3
𝑅1
=
120 Ω × 480 Ω
80 Ω
= 720 Ω
We have seen above that the Wheatstone bridge has two input terminals (A-
B) and two output terminals (C-D). When the bridge is balanced, the voltage
across the output terminals is 0 V. When the bridge is unbalanced, however,
the output voltage may be either positive or negative depending upon the
direction of unbalance.

22
Wheatstone Bridge Light Detector
Balanced bridge circuits find many useful electronics applications such as
being used to measure changes in light intensity, pressure or strain. The
types of resistive sensors that can be used within a wheatstone bridge
circuit include: photoresistive sensors (LDR’s), positional sensors
(potentiometers), piezoresistive sensors (strain gauges) and temperature
sensors (thermistor’s), etc.
There are many wheatstone bridge applications for sensing a whole range
of mechanical and electrical quantities, but one very simple wheatstone
bridge application is in the measurement of light by using a photoresistive
device. One of the resistors within the bridge network is replaced by a
Light Dependent Resistor (LDR).

23
An LDR, also known as a Cadmium Sulphide (Cds) photocell, is a passive
resistive sensor which converts changes in visible light levels into a change
in resistance and hence a voltage. Light dependent resistors can be used for
monitoring and measuring the level of light intensity, or whether a light
source is ON or OFF.
A typical CdS cell such as the ORP12 light dependent resistor typically has
a resistance of about 1 MΩ in dark or dim light, about 900 Ω at a light
intensity of 100 Lux (typical of a well lit room), down to about 30 Ω in
bright sunlight. Then as the light intensity increases the resistance reduces.
By connecting a light dependant resistor to the Wheatstone bridge circuit
above, we can monitor and measure any changes in the light levels as
shown in figure 10.

24
Figure 10: Wheatstone bridge light detector.
R
A
Op- Amp
741
Relay
LDR
ORP 12
𝑅4
10 KΩ
𝑅5
1 KΩ
𝑅3
10 KΩ
𝑉𝑅1
LDR at
Nominal Light
Levels
Out
2N2222
+12 V
D
C
𝑉D
B
A
𝐷1
TR1
−
+

25
The LDR photocell is connected into the Wheatstone bridge circuit as
shown to produce a light sensitive switch that activates when the light level
being sensed goes above or below the pre-set value determined by 𝑉R1. In
this example 𝑉R1 either a 22 KΩ or 47 KΩ potentiometer.
The op-amp is connected as a voltage comparator with the reference
voltage 𝑉D applied to the inverting pin. In this example, as
both 𝑅3 and 𝑅4 are of the same 10 KΩ value, the reference voltage set at
point D will therefore be equal to half of 𝑉
cc. That is
𝑉cc
2
.
The potentiometer, 𝑉R1 sets the trip point voltage 𝑉C, applied to the non-
inverting input and is set to the required nominal light level. The relay turns
“ON” when the voltage at point C is less than the voltage at point D.

26
Adjusting 𝑉R1 sets the voltage at point C to balance the bridge circuit at the
required light level or intensity. The LDR can be any cadmium sulphide
device that has a high impedance at low light levels and a low impedance at
high light levels.
Note that the circuit can be used to act as a “light-activated” switching
circuit or a “dark-activated” switching circuit simply by transposing
the LDR and 𝑅3 positions within the design.
The Wheatstone bridge has many uses in electronic circuits other than
comparing an unknown resistance with a known resistance. When used with
operational amplifier, the Wheatstone bridge circuit can be used to measure
and amplify small changes in resistance, 𝑅X due, for example, to changes in
light intensity as we have seen above.

27
But the bridge circuit is also suitable for measuring the resistance change of
other changing quantities, so by replacing the above photo-resistive LDR
light sensor for a thermistor, pressure sensor, strain gauge, and other such
transducers, as well as swapping the positions of the LDR and 𝑉R1, we can
use them in a variety of other Wheatstone bridge applications.
Also more than one resistive sensor can be used within the four arms (or
branches) of the bridge formed by the resistors 𝑅1 to 𝑅4 to produce “full-
bridge”, “half-bridge” or “quarter-bridge circuit arrangements providing
thermal compensation or automatic balancing of the Wheatstone bridge.

28
Wien Bridge Oscillator
One of the simplest sine wave oscillators which uses a RC network in place of
the conventional LC tuned tank circuit to produce a sinusoidal output
waveform, is called a Wien bridge oscillator.
The Wien bridge oscillator is so called because the circuit is based on a
frequency-selective form of the Wheatstone bridge circuit. The Wien bridge
oscillator is a two-stage RC coupled amplifier circuit that has good stability at
its resonant frequency, low distortion and is very easy to tune making it a
popular circuit as an audio frequency oscillator but the phase shift of the output
signal is considerably different from the phase shift RC oscillator.
The Wien bridge oscillator uses a feedback circuit consisting of a
series RC circuit connected with a parallel RC of the same component values
producing a phase delay or phase advance circuit depending upon the
frequency. At the resonant frequency 𝑓r the phase shift is 0°. Consider the
circuit shown in figure 11.

29
Figure 11: Wien bridge.
Wien bridge oscillator frequency,
𝑓r =
1
2π𝑅𝐶
Where:
𝑓r is the resonant frequency in Hz
R is the resistance in Ω
C is the capacitance in Farads
𝑅1 𝐶1
𝑅2 𝐶2
𝑅1 = 𝑅2 𝐶1 = 𝐶2
High Pass Filter Stage
Low Pass
Filter Stage
𝑉in 𝑉out

30
We know that the magnitude of the output voltage, 𝑉out from the RC
network is at its maximum value and equal to one third
1
3
of the input
voltage, 𝑉in to allow for oscillations to occur. But why one third and not
some other value. In order to understand why the output from the RC
circuit above needs to be one-third, that is 0.333 × 𝑉in , we have to
consider the complex impedance 𝑍 = 𝑅 ± j𝑋 of the two connected RC
circuits.
We know that the real part of the complex impedance is the
resistance, 𝑅 while the imaginary part is the reactance, 𝑋. As we are
dealing with capacitors here, the reactance part will be capacitive
reactance, 𝑋c.

31
The RC Network
If we redraw the above RC network as shown, we can clearly see that
it consists of two RC circuits connected together with the output
taken from their junction. Resistor 𝑅1 and capacitor 𝐶1 form the top
series network, while resistor 𝑅2 and capacitor 𝐶2 form the bottom
parallel network.
Therefore the total impedance of the series combination 𝑅1𝐶1 we
can call, 𝑍S and the total impedance of the parallel combination
𝑅2𝐶2 we can call, 𝑍P. As 𝑍S and 𝑍P are effectively connected
together in series across the input, 𝑉IN, they form a voltage divider
network with the output taken from across 𝑍P as shown in figure 12.

32
Lets assume then that the component values of 𝑅1 and 𝑅2 are the same at
12 KΩ, capacitors 𝐶1 and 𝐶2 are the same at 3.9 nF and the supply
frequency, 𝑓 is 3.4 KHz.
Figure 12
𝑅2 𝐶2
𝐶1
𝑅1
𝑉IN
𝑉OUT
𝑍S
𝑍P

33
Series Circuit
The total impedance of the series combination with resistor, 𝑅1 and
capacitor, 𝐶1 is simply,
𝑅 = 12 KΩ, but 𝑋C =
1
2π𝑓𝐶
∴ 𝑋C =
1
2π × 3.4 KHz × 3.9 nF
= 12 KΩ
𝑍S = 𝑅2 + 𝑋C
2
= 120002 + 120002
= 17 KΩ
We now know that with a supply frequency of 3.4 KHz the reactance of the
capacitor is the same as the resistance of the resistor at 12 KΩ. This then
gives us an upper series impedance 𝑍S of 17 KΩ.
For the lower parallel impedance 𝑍P, as the two components are in parallel,
we have to treat this differently because the impedance of the parallel circuit
is influenced by this parallel combination.

34
Parallel Circuit
The total impedance of the lower parallel combination with
resistor, 𝑅1 and capacitor, 𝐶2 is given as,
𝑅 = 12 KΩ, and 𝑋C = 12 KΩ
1
𝑍
=
1
𝑅
+
1
𝑋C
=
1
12000
+
1
12000
∴ 𝑍 = 6 KΩ
At the supply frequency of 3.4 KHz, the combined resistance and
reactance of the RC parallel circuit becomes 6 KΩ and their parallel
impedance is therefore calculated as,
𝑅 = 6 KΩ and 𝑋C = 6 KΩ (Parallel)
𝑍P = 𝑅2 + 𝑋C
2
= 60002 + 60002
∴ 𝑍P = 8.5 KΩ

35
So we now have the value and for the series impedance, 𝑍S = 17 KΩ
and for the parallel impedance, 𝑍p = 8.5 KΩ. Therefore the output
impedance, 𝑍OUT of the voltage divider network at the given frequency
is,
𝑍OUT =
𝑍P
𝑍P + 𝑍S
=
8.5 KΩ
8.5 KΩ + 17 KΩ
= 0.333
Then at the oscillation frequency, the magnitude of the output
voltage, 𝑉OUT will be equal to 𝑍OUT × 𝑉IN which as shown is equal to
one third
1
3
of the input voltage, 𝑉IN and it is this frequency
selective RC network which forms the basis of the Wien bridge
oscillator circuit. If we now place this RC network across a non-
inverting amplifier which has a gain of 1 +
𝑅1
𝑅2
, then the basic Wien
bridge oscillator circuit is produced as shown in figure 13.

36
Figure 13: Wien bridge oscillator.
The output of the operational amplifier is fed back to both the inputs of
the amplifier. One part of the feedback signal is connected to the
inverting input terminal (negative feedback) via the resistor divider
network of 𝑅1 and 𝑅2 which allows the amplifiers voltage gain to be
adjusted within narrow limits. The other part is fed back to the non-
inverting input terminal (positive feedback) via the RC Wien bridge
network.
+
−
A
𝑅
𝑅 𝐶
𝑅1
𝑅2
1
3
V
𝑉out
Feedback
𝐶

37
The RC network is connected in the positive feedback path of the amplifier
and has zero phase shift a just one frequency. Then at the selected resonant
frequency, 𝑓r the voltages applied to the inverting and non-inverting inputs
will be equal and “in-phase” so the positive feedback will cancel out the
negative feedback signal causing the circuit to oscillate.
The voltage gain of the amplifier circuit MUST be equal too or greater than
three “Gain = 3” for oscillations to start because as we have seen above, the
input is
1
3
of the output. This value, Av ≥ 3 is set by the feedback
resistor network, 𝑅1 and 𝑅2 and for a non-inverting amplifier this is given
as the ratio 1 +
𝑅1
𝑅2
.
Also, due to the open-loop gain limitations of operational amplifiers,
frequencies above 1 MHz are unachievable without the use of special high
frequency op-amps.

38
Example 2:
Determine the maximum and minimum frequency of oscillations of a Wien
bridge oscillator circuit having a resistor of 10 KΩ and a variable capacitor
of 1 nF to 1000 nF.
The frequency of oscillations for a Wien bridge oscillator is given as,
𝑓r =
1
2π𝑅𝐶
Wien bridge oscillator lowest frequency,
𝑓min =
1
2π × 10 × 103 × 1000 × 10−9
= 15.9 Hz
Wien bridge oscillator highest frequency,
𝑓max =
1
2π × 10 × 103 × 1 × 10−9
= 15.9 KHz

39
Example 3:
A Wien bridge oscillator circuit is required to generate a sinusoidal
waveform of 5.2 KHz. Calculate the values of the frequency determining
resistors 𝑅1 and 𝑅2 and the two capacitors 𝐶1 and 𝐶2 to produce the
required frequency.
Also, if the oscillator circuit is based around a non-inverting operational
amplifier configuration, determine the minimum values for the gain
resistors to produce the required oscillations. Finally draw the resulting
oscillator circuit.
𝑓r =
1
2π𝑅𝐶
= 5.2 KHz

40
The frequency of oscillations for the Wien bridge oscillator was given as
5.2 KHz. If resistors 𝑅1 = 𝑅2 and capacitors 𝐶1 = 𝐶2 and we assume a
value for the feedback capacitors of 3.0 nF, then the corresponding value
of the feedback resistors is calculated as,
𝑓r =
1
2π𝑅𝐶
𝑅 =
1
2π𝑓rC
=
1
2π × 5.2 × 103 × 3 × 10−9
= 10.2 KΩ
For sinusoidal oscillations to begin, the voltage gain of the Wien bridge
circuit must be equal too or greater than 3, Av ≥ 3 . For a non-inverting
op-amp configuration, this value is set by the feedback resistor network
of 𝑅3 and 𝑅4 and is given as,
𝐴V =
𝑉OUT
𝑉IN
= 1 +
𝑅3
𝑅4
= 3 or more

41
If we choose a value for resistor 𝑅3 of say, 100 KΩ’s, then the value of
resistor 𝑅4 is calculated as,
1 +
𝑅3
𝑅4
= 3
∴ 𝑅4 =
𝑅3
3 − 1
=
𝑅3
2
=
1
2
𝑅3
if 𝑅3 = 100 KΩ
then, 𝑅4 = 50 KΩ
While a gain of 3 is the minimum value required to ensure oscillations, in
reality a value a little higher than that is generally required. If we assume a
gain value of 3.1 then resistor 𝑅4 is recalculated to give a value of 47 KΩ’s.
This gives the final Wien bridge oscillator circuit as shown in figure 14.

42
Figure 14: Wien bridge oscillator circuit of example 3.
+
−
A
𝑅1
10.2 KΩ
𝐶1
3 nF
𝑅3
𝑅4
47 KΩ
𝑉out
5.2 KHz
100 KΩ
𝑅2
10.2 KΩ
𝐶2
3 nF

43
Wien Bridge Oscillator Summary
Then for oscillations to occur in a Wien bridge oscillator circuit the following
conditions must apply.
• With no input signal a Wien bridge oscillator produces continuous output
oscillations.
• The Wien bridge oscillator can produce a large range of frequencies.
• The Voltage gain of the amplifier must be greater than 3.
• The RC network can be used with a non-inverting amplifier.
• The input resistance of the amplifier must be high compared to R so that
the RC network is not overloaded and alter the required conditions.
• The output resistance of the amplifier must be low so that the effect of external
loading is minimised.
• Some method of stabilizing the amplitude of the oscillations must be provided.
If the voltage gain of the amplifier is too small the desired oscillation will
decay and stop. If it is too large the output will saturate to the value of the
supply rails and distort.
• With amplitude stabilisation in the form of feedback diodes, oscillations from
the Wien Bridge oscillator can continue indefinitely.

44
Instrumentation Amplifier
Example 4:
For the differential amplifier circuit shown in figure 15. Derive the
equation for:
(a) The Voltage Gain.
(b) The Common Mode Rejection Ratio (CMRR).
Solution:
The derivation of the equations are as follows:
(a) The Voltage Gain is given by, 𝐴V =
𝑉out
𝑉in+−𝑉in−
(b) Common Mode Rejection Ratio (CMRR) =
Differentail Gain
Common Gain

45
𝑅1 𝑅2
𝑅1 𝑅2
𝑉in-
𝑉in +
−𝑉
cc
+𝑉
cc
𝑉out
Figure 15: Differential amplifier.

46
Example 5:
The differential amplifier has a Common Mode Rejection Ratio
(CMRR) of about 30,000. If we build a circuit with a differential gain
of 1,000, find the common gain of the circuit.
Solution:
Common Gain =
Differentail Gain
CMRR
=
1000
30000
=
1
30
= 0.03
Example 6:
The design of an Instrumentation amplifier circuit using a buffers and
differential amplifier is shown in figure 16.

47
𝑅3 𝑅4
𝑅3
−𝑉
cc
+𝑉
cc
𝑉out
𝑅2
𝑅4
𝑉in-
𝑉in +
−𝑉
cc
+𝑉
cc
𝑅2
−𝑉
cc
+𝑉
cc
−𝑉
cc
10 K
10 K
47 K
10 K
47 K
Figure 16: Differential amplifier.
Differential Amplifier
Buffers
𝑅1
(No current flow)
Offset
CMRR = 10 log 1 +
2𝑅2
𝑅1
and Gain =
𝑅4
𝑅3
1 +
𝑅2
𝑅1

48
Vector Voltmeter
The vector voltmeter is basically a new type of amplitude and phase measuring
device. It uses two samples to sample the two waves whose amplitudes and
relative phase are to be measured. It measures the voltages at two different points
in the circuit and also measures the phase difference between these voltages at
these two points.
In this voltmeter, two RF signals of same fundamental frequency (1 MHz to
1 GHz) are converted to two IF signals. The amplitudes, waveforms and the phase
relations of IF signals are same as that of RF signals. Thus, the fundamental
components of the RF signals. These fundamental components are filtered from
the IF signals and are measured by a voltmeter and a phase meter.
The block diagram of the vector voltmeter is shown in figure 17.
The instrument consists of four sections:
(i) Two RF to IF converters
(ii) Automatic phase control circuit
(iii) Phase meter circuit
(iv) Voltmeter circuit

49
Sampling
Gate
Sampling
Gate
Sampling
Pulse
Generator
20 KHz
Reference
Oscillator
Automatic
Phase
Control
Voltage
Tuned
Oscillator
20 KHz
Tuned
Amplifier
Amplifier
and
Limiter
+60° Phase
Shifter
Trigger
Amplifier
20 KHz
Tuned
Amplifier
Amplifier
and
Limiter
-120°
Phase
Shifter
Trigger
Amplifier
Constant
Current
Sourse
Current
Switch
Bistable
Multivibrator
Meter
Attenuator
and Amplifier
Phase Meter
Voltmeter
Phase Meter Circuit
Channel “A” RF to IF Converter
Channel “B” RF to IF Converter
Voltmeter Circuit
Automatic
Phase
Control
Circuit
“B”
Probe
RF
Input
1 MHz
-
1 GHz
“A”
Probe
RF
Input
1 MHz
-
1 GHz
CH A
CH B
Figure 17
∅
20 KHz
20 KHz
𝑉C
𝑉C
20 KHz
∅
20 KHz
∅
𝑉A 𝑉A
𝑉B 𝑉B
20 KHz 20 KHz

50
The channel A and B ate the two RF to IF converters. The RF signals are applied
to sampling gates. The sampling pulse generator controls the opening and closing
of the gates. The RF to IF converters and phase control circuit section produce two
20 KHz sine waves with the same amplitudes and the same phase relationship as
that of the same amplitude and the same phase relationship as that of the
fundamental components of the RF signals applied to the channels A and B. The
turned amplifier extracts the 20 KHz fundamental component from these sine
waves.
The pulse control unit generates the sampling pulses for both the RF to IF
converters. The sampling pulse rate is controlled by voltage tuned oscillator for
which the tuning voltage is supplied by the automatic phase control unit. This
section locks the IF signal of channel A to a 20 KHz reference oscillator. Due to
this, the section is also called phase locked section.
The tuned amplifier passes only 20 KHz fundamental component of the IF signal
of each channel. Thus the output of each tuned amplifier maintains the original
phase relationship with respect to the signal in the other channel and also its
correct amplitude relationship.

51
These two filtered signals are then connected to the voltmeter circuit by a front
panel switch marked channel A and channel B. The appropriate meter range is
decided by the input attenuator. This attenuator is also a front panel control
marked amplitude range. It is basically a d.c. voltmeter and it consists of input
attenuator, feedback amplifier having fixed gain, the rectifier and filtering
arrangement and a d.c. voltmeter corresponding to the channel A and channel B.
To determine the phase difference, there exists a phase meter circuit. The signals
from channel A and B are applied to the amplifier and the limiter circuit. Due to
this the signals are amplified and limited i.e. clipped. This produces a square wave
signal at the output of each amplifier and limiter circuit. These square waves are
then applied to the phase shifting network.
The circuit in upper part i.e. channel A shifts the phase of the square waves by
+ 60° while the circuit in lower part i.e. channel B shifts the phase by −120°. The
phase shifts are achieved by using capacitive networks and inverting, non-
inverting amplifiers. The shifted square wave signals are then applied to trigger
amplifiers.

52
These trigger amplifiers convert the square wave signals to the positive spikes
with very fast rise times. These spikes are used to trigger the bistable
multivibrator.
The signal from channel A is connected to set input of the multivibrator while the
signal from channel B is connected to the reset input of the multivibrator. Now of
the phase shift between the two signals is zero then the trigger pulses are +60° −
−120° i.e. 180° out of phase due to phase shift circuitry. Hence in such a case
the bistable multivibrator produces a square waves which is symmetrical about
zero
Thus if there exists a phase shift between the two signals, the bistable
multivibrator produces asymmetrical square wave. Such asymmetrical signal is
used to control the current switch which is transistorised switch is during the
negative portion of the square waves. This switch connects the constant current
supply to the phase meter. When phase shift is 0°, then the current from constant
source is so adjusted that the meter reading is 0°. Depending upon the asymmetric
nature of the square waves, current by current source varies and causes the
appropriate reading of the phase difference, on the meter.

53
The main limitation of the meter is when the shift at the input side is 180° then the
square wave produced by the bistabel multivibrator causes either zero current or
maximum current as in such a case square waves no longer remains square but
collapse into either positive or negative d.c. voltage. These maximum deviations
from the center reading of 0° are marked on the meters as +180° and −180°. The
phase range can be selected by a front panel switch that places a shunt across the
phase meter and changes its sensitivity.
Features Of Vector Voltmeter
(i) The vector voltmeters cover a 1000 to 1 frequency range accomodating
inputs from few microvolts upto about 1 V without input attenuation. Thus it
gives broad frequency range.
(ii) They allow voltage ratios to be measured over 70 to 80 dB range within a
few lengths of a decibel.
(iii) The phase to be measured to an accuracy of about 1°.
(iv) Due to self locking feature, there is automatic tuning of the local oscillator in
each frequency range.
(v) Easy to operate, as simple as normal voltmeters.

54
A TDR is an electronic instrument that uses time domain
reflectometry to characterize and locate faults in metallic cables (for
example, twisted pair wire or coaxial cable). It can also be used to locate
discontinuities in a connector, printed circuit board, or any other
electrical path. The equivalent device for optical fiber is an optical time-
domain reflectometer.
Time Domain Reflectometer (TDR)

55
Signal Transmitted Through And Reflected From A
Discontinuity
Figure 18

56
Generally, the reflections will have the same shape as the incident signal, but
their sign and magnitude depend on the change in impedance level. If there is a
step increase in the impedance, then the reflection will have the same sign as the
incident signal, if there is a step decrease in impedance, the reflection will have
the opposite sign. The magnitude of the reflection depends not only on the
amount of the impedance change, but also upon the loss in the conductor.
The reflections are measured at the output/input to the TDR and displayed or
plotted as a function of time. Alternatively, the display can be read as a function
of cable length because the speed of signal propagation is almost constant for a
given transmission medium.
Because of its sensitivity to impedance variations, a TDR may be used to verify
cable impedance characteristics, splice and connector locations and associated
losses, and estimate cable lengths.
Reflection

57
TDRs use different incident signals. Some TDRs transmit a pulse along the
conductor; the resolution of such instruments is often the width of the pulse.
Narrow pulses can offer good resolution, but they have high frequency
signal components that are attenuated in long cables. The shape of the pulse
is often a half cycle sinusoid. For longer cables, wider pulse widths are
used.
Fast rise time steps are also used. Instead of looking for the reflection of a
complete pulse, the instrument is concerned with the rising edge, which can
be very fast. A 1970s technology TDR used steps with a rise time of 25 ps.
Still other TDRs transmit complex signals and detect reflections with
correlation techniques. See spread-spectrum time-domain reflectometry.
Incident Signal

58
Usage Of TDR
In a TDR-based level measurement device, the device generates an impulse
that propagates down a thin waveguide (referred to as a probe) - typically a
metal rod or a steel cable. When this impulse hits the surface of the medium to
be measured, part of the impulse reflects back up the waveguide. The device
determines the fluid level by measuring the time difference between when the
impulse was sent and when the reflection returned. The sensors can output the
analyzed level as a continuous analog signal or switch output signals. In TDR
technology, the impulse velocity is primarily affected by the permittivity of the
medium through which the pulse propagates, which can vary greatly by the
moisture content and temperature of the medium. In many cases, this effect
can be corrected without undue difficulty. In some cases, such as in boiling
and/or high temperature environments, the correction can be difficult. In
particular, determining the froth (foam) height and the collapsed liquid level in
a frothy/boiling medium can be very difficult.
TDR In Level Measurement

59
The Dam Safety Interest Group of CEA Technologies, Inc. (CEATI), a
consortium of electrical power organizations, has applied spread-spectrum
time domain reflectometry to identify potential faults in concrete dam
anchor cables. The key benefit of time domain reflectometry over other
testing methods is the non-destructive method of these tests.
TDR Used In Anchor Cable In Dam

60
TDR Used In The Earth And Agricultural Sciences
A TDR is used to determine moisture content in soil and porous media. Over
the last two decades, substantial advances have been made measuring
moisture in soil, grain, food stuff, and sediment. The key to TDR’s success is
its ability to accurately determine the permittivity (dielectric constant) of a
material from wave propagation, due to the strong relationship between the
permittivity of a material and its water content, as demonstrated in the
pioneering works of Hoekstra and Delaney (1974) and Topp et al. (1980).
Recent reviews and reference work on the subject include, Topp and
Reynolds (1998), Noborio (2001), Pettinellia et al. (2002), Topp and Ferr
(2002), and Robinson et al. (2003). The TDR method is a transmission line
technique, and determines apparent permittivity (Ka) from the travel time of
an electromagnetic wave that propagates along a transmission line, usually
two or more parallel metal rods embedded in soil or sediment. The probes
are typically between 10 and 30 cm long and connected to the TDR via
coaxial cable.

61
Time domain reflectometry has also been utilized to monitor slope movement
in a variety of geotechnical settings including highway cuts, rail beds, and open
pit mines (Dowding and O'Connor, 1984, 2000a, 2000b; Kane and Beck, 1999).
In stability monitoring applications using TDR, a coaxial cable is installed in a
vertical borehole passing through the region of concern. The electrical
impedance at any point along a coaxial cable changes with deformation of the
insulator between the conductors. A brittle grout surrounds the cable to translate
earth movement into an abrupt cable deformation that shows up as a detectable
peak in the reflectance trace. Until recently, the technique was relatively
insensitive to small slope movements and could not be automated because it
relied on human detection of changes in the reflectance trace over time.
Farrington and Sargand (2004) developed a simple signal processing technique
using numerical derivatives to extract reliable indications of slope movement
from the TDR data much earlier than by conventional interpretation.
TDR In Geotechnical Usage

62
Time domain reflectometry is used in semiconductor failure analysis as a
non-destructive method for the location of defects in semiconductor device
packages. The TDR provides an electrical signature of individual
conductive traces in the device package, and is useful for determining the
location of opens and shorts.
TDR In Semiconductor Device Analysis

63
TDR In Aviation Wiring Maintenance
TDR, specifically spread-spectrum TDR is used on aviation wiring for both
preventative maintenance and fault location. Spread spectrum TDR has the
advantage of precisely locating the fault location within thousands of miles of
aviation wiring. Additionally, this technology is worth considering for real
time aviation monitoring, as spread spectrum TDR can be employed on live
wires. This method has been shown to be useful to locating intermittent
electrical faults.

64
An OTDR is an optoelectronic instrument used to characterise an optical fiber.
An OTDR is the optical equivalent of an electronic TDR. It injects a series of
optical pulses into the fiber under test and extracts, from the same end of the
fiber, light that is scattered (Rayleigh backscatter) or reflected back from
points along the fiber. The scattered or reflected light that is gathered back is
used to characterize the optical fiber. This is equivalent to the way that an
electronic time-domain meter measures reflections caused by changes in
the impedance of the cable under test. The strength of the return pulses is
measured and integrated as a function of time, and plotted as a function of
fiber length.
Optical Time Domain Reflectometer (OTDR)

65
Optoelectronics
Optoelectronics is the study and application of electronic devices and
systems that source, detect and control light, usually considered a sub-
field of photonics. In this context, light often includes invisible forms of
radiation such as gamma rays, X-rays, ultraviolet and infrared, in addition
to visible light. Optoelectronic devices are electrical-to-optical or optical-
to-electrical transducers, or instruments that use such devices in their
operation. Electro-optics is often erroneously used as a synonym, but is a
wider branch of physics that concerns all interactions between light
and electric fields, whether or not they form part of an electronic device.
Optoelectronics is based on the quantum mechanical effects of light on
electronic materials, especially semiconductors, sometimes in the
presence of electric fields.

66
Light is electromagnetic radiation within a certain portion of
the electromagnetic spectrum. The word usually refers to visible light,
which is visible to the human eye and is responsible for the sense of sight.
Visible light is usually defined as having wavelengths in the range of 400 −
700 nm , between the infrared (with longer wavelengths) and
the ultraviolet (with shorter wavelengths). This wavelength means
a frequency range of roughly 430 − 750 THz. The main source of light on
Earth is the Sun. Sunlight provides the energy that green plants use to create
sugars mostly in the form of starches, which release energy into the living
things that digest them. This process of photosynthesis provides virtually all
the energy used by living things. Historically, another important source of
light for humans has been fire, from ancient campfires to modern kerosene
lamps. With the development of electric lights and power systems, electric
lighting has effectively replaced firelight.
Light

68
Reliability And Quality Of OTDR Equipment
The reliability and quality of an OTDR is based on its accuracy,
measurement range, ability to resolve and measure closely spaced events,
measurement speed, and ability to perform satisfactorily under various
environmental extremes and after various types of physical abuse. The
instrument is also judged on the basis of its cost, features provided, size,
weight, and ease of use.
Some of the terms often used in specifying the quality of an OTDR are as
follows:
• Accuracy
• Measurement Range
• Instrument Resolution

69
Defined as the correctness of the measurement i.e., the difference between the
measured value and the true value of the event being measured.
Accuracy
Measurement Range
Defined as the maximum attenuation that can be placed between the instrument
and the event being measured, for which the instrument will still be able to
measure the event within acceptable accuracy limits.

70
Instrument resolution is a measure of how close two events can be spaced
and still be recognized as two separate events. The duration of the
measurement pulse and the data sampling interval create a resolution
limitation for OTDRs. The shorter the pulse duration and the shorter the
data sampling interval, the better the instrument resolution, but the shorter
the measurement range. Resolution is also often limited when powerful
reflections return to the OTDR and temporarily overload the detector. When
this occurs, some time is required before the instrument can resolve a
second fiber event. Some OTDR manufacturers use a “masking” procedure
to improve resolution. The procedure shields or “masks” the detector from
high-power fiber reflections, preventing detector overload and eliminating
the need for detector recovery.
Instrument Resolution

71
This application note provides a summary description of the operation and
capabilities of a Vector Network Analyser (VNA), including general
considerations of front panel operation and measurement methods. Included in
this note are discussions on the following topics:
• System description;
• General discussion about network analysers;
• Basic measurements and how to make them;
• Error correction;
• General discussion on test sets.
For detailed information regarding calibration techniques, accuracy
considerations, or specific measurement applications, pleaser refer to additional
manufacturer application notes and technical papers.
Vector Network Analyser
Introduction

72
Anritsu VNAs measure the magnitude and phase characteristics of networks,
amplifiers, components, cables, and antennas. They compare the incident signal
that leaves the analyzer with either the signal that is transmitted through the test
device or the signal that is reflected from its input. Figure 20 and figure 21
illustrate the types of measurements that the VNA performs.
VNAs are self contained, fully integrated measurement systems that include an
optional time domain capability. The system hardware consists of the following:
• Analyser;
• Precision components required for calibration and performance
verification;
• Optional use of synthesizers used as a second source;
• Optional use of power meters for test port power leveling
and calibration.
General Description

73
Transmission Measurements
Figure 20
Device Under Test
(DUT)
Incident Transmitted
• Gain (dB)
• Insertion Loss (dB)
• Insertion Phase (degrees)
• Transmission Coefficients (S21)
• Separations of Transmission
Components (Real and Imaginary)
• Electrical Length (m)
• Electrical Delay (s)
• Deviation from Linear Phase (degrees)
• Group Delay (s)

74
Reflection Measurements
Figure 21
DUT
Incident
Reflected
Termination
• Return Loss (dB)
• Reflection Coefficients (S11, S22)
• Reflection Coefficients vs Time (Fourier Transform)
• Impedance 𝑅 ± j𝑋
• Standing Wave Ratio (SWR)

75
Source Module
The VNA Internal System Module Perform The Following Functions
This module provides the stimulus to the Device Under Test (DUT). The
frequency ranges of both the source and the test set modules establish the
frequency range of the system. The frequency stability of the source is an
important factor in the accuracy (especially phase accuracy) of the network
analyser. Hence, VNAs always phase lock the source to an internal crystal
reference for a synthesized, step sweep mode of operation. VNAs avoid the
use of unlocked, analog sweep modes because of the sacrifices in
measurement stability, phase performance, and group delay accuracy.

76
Test Set Module
The test set module routes the stimulus signal to the DUT and samples the
reflected and transmitted signals. The type of connector that is used is
important, as is the “Auto Reversing” feature. Auto Reversing means that
the stimulus signal is applied in both the forward and reverse directions.
The direction is reversed automatically. This saves you from having to
reverse the test device physically in order to measure all four Scattering
parameters (S-parameters). It also increases accuracy by reducing
connector repeatability errors. Frequency conversion to the IF range also
occurs in the test set module.

77
Analyser Module
The analyser module receives and interprets the IF signal for phase and
magnitude data. It then displays the results of this analysis on a high
resolution display screen. This display can show all four S-parameters
simultaneously as well as a variety of other forms of displayed information
such as Group Delay, Time and Distance information, and complex
impedance information. In addition to the installed display, you can also
view the measurement results on an external monitor.

78
We will begin this discussion with a subject familiar to most microwave
test equipment users, scalar network analysis. After showing comparisons,
we will proceed to the fundamentals of network analyzer terminology and
techniques. This discussion serves as an introduction to topics that are
presented in greater detail later in this section. This discussion will touch
on new concepts that include the following:
• Reference Delay;
• S-parameters, what they are and how they are displayed;
• Complex Impedance and Smith Charts.
Network Analyser

79
VNAs do everything that scalar analyzers do, plus they add the ability to measure the
phase characteristics of microwave devices over a greater dynamic range and with more
accuracy. If all a vector network analyzer added was the capability for measuring phase
characteristics, its usefulness would be limited. While phase measurements are important
in themselves, the availability of phase information provides the potential for many new
features for complex measurements. These features include Smith Charts, Time Domain,
and Group Delay. Phase information also allows greater accuracy through vector error
correction of the measured signal.
First, let us look at Scalar Network Analyzers (SNAs). SNAs measure microwave signals
by converting them to a DC voltage using a diode detector as shown in figure 22. This DC
voltage is proportional to the magnitude of the incoming signal. The detection process,
however, ignores any information regarding the phase of the microwave signal. Also, a
detector is a broadband detection device, which means that all frequencies (the
fundamental, harmonic, sub harmonic, and spurious signals) are detected and
simultaneously displayed as one signal. This, of course, adds significant error to both the
absolute and relative measurements.
Scalar Analyser Comparison

80
In a VNA, information is extracted of both the magnitude and phase of a
microwave signal. While there are different ways to perform the measurement,
the method the VNA employs is to down convert the signal to a lower
intermediate frequency (i.e. harmonic sampling). This signal can then be
measured directly by a tuned receiver. The tuned receiver approach gives the
system greater dynamic range due to the variable IF filter bandwidth control.
The system is also much less sensitive to interfering signals, including
harmonics.
Figure 22
Microwave
Signal Microwave
Detector
Detector
Output Voltage
Detector Output Voltage is Proportional to Signal Amplitude

81
The VNA is a tuned receiver as shown in figure 23. The microwave signal is
down converted into the passband of the IF. To measure the phase of this
signal as it passes through the DUT, we must have a reference to compare. If
the phase of a signal is 90°, it is 90° different from the reference signal as
shown in figure 24. The vector network analyser would read this as −90°,
since the test signal is delayed by 90° with respect to the reference signal.
The phase reference can be obtained by splitting off a portion of the
microwave signal before the measurement as shown in figure 25.
The phase of the microwave signal after it has passed through the DUT is
then compared with the reference signal. A network analyzer test set
automatically samples the reference signal, so no external hardware is
needed.
VNA Basics

82
VNA Is A Tuned Receiver
Figure 23
Microwave
Signal
Intermediate
Frequency
(IF)
Tunable Local
Oscillator

83
Signals With A 90 Degree Phase Difference
Figure 24: Phase Measurement
Reference Signal
Test Signal
Time

84
Splitting The Microwave Signal
Figure 25
Phase
Detector
DUT
Microwave
Source
Reference
Signal
Splitter
Test
Signal

85
Let us consider the case when the DUT is removed, and a length of
transmission line is substituted as shown in figure 26. Note that the
path length of the test signal is longer than that of the reference signal.
Let us see how this affects our measurement.
Assume that we are making a measurement at 1 GHz, and that the
difference in path length between the two signals is exactly 1
wavelength. This means that test signal is lagging the reference signal
by 360° as shown in figure 27. We cannot really tell the difference
between one sine wave maxima and the next (they are all identical),
so the network analyzer would measure a phase difference of 0°.

86
Split Signal Where A Length Of The Line Replaces DUT
Figure 26
Phase
Detector
Microwave
Source
Reference
Signal
Splitter
Test
Signal
Longer
Path
Length

87
Split Signal Where Path Length Differs By Exactly One Wavelength
Figure 27
Phase
Detector
Microwave
Source
Reference
Signal
Splitter
Test
Signal
Longer By
One Wavelength
Length 360°

88
Now consider that we make this same measurement at 1.1 GHz. Since the
frequency is higher by 10 percent, the wavelength of the signal is shorter by
10 percent. The test signal path length is now 0.1 wavelength longer than that
of the reference signal as shown in figure 28.
This test signal is, 1.1 × 360 = 396°.
This is 36° different from the phase measurement at 1 GHz.
The network analyser will display this phase difference as −36°.
The test signal at 1.1 GHz is delayed by 36° more than the test signal at
1 GHz.
You can see that if the measurement frequency is 1.2 GHz, then we will get a
reading of −72°, −108° for 1.3 GHz, and so forth as shown in figure 29. An
electrical delay occurs between the reference and test signals. For this delay,
we will use the common industry term of reference delay. You also may hear it
called phase delay. In older network analysers, the length of the reference path
had to be constantly adjusted relative to the test path in order to make an
appropriate measurement of phase versus frequency.

89
Figure 28
Split Signal Where Path Length Is Longer Than One Wavelength
Phase
Detector
Microwave
Source
Reference
Signal
Splitter
Test
Signal
Same Path
Length But
Wavelength is
Now Shorter
1.1 Wavelengths = 396°

90
Figure 29
Electrical Delay
Frequency
in GHz
Measured
Phase
1.1 1.2 1.3 1.4
0°
+90°
+180°
-90°
-180°

91
To measure phase on a DUT, we need to remove this phase change
versus frequency due to changes in the electrical length. This will allow
us to view the actual phase characteristics of the device, which may be
much smaller than the phase change due to electrical length difference
of the two paths.
This can be accomplished in two ways. The most obvious way is to
insert a length of line into the reference signal path to make both paths
of equal length as shown in figure 30. With perfect transmission lines
and a perfect splitter, we would then measure a constant phase as we
change the frequency. The problem using this approach is that we must
change the line length with each measurement setup.

92
Figure 30
Split Signals Where Paths Are Of Equal Length
Phase
Detector
Microwave
Source
Reference
Signal
Splitter
Test
Signal
Both Line
Lengths
Now Equal

93
Another approach is to handle the path length difference in software.
Figure 31 displays the phase versus frequency of a device. This device
has different effects on the output phase at different frequencies.
Because of these differences, we do not have a perfectly linear phase
response. We can easily detect this phase deviation by compensating for
the linear phase. The size of the phase difference increases linearly with
frequency, so we can modify the phase display to eliminate this delay.
VNAs offer automatic reference delay compensation with the push of a
button. Figure 32 shows the resultant measurement when we
compensate path length. In a system application, you can usually correct
for length differences, however, the residual phase characteristics are
critical.

94
Figure 31
Phase Difference Increases Linearly With Frequency
Frequency
in GHz
Measured
Phase
1.1 1.2 1.3 1.4
0°
+90°
+180°
-90°
-180°
Subtract Linear
Phase From
Measured Phase

95
Figure 32
Resultant Phase With Path Length
Frequency
in GHz
Resultant
Phase
1.1 1.2 1.3 1.4
0°
+1°
+2°
-1°
-2°

96
Now let us consider measuring the DUT. Consider a two port device, that is a
device with a connector on each end. What measurements would be of interest?
First, we could measure the reflection characteristics at either end with the opposite
end terminated into 50 Ω. If we designate one of the inputs as Port 1 of the device,
then we have a reference port. We can then define the reflection characteristics
from the reference end as forward reflection, and those from the other end as
reverse reflection as shown in figure 33.
Second, we can measure the forward and reverse transmission characteristics.
However, instead of saying “forward,” “reverse,” “reflection,” and “transmission”
all the time, we use a shorthand. That is all that S-parameters are, shorthand! The
“S” stands for scattering. The second number is the device port that the signal is
being injected into, while the first is the device port that the signal is leaving. S11,
therefore, is the signal leaving port 1 relative to the signal injected into port 1.
The four Scattering Parameters (S-Parameters) in figure 34 are:
• S11 Forward Reflection;
• S21 Forward Transmission;
• S22 Reverse Reflection;
• S12 Reverse Transmission.
Network Analyser Measurement

97
Figure 33
Forward And Reverse Measurement
DUT
S22 Reverse
Reflection
S11 Forward
Reflection
Port 1 Port 2

98
Figure 34
S-Parameter
DUT
S22 Reverse
Reflection
S11 Forward
Reflection
Port 1 Port 2
S21 Forward Transmission
S12 Reverse Transmission

99
S-parameters can be displayed in many ways. An S-parameter consists
of a magnitude and a phase. We can display the magnitude in dB, just
like a scalar network analyzer. We often call this term log magnitude.
Another method of magnitude display is to use Units instead of dB.
When displaying magnitude in Units, the value of the reflected or
transmitted signal will be between 0 and 1 relative to the reference.
We can display phase as “linear phase” as shown in figure 35. As
discussed earlier, we cannot tell the difference between one cycle and
the next. Therefore, after going through 360°, we are back to where we
began. We can display the measurement from −180 to +180°, which is
a more common approach. This method keeps the display discontinuity
removed from the important 0 degree area that is used as the phase
reference.

100
Figure 35
Linear Phase With Frequency Waveform
Frequency
Phase
+180°
-180°
0°

101
Several methods are available to display all of the information on one
trace. One method is a polar display as shown in figure 36. The radial
parameter (distance from the center) is magnitude. The rotation
around the circle is phase. We sometimes use polar displays to view
transmission measurements, especially on cascaded devices (i.e.
devices in series). The transmission result is the addition of the phase
and the log magnitude (dB) information in the polar display of each
device.

102
Figure 36
Polar Display
180°
90°
-90°
0°

103
One common method for measuring the reflection and transmission characteristics of
any Device Under Test (DUT), in this case open, short, and matched loads, involves
the using a network analyser. A network analyser allows convenient measurements of
signal reflection and transmission in a variety of formats. It can measure signal
delay, phase, and gain of the DUT. All of these measurements are made with respect
to the source and terminal impedance of the network analyser. The default
impedance of the Agilent network analyser is set at 50 Ω. The signal reflected from
the DUT is usually measured as a ratio to the incident signal. It can be expressed as
reflection coefficient or return loss. These measurements are described
mathematically as,
Reflection coefficient ≡
reflected power
incident power
=
𝐸refl
𝐸inc
= 𝜌 (magnitude only)
= Γ (Reflection magnitude and phase)
Return loss (dB) = −20 log 𝜌
Standing Waves Ratio, 𝑆𝑊𝑅 =
1+ Γ
1− Γ
Network Analysis

104
Displaying the reflection measurement in polar form on the network analyser
with a marker allows direct determination of the complex impedance of the
DUT. The center of the circle represents a coefficient Γ of 0, a perfect match,
no reflected signal. The outermost circumference of the scale represents a Γ
of 1, 100 % reflection. The phase angle is directly read from the display. The
magnitude and phase will be directly displayed in the marker data readout for
any frequency.
The amount of power reflected from a device is directly related to the
impedances of the DUT and the measurement instrument. Γ=0 occurs when
the DUT and the analyser have identical impedances. A short circuit has
Γ=1∠180°. Every other value of Γ corresponds uniquely to complex device
impedance. In terms of impedances,
𝑍o is the impedance of the measurement instrument,
𝑍DUT is the impedance of the DUT.
To facilitate computations, the normalised (in this case normalised to 50 Ω)
impedance is,
𝑍N =
𝑍DUT
𝑍o
=
1 + Γ
1 − Γ

105
Scattering parameters (S-parameters) are commonly used to characterise high
frequency circuits. S-parameters basically are two-port characteristics of the
DUT. Additionally, the behaviour of traveling waves is readily deduced from
S-parameters. S-parameters can readily be found using the schematic of the
test set up shown in figure 37.
DUT
2-Port Network
Figure 37: Two port network used for S-parameters measurements.
𝑍𝐿
+
-
𝑍0
𝐸r2
𝐸i2
𝐸r1
𝐸i1

106
Define new variables with respect to the characteristic impedance of the
measurement instrument,
𝑎1 =
𝐸i1
𝑍o
𝑎2 =
𝐸i2
𝑍o
𝑏1 =
𝐸r1
𝑍o
𝑏2 =
𝐸r2
𝑍o
S-parameters relates these four waves as follows:
𝑏1 = 𝑆11𝑎1 + 𝑆12𝑎2
𝑏2 = 𝑆21𝑎1 + 𝑆22𝑎2
For 𝑆11, the output port of the DUT is terminated, with 𝑍o = 50 Ω and the
ratio of 𝑏1 to 𝑎1 is measured,
𝑆11 =
𝑏1
𝑎1 𝑎2=0

107
Terminating the output port of the DUT with the impedance of the
measurement instrument is equivalent to setting 𝑎2 = 0 since a traveling wave
incident on this load will be totally absorbed. 𝑆11 is the input reflection
coefficient of the DUT. The forward transmission through the DUT is the ratio
of 𝑏2 to 𝑎1. This could either be the gain of the amplifier or the attenuation of a
passive network,
𝑆21 =
𝑏2
𝑎1 𝑎2=0
By terminating the input side of the network, we set 𝑎1 = 0 and can then
measure the output reflection coefficient, 𝑆22, and the reverse transmission
coefficient, 𝑆12, defined as,
𝑆22 =
𝑏2
𝑎2 𝑎1=0
𝑆12 =
𝑏1
𝑎2 𝑎1=0
S-parameters are typically expressed as a magnitude and phase.

108
Spectrum Analyser
Introduction
• A spectrum in the practical sense is a collection of sine waves, when
combined properly produces the required time domain signal.
• The frequency domain also has its measurement strengths.
• The frequency domain is better for determining the harmonic
content of a signal.
A spectrum analyser is a device used to examine the spectral
composition of some electrical, acoustic, or optical waveform. Mostly it
finds application in measurement of power spectrum .

109
Figure 38
Amplitude
(Power)
Time Domain
Measurements Frequency
Domain
Measurements

111
Analog Spectrum Analyser
An analog spectrum analyser uses either a variable bandpass filter
whose mid-frequency is automatically tuned (shifted, swept) through
the range of frequencies of which the spectrum is to be measured or a
superheterodyne receiver where the local oscillator is swept through
a range of frequencies.
Figure 40

112
Digital Spectrum Analyser
A digital spectrum analyser computes the Fast Fourier Transform
(FFT), a mathematical process that transforms a waveform into the
components of its frequency spectrum
Figure 41

113
Spectrum Analysis
• In various field operations involving signals there is need to ascertain
the nature of the signal at several points.
• Signal characteristics affect the parameters of operation of a system.
• Spectrum analysis mostly involves study of the signal entering a
system or that produced by it.
• Spectrum analysers usually display raw, unprocessed signal
information such as voltage, power, period, waveshape, sidebands
and frequency. They can provide with a clear and precise window
into the frequency spectrum.

114
Fast Fourier Transform (FFT) Spectrum Analyser
The Fourier analyser basically takes a time-domain signal, digitizes it
using digital sampling, and then performs the mathematics required to
convert it to the frequency domain, and display the resulting spectrum
as shown in figure 42.
Figure 42: Parallel filters measured simultaneously.
𝑓1 𝑓2
A
𝑓

115
Swept Spectrum Analyser
The most common type of spectrum analyser is the swept-tuned
receiver. It is the most widely accepted, general-purpose tool for
frequency-domain measurements. The technique most widely used is
superheterodyne.
𝑓1 𝑓2
A
𝑓
Figure 43: Filter sweeps over range of interest.

116
FFT Spectrum Analyser
The Measurement System
• The analyser is looking at the entire frequency range at the same time
using parallel filters measuring simultaneously.
• It is actually capturing the time domain information which contains all
the frequency information in it.
• With its real-time signal analysis capability, the Fourier analyser is able
to capture periodic as well as random and transient events.
• It also can provide significant speed improvement over the more
traditional swept analyser and can measure phase as well as magnitude.

117
Swept Spectrum Analyser
• Very basically, these analysers "sweep" across the frequency range of
interest, displaying all the frequency components present.
• The swept-tuned analyser works just like the AM radio in your home
except that on your radio, the dial controls the tuning and instead of a
display, your radio has a speaker.
• The swept receiver technique enables frequency domain measurements
to be made over a large dynamic range and a wide frequency range.
• It has significant contributions to frequency-domain signal analysis for
numerous applications, including the manufacture and maintenance of
microwave communications links, radar, telecommunications
equipment, cable TV systems, and broadcast equipment; mobile
communication systems; EMI diagnostic testing; component testing;
and signal surveillance.

118
Theory Of Operation
Figure 44
RF Input
Attenuator
Input
Signal
Local
Oscillator
Crystal
Reference
Mixer
IF
Gain
IF
Filter
Detector
Log
Amplifier Video
Filter
Sweep
Generator
CRT
Display
Pre Selector
(Low Pass Filter)

119
The major components in a spectrum analyser are:
• RF input attenuator;
• Mixer;
• IF (Intermediate Frequency) gain;
• IF filter;
• Detector;
• Video filter;
• Local oscillator;
• Sweep generator;
• CRT display.
Components In Spectrum Analyser

120
Mixer
Figure 45
RF IF
LO
𝑓sig
𝑓LO
𝑓sig
𝑓LO − 𝑓sig 𝑓LO + 𝑓sig
𝑓LO

121
• A mixer is a device that converts a signal from one frequency to another.
• It is sometimes called a frequency-translation device.
• A mixer is a non-linear device (frequencies are present at the output that
were not present at the input).
• The output of a mixer consists of the two original signals 𝑓Sig and
𝑓LO as well as the sum 𝑓LO + 𝑓Sig and difference 𝑓LO − 𝑓Sig
frequencies of these two signals.
• In a spectrum analyser, the difference frequency is actually the
frequency of interest. The mixer has converted our RF input signal to an
IF (Intermediate Frequency) signal that the analyser can now filter,
amplify and detect for the purpose of displaying the signal on the
screen.

122
IF Filter
Figure 46
Display
IF
Bandwidth
(RBW)
Input
Spectrum

123
• The IF filter is a bandpass filter which is used as the “window” for
detecting signals.
• It's bandwidth is also called the Resolution Bandwidth (RBW) of the
analyser and can be changed via the front panel of the analyser.
• By giving a broad range of variable resolution bandwidth settings , the
instrument can be optimized for the sweep and signal conditions,
letting trade-off frequency selectivity (the ability to resolve signals),
Signal-to-Noise Ratio (SNR), and measurement speed.
• As RBW is narrowed, selectivity is improved (we are able to resolve
the two input signals). This will also often improve SNR.

124
Detector
Figure 47
Amplitude
■ Positive detection: Largest value in
bin displayed
● Negative detection: Smallest value
in bin displayed
♦ Sample detection: Last value in bin
displayed
■ ■
■ ■
■
■ ■
■
■
■
● ●
● ●
●
●
● ● ●
♦ ♦
●
♦ ♦ ♦
♦ ♦
♦ ♦
♦
Bins
Detector

125
• The analyser must convert the IF signal to a baseband or video signal
so it can be viewed on the instrument's display. This is accomplished
with an envelope detector which then deflects the CRT beam on the y-
axis, or amplitude axis.
• Many modern spectrum analysers have digital displays which first
digitise the video signal with an analog-to-digital converter (ADC).
• The positive-peak detector mode captures and displays the peak value
of the signal over the duration of one trace element.
• The negative-peak detector mode captures the minimum value of the
signal for each bin.

126
Video Filter
Figure 48
Video
Filter

127
• The video filter is a low-pass filter that is located after the
envelope detector and before the ADC.
• This filter determines the bandwidth of the video amplifier, and is
used to average or smooth the trace seen on the screen.
• By changing the video bandwidth (VBW) setting, we can decrease
the peak-to-peak variations of noise.

128
Other Components
Figure 49
Sweep
Generator
Frequency
IF
Gain
CRT Display
Local
Oscillator
RF Input
Attenuator

129
• The local oscillator is a Voltage Controlled Oscillator (VCO) which in effect
tunes the analyser.
• The sweep generator actually tunes the LO so that its frequency changes in
proportion to the ramp voltage.
• This also deflects the CRT beam horizontally across the screen from left to
right, creating the frequency domain in the x-axis.
• The RF input attenuator is a step attenuator located between the input
connector and the first mixer. It is also called the RF attenuator.
• This is used to adjust the level of the signal incident upon the first mixer.
• This is important in order to prevent mixer gain compression and distortion due
to high-level and/or broadband signals.
• The IF gain is located after the mixer but before the IF, or RBW, filter.
• This is used to adjust the vertical position of signals on the display without
affecting the signal level at the input mixer.
• When it changed, the value of the reference level is changed accordingly.
• The IF gain will automatically be changed to compensate for input attenuator
changes, so signals remain stationary on the CRT display, and the reference
level is not changed.
The Auxillaries

130
How It All Work Together
Figure 50
IF Filter
Detector
Input
Mixer
Local
Oscillator
CRT Display
Sweep Generator
0 1 2 3 4 5 6
3.6 6.5
0 1 2 3
𝑓s
Signal Range LO Range
3 4 5 6
3.6 6.5
𝑓LO
GHz
0 1 2 3
A
𝑓 GHz
GHz
𝑓LO − 𝑓s
𝑓s
𝑓LO
𝑓LO − 𝑓s
3.6
𝑓IF

131
• First of all, the signal to be analyzed is connected to the input of the
spectrum analyser. This input signal is then combined with the LO through
the mixer, to convert or translate it to an intermediate frequency (IF).
• These signals are then sent to the IF filter.
• The output of this filter is detected, indicating the presence of a signal
component at the analyser’s tuned frequency. The output voltage of the
detector is used to drive the vertical axis (amplitude) of the analyser display.
• The sweep generator provides synchronization between the horizontal axis of
the display (frequency) and tuning of the LO. The resulting display shows
amplitude versus frequency of spectral components of each incoming signal.
• The horizontal arrows are intended to illustrate the "sweeping" of the
analyser. Starting with LO at 3.6 GHz, the output of the mixer has four
signals, one of which is at 3.6 GHz 𝑓LO .

132
• IF filter is also at 3.6 GHz (it’s shape has been imposed onto the frequency
graph for clarity). Therefore, we expect to see this signal on the display. At
0 Hz on the CRT, we do indeed see a signal - this is called “LO Feed
through”.
• Sweep generator moving to the right, causes the LO to sweep upward in
frequency. As the LO sweeps, so two will three of the mixer output signals
(the input signal is stationary).
• As the LO Feed through moves out of the IF filter bandwidth, we see it taper
off on the display. As soon as the difference frequency 𝑓LO − 𝑓S comes into
the envelop of the IF filter, we start to see it.
• When it is at the center (e.g. 3.6 GHz) we see the full amplitude of this signal
on the display.
• And, as it moves further to the right, it leaves the filter envelop, and no signal
is seen on the display.
• The signal is being swept through the fixed IF filter, and properly displayed
on the analyser screen.

133
Figure 51
Front Panel Operation
Primary Functions
(Frequency, Amplitude, Span)
Softkeys
Control Functions
(RBW, Sweep Time, VBW)
RF Input
Numerical
Keypad

References
134
(1) Chaniotakis and Cory, Introduction to Electronics, Signals and
Measurement, Massachusetts Institute of Technology, 2006.
(2) A. V. Bakshi and U. A. Bakshi, Electronic Measurements and
Instrumentation, 2008.
(3) Anritsu, Vector Network Analyser Primer, Application Note, 2009.

Lecture Notes: EEEC6430312 Measurements And Instrumentation - Instrumentation

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Lecture Notes: EEEC6430312 Measurements And Instrumentation - Instrumentation