EENG 32131 MEASUREMENTS AND INSTRUMENTATION

FACULTY OF ENGINEERING AND COMPUTER TECHNOLOGY

BENG (HONS) IN ELECTRICAL AND ELECTRONIC ENGINEERING

Ravandran Muttiah BEng (Hons) MSc MIET

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

Figure 1

2

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 ln𝑅 + 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 ln𝑅1 + 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 degree Celcius 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.

(1) If resistance is known, the temperature may be determined from equation 1.

(2) If temperature is known the resistance is determined from the following equation:

𝑅 = 𝑒𝑥𝑝 𝛽 −𝛼

2

13− 𝛽 +

𝛼

2

13

where, α =𝑎−

1

𝑇

𝑐and 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 100Ω/degree Celsius which results in the design of sensitive and

robust systems.

5

6

Figure 2

Electronic Transducer

7

Figure 3

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 degrees Celsius. 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

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.

Figure 4: Wheatstone Bridge

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 below.

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 = 12V ÷ (10Ω + 20Ω) = 0.4A

The voltage at point C, which is also the voltage drop across the lower

resistor, R2 is calculated as:

VR2 = I × R2 = 0.4A × 20Ω = 8 volts

12

Then we can see that the source voltage VS is divided among the two series

resistors in direct proportion to their resistances as VR1 = 4V and VR2 = 8V.

This is the principle of voltage division, producing what is commonly called a

potential divider circuit or voltage divider network.

Now if we add another series resistor circuit using the same resistor values in

parallel with the first we would have the following circuit.

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 volts, with respect to zero (battery negative), as the voltage is

common and the two resistive networks are the same.

13

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

volts as: C = D = 8 volts, then the voltage difference is: 0 volts

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.

14

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 = 0.4A × 10Ω = 4 volts

Now with VR4 having 4 volts dropped across it, the voltage difference between

points C and D will be 4 volts as: C = 8 volts and D = 4 volts. Then the

difference this time is: 8 – 4 = 4 volts

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 volts (balanced)

and the maximum supply voltage (unbalanced), and this is the basic principal of

the Wheatstone Bridge Circuit.

15

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.

Figure 5: Wheatstone Bridge Circuit

16

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:

The Wheatstone Bridge equation required to give the value of the unknown

resistance, RX at balance is given as:

17

Where resistors, R1 and R2 are known or preset values.

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 6

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For the first series arm, ACB

For the second series arm, ADB

The voltage across points C-D is given as:

19

The value of resistor, R4 required to balance the bridge is given as:

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 volts. When the bridge is unbalanced,

however, the output voltage may be either positive or negative depending

upon the direction of unbalance.

20

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, or LDR.

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.

21

A typical Cadmium Sulphide (CdS) cell such as the ORP12 light dependent

resistor typically has a resistance of about one Mega ohm (MΩ) in dark or

dim light, about 900Ω at a light intensity of 100 Lux (typical of a well lit

room), down to about 30Ω 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.

Figure 7: Wheatstone Bridge Light Detector

22

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 22k or 47k 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 10kΩ value, the reference voltage set at

point D will therefore be equal to half of Vcc. 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.

23

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.

24

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.

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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 ƒr the phase shift is 0o. Consider the

circuit below.

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Figure 8: Wien Bridge

Wien Bridge Oscillator Frequency,

Where:

ƒr is the Resonant Frequency in Hertz

R is the Resistance in Ohms

C is the Capacitance in Farads

27

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 0.333xVin, 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.

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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 ZPas shown.

Lets assume then that the component values of R1 and R2 are the same

at: 12kΩ, capacitors C1 and C2 are the same at: 3.9nF and the supply

frequency, ƒ is 3.4kHz.

29

Series Circuit

The total impedance of the series combination with resistor, R1 and

capacitor, C1 is simply:

30

We now know that with a supply frequency of 3.4kHz, the reactance of

the capacitor is the same as the resistance of the resistor at 12kΩ. This

then gives us an upper series impedance ZS of 17kΩ.

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.

Parallel Circuit

The total impedance of the lower parallel combination with resistor, R2 and

capacitor, C2 is given as:

31

At the supply frequency of 3400Hz, or 3.4kHz, the combined resistance

and reactance of the RC parallel circuit becomes 6kΩ (R||Xc) and their

parallel impedance is therefore calculated as:

So we now have the value for the series impedance of: 17kΩ’s,

( ZS = 17kΩ ) and for the parallel impedance of: 8.5kΩ’s, ( ZS = 8.5kΩ ).

Therefore the output impedance, Zout of the voltage divider network at the

given frequency is:

32

Then at the oscillation frequency, the magnitude of the output

voltage, Vout will be equal to Zout x 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 the following basic Wien bridge oscillator circuit is

produced.

Figure 9: Wien bridge oscillator

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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.

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, (ƒr) 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).

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Also, due to the open-loop gain limitations of operational amplifiers,

frequencies above 1MHz are unachievable without the use of special high

frequency op-amps.

Example 2:

Determine the maximum and minimum frequency of oscillations of a Wien

Bridge Oscillator circuit having a resistor of 10kΩ and a variable capacitor

of 1nF to 1000nF.

The frequency of oscillations for a Wien Bridge Oscillator is given as:

Wien Bridge Oscillator Lowest Frequency,

35

Wien Bridge Oscillator Highest Frequency,

Example 3:

A Wien Bridge Oscillator circuit is required to generate a sinusoidal

waveform of 5,200 Hertz (5.2kHz). Calculate the values of the frequency

determining resistors R1 and R2and 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.

36

The frequency of oscillations for the Wien Bridge Oscillator was given as

5200 Hertz. If resistors R1 = R2 and capacitors C1 = C2 and we assume a

value for the feedback capacitors of 3.0nF, then the corresponding value

of the feedback resistors is calculated as:

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:

37

If we choose a value for resistor R3 of say, 100kΩ’s, then the value of

resistor R4 is calculated as:

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 47kΩ’s.

This gives the final Wien Bridge Oscillator circuit as:

38

Figure 10: Wien bridge oscillator circuit of example 3

39

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.

40

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 below.

The instrument consists of four sections:

(i) Two RF to IF converters

(ii) Automatic phase control circuit

(iii) Phase meter circuit

(iv) Voltmeter circuit

41

42

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.

43

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.

44

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.

45

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 cuases 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 centre 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

(1) 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.

(2) They allow voltage ratios to be measured over 70 to 80 dB range within a few

lengths of a decibel.

(3) The phase to be measured to an accuracy of about 1°.(4) Due to self locking feature, there is automatic tuning of the local oscillator in

each frequency range.

(5) Easy to operate, as simple as normal voltmeters.

46

A time-domain reflectometer (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

47

Signal Transmitted Through And Reflected From A

Discontinuity

48

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

49

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

50

Usage Of Time Domain Reflectometer (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

51

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

52

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 Ferre

(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.

53

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 & O'Connor, 1984, 2000a, 2000b; Kane & 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

54

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

55

TDR In Aviation Wiring Maintenance

Time domain reflectometry, specifically spread-spectrum time-domain

reflectometry is used on aviation wiring for both preventative maintenance

and fault location. Spread spectrum time domain reflectometry 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 reflectometry can be employed

on live wires. This method has been shown to be useful to locating

intermittent electrical faults.

56

An optical time-domain reflectometer (OTDR) is an optoelectronic instrument

used to characterize an optical fiber. An OTDR is the optical equivalent of an

electronic time domain reflectometer. 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

57

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.

58

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 nanometres (nm), or 4.00 × 10−7 to 7.00 × 10−7 m, between

the infrared (with longer wavelengths) and the ultraviolet (with shorter

wavelengths). This wavelength means a frequency range of roughly 430–

750 terahertz (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

59

60

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

61

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.

62

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

63

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 paper 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

64

Anritsu Vector Network Analyzers 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 11 and Figure 12 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

65

Transmission Measurements

Figure 11

66

Reflection Measurements

Figure 12

67

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.

68

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.

69

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.

70

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

71

Vector Network Analyzers 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 (Figure 13). 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

72

In a vector network analyser, 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 (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 13

73

The vector network analyser is a tuned receiver (Figure 14). 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 degrees, it is 90 degrees different

from the reference signal (Figure 15). The vector network analyzer would

read this as –90 degrees, since the test signal is delayed by 90 degrees with

respect to the reference signal.

The phase reference can be obtained by splitting off a portion of the

microwave signal before the measurement (Figure 16).

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.

Vector Network Analyser Basics

74

Vector Network Analyser Is A Tuned Receiver

Figure 14

75

Signals With A 90 Degree Phase Difference

Figure 15

76

Splitting The Microwave Signal

Figure 16

77

Let us consider the case when the DUT is removed, and a length of

transmission line is substituted (Figure 17). 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 degrees (Figure 18). 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

degrees.

78

Split Signal Where A Length Of The Line Replaces DUT

Figure 17

79

Split Signal Where Path Length Differs By Exactly One Wavelength

Figure 18

80

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 (Figure 19).

This test signal is: 1.1 X 360 = 396 degrees

This is 36 degrees different from the phase measurement at 1 GHz.

The network analyzer will display this phase difference as –36 degrees.

The test signal at 1.1 GHz is delayed by 36 degrees 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 degrees, –108 degrees for 1.3 GHz, and so forth. (Figure 20).

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 analyzers, 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.

81

Figure 19

Split Signal Where Path Length Is Longer Than One Wavelength

82

Figure 20

Electrical Delay

83

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 (Figure 21). 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.

84

Figure 21

Split Signals Where Paths Are Of Equal Length

85

Another approach is to handle the path length difference in

software. Figure 22 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 23 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.

86

Figure 22

Phase Difference Increases Linearly With Frequency

87

Figure 23

Resultant Phase With Path Length

88

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 ohms. 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 (Figure 24).

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 (Figure 25) are:

• S11 Forward Reflection

• S21 Forward Transmission

• S22 Reverse Reflection

• S12 Reverse Transmission

Network Analyser Measurement

89

Figure 24

Forward And Reverse Measurement

90

Figure 25

S-Parameter

91

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” (Figure 26). As discussed

earlier, we cannot tell the difference between one cycle and the

next. Therefore, after going through 360 degrees, we are back to

where we began. We can display the measurement from –180 to

+180 degrees, 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.

92

Figure 26

Linear Phase With Frequency Waveform

93

Several methods are available to display all of the information

on one trace. One method is a polar display (Figure 27). 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 (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.

94

Figure 27

Polar Display

95

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 .

96

97

98

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.

99

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

100

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.

101

The Basic Types

Fast Fourier Transform (FFT) Spectrum Analyser

The Fourier analyser basically takes a time-domain signal,

digitises it using digital sampling, and then performs the

mathematics required to convert it to the frequency domain, and

display the resulting spectrum.

102

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.

103

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.

104

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.

105

Theory Of Operation

106

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

107

Mixer

108

• 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 − 𝑓Sigfrequencies 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.

109

IF Filter

IF Filter

110

• 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.

111

Detector

112

• 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.

113

Video Filter

114

• 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.

115

Other Components

116

• 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

117

How It All Work Together

118

• 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 .

119

• 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 Feedthrough 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.

120

Front Panel Operation

References

121

(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