Courseware Samplein a waveguide. Converting impedances to admittances, and vice versa, using the...

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Courseware Sample

85756-F0

A

TELECOMMUNICATIONS

COURSEWARE SAMPLE

bythe Staff

ofLab-Volt Ltd.

Copyright © 2008 Lab-Volt Ltd.

All rights reserved. No part of this publication may be reproduced,in any form or by any means, without the prior written permissionof Lab-Volt Ltd.

Printed in CanadaFebruary 2009

III

Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V

Courseware Outline

Microwave Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII

Sample Exercise Extracted from Microwave Fundamentals

Exercise 7 Standing Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Instructor Guide Sample Exercise Extracted from Microwave Fundamentals

Exercise 7 Standing Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Bibliography

V

Introduction

The Lab-Volt Computer-Assisted Microwave Technology Training System,Model 8091, is a complete, state-of-the-art microwave training system, including dataacquisition and instrumentation.

Specifically designed for hands-on training, this integrated package of software,hardware, and courseware comes with all power supplies, high-quality microwavecomponents, and accessories required to perform the experiments.

The courseware experiments are performed by using the Lab-Volt software DataAcquisition and Management for Microwave systems (LVDAM-MW®). This modernsoftware is built around a Data Acquisition Interface (DAI), that performs 12-bitA/D acquisition on four channels.

The software uses the acquired data received from the interface to calculate anddisplay the values of power and SWR measurements on a computer screen. Thesoftware also features an oscilloscope, a Smith Chart displaying the values of thetransmission line parameters and used to perform impedance matching, and a datatable used to record, save, and graph all the measured parameters.

The microwave components and accessories include:

• A Gunn diode oscillator running at 10.5 GHz in continuous wave (CW) mode ormodulated by a 1-kHz square wave.

• A crystal detector, a thermistor, and a slotted line used with the LVDAM--MWsoftware to detect microwave signals and power and to take SWRmeasurements. The Gunn Oscillator Power Supply provides power to the DataAcquisition Interface through a connector that aligns when this interface isstacked on top of the power supply.

• An antenna azimuth indicator for accurate plotting of antenna field patterns.

• Inductive and capacitive irises used to measure reactive impedance.

• Three lenses, a metal plate, and a dielectric plate for microwave opticsexperiments.

• A PIN diode to teach microwave switching, variable attenuation, and amplitudemodulation of microwave signals.

• A hybrid tee to teach microwave signals' splitting and coupling.

MICROWAVE FUNDAMENTALS

Courseware Outline

VII

Exercise 1 Familiarization with Microwave Equipment

Identifying the basic components of a microwave setup. Assemblinga typical microwave setup and measuring power. Learning how to usethe Power Meter of the LVDAM-MW Software.

Exercise 2 Power Measurements

Familiarization with the operating principles of a microwave powermeter. Performing power calculation and measurements.

Exercise 3 The Gunn Oscillator

Familiarization with the basic operating principles of a Gunn oscillator.Characterizing a Gunn oscillator by plotting the following curves: thecurrent-versus-voltage curve, the delivered power-versus-voltagecurve, and the efficiency-versus-voltage curve.

Exercise 4 Calibration of the Variable Attenuator

Familiarization with the concepts of attenuation and insertion losses.Characterizing a variable attenuator by plotting its attenuation-versus-blade position curve.

Exercise 5 Detection of Microwave Signals

Familiarization with a crystal detector operating in the square-lawregion. Plotting the sensitivity curve of a crystal detector andevaluating its tangential sensitivity.

Exercise 6 Attenuation Measurements

Using the SWR Meter of LVDAM-MW and the Crystal Detector tomeasure attenuation. Measuring attenuation with the RF substitutionmethod.

Exercise 7 Standing Waves

Creation of standing waves in waveguides. Performing microwavefrequency measurements and standing wave measurements with theSlotted Line and the SWR Meter.


Courseware Outline

VIII

Exercise 8 The Directional Coupler

Familiarization with the operating principles of a directional coupler.Defining and measuring the coupling factor and the directivity of adirectional coupler.

Exercise 9 Reflection Coefficient Measurements

Familiarization with the concepts of reflection coefficient and returnloss. Measuring the reflection coefficient of a load. Determining thepower absorbed by a load based on its reflection coefficient.

Exercise 10 SWR Measurements

Familiarization with the concept of standing-wave ratio (SWR). Usingthe SWR Meter and the Slotted Line to measure the SWR.

Exercise 11 Impedance Measurements

Relationship between the reflection coefficient at the load and the loadimpedance. The Smith Chart. Plotting a normalized impedance on theSmith Chart. Determining the SWR produced by a given load.Determining the magnitude and phase of the reflection coefficientproduced by a given load. Determining the impedance of a load witha slotted line (short-circuit minima-shift method).

Exercise 12 Reactive Impedances

Effect of discontinuities in the relationship between the electric fieldand the magnetic field. Familiarization with the followingdiscontinuities: the capacitive iris, the inductive iris, and the screwtuner. Determining the reactance produced by an iris or a screw tunerin a waveguide. Converting impedances to admittances, and viceversa, using the Smith Chart. Determining the admittance and theimpedance of an iris with the Smith Chart.

Exercise 13 Impedance Matching

Reflection coefficient along a waveguide. Measuring an impedancealong a waveguide, using the Smith Chart. Determining theimpedance and the location of the matching device required to matcha load, using the Smith Chart. Using a slide-screw tuner.


Courseware Outline

IX

Exercise 14 Antennas and Propagation

Propagation in free space. Propagation loss due to the separationbetween the antennas. Isotropic radiators. Attenuation of a transmittedsignal as a function of the distance between the transmitting andreceiving antennas. Power received by an antenna as a function of itsorientation with respect to the transmitting antenna. Plotting aradiation pattern. Characterization of an antenna with two radiationpatterns (E- and H-plane patterns). Methods used to measure the gainof an antenna.

Exercise 15 Microwave Optics

Phenomena usually encountered in optics. Index of refraction of amaterial as a function of the frequency. The reflection coefficient andthe coefficient of transmission. The Snell's Law. Lenses and parabolicantennas.

Exercise 16 A Microwave Transmission Demonstration (Requires OptionalEquipment)

A simple demonstration to show how a microwave signal can be usedto carry information along a line of sight from one point to another.

Exercise 17 PIN Diodes

Construction of PIN diodes. Operation of a PIN diode when forwardand reverse biased. Typical resistance-versus-bias current responseof a forward biased PIN diode. Equivalent RF circuit of a forwardbiased PIN diode. Attenuation of a reverse biased PIN diode as afunction of frequency. Typical applications of PIN diodes.

Exercise 18 Wireless Video Transmission System (Requires OptionalEquipment)

Implementation and testing of a wireless video transmission systemthat uses a PIN diode as a microwave AM modulator. Effects thatconstructive and destructive interference has on the strength of thesignal received and on the image displayed by the video/TV receiver.

Exercise 19 Hybrid Tees

Introduction to waveguide tees. The hybrid (magic) tee. Using a hybridtee as a power splitter or a power combiner. Attenuation between theH- and E-plane arms of the tee and each of its lateral arms. Typicalapplications of hybrid tees.


Courseware Outline

X

Appendices A Common SymbolsB Module Front PanelsC Answers to Procedure Step QuestionsD Answers to Review QuestionsE New Terms and WordsF Equipment Utilization Chart

Bibliography

Sample Exercise

Extracted from

Microwave Fundamentals

3

Exercise 7

Standing Waves

EXERCISE OBJECTIVES

When you have completed this exercise, you will know how standing waves arecreated in waveguides. You will be able to perform microwave frequencymeasurements and standing wave measurements with the Slotted Line and theSWR Meter of LVDAM-MW.

DISCUSSION

Creation of Standing Waves

When a sinusoidal microwave source is connected to a waveguide, sinusoidal wavesof voltage and current propagate along it.

Note: In fact, we could also say that both an electric field wave and a magneticfield wave propagate inside the waveguide. Considering voltages and currentsinstead of electric and magnetic fields is simply a different way of viewingthings. The voltage is present between the top and the bottom of thewaveguide, whereas the current flows in the side walls. Throughout thisexercise, we will deal with voltages and currents to facilitate the understanding.

The amplitude of the voltage and the current depend on the characteristic impedanceof the waveguide and on the impedance of the terminating load.

When the impedance of the load is equal to the characteristic impedance of thewaveguide, the load continually absorbs all the received energy. No energy isreflected back toward the source. The waves travel only from the source to the load.

Conversely, when the impedance of the load is not equal to the characteristicimpedance of the waveguide, not all the received energy is absorbed by the load.Instead, part of it is reflected back toward the source.

Figure 7-1, for example, shows the waves traveling along a waveguide when theimpedance of the load is not equal to the characteristic impedance of the waveguide.

In this example, the load is in the short-circuit condition:

• the incident wave is completely reflected at the load end.

• the reflected and incident waves travel through each other, but in oppositedirections, thereby combining vectorially.

This results in the creation of a standing wave along the waveguide. The standingwave is the sum of the instantaneous values of the incident and reflected waves ateach point all along the line. This wave does not move or travel along the line, hencethe term "standing".

Standing Waves

4

Figure 7-1. Creation of a standing wave along a short-circuited waveguide.

Conventional Representation of Standing Waves

Even if the voltage or current of standing waves continually changes polarity withtime, the conventional way of representing these waves is with their negative andpositive half-cycles pointing upward.

Figure 7-2 shows the conventional representation of a standing wave of voltagealong a short-circuited waveguide.

• The points where the voltage is minimum are called minima, or nodes.

• The points where the voltage is maximum are called maxima, or loops.

The amplitude of the minima and maxima is determined by the amplitude of thereflected wave. The amplitude of the reflected wave is determined by the nature ofthe load.

When the load is a short circuit or an open circuit, the amplitude of the reflectedwave is maximum. In fact, the amplitude of the maxima is theoretically equal to twicethe amplitude of the incident wave, while the amplitude of the minima is null (orpractically zero).

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Figure 7-2. Conventional representation of a standing wave of voltage along a short-circuitedwaveguide.

Frequency Measurement

When examining Figure 7-2, the statements below can be inferred.

• At the load end of the waveguide, a minimum invariably occurs.

• Minima also occur at every even multiple of λg/4 from the load end (where λg isthe wavelength of the propagating wave in the waveguide.)

• Maxima occur at every odd multiple of λg/4 from the load end.

Figure 7-2 allows you to determine the frequency of a microwave signal propagatingin a short-circuited waveguide:

1. Measure the distance d between two successive minima.

(Since minima are usually more sharply defined than maxima, measuring thedistance between minima provides more accurate results. The presence of largereflections is also advantageous. Terminating the waveguide by a short-circuitedload provides large reflection. A matched load could not be used as there wouldbe no standing wave in this case.)

2. Multiply the measured distance by 2 to obtain the wavelength of the guidedsignal, λg.

3. Calculate the frequency of the guided signal, f, using the following equation:

where c = velocity of propagation of the signal in free space (3.0 @ 108 m/s);λg = wavelength of the guided signal (m);a = width of the waveguide (m);f = frequency of the guided signal (Hz).

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The Lab-Volt Slotted Line

Figures 7-3 and 7-4 show the Lab-Volt Slotted Line, Model 9520. This device can beused to measure the distance between the minima and the maxima of a standingwave.

The Slotted Line consists of a low-loss waveguide section with a narrow, longitudinalslot in the top wall, as Figure 7-3 shows. A sliding carriage, containing a probeconnected to a crystal detector, can be moved along the waveguide.

The probe is inserted into the waveguide to sense the electric field, as Figure 7-4shows. This causes a microwave signal to be induced at the probe output. Thecrystal detector detects this signal and produces a proportional DC voltage. Thisvoltage is available at the BNC output of the probe holder.

A thumbscrew allows you to adjust the depth of the probe and, therefore, themagnitude of the DC voltage at the BNC output. The marks and the pointer providean indication of the depth of the probe.

The voltage produced at the BNC output of the Slotted Line decreases as the probeis withdrawn from the waveguide; conversely, the voltage increases as the depth ofpenetration of the probe is increased.

Figure 7-3. The Lab-Volt Slotted Line and its symbolic representation.

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7

Figure 7-4. Cut-away view of the Lab-Volt Slotted Line.

Microwave Frequency Measurements and Standing Wave Measurements

The Lab-Volt Slotted Line can be used with the SWR Meter of LVDAM-MW toperform microwave frequency measurements and standing wave measurements.

To do this, the Slotted Line is connected to the input of the Data AcquisitionInterface (DAI) that is dedicated to the SWR Meter: MULTI-FUNCTION INPUT 3.This connection is usually made via the Lab-Volt 60-dB Amplifier, Model 9593, toobtain the maximum dynamic range.

The SWR Meter is set to read power. Its power reading is directly related to theDC voltage at the Slotted Line output and, therefore, to the magnitude of the electricfield in the waveguide.

When the carriage is moved along the waveguide, the position of the probe changes,causing the DC voltage produced by the crystal detector to change as a function ofthe variation in magnitude of the electric field along the waveguide.

Two positioning scales on the waveguide and the carriage indicate the location of thecarriage. This allows you to locate the minima and the maxima in the standing waveproduced by various loads, and to measure the wavelength and the frequency of themicrowave signal in the waveguide.

The measurements made with a slotted line are limited by the scale graduations. Theaccuracy of measurement decreases as the frequency of the guided signal isincreased.

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Startup Procedure to Follow When Using the Lab-Volt Slotted Line and theSWR Meter of LVDAM-MW

Before using the Lab-Volt Slotted Line and the SWR Meter, the following startupprocedure must be performed. This procedure allows you to obtain the maximumdynamic range on the SWR Meter, while operating the crystal detector of the SlottedLine in its square-law region to obtain valid SWR Meter readings.

1. The microwave signal injected into circuit is amplitude modulated by a 1-kHzsquare wave, provided by the Gunn Oscillator Power Supply. The microwavesignal is then attenuated in order for the crystal detector of the Slotted Line tooperate in its square-law region and the SWR Meter to provide valid readings.

2. The Slotted Line's probe is located close to the maximum nearest the load inorder for the Slotted Line output voltage to be maximum. This voltage is appliedto MULTI-FUNCTION INPUT 3 of the DAI (input dedicated to the SWR Meter ofLVDAM-MW).

3. The depth of the Slotted Line's probe is set to the initial default position of 1/3 ofmaximum.

4. With the minimum sensitivity (0-dB gain) on Input 3, the frequency of the SWRMeter's amplifier is tuned to obtain the maximum signal level on the SWR Meter.

5. The Slotted Line's probe depth is then adjusted so that the maximum signal levelindicated by the SWR Meter is between 70 and 90% of full scale.

6. The Slotted Line's probe is accurately positioned over the maximum, and theprobe depth is fine tuned, if necessary, to obtain the maximum signal level on theSWR Meter.

7. The reference level (0.0 dB) is set on the SWR Meter.

Particular attention must be paid to the adjustment of the probe depth inside theSlotted Line. If the probe penetrates too deep into the Slotted Line, the fielddistribution can be distorted, especially when the SWR is high. Moreover, the probe'scrystal detector is then more likely to operate outside of its square-law region,causing the measurements to be erroneous.

To obtain a good accuracy of measurement, the central frequency of theSWR Meter must be readjusted whenever the microwave circuit is modified or usedfor a prolonged period of time, as the central frequency drifts over time. The drift inthe central frequency of the SWR Meter is due, among other things, to variations inambient temperature and equipment temperature.

Similarly, the SWR Meter's reference may vary slightly over time. Small drifts areacceptable. However, it is recommended that you verify the reference from time totime and readjust it to 0.0 dB, to maintain a good accuracy of measurement.

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Procedure Summary

In this exercise, you will measure the guided wavelength and the frequency of amicrowave signal, using the Slotted Line and the SWR Meter.

You will then plot the standing-wave patterns for a short circuit, an attenuator andshort-circuit load, and a matched load.

EQUIPMENT REQUIRED

Refer to the Equipment Utilization Chart, in Appendix F of this manual, to obtain thelist of equipment required to perform this exercise.

PROCEDURE

System Setup

G 1. Make sure that all power switches are in the O (off) position. Set up themodules and assemble the microwave components as shown in Figure 7-5.

The Slotted Line must be connected, via the 60-dB Amplifier, to the analoginput of the Data Acquisition Interface (DAI) that is dedicated to the SWRMeter of LVDAM-MW: MULTI-FUNCTION INPUT 3.

The supply cable of the 60-dB Amplifier must be connected to theDB-9 connector on the bottom of the Data Acquisition Interface.

G 2. Referring to the attenuation-versus-blade position curve (or thecorresponding Data Table) of the Lab-Volt Variable Attenuator obtained inExercise 4, determine the attenuator blade's position required for thisattenuator to provide an attenuation of 20 dB approximately.

Set the Variable Attenuator’s blade to this position, which will limit themicrowave signal incident to the Slotted Line's Crystal Detector to make itoperate in its square-law region.

Attenuator blade’s position: mm

G 3. Make the following settings on the Gunn Oscillator Power Supply:

VOLTAGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MIN.MODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 kHzMETER SCALE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 V

G 4. Turn on the Gunn Oscillator Power Supply and the Data AcquisitionInterface (DAI) by setting their POWER switch to the "I" (ON) position.

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Set the Gunn Oscillator supply voltage to 8.5 V. Wait for about 5 minutes toallow the modules to warm up.

Figure 7-5. Computer and module arrangement (showing electrical connections to microwavecomponents), and microwave setup.

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Preliminary Adjustment of the Slotted Line and SWR Meter

G 5. Move the probe of the Slotted Line along the waveguide and set it over the50-mm position. (The 50-mm mark on the waveguide scale intersects therightmost ("0") mark on the carriage scale, as Figure 7-6 shows).

The 50-mm position approximately corresponds to the location of thestanding wave maximum nearest the load.

Figure 7-6. Locating the Slotted Line's probe over the 50-mm position and adjusting the probe'sdepth to 1/3 of maximum (pointer aligned with the second lowermost mark).

G 6. On the Slotted Line, loosen the thumbscrew of the sliding carriage andpartially withdraw the probe holder (by gently pulling up on the 60-dBAmplifier connected to the probe holder).

Adjust the depth of the Slotted Line's probe to approximately 1/3 ofmaximum (the Slotted Line's pointer must be aligned with the secondlowermost mark approximately, as Figure 7-6 shows); then tighten thethumbscrew.

Note: Particular attention must be paid to the adjustment of theprobe depth inside the Slotted Line. If the probe penetrates toodeep into the Slotted Line, the field distribution can be distorted,especially when the SWR is high. Moreover, the probe's crystaldetector is then more likely to operate outside of its square-lawregion, causing the measurements to be erroneous.

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G 7. On the host computer, start the LVDAM-MW software. In the ApplicationSelection window, make sure the Work in stand-alone box is unchecked,and click OK.

In the Settings panel of LVDAM-MW, make the following settings:

Gunn Oscillator/VCO Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ONFunction Input 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SWR MeterInput 3 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 dB60 dB Ampli on Input 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ON

G 8. In LVDAM-MW, start the SWR Meter and set it to display decibels (dB).

G 9. Tune the frequency of the SWR Meter's amplifier: using the cursor of theSWR Meter, scan through the frequency tuning range of this meter (from900 to 1100 Hz) to find the frequency at which the Signal Level (indicatedas a percentage below the horizontal indicator bar of the meter) ismaximum.

a. If the maximum signal level obtained on the SWR Meter is between 70and 90% of full scale and the horizontal indicator bar stays green, theequipment is properly adjusted. Go immediately to step 10.

Note: To obtain the maximum dynamic range of measurement onthe SWR Meter (once its amplifier has been tuned), a maximumlevel between 70 and 90% on the SWR Meter with Input 3 Gainset to 0 dB is ideal.

b. If the maximum signal level obtained on the SWR Meter is between10% and 70% of full scale, loosen the thumbscrew of the Slotted Lineand very slightly readjust the depth of its probe so that the maximumsignal level indicated by the SWR Meter is between 70 and 90% of fullscale (and the green bar stays green) once the thumbscrew of theSlotted Line has been re-tightened (the tightening of the thumbscrewwill cause the signal level to vary slightly).

Make sure not to insert the probe too deep inside the Slotted Line,otherwise the measurements may be erroneous. Instead slightlyreadjust the attenuation provided by the Variable Attenuator if themaximum reachable Signal Level stays below 70% of full scale, untilthis signal is within 70 and 90% of full scale.

Note: The adjustment process may be tedious at first, since asmall change in probe depth results in a significant change in theSWR Meter's signal level, however it will become easier withpractice.

c. If you are unable to tune the SWR Meter's amplifier because themaximum signal level exceeds the measurement scale (the horizontalindicator bar of the meter turns to red), loosen the thumbscrew of theSlotted Line. Readjust the depth of the Slotted Line's probe in order toobtain a significant reading on the SWR Meter (a signal level of, forexample, about 25% of full scale, once the thumbscrew of the Slotted

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Line has been re-tightened since its tightening will cause the signal levelto change slightly). Then, tune the frequency of the SWR Meter toobtain the maximum signal level on this meter. If this level is notbetween 70 and 90% of full scale, very slightly readjust the depth of theSlotted Line's probe so that the maximum signal level indicated by theSWR Meter is between 70 and 90% of full scale (and the green barnever turns from green to red) once the thumbscrew of the Slotted Linehas been re-tightened.

d. If the maximum signal level stays null or too low (below 10% of full scalewith a blue indicator bar or no bar displayed) when trying to tune theSWR Meter's amplifier, slightly decrease the attenuation produced bythe Variable Attenuator in order to obtain a significant level on the SWRMeter (a signal level of, for example, about 25% of full scale). Then,tune the meter frequency in order to obtain the maximum signal level onthis meter. If the maximum signal level is not between 70 and 90% offull scale, slightly readjust the Variable Attenuator for the signal to bewithin this range.

Note: The voltage produced by the Slotted Line decreases as theprobe is withdrawn from the waveguide; conversely, the voltageincreases as the depth of penetration of the probe is increased.The probe needs to be partially withdrawn from the Slotted Line'swaveguide to obtain valid measurements on the SWR Meter anda good dynamic range. The probe must not be fully inserted intothe Slotted Line's waveguide, otherwise its crystal detector maynot operate in the square-law region, causing the SWR Meterreadings to be erroneous.

G 10. Very slightly move the probe of the Slotted Line around the 50-mm positionon the graduated waveguide, while observing the Signal Level on the SWRMeter; locate the probe over the maximum (if not already there) to obtain themaximum Signal Level on the SWR Meter.

Note: If this causes the Signal Level to become lower than 70%or higher than 90% of full scale, very slightly readjust the depth ofthe Slotted Line's probe to bring the Signal Level back to 70-90%of full scale, with a green bar that never turns to red, when theprobe is at the maximum.

G 11. Click on the REFERENCE button of the SWR Meter to set the referencelevel to 0.0 dB.

Measuring the Guided Wavelength and the Microwave Signal Frequency

G 12. Move the Slotted Line's probe along the waveguide to locate the minimaand the maxima. Record the position of each of them in Table 7-1. Do notmodify any equipment setting, except Gain Input 3 when necessary.

– To locate the maxima, set Gain Input 3 to 0 dB and find the probelocations for which the signal level is maximum on the SWR Meter.

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– To locate the minima, set Gain Input 3 to 20 dB and then 40 dB to findthe probe locations for which the signal level is minimum on theSWR Meter—this level will be approximately null, causing jerky andsmall irregular moves of the SWR Meter's indicator bar in the blue(lowest) range area.

MINIMUM DISTANCE FROM THELOAD (mm) MAXIMUM DISTANCE FROM THE

LOAD (mm)

m1 (nearest from load) M1 (nearest from load)

m2 M2

m3 M3

m4 M4

m5 M5 —

Table 7-1. Location of minima and maxima when the load consists of a short circuit.

G 13. Based on the data recorded in Table 7-1, evaluate the distance, d, betweentwo successive minima.

d = mm

Multiply the distance, d, by 2 to obtain the wavelength of the signal in thewaveguide, λg.

λg = 2d = mm

Based on the obtained wavelength, λg, calculate the frequency of the signalin the waveguide, f, using the formula below.

where c = velocity of propagation of the signal in free space (3.0 @ 108 m/s);λg = wavelength of the signal in the waveguide (m);a = width of the waveguide, equal to 0.0229 m;f = frequency of the signal in the waveguide (Hz).

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Standing Wave Produced Along the Slotted Line when the Waveguide Is Short-Circuited

G 14. In LVDAM-MW, select the Data Table function and enter the column titlesand figures already recorded in Table 7-2 below. Save your Data Table.

DISTANCE FROM THELOAD (mm) SWR METER READING (dB) E/E MAX.

50 0 1

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

Table 7-2. E/E MAX. ratios along the Slotted Line when the waveguide is short-circuited.

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G 15. Set the Gain on Input 3 to 0 dB.

Locate the Slotted Line's probe over the maximum nearest the load (aroundthe 50.0-mm position) in order to obtain the maximum signal level on theSWR Meter.

Verify that the frequency of the SWR Meter is properly tuned for the SignalLevel displayed on the SWR Meter to be maximum. Click on theREFERENCE button of the SWR Meter to set the reference level to 0.0 dB.

G 16. Fill in your Data Table: by moving the Slotted Line's probe away from theload in steps of 1.0 mm, set this probe to each of the locations listed in theData Table and, for each location, perform the steps below.

a. Note the SWR Meter power reading and record it under the column"SWR METER READING" (increase or decrease Gain Input 3 asnecessary, but do not change the Reference on the SWR Meter).

b. Using the SWR Meter reading recorded in step a., use the equationbelow to calculate the ratio E/E MAX.. Record your result under thecolumn "E/E MAX.". Save your table.

where E = Voltage of the standing wave at the current probelocation (V);

E MAX. = Voltage of the standing wave at the location of themaximum (V);

SWR Meter Reading = Ratio of the standing wave voltage, E, to themaximum voltage, E MAX. of this wave, in decibels(dB).

G 17. In LVDAM, select the Graph function of the Data Table and plot theE/E MAX.-versus-distance from the load curve: select "DISTANCE FROMTHE LOAD" for the X-Axis and "E/E max" for the Y-Axis.

Have the X-Axis coordinates of your graph graduated like the Slotted Line'sruler (right-to-left increase) by making the following settings in the Graphwindow:

X-Axis CoordinatesInversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ON

ScaleX-Axis Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ManualX Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10X Max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150X Min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

Your graph should show part of the standing-wave pattern, as Figure 7-7shows. Print your graph, then plot the rest of the standing wave freehandbased on the minima and the maxima recorded in Table 7-1.

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Remember that a standing wave repeats itself every half-wavelength. Thedistance between the minima and maxima remains constant.

Figure 7-7. Standing wave produced along the Slotted Line when the waveguide is short-circuited.

G 18. Save and close your Data Table.

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Standing Wave Produced Along the Slotted Line When the Load Consists ofa 6-dB Attenuator and a Short Circuit

G 19. In the Settings panel of LVDAM-MW, set the Gunn Oscillator/VCO Powerto OFF.

G 20. Taking care not to modify the adjustment of the Variable Attenuatorand Slotted Line’s probe depth, modify your microwave circuit in order toobtain the circuit shown in Figure 7-8.

Leave the rest of the equipment connected and set as before.

Figure 7-8. Modified microwave circuit to plot the standing-wave pattern when the load consistsof a 6-dB attenuator and a short circuit.

G 21. In the Settings panel of LVDAM-MW, make the following settings:

Gunn Oscillator/VCO Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ONInput 3 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 dB

Wait for about 5 minutes to allow the modules to warm up.

G 22. Locate the Slotted Line's probe over the maximum nearest the load (aroundthe 41.0-mm position) in order to obtain the maximum signal level on theSWR Meter.

Verify that the frequency of the SWR Meter is properly tuned for the SignalLevel displayed on the SWR Meter to be maximum. Slightly move the

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19

Slotted Line's probe around the 41-mm position to locate the probe over themaximum (if not already there) and obtain the maximum Signal Level on theSWR Meter. If the maximum signal level is below 70% of full scale, veryslightly readjust the attenuation provided by the Variable Attenuator or thedepth of the Slotted Line's probe so that the maximum level is between 70and 90% of full scale.

Click on the REFERENCE button of the SWR Meter to set the referencelevel to 0.0 dB.

G 23. Move the probe of the Slotted Line along the graduated waveguide to locatethe minima and the maxima. Record the position of each of them inTable 7-3. Do not modify any equipment setting, except Gain Input 3 ifnecessary.

Note: The magnitude of the minima and the maxima may slightlychange as the probe is moved along the line due to power lost byreflection along the guide. Reflections and reflection losses will bestudied in another exercise.

MINIMUM DISTANCE FROM THELOAD (mm) MAXIMUM DISTANCE FROM THE

LOAD (mm)

m1 (nearest from load) M1 (nearest from load)

m2 M2

m3 M3

m4 M4

m5 — M5

Table 7-3. Location of minima and maxima when the load consists of a 6-dB attenuator and a shortcircuit.

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DISTANCE FROM THELOAD (mm) SWR METER READING (dB) E/E MAX.

41 0 1

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

Table 7-4. E/E MAX. ratios along the Slotted Line when the load consists of a 6-dB attenuator and ashort circuit.

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21

G 25. Locate the Slotted Line's probe over the maximum nearest the load (aroundthe 41.0-mm position) in order to obtain the maximum signal level on theSWR Meter.

Verify that the frequency of the SWR Meter is properly tuned for the SignalLevel displayed on the SWR Meter to be maximum. Click on theREFERENCE button of the SWR Meter to set the reference level to 0.0 dB.

G 26. Fill in your Data Table: by moving the Slotted Line's probe away from theload in steps of 1.0 mm, set this probe to each of the locations listed in theData Table and, for each location, perform the steps below.

a. Note the SWR Meter power reading and record it under the column"SWR METER READING".

Note: When the SWR Meter's Signal Level fluctuates,approximate this level.

b. Using the SWR Meter reading recorded in step a., use the equationbelow to calculate the ratio E/E MAX. Record your result under thecolumn "E/E MAX.". Save your table.




G 27. In LVDAM, select the Graph function of the Data Table and plot theE/E MAX.-versus-distance from the load curve.

Have the X-Axis coordinates of your graph graduated like the Slotted Line'sruler by making the following settings in the Graph window:



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22

Your graph should show part of the standing-wave pattern, as Figure 7-9shows. Observe that the peak-to-peak amplitude of the standing wave islower than that of the standing wave previously obtained with the short-circuited load.

Print your graph, then plot the rest of the standing wave freehand based onthe minima and the maxima recorded in Table 7-3.

Remember that a standing wave repeats itself every half-wavelength. Thedistance between the minima and maxima remains constant.

Figure 7-9. Standing wave produced along the Slotted Line when the load consists of a 6-dBattenuator and a short circuit.


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23

Standing Wave Produced Along the Slotted Line with a Matched Load

G 29. In the Settings panel of LVDAM-MW, set the Gunn Oscillator/VCO Powerto OFF.

G 30. Taking care not to modify the adjustment of the Variable Attenuatorand Slotted Line's probe, modify your microwave circuit in order to obtainthe circuit shown in Figure 7-10.

Leave the rest of the equipment connected and set as before.

Figure 7-10. Modified microwave circuit to plot the standing-wave pattern with a matched load.

G 31. In the Settings panel of LVDAM-MW, make the following settings:

Gunn Oscillator/VCO Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ONInput 3 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 dB


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24

PROBE LOCATION (mm) SWR METER READING (dB) E/E MAX.

40 0 1

50

60

70

80

90

100

110

Table 7-5. E/E MAX. ratios along the Slotted Line with a matched load.

G 33. Locate the Slotted Line's probe over the 40-mm position.

Verify that the frequency of the SWR Meter is properly tuned for the SignalLevel displayed on the SWR Meter to be maximum. If this level is below70% of full scale, very slightly readjust the attenuation provided by theVariable Attenuator or the depth of the Slotted Line's probe so that themaximum level is between 70 and 90% of full scale.

Click on the REFERENCE button of the SWR Meter to set the referencelevel to 0.0 dB.

G 34. Fill in your Data Table: by moving the Slotted Line's probe away from theload, set this probe to each of the locations listed in the Data Table and, foreach location, perform the steps below.

a. Note the SWR Meter power reading and record it under the column"SWR METER READING".

Note: When the SWR Meter's Signal Level fluctuates,approximate this level.

b. Using the SWR Meter reading recorded in step a., use the equationbelow to calculate the ratio E/E MAX. Record your result under thecolumn "E/E MAX." Save your table.



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25


G 35. In LVDAM, select the Graph function of the Data Table and plot theE/E MAX.-versus-distance from the load curve.

Have the X-Axis coordinates of your graph graduated like the Slotted Line'sruler by making the following settings in the Graph window:



Your graph should resemble that shown in Figure 7-11.

Observe that the amplitude of the standing wave stays nearly constantaround a ratio E./EMAX. of 1, since the impedance of the load is matched tothe characteristic impedance of the waveguide.


G 37. Turn off the Gunn Oscillator Power Supply and the Data AcquisitionInterface by setting their POWER switch to the O (OFF) position.Disassemble the setup and return all components to their storage location.

G 38. Close the LVDAM-MW software.

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26

Figure 7-11. Standing wave produced along the Slotted Line with a matched load.

CONCLUSION

In this exercise, the concepts of characteristic impedance, reflected waves, andstanding-waves were introduced. You became familiar with the use of a slotted lineby evaluating the guided wavelength and the frequency of a microwave signal. Youalso determined the standing-wave patterns for a short circuit, an attenuator andshort-circuit load, and a matched load.

REVIEW QUESTIONS

1. What does a standing-wave pattern represent?

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27

2. What is the distance, in terms of wavelengths, between successive minima in astanding-wave pattern?

3. What causes a maximum on a standing-wave?

4. Explain how to determine a microwave signal's frequency with a slotted line.

5. What physical parameter does a slotted line measure?

Instructor Guide

Sample Exercise

Extracted from

Microwave Fundamentals

31

Exercise 7

Standing Waves

INTRODUCTORY INFORMATION

Exercise 7 introduces standing waves. Standing waves are the result of two wavesof the same frequency and amplitude travelling in opposite directions in a waveguideadding to and subtracting from each other. In waveguides, two waves travelling inopposite directions exist when an incident wave encounters a discontinuity, obstacle,or load and a reflected wave is produced. A standing wave can be defined for anycomponent of the microwave field. Generally, the electric field component isconsidered.

When the two waves are of the same magnitude, the resulting wave is called a purestanding wave. This wave is stationary; that is, a constant-phase point does notmove, but remains at the same point as time goes by. If one of the waves is smallerthan the other, the resulting wave will not be stationary and the constant-phase pointwill move in the same direction as the larger wave. However, the envelope of theinstantaneous curves will be stationary. This envelope is called a standing-wavepattern.

Normally, it is not the shape of the standing-wave pattern that is of interest; it israther the ratio of the maximum to the minimum values of the pattern, called theStanding-Wave Ratio (SWR), that is of interest. A maximum of a standing-wavepattern is the sum of the amplitudes of the two waves. A minimum is the differencebetween the amplitudes of the two waves.

A common cause of standing-wave patterns is the reflection of a portion of thepropagating wave by a load in the microwave system. If the impedance of the loadis not equal to the characteristic impedance of the system, some of the propagatingwave will be reflected back towards the microwave source. The size of the reflectedwave will depend on the mismatch between the load and the system. Obviously, ifa part of the signal sent to the load is reflected, the load will not have absorbed allof the signal. From the SWR produced by the resulting standing-wave pattern, youcan determine the fraction of the incident wave that has been reflected.

In the first part of the exercise, the students will use the Lab-Volt Slotted Line and theSWR Meter of LVDAM-MW to measure the guided wavelength of a microwavesignal. To do this, the students will first measure the distance between twosuccessive minima near the load (in the short-circuited condition) and multiply thisdistance by two to obtain the wavelength. Based on this wavelength, the studentswill use a formula to calculate the frequency of the microwave signal.

The students will then use the Slotted Line and the SWR Meter to determine thestanding-wave pattern produced by three different loads: a short circuit, anattenuator and short-circuit load, and a matched load. The students will record andsave all the measurements made with the Slotted Line and the SWR Meter in theData Table of LVDAM-MW; the Graph function of this software will automatically plotthe standing-wave pattern corresponding to the results recorded in the Data Table.

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Microwave Frequency Measurements and Standing Wave Plotting with theLab-Volt Slotted Line and LVDAM-MW SWR Meter

The Lab-Volt Slotted Line is used with the SWR Meter of LVDAM-MW to performmicrowave frequency measurements and standing wave plotting.

To do this, the Slotted Line must be connected to the input of the Data AcquisitionInterface (DAI) that is dedicated to the SWR Meter: DAI Input 3. This connection isusually made via the Lab-Volt 60-dB Amplifier, Model 9593, to obtain the maximumdynamic range.

The SWR Meter is set to read power, in dB. Its power reading is directly related tothe DC voltage at the Slotted Line output and, therefore, to the magnitude of theelectric field in the waveguide.

When the carriage is moved along the waveguide, the position of the probe changes,causing the DC voltage produced by the crystal detector to change as a function ofthe variation in magnitude of the electric field along the waveguide.

Two positioning scales on the waveguide and the carriage indicate the location of thecarriage. This allows the students to locate the minima and the maxima in thestanding wave produced by various loads, and to measure the wavelength and thefrequency of the microwave signal in the waveguide.

The measurements made with the Slotted Line are limited by the scale graduations.

Startup Procedure to Follow When Using the Lab-Volt Slotted Line and the SWRMeter of LVDAM-MW

Before using the Lab-Volt Slotted Line and the SWR Meter, the following startupprocedure must be performed. This procedure allows students to obtain themaximum dynamic range on the SWR Meter, while operating the crystal detector ofthe Slotted Line in its square-law region to obtain valid SWR Meter readings.

1. The microwave signal injected into circuit is amplitude modulated by a 1-kHzsquare wave, provided by the Gunn Oscillator Power Supply. The microwavesignal is then attenuated in order for the crystal detector of the Slotted Line tooperate in its square-law region and the SWR Meter to provide valid readings.

2. The Slotted Line's probe is located over the standing-wave maximum nearest theload in order for the Slotted Line output voltage to be maximum. This voltage isapplied to DAI Input 3 (input dedicated to the SWR Meter of LVDAM-MW).

3. The depth of the Slotted Line's probe is set to the initial default position of 1/3 ofmaximum.

4. With the minimum sensitivity (0-dB gain) on DAI Input 3, the frequency of theSWR Meter's amplifier is tuned to obtain the maximum signal level on theSWR Meter.

5. The Slotted Line's probe depth is then adjusted so that the maximum signal levelindicated by the SWR Meter is between 70 and 90% of full scale.

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33

6. The Slotted Line's probe is accurately positioned over the maximum, and theprobe depth is fine tuned, if necessary, to obtain the maximum signal level on theSWR Meter.

7. Finally, the reference level (0.0 dB) is set on the SWR Meter. All subsequentSWR Meter readings will be the ratio, in decibels (dB), of the measured power tothe reference level of 0.0 dB (relative power level).

Particular attention must be paid to the adjustment of the probe depth inside theSlotted Line. If the probe penetrates too deep into the Slotted Line, the fielddistribution can be distorted, especially when the SWR is high. Moreover, the probe'scrystal detector is then more likely to operate outside of its square-law region,causing the measurements to be erroneous.

To obtain a good accuracy of measurement, the tuning of the amplifier frequencyof the SWR Meter must be readjusted whenever the microwave circuit is modifiedor used for a prolonged period of time, as the central frequency drifts over time. Thedrift in the central frequency of the SWR Meter’s amplifier is due, among otherthings, to variations in ambient temperature and equipment temperature.

Similarly, the SWR Meter's reference may vary slightly over time. Small drifts areacceptable. However, it is recommended that you verify the reference from time totime and readjust it to 0.0 dB, to maintain a good accuracy of measurement.

INSTRUCTIONAL PLAN

A. Explain how standing-wave patterns are formed from two waves travelling inopposite directions:

1. Waves of the same frequency and amplitude (produce a pure standing wave).2. Waves of the same frequency, but different amplitude (produce a

standing-wave pattern).

B. Describe a standing-wave pattern showing the minima and maxima. Emphasizethe fact that the distance between successive minima or maxima is equal to halfthe guided wavelength of the microwave signal.

C. Briefly explain that the size of the reflected wave depends on the mismatchbetween the characteristic impedance of the waveguide system and theimpedance of the load.

D. Briefly explain the standing-wave ratio. (More will be said about the SWR inExercise 10):

E. Familiarize the students with the Slotted Line.

F. Explain how to use the SWR Meter of LVDAM-MW to perform measurementswith the Slotted Line, and the startup procedure to perform.

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34

G. Explain how the Slotted Line and the SWR Meter are used to determine theguided wavelength of the microwave signal:

1. Measure the distance between successive minima. Also explain why minimaare used rather than maxima.

2.

where c = velocity of propagation of the signal in free space (3.0 @ 108 m/s);λg = wavelength of the signal in the waveguide (m);a = width of the waveguide, equal to 0.0229 m;f = frequency of the signal in the waveguide (Hz).

DEMONSTRATIONS

• Show why minima of the standing-wave pattern are used to determine thewavelength of a signal in the guide. You could use a sketch of a standing-wavepattern and a set-up with a Slotted Line and a Fixed Short Circuit. Show that theprecise location of a minimum is much easier to determine than that of amaximum.

• By changing loads, show that, although the standing-wave pattern may shift andits amplitude may vary, the distance between minima and maxima remainsconstant.

PRESENTATION AIDS

1. Use diagrams to show how a standing-wave pattern is formed. Many textbookshave diagrams that might prove helpful.

2. Use the explanations given above to explain how to use the SWR Meter with theSlotted Line and how to perform the startup procedure.

Bibliography

BADENFULLER, A.J., Microwaves: An Introduction to Microwave Theory andTechniques, 2nd Edition, Oxford, U.K., Pergammon Press, 1979.ISBN 0-08-024297-8

CHEUNG, W.S., LEVIEW, F.H., Microwave Made Simple. Principles andApplications, Dadham, Mass (U.S.A.), Artech House Inc., 1985.ISBN 0-89006-173-4

CROSS, A.W., Experimental Microwave, Stevenage, U.K., Marconi Instruments Ltd.,1977.

GANDHI, O.P., Microwave Engineering and Applications, Elsmsford, New York,Pergamon Press Inc., 1981.ISBN 0-08-025588-4

GARDIOL, F., Hyperfréquences, Paris, France, Dunod, 1987.ISBN 2-04-016953-9

GRIVET, P., Physique des Lignes de Haute Fréquence et d'Ultra-Haute Fréquence,Paris, France, Masson et Cie, 1969.

GUPTA, K.C., Microwaves, New Delhi, India, Wiley Eastern Ltd., 1979.ISBN 0-85226-346-5

JOUQUET, M., Ondes Électromagnétiques – Vol. 2: Propagation Guidée, Paris,France, Bordas-Dunod, 1973.ISBN 2-04-010141-1

KENNEDY, G., Electric Communication Systems, 3rd Ed., New York, N.Y. (U.S.A.),McGraw Hill Book Co., 1985.ISBN 0-070-34054-4

LAVERGHETTA, T.S., Handbook of Microwave Testing, Dadham, Mass (U.S.A.),Artech House Inc., 1981.ISBN 0-89006-070-3

LIAO, S.Y., Microwave Devices and Circuits, Englewood Cliffs, New Jersey (U.S.A.),Prentice Hall Inc., 1980.ISBN 0-13-581297-0

VASSALLO, C., Théorie des Guides d'Ondes Électromagnétiques – Tome 1 etTome 2, Paris, France, Éditions Eyrolles, 1985.

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