MICROWAVE MEASUREMENT by PolisasLib3

MICROWAVE MEASUREMENT

NOOR HAYATI BINTI HAMZAH Published by POLITEKNIK SULTAN HAJI AHMAD SHAH SEMAMBU 25350 KUANTAN Copyright ©2021, by Politeknik Sultan Haji Ahmad Shah Materials published in this book under the copyright of Politeknik Sultan Haji Ahmad Shah. All rights reserved. No part of this publication may be reproduced or distributed in any form or by means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of the publishers.

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MICROWAVE MEASUREMENT

Contents ACKNOWLEDGEMENT .......................................................................................................... 3 PREFACE ................................................................................................................................... 4 3.0 INTRODUCTION ................................................................................................................ 5 3.1 EQUIVALENT CIRCUIT .................................................................................................... 5 3.2 TRANSMISSION LINE PARAMETERS AND EQUATIONS .......................................... 6 3.2.1 Line parameters ............................................................................................................. 6 3.2.2 Impedances .................................................................................................................... 7 3.2.3 STANDING WAVE ...................................................................................................... 9 3.3 TYPE OF MICROWAVE MEASUREMENT................................................................... 12 3.3.1 Block diagram of Microwave testing .......................................................................... 12 3.3.2 The functions for each block in Figure 3.3.0. .............................................................. 12 3.3.3 Type of microwave measurement............................................................................... 13 3.4 SMITH CHART ................................................................................................................ 18 3.4.1 Smith Chart Parameters ............................................................................................... 19 3.4.2 Scale for length or distances (Figure 3.4.2) ................................................................ 22 3.4.3 VSWR and Reflection coefficient of the transmission line ......................................... 22 3.4.4 Admittances on the Smith Chart .................................................................................. 26 3.4.5 Distance from load to Vmax and Vmin of the standing wave ......................................... 26 3.4.6 Input impedance Z IN ................................................................................................... 29 3.4.7 Stub matching .............................................................................................................. 30 PROBLEMS ............................................................................................................................. 35 ANSWERS ............................................................................................................................... 36 Exercise 1 : ........................................................................................................................... 36 Exercise 2 ............................................................................................................................. 36 Exercise 3 ............................................................................................................................. 36 Exercise 4 ............................................................................................................................. 36 PROBLEMS 1 ...................................................................................................................... 40 PROBLEM 2 ........................................................................................................................ 41 PROBLEM 3 ........................................................................................................................ 42 REFERENCES: ........................................................................................................................ 43

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MICROWAVE MEASUREMENT

ACKNOWLEDGEMENT In the name of Allah, the Most Gracious and the Most Merciful, Alhamdulillah and ll the praises to Allah for the strenghth and His Blessing which enabled us to complete the documentation of this eBook. I would like to express our appreciation to our POLISAS Head of Electrical and Engineering Department , Head of DEP program for their support and encouragement in producing this eBook. Thank you as well to Mr Nor Shukor Ali who is patiently giving advices along the way. My gratitude also to family and friends who have been involved either directly or indirectly because without their supports, this eBook would not have been completed.

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MICROWAVE MEASUREMENT

PREFACE The contents of this eBook is written based on the Malaysian polytechnic syllabus for DEP50043 MicroDevices course taken by Electrical and Electronic Engineering (Communication) students. There are four topics in this course. Each topic will be compiled in eBook format separately. So the first compilation of this eBook is related to topic 3 , titled Microwave Measuremet. The content of the eBook is divided into 3 sections which begin with a description related to the transmission line that carries the signal in the highest frequency in the form of an equivalent circuit consisting of the lump parameters. Next is a description on types of measurements performed on microwave systems. The third section deals with the Smith chart that is used to simplify the calculation of transmitter line parameters without using equations. Exercises and probles are also provided to test the readers’s understanding and the answers are given at the end of the chapter. We hope this eBook will be useful to the students, instructors as well as others interested in microwave measurement. We welcome feedback and comments for further improvement.

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MICROWAVE MEASUREMENT 3.0 INTRODUCTION Figure 3.0 show a simple microwave communications link that uses a beam of radio waves in the microwave frequency range to transmit information between two fixed locations on the earth. The transmission line carries the signal from the transmitter to the antenna and, at the receiving end of the link, from the antenna to the receiver. In electrical engineering, a transmission line is anything that conducts current from one point to another. In low frequency circuit, the transmission line(wire) does not effect the power transfer since the wire that connect the components have zero resistance.

Figure 3.0: Simplified block diagram of microwave communication Link from location A to location B. (https://www.eeeguide.com/microwave-link-in-electroniccommunication)

However, at microwave frequencies, those media excessively weaken the signal. Thus, special transmission lines are used such as hollow pipes called waveguides. At high frequency the length of the transmission line will significantly effect the propagation of the signal and therefore, the behavior of the transmission is analyzed using transmission line theory.

3.1 EQUIVALENT CIRCUIT In transmission line theory, the transmission line is represented by an equivalent circuit as shown in Figure 3.1.0 , with its electrical properties characterized by groups of parameters such as resistance R, inductance(L), Capacitance(C) and Conductance (G) that are distributed uniformly along the line. Generator

𝐕𝐆

Load

Transmission Line

𝐙𝐋

Figure 3.1.0: The equivalent circuit to representation the transmission line. Page 5

MICROWAVE MEASUREMENT

Figure 3.1.1 shows how the distribution of the transmission parameters within the small section of the line, dz, that is consist of series resistance and inductance with parallel conductance and capacitance, and this lumped parameter is repeated or distributed uniformly along the length of transmission line .

Figure 3.1.1: Distributed (lumped) parameters within the transmission line. (http://www.amanogawa.co m/archive/docs/C-tutorial.pdf)

3.2 TRANSMISSION LINE PARAMETERS AND EQUATIONS 3.2.1 Line parameters Parellel parameters  C-Shunt Capacitance (F/m)  G-Shunt conductance (S/m)

Series parameters  R- Series Resistance per unit length (Ω/m)  L - Series Inductance perunit length (H/m)

Figure 3.1.2: The series parameters and parallel parameters within the small part dz of the transmission line. (http://www.amanogawa.co m/archive/docs/C-tutorial.pdf)

Figure 3.1.2 shows the lumped parameter in series and parallel within the small part of the transmission line dz where; 

parameter R represent the loss of the conductor due to material, width, height, and length of the conductor.



represent the layout of the conductor



represent dielectric material used inside the transmission line Page 6

MICROWAVE MEASUREMENT 

represent the loss of the dielectric

Combination of the series and parallel parameters present an opposition to the current flowing through the line and is called an Impedance Z, where 𝑍 = (𝑅 ∓ 𝑗𝑋) 𝑜ℎ𝑚 A measure of how easily a circuit or device will allow a current to flow is called an admittance Y, where, 𝑌=

1 = (𝐺 ∓ 𝑗𝐵) 𝑆 𝑍

Therefore, admittance can be calculated from given impedance Z and vice versa.

EXAMPLE 1: (a) Determine the admittance Y1 for the given Z1= (100 + j50) Ω and

(b) Z2 for given Y2= (0.015 – j0.023) S

(a) Y1 (S) =

1 1 = = ⋯… Z1 100 + j50

(𝑏) 𝑍2 ( ) =

1 1 = = ⋯… 𝑌2 0.015 − 𝑗0.023

3.2.2 Impedances In high frequency transmision line, signal propagates inside the line using electromagnetic wave. The input signal will be referred as incident wave that will travel along the transmission line of length l. When the wave reaches the load at the end of the line, part of the wave will be reflected back as shown by Figure 3.1.3. The magnitude or the strength of the reflected wave will be determined by the characteristic of the load.

𝐙𝐢𝐧 Figure 3.1.3: Propagation of signal or wave inside the transmission line where the incident wave is reflected back by the load at the end of the line. Page 7

MICROWAVE MEASUREMENT 3.2.2.1 Characteristic impedance Z0 In high frequency transmission line, the impedance Z, can be also represented by the ratio of E field to the H field of the wave or the ratio of Voltage to Current. If the ratio of voltage amplitude to current amplitude is constant (that a wave travelling in one direction only with no reflection, then, it is called Characteristic Impedance Zo, and can be determine by the following according to type of transmission line 𝑅 + 𝑗𝜔𝐿 Lossy Line 𝑍0 = √ = 𝑅𝑜 + 𝑗𝑋𝑜 𝐺 + 𝑗𝜔𝐶 For lossless line G = R = 0, thus,

Lossless Line 𝑍0 = √

𝐿 𝐶

From the above equations, Zo, is determined by the material of the conductor and the dielectric surrounding the conductor and length of transmission line does not effect the value of Zo 3.2.2.2 Input impedance Zin Generally, the impedance at a position near the generator is not the same as the impedance of the load, because of the presence of the transmission line. It is called input impedance Zin. The input impedance is the impedance of the transmission line at an input position looking towards to the load. The input impedance is determined according to type of transmission line as follows; For lossy line , 𝑍𝐿 + 𝑗𝑍0 𝑡𝑎𝑛ℎ𝛾𝐿 𝑍𝑖𝑛 = 𝑍0 ( ) 𝑍0 + 𝑗𝑍𝐿 𝑡𝑎𝑛ℎ𝛾𝐿 For lossless line , 𝑍𝐿 + 𝑗𝑍0 𝑡𝑎𝑛ℎ𝛽𝐿 𝑍𝑖𝑛 = 𝑍0 ( ) 𝑍0 + 𝑗𝑍𝐿 𝑡𝑎𝑛ℎ𝛽𝐿 Where 𝛾 is the propagation constant 𝛾 = √𝑍𝑌 = √(𝑅 + 𝑗𝜔𝐿)(𝐺 + 𝑗𝜔𝐶) And is also stated in term of attenuation constant α and phase constant β, 𝛾 = 𝛼 + 𝑗𝛽 Page 8

MICROWAVE MEASUREMENT 3.2.3 Standing Wave

When a transmission line is terminated by the load ZL that does not match with the characteristic impedence Zo of the line, not all power is absorbed bt the load. Part of the power will be reflected by the load as shown by Figure 3.2.1. The forward wave(incident) wave mixes with the reflected wave to produce standing wave. The standing wave can be view in terms of current or voltage. The point of minimum value for the standing wave is called nodes and the maximum value is called antinodes. All the nodes are permanently fixed, and the positions of all antinodes are constant. They are separated by half the wavelength of the signal. ANTINODE NODE

Figure 3.2.1: Creation of standing wave due to short circuit termination How well matched the load is to the transmission line or receiver can be measured by the following parameters with respective equations. 3.2.3.1 Reflection coefficient Г At any point of the transmission line reflection coefficient is defined as magnitude of the reflected voltage to incident voltage; Reflection coeficient Г =

ZL − ZO SWR − 1 = = |Г| 𝑒 𝑗𝜃 = |Г| < 𝜃 ZL + ZO SWR + 1

3.2.3.2 Voltage Standing Wave Ratio, VSWR Voltage standing wave ratio is a ratio of maximum value to the minimum value of the standing wave pattern ; VSWR =

Vmax Imax =√ Vmin Imin

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MICROWAVE MEASUREMENT Voltage Standing Wave Ratio, VSWR is a ratio of maximum value to the minimum value of the standing wave pattern ;

Г =

SWR − 1 1+ Г … … … … … … … VSWR = SWR + 1 1−Г

The greater the mismatch between line and load, the higher the SWR will be between generator and line. In practical lines, power loss increases with SWR, and so a low value of standing wave ratio is always sought, except when the transmission line is being used as a pure reactance or as a tuned circuit.

Figure 3.2.2 (a) show a standing wave due to short circuit load while Figure 3.2.2(b) show standing wave for load ZL with resistance value larger that Zo. ZL= Zsc

V I

λ/2

Distance along the line l

Figure 3.2.2(a) : Lossless line terminated with short circuit load Zsc. (https://www.eeeguide.com/standing-waves-in-transmission-lines/)

A half-wavelength from the load is a point at which there will be a voltage zero and a current maximum. These conditions will repeat at half-wavelength distances, as shown in Figure 3.2.2(a). The same conditions apply if the load is an open circuit in Figure 3.3(b), except that the first current minimum (and voltage maximum) is now at the load, instead of a quarter-wavelength away from it. ZL= RL> Zo

V I

λ/2 Distance along the line l

Figure 3.2.2(b) : Lossless line terminated in pure ressitance greater than Zo. (https://www.eeeguide.com/standing-waves-in-transmission-lines/) Page 10

MICROWAVE MEASUREMENT Table 3.0 The relationship between reflection coefficient and standing wave ratio for different type of termination or load.

Table 3.0: The relationship between type of load, reflection coefficient and standing wave ratio. Reflection Load VSWR coefficient REMARK Z σ L Г Matching load, ZL = Z 0

Г=0 ⃒Г⃒ = 0

σ=1

No reflection - only have incident wave.

General case ZL = R ± jX

Г = ⃒Г⃒ ∠θ°

σ >1

Reflection occurs – refelected wave at arbitrary phase

short circuit, ZL = 0;

Г = -1 ⃒Г⃒ = 1, θ = 180°

σ=0

Due to phase reversal of reflected wave, i.e change of phase , the incident and reflected wave will be cancelled.

open circuit ZL = ∞

Г=1 ⃒Г⃒ = 1, θ = 0°

σ=∞

Reflection occurs because the incident and reflected waves are in phase.

EXAMPLE 2: Calculate the reflection and VSWR for the transmission line with characteristic impedance Z o = 50Ω that is terminated with load ZL = 100 + j50 Ω. Г =

ZL − ZO ZL + ZO (100 + j50) − (50) 50 + j50 70.7 < 45 = = = 0.447 < −44.6 (100 + j50) + (50) 150 + j50 158.114 < 89.6

VSWR =

1 + |Г| 1 − |Г| 1 + 0.447 = 2.62 1 − 0.447

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MICROWAVE MEASUREMENT 3.3 TYPE OF MICROWAVE MEASUREMENT There are two categories for microwave measurement; i. Gred 1 – to get accurate data or readings with error less tah 5%. ii. Gred 2 – to observe the characteristic or behaviour of the signal Measurement for the high frequency signal involves special components that are required to be assembled on a flat surface. All the components have to be assembled together by screwing together the components and all components must be aligned with each other as to prevent signal leaking at the joints (the connected part). High frequency signal propagates throughout the waveguide in various mode. Mode is a pattern or configuration of electric field E and magnetic field H of the signal that propagate inside the waveguide. Most test bench uses rectangular waveguide as the transmission line and propagation dominant mode TE 1,0. Microwave system also require special components called basic accessories for special purposes, for example when the direction of the signal or the polarization of the signal need to be changed. The basic accessories must come with a specific dimension and shape in order to minimize the internal reflection or to reduce the VSWR that will occur inside this irregular shape. Figure 3.3.1 shows the assembling of block diagrams for components to perform measurement for the system

3.3.1 Block diagram of Microwave testing Uwave Source

Isolator

Attenuator

Wave Meter

Power Meter

VSWR Display

Directiona l Coupler

Slotted Line

Tuner

Terminatio n

Figure 3.3.1 : A block diagram for Microwave measurement.

3.3.2 The functions for each block in Figure 3.3.0. Block Microwave source Isolator

Function To produce carrier wave(signal) in microwave spectrum. To block the reflected wave that travel back to the generator/source. The wave which travel in opposite direction will be attenuated. Page 12

MICROWAVE MEASUREMENT Attenuator Wave meter Directional Coupler Power meter Slotted line and diode detector VSWR meter Tuner Termination

To control the power level in the system to a suitable value. To measure the frequency in the system To divide the signal with certain ratio to Power meter for power measurement To measure power in the system To sampled the strength of the signal and sent to VSWR display. To show the value of VSWR generated in the system To allow the correct frequency exist in the system To terminate the system with match or short circuit or open circuit or complex load.

3.3.3 Type of microwave measurement. 3.3.3.1 Frequency measurement using Wave Meter A measurement to make sure that the oscillator or source produces a signal with a correct frequency. Basic method used is a meter with resonant cavity. Figure 3.3.2 shows a structure of a Wave Meter with resonant cavity. Different frequency will oscillate inside different volume of the resonant cavity.

Micrometer Plunger Plunger

Figure 3.3.2: Internal structure of Frequency meter (Microwave Trainer Feedback MWT)

Operation: Figure 3.3.3 shows the blocks diagram to measure frequency of microwave signal. Microwave signal is generated by the microwave source. The level of power of the generated signal is controlled by the attenuator to a suitable value that can be displayed within the range of of ampere meter. The signal generated in the system is sampled by the diode detector probe mounted onto slotted line. The samples signal is rectified by the diode and then Page 13

MICROWAVE MEASUREMENT displayed by ampere meter. The system is then terminated with appropriate impedance. Meter Ampere

Source

Attenuator

Wave meter

Slotted line & Diode Detector

Termination

Figure 3.3.3: Block diagram for frequency measurement The volume of resonant cavity is controlled by the plunger. The plunger is connected directly to the micrometer anad the rotation of micrometer will adjust the depth of the plunger inside the cavity. When the resonant frequency of the cavity is the same as the frequency of the signal that propagate inside the waveguide, a large amount of signal that propagate along the waveguide will be absorbed by the cavity. Thus, only small amount of signal will continue to propagate through the waveguide and sampled by diode detector. At this moment, the meter ampere will show the decreasing of reading as shown by Figure 3.3.4(a) (or DIPPING in meter ampere reading has occurred). The reading of the micrometer is recorded and is used with Frequency-calibrated Chart in Figure 3.3.4(b) to get the value of frequency in GHz.

Figure 3.3.4(a) : Dipping of power output detected during resonant (Microwave Trainer Feedback MWT) Frequency(GHz)

Micrometer (mm)

Figure 3.3.4(b) : Calibrated Chart - Micrometer vs frequency Page 14

MICROWAVE MEASUREMENT 3.3.3.2 VSWR measurement using Slotted Line with Diode Detected When the system is terminated with unmatched termination, the standing wave will be generated. Figure 3.3.5(a) shows standing waves generated by different unmatched termination. Standing wave can be represented by current, voltage or power. Standing wave consist of sequences of maximum(max) and minimum(min) values. The distance between the max and min value is half of guide wavelength λg/2. ZL= Zsc

λ/2

Figure 3.3.5(a) : Lossless line terminated with short circuit load Zsc. https://www.eeeguide.com/standing-waves-in-transmission-lines/

The slotted line is a waveguide with a narrow axial slot cut in the centre of the broad section of the guide, as shown in Fig 3.6.6. This narrow slot is in the position of non-radiating and causes negligible distortion to the wave within the guide. The sampling of signal is done by the probe connected to the diode detector. The diode detector then rectifies the sampled microwave signal and the rectified current is shown by the DC milliammeter.

Slotted section

Crystal Detector Carriage

Probe Figure 3.3.5(b): The internal structure of Diode detector mounted on slotted section. (Microwave Trainer Feedback MWT)

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MICROWAVE MEASUREMENT

The selection of suitable method to measure VSWR depends on whether the Diode detector is operating whithin its Square-law characteristic , that is i = kv2 , where, i – the current detected by diode detector v – rf voltage propagate in the system. Operation: Figure 3.3.5(c) is the block diagram to measure VSWR. Microwave signal is generated by the microwave source. The level of power of the generated signal is controlled by the attenuator to a suitable value so that can be displayed within the range of by meter ampere. Standing wave generated in the system is sampled by the diode detector probe mounted onto slotted line. The samples signal is rectified by the diode and then displayed by meter ampere. The tuner is set so that only the signal with the right frequency is exist in the system. Termination that has impedance not equal to characteristic impedance will generate standing wave in the system.

Uwave Source

Attenuator

Diode Detector

Meter Ampere

Slotted Line

Tuner

Terminatio n

Figure 3.3.5(c): Block diagram for VSWR measurement.

There are TWO ways to measure VSWR: i. Direct Method – is used for the diode detector that operate with Squarelaw characteristic. The detector is slided along the slotted line to detect the maximum and minimum current or voltage. These values are used with the following formula to get the VSWR value, 2 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒 𝐼𝑚𝑎𝑥 𝑣𝑚𝑎𝑥 𝑣𝑚𝑎𝑥 √ √ 𝑉𝑆𝑊𝑅 = = √ = = … … … … . (1) 2 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒 𝐼𝑚𝑖𝑛 𝑣𝑚𝑖𝑛 𝑣𝑚𝑖𝑛

ii. Double Minimum Method –is used for a large value of VSWR, typically > 3. The detector current will become very small and the ratio of formula (1) is increasingly difficult to measure accurately, that is the diode does not operating with its squre-law characteristic. Thus, we use the method based on locating the minimums and the distance between points at Page 16

MICROWAVE MEASUREMENT which the value is twice the minimum value. By referring to Figure 3.3.5(d);  Slide the detector somewhere to the middle position of the slotted line so that it can detect one Imin value of the standing wave. Take the reading of the slotted line and this position is called x0 .  From position x0 , slide the detector to the right until it ampere meter shows a value of 2xImin. Record the slotted line at this position, x1.  From position x1 , slide the detector to the left, passing by x0 to a position where ampere meter shows another value of 2xImin. Record the slotted line at this position, x2.  From position x2 , slide the detector further down to the left, until the ampere meter shows the next Imin value Record the slotted line at this position, x3.  Use the slotted line position from above steps with the following formula to calculate the VSWR.  Sketch the standing wave with the output voltage values vs slotted line readings from above steps, Figure 3.5.

𝑉𝑆𝑊𝑅 = √1 +

∝=

1 1 = 1 + … … … … … (2) √ 𝜋𝑑 𝑠𝑖𝑛2 ∝ 2 𝑠𝑖𝑛 λ𝑔

𝜋𝑑 𝜋 ∣ (𝑥2 − 𝑥1 ) ∣ = … … … … … … … … … … … . (3) λ𝑔 2 ∣ (𝑥3 − 𝑥0 ) ∣

Detector Output

V2max

2V2min

V2min

X2 X1

Position on Slotted line(mm)

Figure 3.3.5(d) : Standing wave for Double Minimum Page 17

MICROWAVE MEASUREMENT 3.4 SMITH CHART Philip H. Smith

Philip H. Smith develop a simple graphic tool called SMITH CHART, in order to avoid the tedious solution methods in calculating the transmission Line parameters using equations.

Figure 3.4.0 : Thestandard Smith (Charthttps://www.digikey.be/nl/articles/the-smith-chart-an-ancientgraphical-tool-still-vital-in-rf-design)

Smith Chart is a circular graph with rectangular and polar coordinate and is used to solve transmission line problems.

Application of Smith Chart are: (a) Impedances(Z), Admittances(Y  Position of ZL from ZIN and viceversa.  Position of YL from YIN and viceversa (b) Standing wave ratio VSWR  

Value of SWR Distance of maximum Dmax and minimum Dmin value on the standing wave from the Load (c) Reflection coefficients  Magnitude |Г|  Angle < 𝜃 (d) Matching  

Parallel technique Single stub Page 18

MICROWAVE MEASUREMENT 3.4.1 Smith Chart Parameters Smith chart consists of transmission line parameters such as normalized impedance, Z’ (the most common) or normalized admittance, Y’ or both. The normalized parameters are constructed on the complex reflection coefficient plane in two dimensions, that is using rectangular (i,j) and polar (r,ϴ) scale. Normalized scaling allows the Smith chart to be used for problems involving various characteristic impedance /admittance for various transmission line or systems. Figure 3.4.1 shows separately the Smith Chart parameters that are: (a) the normalized resistances circles, where the value of the circles is shown by the horizontal line begin with 0 on the left of the green line and increasing to the right. (b) the normalized reactance curves, where the value of the curve is shown at the edge of the circle; i. half circle in red to represent pure inductive reactance + jxL(pure inductive susceptance, + jbL) ii. half circle in blue to represesny pure capacitive raectance -jxC (pure capacitive susceptance, - jbC)

(a)

(b) Figure 3.4.1: Elemen of Smith Chart - (a) Sets of normalized resistance(r)/conductance(g), and (b) set of normalized reactance(x)/susceptance(b) that touch at a point on the righthand side Page 19

MICROWAVE MEASUREMENT

Figure 3.4.1(c): The basic graphical elements of the Smith chart are circles that touch at a point on the right-hand side to represent real part R of a complex impedance Z = R + jX, and arcs. (Charthttps://www.digikey.be/nl/articles/the-smith-chart-an-ancientgraphical-tool-still-vital-in-rf-design)

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MICROWAVE MEASUREMENT

EXERCISE 1: Express the value of the normalized impedance based on the locations given in Figure E3;

Figure E3

EXERCISE 2: Gives the name for the elemen of Smith Chart labeled A, B, C and D. A

Figure E4 Page 21

MICROWAVE MEASUREMENT 3.4.2 Scale for length or distances (Figure 3.4.2) Figure 3.4.2 shows the real Smith Chart template that shows the sets of normalized resistance circles and normalized reactance, the related scales on the chart and also the radially scaled at the bottom of the chart. Length or distances of the transmission line is measure in metric. In order for Smith Chart to be used for various length of transmission line, the length in metric is converted to the wavelength of the signal. The Smith chart has circumferential scaling in wavelengths and degrees; o the wavelengths scale represents the distance measured along the transmission line connected between the generator or source and the load to the point under consideration. o 1 complete circle (rotation) of Smith Chart is equal to 1 ʎ o conversion OF LENGTH FROM ʎ to metric is calculated from the freqency of the signal that propagate inside the transmission line

3.4.3 VSWR and Reflection coefficient of the transmission line The following list is the steps that need to be followed to obtain the VSWR value due to the load that does not match the characteristic impedance of the transmission line system (Figure 3.4.3(a) and (b)) 1. Normalized the real impedance (Ω) with the transmission line characteristic Zo. 2. Trace the normalized resistance, r 3. Trace the normalized reactance, x 4. The meeting point between these two parameter will give the normalized impedance Z’ = r ± jx 5. Draw the VSWR circle with the centre is at point 1.0 of the chart and the radius is the length from the poin 1.0 to the Z’ location. 6. The intersection of this VSWR circle with the right side of resistance scale will give the value of VSWR. 7. Measure the radius of VSWR circle 8. Map the radius of the VSWR circle onto the radial scale at the bottom of the chart titled “RFL COEFF, E OR I” to get the value of MAGNITUDE of reflection coefficient. Page 22

MICROWAVE MEASUREMENT 9. Extend a straight line from the centre of the chart (1.0,0) outward to Z’ and ends at “Angle of reflection coefficient in degree” to get the ANGLE of reflection coefficient

SCALE WAVELENGTH

r = 0.22 SCALE REFLECTION ANGLE

x = -j 2.5

CENTRE

VSWR

Figure 3.4.2: Real template Smith Chart with normalized resistance circle, normalized reactance curves and related scales

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MICROWAVE MEASUREMENT EXAMPLE 3

The above transmission line with length L has a characteristic impedance of 50 Ω and is terminated by load 60 +j 70 Ω. Use Smith Chart to determine: (a) VSWR (b) Reflection coefficient at the load. ZL 60 + j70 Normalized ZL′ = = = 1.2 + j1.4 ZO 50 Trace the resistance 1.2 circle and reactance +j1.4 curve on Smith chart. The intersection between these two parameter is the location of ZL’ as shown by Figure 3.4.3(a). Draw the VSWR circle (red circle) and the intersection between red circle and the right side of resistance circle gives the value of VSWR = 3.3

Figure 3.4.3(a): VSWR circle and its value for a 50 Ω lossless transmission line that is connected to an antenna of impedances 60 +j 70 Ω. Page 24

MICROWAVE MEASUREMENT

Figure 3.4.3(b): The radially scaled parameter- use SWR scale to get the VSW value in unitless or dBs and the magnitude |Г| of reflection coefficient.

Map the radius of the VSWR circle onto the radial scale at the bottom of the chart and the magnitude of reflection coefficient |Г|=0.53 Extend a straight line from the centre of the chart (1.0,0) outward to ZL’ and ends at “Angle of reflection coefficient in degree” scale and ѲL= 49֯ (Figure 3.43(c))

Figure 3.4.3(c) : A straight line from centre of chart at 1.0 to the Angle of reflection scale to get the angle of the reflection coefficient Ѳ = 49 ֯

Page 25

MICROWAVE MEASUREMENT 3.4.4 Admittances on the Smith Chart The admittances of the system is located on the same VSWR circle of the impedances but at 180֯ away from the impedance location. Step to determine Admitances is shown by Figure 3.4.4. 1) Normalized the real impedance (Ω) with the transmission line characteristic Zo. 2) Trace the normalized resistance, r and trace the normalized reactance, x 3) The meeting point between these two parameter will give the normalized impedance Z’ 4) The admittance is located at 180° from load impedance on VSWR circle.

EXERCISE 3: Show the location of the NORMALIZED ADMITTANCE Y’ for following impedances and NORMALIZED IMPEDANCE Z’ FOR THE FOLLOWING admittance on the Smith Chart if the characteristic impedance is 50 Ω. a) Z1 = (100 + j50) Ω c) Z3 = j200 Ω b) Z2 = (50 –j25) Ω d) Z4 = 150 Ω

a) Y1 = 0.02 S b) Y2 = (0.015 – j0.023) S

c) Y3 = (0.024 + j0.006) S

3.4.5 Distance from load to Vmax and Vmin of the standing wave Step to determine Vmax and Vmin of the standing wave for termination with load ZL: Figure 3.4.5; 1) Normalized ZL and then trace circle r and curve x. 2) Draw VSWR circle for the normalized load. 3) Draw straight line from the centre of chart at 1.0 toward z L and to the outer wavelength scale, PL. 4) To get the first position of Vmax from the load - rotate in clockwise direction from PL to the position of Pmax. 5) The distance of the first Vmax from the normalized load is the distance Dmax = (B)Pmax - (A) PL. 6) For first Vmin , continue rotating in clockwise direction from PL to the position of Pmax. and continue till reach position (C)Pmin. 7) Distance Dvmin = Pmin - Pload Page 26

MICROWAVE MEASUREMENT EXAMPLE 3…CONTINUE - Determine the load admittance on the Smith chart

ZL’ = 1.2+j1.4

𝒀′𝑳 =0.36-j0.41

Figure 3.4.4: Location of normalized load admittance yL is on the same VSWR circle of the normalized load but at a pooint of 180 from the load z L.

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MICROWAVE MEASUREMENT EXAMPLE 3…CONTINUE - Use Smith Chart to determine Dmax and Dmin

Figure 3.4.5: Measurement of distance for Vmax and Vmin from the load Page 28

MICROWAVE MEASUREMENT 3.4.6 Input impedance Z IN Step to determine Zin from termination with load ZL: Figure 3.4.6; 1) Distance input impedance from load impedance is PZIN = PZL + L 2) Draw a straight line from point PZIN back to centre point of chart 1.0. 3) The intersection of this straight line with the VSWR circle is the reading of Z’IN values. 4) The real value ZIN (Ω) = (Zo)(Z’IN)

Figure 3.4.6: Position of normalized ZIN from the ZL

EXERCISE 4: Determine the following for impedances (a) and (b) in Exercise 3 for transmission line of length 0.12λ; (a)

the Vmax and Vmin of the standing wave

(b)

the real input impedance Zin Page 29

MICROWAVE MEASUREMENT 3.4.7 Stub matching Impedance matching in a transmission lines is done to prevent reflections along an interconnect as well as by the load. Impedance matching can be achieved by inserting another transmission line (or known as stub) to the main transmission line. Matching can be done by using one or more stub and is called ‘stub matching’.

The stub can be connected in parallel or series to main line. The stub can be a short or an open circuit stub. It is convenient to work with admittance, when placing a stub parallel with the line and load as shown by Figure 3.4.7(a) and (b). Whereas Figure 3.4.7(c) show the summary of steps taken to perform the stub matching.

Figure 3.4.7 (a) Stub is connected in parallel to the load and the line parameters to be determine.

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MICROWAVE MEASUREMENT

Figure 3.4.7(b): Impedances are converted to admittances for easy calculation.(Amogawa,2006-Digital Maestro Series)

Figure 3.4.7(c): Summary of steps and parameters to be calculated for matching purpose.(Amogawa,2006-Digital Maestro Series) Step to matched the transmission line: Figure 3.4.7(d); Page 31

MICROWAVE MEASUREMENT 1) Normalize ZL and Locate ZL on the chart 2) Draw (SWR) circle and locate YL at the opposite site of the same VSWR circle. 3) Trace circle g=1 4) Find intersection of  circle and g=1 circle (ydstub1) and draw the straight line fron poin 1.0 to Ydstub1 till the λ scale. This is a normalized line admittance ydstub1 = 1 + j1.4 5) Find distance traveled (WTG) to get to this admittance, that is dSTUB1 =PYdstub1 – PYL dSTUB1 = 0.166 – 0.101 = 0.065

PYL = 0.101

PYdstub1 = 0.166

ydstub1

Figure 3.4.2 : The real Smith Chart

Figure 4.3.7(d)

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MICROWAVE MEASUREMENT 6) Identify the normalized input admittance of stub ySTUB1 = 0 - jbStub1 = 0 – j1.4 7) Locate short circuit stub PSC 8) LSTUB1 =The distance traveled (WTG) from PSC to PYSTUB1=0.348 - 0.25 = 0.098 .

**Our solution is to place a short-circuited stub of length 0.098 a distance of .065 from the load.

PSC

ydstub1 = - j1.4

PYstub1 = 0.348 FOR MATCHING , WE NEED TO bstub1 = -j bdstub1

Figure 4.3.7(d)

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MICROWAVE MEASUREMENT There is a second solution where the  circle and g=1 circle intersect. From Figure 4.3.(e), this is also a solution to the problem, but requires a longer dstub and Lstub so is less desireable, unless practical constraints require it. dstub2 = (0.328 - 0.101)= 0.227 Lstub2 = (0.25 + 0.151) = 0.351

PYL = 0.101

ystub2

yL ydstub1

PSC

ydstub2

PYdstub2 = 0.328

Figure 4.3.7(e)

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MICROWAVE MEASUREMENT PROBLEMS (1)

Apply Smith chart to get the following line parameters if the reflection coefficient of the load is 0.4< -46֯ and the characteristic of the transmission line is 50Ω.

(2)

The following lossy transmission line has a characteristic impedance of 50Ω and is terminated with a horn antenna ZL = 12 + j25 Ω. Illustrate by using Smith Chart, how to determine the parameters shown on the transmission line, in oder to match the transmission line with parallel connected stub.

Ydstub1 Dstub1

Ystub1 YL

Lstub1

(3)

To ensure an optimum transmission of a signal, the impedance of a transmitted antenna must be as close as to the characteristic impedance of the transmission line Zo. As a trainee technician in Telco Sdn. Bhd, you are assigned to determine the VSWR produced in this 50 Ω communication system. The antenna is a parabolic antenna with normalized admittance YL’= 0.3 + j 0.6. Then, using the same Smith Chart, you need to investigate how to match the antenna to the system by using a single closedcircuit stub which is connected in parallel to the transmission line. Your answer must include TWO (2) possible stub positions and the designated stub lengths.

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MICROWAVE MEASUREMENT ANSWERS Exercise 1 Normalized impedances for following locations on Figure E1 are: Green point = 0.2 + j0.5 Black point = 0.0 + j0 or short circuit Blue point .0 - j0.5 Red point = 1.0 - j0.2 Orange point = 1.0 – j 1.0 Yellow point = infinity Light blue = 2 + j2

Exercise 2 A – Normalized resistance/conductance circles B – Scale for normalized capacitive reactances/inductive susceptance C – Scale for normalized inductive reactance/capacitive susceptance D – Normalized capacitive reactance/inductive susceptance curves

Exercise 3 Refer Attachment Exercise 3

Exercise 4 Refer Attachment Exercise 4

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MICROWAVE MEASUREMENT ATTACHMENT Exercise 3

X X X

𝑧1 =

100 + 𝑗50 = 2 + 𝑗1 50

𝑦1 = 𝑌1 𝑍𝑜 = (0.02)(50) = 1

𝑧2 =

50 − 𝑗25 = 1 − 𝑗0.5 50

𝑦1 = 𝑌1 𝑍𝑜 = (0.015 − 𝑗0.023)(50) = 0.75 − 𝑗1.15

Page 37

𝑧2 =

0 − 𝑗200 = 0 − 𝑗4 50

𝑦1 = 𝑌1 𝑍𝑜 = (0.024 − 𝑗0.006)(50) = 1.2 − 𝑗0.3

MICROWAVE MEASUREMENT Continue from Exercise 3

𝑧1 =

50 + 𝑗25 = 1 + 𝑗0.5 50

VSWR = 1.65

𝑧2 =

0 − 𝑗200 = 0 − 𝑗4 50

VSWR = infinity

Page 38

𝑧3 =

150 − 𝑗0 = 3 − 𝑗0 50

VSWR = 3.0

MICROWAVE MEASUREMENT Exercise 4

VSWR=2.6 X

𝑧1 =

100 + 𝑗50 = 2 + 𝑗1 50

𝑧2 =

VSWR = 2.6

VSWR=1.65

50 − 𝑗25 = 1 − 𝑗0.5 50

VSWR = 1.65

Page 39

MICROWAVE MEASUREMENT Problem 1

PVmax= 0.186+0.25 = 0.436λ

PYL’=0.091 λ

yL’ = 0.38 + j0.37

VSWR= 3.0 7

Vmax

ZL’ = 1.35 - j1.29

PZL’WTL = 0.186λ

Dstub1 = 0.172 + 0.84 = 0.585λ

Length stub1 = 0.331 - 0.25 = 0.081λ

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MICROWAVE MEASUREMENT Problem 2

PYL’=0.091 λ PYdstub1’= 0.184λ

ZL’ = 0.24 + j0.5 Ydstub1’ = 1.0 - j1.8 7

Y SC

YL’ = 0.78 + j1.6

Ystub1’ = 0 - j1.8 7 PYstub1’= 0.331 λ

Dstub1 = 0.172 + 0.84 = 0.585λ

Length stub1 = 0.331 - 0.25 = 0.081λ

Page 41

MICROWAVE MEASUREMENT Problem 3

Length stub2 = 0.25 + 0.163= 0.413λ

PYL’=0.091 λ

PYDSTUB1’= 0.18 λ

Ystub2’ = 0 + j1.65 7

YL’ = 0.3 + j0.6 Ydstub1’ = 1.0 + j1.65

Y SC

Ydstub2’ = 1.0 - j1.65 7 ZL’ = 0.28 + j0.525

PYstub1’= 0.341 λ Ystub1’ = 0.0 - j1.65 7

Page 42

Length stub1 = 0.341 - 0.25 = 0.091λ

MICROWAVE MEASUREMENT REFERENCES (1) Annapurna D., Sisir KD. (2001).Microwave Engineering. McGraw Hill. (ISBN0-07-463577-8) (2) Pozar D.M. (2005). Microwave Engineering. John Wiley & Sons, 3rd Edition (3) Amogawa,2006-Digital Maestro Series (4) Microwave Trainer Feedback MWT (5) https://www.eeeguide.com/standing-waves-in-transmission-lines/ (6) Microwave Trainer Feedback MWT (7) Charthttps://www.digikey.be/nl/articles/the-smith-chart-an-ancient-graphical-tool-stillvital-in-rf-design

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MICROWAVE MEASUREMENT

Articles inside

PROBLEMS

3.4.1 Smith Chart Parameters

ACKNOWLEDGEMENT

3.2.2 Impedances

PREFACE