Download CODE/COURSE : EP603/ MICROWAVE DEVICES PROGRAM: DEP

CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
3.1
PROGRAM: DEP
Transmission line characteristics.
In the microwave frequency region, power is considered to be in electric and magnetic
fields that are guided from place to place by some physical structure. Any physical
structure that will guide an electromagnetic wave place to place is called a Transmission
Line.
Transmission lines are distributed devices. RLCG type models are commonly used to
approximate the distributed behavior of a transmission line. The single transmission line
shown below can be modeled by a network consisting of a series resistance and
inductance with parallel capacitance and conductance.
RLCG Model for Single Transmission Line
The different terms included in the model describe the following physical
phenomena:
R Resistive loss of the conductor (transmission line trace). Determined by the
conductance of the metal, width, height, and length of the conductor.
L
Inductive part of the circuit resulting from the layout of the conductors.
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
Determined by the dimensions of the conductor, permeability of the metal, and
layout.
C
Capacitive part of the circuit resulting from the layout of the conductors.
Determined by the permittivity and thickness of the board material and the area
of the conductor.
G
Shunt loss of the dielectric. Determined by the layout of the conductors,
permittivity, loss tangent and thickness of the board material.
General Characteristics of Transmission Line
Propagation delay per unit length (T0) { time/distance} [ps/in] Or Velocity (v0)
{distance/ time} [in/ps]
Characteristic Impedance (Z0)
Per-unit-length Capacitance (C0) [pf/in]
Per-unit-length Inductance (L0) [nf/in]
Per-unit-length (Series) Resistance (R0) [W/in]
Per-unit-length (Parallel) Conductance (G0) [S/in]
Transmission Line Equations
Propagation equation
  ( R  jL)(G  jC)    j
 is the attenuation (loss) factor
 is the phase (velocity) factor
Characteristic Impedance equation
Z0 
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( R  jL )
(G  jC )
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
SPECIAL CASES TO REMEMBER
A: Termnated in
Zo
Zs
Vs
Zo
 Zo
Zo   Zo
0
 Zo
ZoZo
If the end of the transmission line is terminated in a resistor equal in value to the
characteristic impedance of the line as calculated by the formula Z=(L/C)0.5 , then the
voltage and current are compatible and no reflections occur.
B: Short Circuit
C
Vs
:
Zs
Zo
Zo
0 
Z
  ISOLATOR  1
o
0  Zo
Z
O
o
p
e When the end of the transmission line is terminated in a short (RL = 0), the voltage at the
n short must be equal to the product of the current and the resistance.
C
i
r
c
u
i
t
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
Zs

Vs

PROGRAM: DEP
 
1
A
 
Vs
When the line is terminated in an open, the resistance between the open ends of the
line must be infinite. Thus the current at the open end is z
THE REFLECTION AND TRANSMISSION LOSSES.
When the resistive load termination is not equal to the characteristic impedance, part of
the power is reflected back and the remainder is absorbed by the load. The amount of
voltage reflected back is called voltage reflection coefficient.
Γ = Vr/Vi
where Vr = incident voltage
Vi = reflected voltage
The reflection coefficient is also given by
Γ = (ZL - ZO)/(ZL + ZO)
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
VOLTAGE STANDING WAVE RATIO (VSWR).
A standing wave is formed by the addition of incident and reflected waves and has
nodal points that remain stationary with time.
Voltage Standing Wave Ratio:
VSWR = Vmax/Vmin
Voltage standing wave ratio expressed in decibels is called the Standing Wave
Ratio:
SWR (dB) = 20log10VSWR
The maximum impedance of the line is given by:
Zmax = Vmax/Imin
The minimum impedance of the line is given by:
Zmin = Vmin/Imax
or alternatively:
Zmin = Zo/VSWR
Relationship between VSWR and Reflection Coefficient:
VSWR = (1 + | Γ |)/(1 - | Γ |)
Γ = (VSWR – 1)/(VSWR + 1)
 OBJECTIVES:
To survey the fields of microwave measurements.

To provide insight into the concepts behind the measurements.
 The measurement of microwave involves measuring of : Frequency
 Power
 Impedance
 Wavelength
 Attenuation
 Noise
 VSWR

Test equipments required for microwave measurements may be divided into :-
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
TYPES OF MEASUREMENT
EQUIPMENTS
FREQUENCY-DOMAIN
 Wavemeter s (absorption, transmission or reaction).
 Slotted lines.
 Spectrum analyzer, frequency sweepers and frequency counters.
DISPLAY OF TIME-DOMAIN
 Sampling oscilloscope.
 Oscilloscope.
VSWR
 Slotted lines ( direct method or double minimum method)
POWER
 Powermeters.
 Detectors with oscilloscopes.
 Spectrum analyzers.
WAVELENGTH
 Coaxial and waveguide slotted lines
NOISE
 Noise meters.
 Network analyzer – multifunctional test equipment.
 Microwave measurement required a set of test-desk which comprise of 2 types of test-desk i.e : GRED 1
 Are measurement used to obtain Merupakan pengukuran untuk mendapatkan nilai-nilai yang tepat. Ralat
daipada pengukuran ini kurang daripada 5 %.
 GRED 2
 Merupakan pengukuran gelombang mikro secara umum dan bukan bertujuan untuk mendapatkan data-data
yang tepat tetapi hanya sebagai pemerhatian terhadap perlakuan gelombang mikro sahaja.

FIG.1 : BLOCK DIAGRAM OF MICROWAVE TESTDESK LAYOUT :
MICROWAVE SOURCE
POWER METER
ATTENUATOR
WAVEMETER
DIRECTIONAL
COUPLER
VSWR INDICATOR
SLOTTED LINE
TUNER
TERMINATOR
 FUNCTION
 MICROWAVE SOURCE
 Generates microwave source in X-band (8 – 12 GHz); e.g klystron, magnetron or TWT
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
 ISOLATOR /CIRCULATOR
 Allow wave to travel through in one direction while being attenuated in the other direction or it is use to
eliminate the unwanted generator frequency pulling (changing the frequency of the generator) due to system
mismatch or discontinuity. (to prevent reflected energy from reaching the source)
 ATTENUATOR
 Control the amount of power level in a fixed amount, variable amount or in a series of fixed steps from the
from the microwave source to the wavemeter.
 WAVEMETER
 Used to select / measure resonant cavity frequencies by having a plunger move in and out of the cavity
thus causes the the cavity to resonate at different frequencies.
 DIRECTIONAL COUPLER

Samples part of the power travelling through the main waveguide and allows part of its energy to feed to a
secondary output port. Ideally it is used to separate the incident and reflected wave in a transmission line.
 SLOTTED LINE
 Used to determine the field strength through the use of a detector probe that slides along the top of the
waveguide.
 VSWR INDICATOR
 Denotes the value of VSWR measured by the slotted line.
 TUNER
 Allows only the desired frequency to appear at the output. Any harmonic frequencies that appear at the
output are reduced to an acceptable level.
 TERMINATOR
 May range from a simple resistive termination to some sort of deep-space antenna array, active repeater or
similar devices. 3 special cases of transmission line i.e short circuit, open circuit, match impedance.
 FREQUENCY MEASUREMENT
 It is important to select a particular resonance mode( normally that which makes the effective cavity size smallest
i.e that for which the srew is srewed farthest inward) since there are several possible modes of resonances.
 The frquency meter used has a cavity which is coupled to the waveguide by a small coupling hole which is used
to absorb only a tiny fraction of energy passing along the waveguide.
 Adjusting the micrometer of the Frequency Meter will vary the plunger into the cavity. This will alters the cavity
size and hence the resonance frequency.
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
 The readings on the micrometer scales are calibrated against frequency. As the plunger enters the caviy, its
sized is reduced and the frequency increases.
 The wavemeter is adjusted for maximum or minimum power meter readings depending on whether the cavity is
a transmission or absorption type device. With the tarnsmission-type device, the power meter will be adjusted
for a maximum. It only allows frequency close to resonance to be transmitted through them. Other frequencies
are reflected down the waveguide. The wavemeter acts as a short circui for all other frequencies.
 For the absorption-type wavemeter, the power meter will be adjusted for a minimum. Its absorp power from the
line around resonant frequency and act as a short to other frequencies.
 The absorbing material used is to absorb any unwanted signal that will cause disturbance to the system.
 VSWR ( VOLTAGE STANDING WAVE RATIO ) MEASUREMENT
 Used to determine the degree of mismatch between the source and load when the value VSWR ≠ 1.
 Can be measured by using a slotted line. Direct Method Measurement is used for VSWR values upto about 10.
Its value can be read directly using a standing wave detector .
 The measurement consists simply of adjusting attenuator to give an adequate reading, making sure that the
frequency is correct and then using the dc voltmeter to measure the detector output at a maximum on the slotted
section and then at the nearest minimum.
 The ratio of the voltage maximum to the minimum gives the VSWR i.e
VSWR = Vmax / Vmin
ISWR = Imax / Imin
= k (V max)2 / k (V min)2
= ( V max / V min)2
= VSWR2
VSWR = √ ( Imax / Imin ) = √ ISWR
 Methods used depends on the value of VSWR whether it is high or low. If the load is not exactly matched to the
line, standing wave pattern is produced.
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
 Reflections can be measured in terms of voltage, current or power. Measurement using voltage is preffered
because it is simplicity.
 When reflection occured, the incident and the reflected waves will reinforce each other in some places, and in
others they will tend to cancel each other out.
 DOUBLE MINIMUM METHOD MEASUREMENT ( VSWR > 10)
‘Double Minimum’ method is usually employed for VSWR values greater than about 10.

E2MAX
d
SWR PATTERN
2E2MIN
E2MIN
λ/2
0
d/2
distance along the line
 The detector output (proportional to field strength squared) is plotted against position. The probe is moved aling
the line to find the minimum value of signal.
 It is then moved either side to determine 2 positions at which twice as much detector signal is obtained. The
distance d between these two positions then gives the VSWR according to the formula :
S = √ 1 + 1/Sin2(πd/λ)
 POWER MEASUREMENT
 Methods of measurement of power depend on the frequency of operation, levels of power and whether the
power is continuous or pulsed.
 Power measurements can be divided into 3 power ranges: Low power ( < 1mW @ 0dBm)
 Medium power ( antara 1 mW - 10 W @ 0 – 40 dBm)
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MICROWAVE MEASUREMENT
PROGRAM: DEP
 High power ( > 10 W @ 40 dBm)
 Power is detected at microwave frequencies by the following devices. Bridge circuit is used to measure absolute
power of 10 mW whereby one of the resistance is used as part of the circiutry : Bolometers (therrmistors dan baretters).
 Thermocouples
 Microwave crystal
 BOLOMETERS
 Are power detectors that operate on thermal principles. Resistance of the bolometer changes in proportion
to its temperature. Since the temperature of the resistance is dependent on the signal power power
absorbed, the resistance must also be in proportion to the signal power.
 2 kinds of bolometers are available, baretters and thermistors. Both are sensitive power detectors and is
used to indicate microwatts of power. They are used with bridge circuits to convert resistance to power
using a meter or other indicating devices.
 BARETTERS
 Are usually thin pieces of wire such as platinum. They are mounted as terminating devices in a section of
transmission line. The section of transmission line with the mounting structure is called a detector mount.
 The increase of temperature of the baretter due to the power absorbed from the signal in the line causes the
temperature of the device to increase.
 The temperature coefficient of the device causes the resistance to change in value in proportion to the change in
temperature of the device (positive temperature coefficient i.e the resistance increases with increasing
temperature; R α t).
 THERMISTOR
 Are beads of semiconductor material that are mounted across the line. They have a negative temperature
coefficient i.e the resistance decreases with increasing temperature; R α 1/ t.
 The impedance of baretters and thermistors must match that of the transmission so that all power is absorbed by
the device.
 Variations in resistance due to thermal-sensing devices must be converted to a reading on an indicating device
such as a meter. This can be done accurately using a balanced bridge arramgement as shown below:-
R
R1
DC VOLTAGE
DETECTORS
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
 With no power to the detector that contains the sensor element, the sensor-line R1 is adjusted to zero reading
through the meter M1 and the bridge circuit is balanced.
 When signal is applied to the sensor element, causing its temperature to change, the sensor resistance
changes, causing the bridge to become unbalanced.
 Resistor R1 is adjusted to balance meter M1. The change in the reading of meter M2 in the sensor element leg
is a direct measure of the microwave power.
 THERMOCOUPLES
 Are used as power monitors in the low-to-medium power regions and are very sensitve.
 Is a thin wire made of two disimilar metals. Hence there will be two junctions (hot & cold).
 When the temperature at two junctions are different, a voltage is developed across the thermocouple (i.e across
both junctions). This developed voltage is proportional to the difference between the two junction temperatures.
 When the temperature at both junctions are the same, the difference in voltage = 0.
 MICROWAVE CRYSTALS
 Are non-linear detectors that provide current in proportion to the power. It is limited to making low-power
measurements.
 The current is proportional to the power due to the square-law characteristic of the crystal. This square-law
characteristic only occurs for small signal levels.
 At larger signal levels the relationship is linear, as with any diode. Therefore the proportional relationship
between power and current output is only true at power levels below 10mW.
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT

PROGRAM: DEP
SMITH CHART
Sometimes called polar impedance diagram or transmission line calculator.
For complex transmission line problems, the use of the formulae becomes increasingly
difficult and inconvenient. An indispensable graphical method of solution is the use of
Smith Chart.
COMPONENTS OF A SMITH CHART
Horizontal line:
The horizontal line running through the center of the Smith chart represents either the
resistive ir the conductive component. Zero resistance or conductance is located on the
left end and infinite resistance or conductance is located on the right end of the line.
Circles of constant resistance and conductance:
Circles of constant resistance are drawn on the Smith chart tangent to the right-hand
side of the chart and its intersection with the centerline. These circles of constant
resistance are used to locate complex impedances and to assist in obtaining solutions
to problems involving the Smith chart.
Lines of constant reactance:
Lines of constant reactance are shown on the Smith chart with curves that start from a
given reactance value on the outer circle and end at the right-hand side of the center
line.
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
SOLUTIONS TO MICROWAVE PROBLEMS USING SMITH CHART
 The types of problems for which Smith charts are used include the following:
1. Plotting a complex impedance on a Smith chart
2. Finding VSWR for a given load
3. Finding the admittance for a given impedance
4. Finding the input impedance of a transmission line terminated in a short or
open.
5. Finding the input impedance at any distance from a load ZL.
6. Locating the first maximum and minimum from any load
7. Matching a transmission line to a load with a single series stub.
8. Matching a transmission line with a single parallel stub
9. Matching a transmission line to a load with two parallel stubs.
PLOTTING A COMPLEX IMPEDANCE ON A SMITH CHART
 To locate a complex impedance, Z = R+-jX or admittance Y = G +- jB on a Smith
chart, normalize the real and imaginary part of the complex impedance. Locating the
value of the normalized real term on the horizontal line scale locates the resistance
circle. Locating the normalized value of the imaginary term on the outer circle
locates the curve of constant reactance. The intersection of the circle and the curve
locates the complex impedance on the Smith chart.
FINDING THE VSWR FOR A GIVEN LOAD
 Normalize the load and plot its location on the Smith chart.
 Draw a circle with a radius equal to the distance between the 1.0 point and the
location of the normalized load and the center of the Smith chart as the center.
 The intersection of the right-hand side of the circle with the horizontal resistance line
locates the value of the VSWR.
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MICROWAVE MEASUREMENT
PROGRAM: DEP
FINDING THE INPUT IMPEDANCE AT ANY DISTANCE FROM THE LOAD
 The load impedance is first normalized and is located on the Smith chart.
 The VSWR circle is drawn for the load.
 A line is drawn from the 1.0 point through the load to the outer wavelength scale.
 To locate the input impedance on a Smith chart of the transmission line at any given
distance from the load, advance in clockwise direction from the located point, a
distance in wavelength equal to the distance to the new location on the transmission
line.
POWER LOSS
 Return Power Loss: When an electromagnetic wave travels down a transmission line
and encounters a mismatched load or a discontinuity in the line, part of the incident
power is reflected back down the line. The return loss is defined as:
Preturn = 10 log10 Pi/Pr
Preturn = 20 log10 1/ Γ
 Mismatch Power Loss: The term mismatch loss is used to describe the loss caused
by the reflection due to a mismatched line. It is defined as
Pmismatch = 10 log10 Pi/(Pi - Pr)
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CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
 WITH REFERENCE TO SMITH CHART :
 At the very bottom of the chart the word CENTER printed beneath a small straight vertical line.
 This line will intersects the horizontal line (which cuts the circular chart into half) at a point marked 1.0 
this is the start of the chart i.e the center of the circle.
Arcs of + jx
Center
Of Chart
Axis of Normalized
Resistance
Arcs of - jx
CENTER
 Axis of normalized resistance begins at the left : 0, 0.1, 0.2. ......1.0 (at the center ...... 20, 50 and infinity / ∞ at
the right). These numbers represent normalized resistance values as given by :
Normalized Resistance, r = R / Z0
where; R = actual resistive part of complex load
Z0 = characteristic impedance
 There are also 2 sets of arcs on the chart. One set curves upward from its common point of tangency and
represents normalized values of inductive reactance as given by :
Normalized Inductive Reactance, x = jX / Z0
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MICROWAVE MEASUREMENT
PROGRAM: DEP
 The other set of arcs curves downward from a common point of tangency and represents normalized values of
capacitive reactance as given by :
Normalized Capacitive Reactance, x = - jX / Z0
 All the complete circles intersect all the arcs. Any given point of intersection is a normalized load impedance
value as given by :
Normalized Load Impedance,
z L = ZL / Z0
= R ± jX
Z0
= r ± jx
 The outermost circular scale represents distance in normalized wavelengths. The direction towards the
load on the SC is always counterclockwise. The direction towards the generator on the SC is always
clockwise. One revolution on the chart represents one-half wavelength (λ/2) of a tansmission line.
 SC can be used with any characteristic impedance of the transmission line or any frequency of operation.
 USAGE OF SMITH CHART
 USE TO SOLVE A VARIETY OF MICROWAVE PROBLEMS :i ) Plotting real, imaginary and complex loads.
iv ) Locating the distance to the minimum and maximum
points of the standing waves in front of any line
ii ) Finding VSWR for a given transmission line
termination.
termination.
v ) Matching a line termination to the transmission line
iii ) Finding input impedance at any point in front of a
using single stub or double stub tuners or ‘quarter transmission line terminated in an open, short or
wave transformer’.
complex load.
 REFLECTION ON LINES
 If a transmission lines has infinite length (∞) or it is terminated in its characteristic impedance, all the power
applied (incident wave) to the line by the generator is absorbed by the load at the othe end.
 On the other hand, if a finite piece of line is terminated, ZL ≠ Z0 some of the power (incident wave) will be
absorbed by the termination. The remaining power will be reflected. Thus there are two waves on the line i.e,
incident wave and reflected wave.
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MICROWAVE MEASUREMENT
PROGRAM: DEP
 The resultant wave at any part of the line is the algebraic sum of the two waves and it produces a standing wave
on the line.
REFLECTION COEFFICIENT
REFLECTION
COEFFICIENT, ρ
LOAD, ZL
VSWR, σ
REMARK
ρ = -1
short circuit,
ZL = 0;
σ=0
Due to phase reversal i.e change of phase thus
the incident and reflected wave will be cancelled.
ρ=1
open circuit ,
ZL = ∞
σ=∞
Total refelection occurs because the 2 waves are
in phase.
ρ=0
Matching load, ZL = Z0
σ=1
No reflection occurs only have incident wave.
 STUB MATCHING
 When a line is ‘matched’ the reflection coefficient ρ = 0 and so the standing wave ratio, S = 1. Most system are
therefore designed to work with S as near to 1 as possible.
 A value of S > 1, represent mismatched and end to loss of power at the receiving end. In other cases it may
caused a voltage breakdown as in high power radar system or distortion in tv.
 It it therefore necessary to match a line. Matching in the case of two wire lines, may be done by using one or
more stub and is called ‘stub matching’ or by the use of quarter wave transformer.
 The use of stub in matching a complex load to the line is to achieve a complete power transfer (VSWR = 1.0).
The stub used has to be placed in parallel with the line and load, thus has to deal with admittance, not
impedance.
EXAMPLE 1
Given : ZL = 50 + j 50 Ω , Z0 = 50 Ω. Calculate (i) normalize impedance (ii) draw the SWR circle
(iii) VSWR (iv) reflection coefficient (v) angle of reflection (vi) Rmin and Rmax (v) stub length (vi)
stub distance.
(i)
Normalize impedance,
zL = ZL / Z0 = 50 + j 50 Ω
50
= 1 + j 1 Ω. (point A)
(ii) Plot zL on SC
(iii) Construct SWR circle with center C passing through zL .
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PROGRAM: DEP
s = 2.6
(iv) Draw a radial line passing through zL from center C, λA = 0.162 λ B/W
(v)
B / W = 0.162 λ + 0.25 λ
= 0.412 λ (i.e towards generator)
(vi) At point B, admittance y = 1/ zL = 0.5 + j 0.5 Ω
reference wavelength, λB = 0.413 λ
(vii) At point C, admittance y = 1 + j x = 1 + j 1 Ω
wavelength, λC = 0.162 λ
Therefore, stub distance, d = 0.5 λ - λB - λC = 0.5 λ - 0.413 λ + 0.162 λ
= 0.249 λ.
(viii) At point D,
subsceptance = - j x = -j 1
wavelength λD = 0.375 λ
the stub will have a short circuit at its far end, admittance at this point ∞,
the wavelength at this point is = 0.25 λ
therefore,
stub length, l = λD - 0.25 λ = 0.375 λ - 0.25 λ
= 0.125 λ
Rmin = r min x Z0
= 0.38 x 50
= 19 Ω
Rmax = r max x Z0
= 2.6 x 50
= 130 Ω
reflection coefficient, ρ = 0.42
angle of reflection , Ө = 63°
EXAMPLE 2
A complex load of ZL = 35 + j 65 Ω terminating a 50 Ω transmission line. Using a SC (i) plot the point of the load
normalized impedance and find the value of (iii) SWR (ii) coefficient reflection (v) angle of reflection (vi) Rmin and
Rmax (v) stub length and the distance required to obtain a matched line-load
1. Normalized load impedance, zL = ZL / Z0 = 35 + j 65 Ω
50
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PROGRAM: DEP
= 0.7 + j 1.3 Ω. (point A)
2. Plot zL on Smith Chart.
3. Construct the SWR circle ( at point C = 1.0 – passing through zL )
VSWR, s = 4.3
Reflection coefficient, ρ = 0.623
Rmin = r min x Z0
= 0.23 x 50
= 11.5 Ω
4. At Point B, admittance
;
angle of reflection, Ө = 65.6°
Rmax = r max x Z0
= 4.3 x 50
= 215 Ω
y = 1/ zL = 0.32 - j 0.6 Ω
Reference Wavelength , λB = 0.409 λ
5. At Point C, admittance
y = 1 + j x = 1 + j 1 .6 Ω
Wavelength, λC = 0.179 λ
therefore,
stub distance, d = 0.5 λ - λB - λC = 0.5 λ - 0.409 λ + 0.179 λ
= 0.27 λ.
Stub length, l;
6. At Point D, subsceptance = - j x = -j 1.6
Wavelength, λD = 0.339 λ
For short circuit stub, admittance  ∞, wavelenth at this point is = 0.25 λ
Therefore , stub length, l = λD - 0.25 λ = 0.339 λ - 0.25 λ
= 0.089 λ
CONCLUSION
A short circuitted-stub 0.089 wavelength long located on the line 0.27 away from a complex load of ZL = 35 + j 65 Ω
will reduce the VSWR on the line to 1.00 (no reflection) and a maximum transfer of power from source to load will be
achieved.
PREPARED BY :
ROHANA IBRAHIM
PTSS
28/07/2007
19
CODE/COURSE : EP603/ MICROWAVE DEVICES
MICROWAVE MEASUREMENT
PROGRAM: DEP
EXERCISES :
Construct the SWR circle for the given complex load :
1. ZL = 28 - j 60 Ω , Z0 = 50
2. ZL = 70 - j 55 Ω , Z0 = 50
3. Find the distance and stub length required to obtain a matched line-load condition between :(a) ZL = 31.25 + j 10 Ω & Z0 = 50
(b) ZL = 41.25 - j 22.5 Ω
& Z0 = 75
4. Given : R = 45 Ω, C = 26.5pF, f = 0.12 GHz, Z0 = 30 Ω.
Find :- (i) stub distance (ii) stub length (iii) reflection coefficient & angle of reflection (iv) actual Rmin and Rmax
PREPARED BY :
ROHANA IBRAHIM
PTSS
28/07/2007
20