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Transcript of microwave lab manual
ECE402 – Microwave Engineering Lab
School of Electronics Engineering
Microwave Lab Manual Winter Semester
2012 -13
VIT U N I V E R S I T Y
(Estd. u/s 3 of UGC Act 1956)
List of MW Lab experiments
• Gunn Diode Oscillator
• Directional Coupler & Circulator
• Waveguide Tee Junctions
• Magic Tee
• Measurement of impedance of a device (Antenna)
• Measurement of Antenna Radiation Pattern
• MIC Power Dividers
• Two Port Networks
• Wilkinson Power Divider ( Equal & Unequal )
• Branch Line Coupler
• 180o Hybrid Coupler
• LPF – Richard’s Transformation Method
• LPF – Stepped Impedance Method
Gunn Diode Objectives: To study Gunn diode as a microwave source and hence to study
1. I-V characteristics 2. Power – Bias voltage characteristics 3. Power – Frequency characteristics
Equipment & Components required : Gunn Oscillator Gunn power supply PIN modulator Isolator Variable attenuator Detector mount VSWR meter Cables Theory : The Gunn diode is a very useful microwave source and is widely used. The Gunn oscillator
is based on negative differential conductivity effect in bulk semiconductors such as GaAs. From
the DC V-I characteristics, we will see that the Gunn diode has a negative differential resistance
region. In GaAs, electrons can exist in a high-mass low velocity state as well as their normal low-
mass high-velocity state and they can be forced into the high-mass state by a steady electric field of
sufficient strength. In this state they form domains which cross the field at a constant rate causing
current to flow as a series of pulses. This is the Gunn effect and one form of diode which makes use
of it consists of an epitaxial layer of n-type GaAs grown on a GaAs substrate. A potential of a few
volts applied between ohmic contacts to the n-layer and substrate produces the electric field which
causes clusters. The frequency of the current pulses so generated depends on the transit time
through the n-layer and hence on its thickness. If the diode is mounted in a suitably tuned cavity
resonator, the current pulses cause oscillation by shock excitation and r.f. power up to 1 W at
frequencies between 10 and 30 GHz is obtainable.
Block diagram:
Gunn power supply
Gunn Oscillator
PIN Modulator Isolator Variable
Attenudator Detector Mount
VSWR Meter
Expt. No. : Date :
Figure (1)
Procedure: 1. Set the components as shown in figure 1.
2. Set the micrometer of Gunn Oscillator for required frequency of operation (9 GHz).
3. Change the Gunn bias voltage in steps of 0.5 V and measure the Gunn diode current
through the digital panel meter.
4. Plot the voltage & current readings on a graph.
5. Measure the threshold voltage (Vo) which corresponds to maximum current.
6. Set Gunn biasing just above Vo and note down corresponding power.
7. Change the Gunn bias voltage in steps of 0.5 V and measure the power VSWR meter.
8. Plot power – bias voltage characteristics.
9. Set Gunn biasing for maximum power output and note down this power.
10. Move micrometer screw in steps of 0.5 mm and note down corresponding power till the
screw reaches one extreme.
11. Plot power – frequency characteristics.
Sample Observations:
Bias voltage = 4 V Frequency = 10 GHz
Bias Voltage
(V) Current (mA) Power (dB)
1 0.176 -70
2 0.306 -70
3 0.362 -46
3.28 0.367 -44
4 0.198 -40
5 0.147 -47
6 0.301 -58
7 0.298 -58
8 0.296 -58
9 0.294 -58
10 0.293 -58
Frequency
(GHz) Power (dB)
9 -58
9.2 -62
9.4 -58
9.6 -44
10 -40
10.4 -33
10.6 -38
11 -32
11.4 -36.5
11.75 -39
12.4 -46
Model graph:
0 2 4 6 8 10
0.15
0.20
0.25
0.30
0.35
0.40
Cur
rent
(mA
)
Voltage (V)
I-V characteristics Practical Observations: Bias voltage = Frequency =
Bias Voltage
(V) Current (mA) Power (dB)
Frequency
(GHz) Power (dB)
Conclusions:
Expt. No. : Date :
Directional Coupler Objective: To study the function of a directional coupler by measuring the following parameters.
4. Insertion loss 5. Coupling coefficient 6. Directivity 7. Isolation
Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Directional coupler Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Theory : A directional coupler is a four port wave guide junction as shown in figure 1. Directional
couplers are used to divide signals from a single channel into multiple channels in both small signal
and large signal applications. Also directional couplers are used to sample propagating microwave
energy for the purpose of monitoring or measuring. It consists of a primary wave guide called main
arm (1 & 2 ports) and a secondary wave guide called auxiliary arm ( 3 & 4 ports).
The operation of a directional coupler can be illustrated with the help of figure 1. If power
fed at port 1 is coupled to port 3 (coupled port) with the coupling factor while the remainder of the
in put power is delivered fed to port 2 (through port). In an ideal directional coupler, no power is
delivered to port 4 (Isolated port). The following quantities are generally used to characterize
directional coupler
Insertion loss = 1
2
10 log PP
dB
Coupling coefficient = 1
3
10 log PP
dB
Directivity = 3
4
10 log PP
dB
Isolation = 1
4
10 log PP
dB
Isolated Coupled
Input Through
34
21
Figure (1) Block diagram:
Klystron power supply
Klysron Oscillator
Isolator Slotted Section
Main arm Matched termination
Detector VSWR Meter
Auxiliary arm
Figure (2)
Procedure:
1. Set the components as shown in figure 2 without directional coupler.
2. Energise the microwave source for particular frequency of operation.
3. Set any reference level of power on VSWR meter with the help of gain control knob of
VSWR meter, and note down the reading (P1 in dB).
4. Insert the directional coupler as shown in figure 2 with detector to the auxiliary port 3
and matched termination to port 2, without changing the position of gain control knob of
VSWR meter.
5. Note down the reading of VSWR meter with the help of range-dB switch if required (P3
in dB).
6. Calculate coupling coefficient C = P1 – P3 (dB).
7. Now carefully disconnect the detector from the auxiliary port 3 and matched termination
from port 2 without disturbing the set-up.
8. Connect the matched termination to the auxiliary port 3 and detector to port 2 and
measure the reading on VSWR meter (P2 in dB).
9. Compute insertion loss I.L. = P1 – P2 (dB).
10. Connect the directional coupler in the reverse direction, i.e. port 2 to slotted section side,
matched termination to port 1 and detector mount to port 3 without disturbing the
position of the gain control knob of VSWR meter.
11. Note down the reading on VSWR meter (P4 in dB ).
12. Compute Isolation = P1 – P4 (dB) and Directivity = P3 – P4 (dB).
Sample Observations:
I/P port
P1(dB)
O/P port
P2(dB)
Coupled
port P3(dB)
Isolated
port P4(dB) I.L. (dB) C.C. (dB)
Directivity
(dB)
Isolation
(dB)
-20 -21 -30 -60 1 10 30 40
Practical Observations:
I/P port
P1(dB)
O/P port
P2(dB)
Coupled
port P3(dB)
Isolated
port P4(dB) I.L. (dB) C.C. (dB)
Directivity
(dB)
Isolation
(dB)
Conclusions:
Expt. No. : Date :
Circulator Objective: To study the function of a 3-port circulator by measuring the following parameters.
1. Insertion loss 2. Isolation
Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Circulator Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Theory :
A circulator is a non reciprocal device with ports arranged in such a way that power
entering at a port is coupled to an adjacent port but not coupled to the other ports. Based on the
direction of the energy propagation to the adjacent ports we have clockwise and anti-clockwise
circulators. Circulators can have any number of ports. Wave propagation in a 3-port clockwise
circulator is shown in figure 1. The following quantities are generally used to characterize
circulator
Insertion loss = 1
2
10 log PP
dB
Isolation = 1
3
10 log PP
dB
Port 2
Port 1
Port 3
Figure (1) Block diagram:
Klystron power supply
Klysron Oscillator
Isolator Slotted Section
Circulator Matched termination
Detector VSWR Meter
Figure (2)
Procedure:
1. Set the components as shown in figure 2 without circulator.
2. Energise the microwave source for particular frequency of operation.
3. Set any reference level of power on VSWR meter with the help of gain control knob of
VSWR meter, and note down the reading (P1 in dB).
4. Insert the circulator as shown in figure 2 with detector to adjacent port 2 and matched
termination to port 3, without changing the position of gain control knob of VSWR
meter.
5. Note down the reading of VSWR meter with the help of range-dB switch if required (P2
in dB).
6. Calculate insertion loss I.L. = P1 – P2 (dB).
7. Now carefully disconnect the detector from port 2 and matched termination from port 3
without disturbing the set-up.
8. Connect the matched termination to port 2 and detector to port 3 and measure the
reading on VSWR meter (P3 in dB).
9. Compute Isolation. = P1 – P3 (dB).
10. Repeat the experiment for other ports similar way.
Sample Observations:
I/P port
power(dB)
O/P port
power(dB)
Isolated port
power(dB) I.L. (dB)
Isolation
(dB)
P1= -20 P2=-20.5 P3=-60 0.5 40
P2= -20 P3=-20.8 P1=-62 0.8 42
P3= -20 P1=-20.9 P2=-61 0.9 41
Practical Observations:
I/P port
power(dB)
O/P port
power(dB)
Isolated port
power(dB) I.L. (dB)
Isolation
(dB)
Conclusions:
Waveguide Tee junctions
Expt. No. : Date :
Objectives: 1. To study the function of a E-plane and H-plane Tee 2. To determine scattering parameters of a E-plane and H-plane Tee
Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator E or H-plane Tee Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Theory : A waveguide T-junction is a simple three port network that can be used for power
division or combining. These junctions are not matched perfectly at all ports. Waveguide tees may
be consists of E-plane tee, H-plane Tee or Magic Tee.
E-plane Tee :
An E-pane tee is a waveguide in which the axis of its side arm is parallel to the E filed of
the main guide as shown in figure 1. If the collinear arms are symmetric about the side arm, there
are two different transmission characteristics. E-plane tee can be perfectly matched with the aid of
screw tuners or capacitive or inductive windows at the junction, the diagonal elements of the S-
matrix S11, S22, S33 are zero because there is no reflection. When the waves are fed into side arm
(port 3), the waves appearing at port 1 and port 2 of the collinear arm will be in opposite phase and
in the same magnitude as shown in figure 2.
Figure 1 Figure 2
H-plane Tee : An H-plane tee is a waveguide tee in which the axis of its side arm(port 3) is
shunting the E-field or parallel to the H filed of the main arm as shown in figure 3. If two input
waves are fed at port 1 and port 2 in same phase, the output wave at port 3 will be additive and in
phase. On the other hand, if the input is fed into port 3, the wave will split equally into port 1 and
port 2 in phase and in the same magnitude.
Figure 3
Block diagram:
Klystron power supply
Klysron Oscillator
Isolator Slotted Section
Tee junction Matched termination
Detector VSWR Meter
Figure (4)
Procedure:
1. Set the components as shown in figure 4 without Tee junction.
2. Energize the microwave source for particular frequency of operation.
3. Set any reference level of power on VSWR meter with the help of gain control knob of
VSWR meter, and note down the reading (P1 in dB).
4. Insert the Tee junction as shown in figure 4 with detector to port 2 and matched
termination to port 1, without changing the position of gain control knob of VSWR
meter.
5. Note down the reading of VSWR meter with the help of range-dB switch if required (P2
in dB).
6. Now carefully disconnect the detector from port 2 and matched termination from port 1
without disturbing the set-up.
7. Connect the matched termination to port 2 and detector to port 1 and measure the
reading on VSWR meter (P1 in dB).
8. Repeat the experiment by keeping port 2 and port 3 as input ports.
9. Scattering parameters of the Tee junction are calculated as follows
Port 1 as input port then, 221
1
PSP
= ; 331
1
PSP
=
Port 2 as input port then 112
2
PSP
= ; 332
2
PSP
=
Port 3 as input port then 113
3
PSP
= ; 223
3
PSP
=
Sample Observations:
I/P port
power(dB)
O/P port 1
power(dB)
O/P port 2
power(dB)
P3= -20 P1=-25.5 P2=-25.4
P2= -20 P3=-22.6 P1=-29
P1= -20 P2=-22.6 P3=-29
Practical Observations: I/P port
power(dB)
O/P port 1
power(dB)
O/P port 2
power(dB)
Conclusions:
Expt. No. : Date :
Magic Tee Objective: To study the function of a Magic Tee by measuring Isolation. Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Magic Tee Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Theory : A magic tee is a combination of E-plane and H-plane tee, shown in figure 1. The magic
tee is commonly used for mixing, duplexing and impedance measurements. The magic tee has
several characteristics.
1. If two waves of equal magnitude and the same phase are fed into port 1 and port 2, the
output will be zero at port 3 and additive at port 4.
2. If a wave is fed into port 4 (the H arm) , it will be divided equally between port 1 and port 2
of the collinear arms and will not appear at port 3 (the E arm).
3. If a wave is fed into port 3 (the E arm), it will produce output of equal magnitude and
opposite phase at port 1 and port 2. The output at port 4 is zero. That is S34=S43=0.
4. If a wave is fed into one of the collinear arms at port 1 or port2 , it will not appear in the
other collinear arm at port 2 or port 1 because the E arm causes a phase delay while H arm
causes a phase advance. That is S12=S21=0.
Therefore the S matrix of a magic tee can be expressed as
13 14
23 24
31 32
41 42
0 00 0
0 00 0
S SS S
SS SS S
⎛ ⎞⎜ ⎟⎜ ⎟ =⎜ ⎟⎜ ⎟⎝ ⎠
Figure (1)
Block diagram:
Figure (2)
Klystron power supply
Klysron Oscillator
Isolator Slotted Section
Magic Tee Matched termination
VSWR Meter
Detector Mount
Matched termination
Procedure:
1. Set the components as shown in figure 2 without magic tee
2. Energize the microwave source for particular frequency of operation.
3. Set any reference level of power on VSWR meter with the help of gain control knob of
VSWR meter, and note down the reading (Pin in dB).
4. Insert the Tee junction as shown in figure 2 with detector to port 3 and matched
termination to port 1 and port 2, without changing the position of gain control knob of
VSWR meter.
5. Note down the reading of VSWR meter with the help of range-dB switch if required (P3
in dB).
6. Repeat the experiment by keeping port 1, Port 2 and port 3 as input ports.
Sample Observations:
I/P port power(dB) O/P port power(dB)
E-arm
P3= -20
P1 = -25.5
P2 = -25.4
P4 = - 65
H-arm
P4= -20
P1 = -26.1
P2 = -25.7
P3 = -68
Practical Observations:
I/P port power(dB) O/P port power(dB)
E-arm
H-arm
Conclusions:
Expt. No. : Date :
Measurement of Unknown Impedance Objectives: To measure the impedance of an Unknown load. Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Directional coupler Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Short plate Unknown load Theory :
The impedance at any point on a transmission line can be written in the form (R + jX).
For comparison VSWR can be calculated as
1 | |1 | |
VSWR + Γ =
− Γ
11
ref L oL L
inc L o
V Z Z VSWRV Z Z VSWR
− −Γ = ; Γ = ; Γ =
+ +
Z0 = Characteristics impedance of waveguide at operating frequency.
ZL is the load impedance.
The unknown device is connected to the slotted line and the position of the minima is
determined. The unknown device is replaced by movable short to the slotted line. Two successive
minima positions are noted. The twice the difference between minima position will be guided
wavelength. One of the minima is used as reference for Impedance measurement. Find the
difference of reference minima and minima position obtained from unknown load. Let it be d.
Take a Smith Chart towards load side at a distance equal to d/λg. Join the centre with this point.
Find the point where it cut the drawn circle. The co-ordinates of this point will show the
normalized impedance of load.
Block diagram:
Klystron power supply
Klysron Oscillator
Isolator Slotted Section
Main arm Matched termination
Detector VSWR Meter/CRO
Auxiliary arm
Procedure:
1. Set the components as shown in figure with a matched load.
2. Energise the microwave source for particular frequency of operation.
3. Keep the Controls knobs of klystron power supply (SKPS-610) as below:-
i) Beam voltage Switch- ‘OFF’
ii) Beam voltage control knob- Fully anticlockwise
iii) Repeller voltage control knob- Fully clockwise
iv) Mod Switch- AM
v) AM Amplitude- Around fully clockwise
vi) AM Frequency knob- Around mid position.
4. Switch ‘ON’ the klystron power supply, VSWR meter and cooling fan.
5. Switch ‘ON’ the Beam voltage Switch and set and rotated the beam voltage knob
clockwise slowly up to 270 volt meter reading and observe beam current position, “The
beam current should not increase more than 30 mA”.
6. Adjust the repeller voltage knob to get some deflection in VSWR meter.
7. Maximize the deflection with AM amplitude and frequency control knob of power supply.
8. Tune the repeller voltage knob for maximum deflection.
9. Now connect a movable short at the slotted line.
10. Move the probe along the Slotted line. Note the two successive minima positions; let it be
as d1 and d2. Hence λg = 2(d1- d2).
11. One of the minima is used as reference for Impedance measurement. Let it be DR.
12. The unknown device is connected to the slotted line and the position of minima is
determined. Let it be DU. Measure VSWR S0.
13. Find d = (DR - DU). Calculate:- d / λg
Impedance measurement using Smitch Chart:
Take a Smith Chart, taking ‘(1,0)’ as centre, draw a circle of radius equal to VSWR S0.
Fix the voltage minimum point at the extreme left of the horizontal axis of the smith chart. Mark a
point on circumference on VSWR circle towards load side at a distance equal to d / λg. Join the centre
with this point. Find the point where it cut the drawn circle. The co-ordinates of this point will show
the normalized Impedance of load. Multiply with the wave impedance of the waveguide at the
operating frequency.
Impedance measurement using Calculation:
min
min
L
11
2
2where ;
distance between two minima of short circuit & unknown load
The load impedance is then 1Z1
g
i
o
VSWRVSWR
l
l
e
Z
θ
θ π β
πβλ
− | Γ | =
+
= +
=
=
Γ =| Γ |
+ Γ⎛ ⎞= ⎜ ⎟− Γ⎝ ⎠
Practical Observations:
Unknown Impedance
Ref Min Position
(Cm) (DR)
Guided Wave
length (without Sample)
λg = 2*(d1- d2) Cm
Minima with the sample (Cm) (DU)
VSWR with the
Sample (S0)
d =(DR- DU)
d -- λg
Calculated Impedance
1 2 3
4 Conclusions:
Expt. No. : Date :
Measurement of Radiation Pattern Objective: 1. To measure the E plane and H plane radiation pattern of a pyramidal horn antenna. 2. To compute the 3 dB beam width and directivity of horn antenna. Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Waveguide twist Detector mount VSWR meter Matched termination Pyramidal horn antennas Theory : The radiation pattern of an antenna is a plot of field strength of the power intensity as a
function of the aspect angle at a constant distance from the radiating antenna. It is a 3D plot of the
radiation properties far from the source such as the radiation intensity, power density, directivity
and polarization of an antenna as a function of the spatial coordinates which are described in terms
of spherical coordinates. An antenna pattern consists of several lobes, the main lobe, side lobes,
and the back lobe. The major power is concentrated in the main lobe and it is required to keep the
power in the side lobes and back lobe as low as possible.
Usually the radiation pattern is shown in principal planes of interest. Further, for linearly
polarized antennas, patterns may be plotted in E – plane or H – plane. E- plane is defined as the
plane passing through the antenna in the direction of beam maximum and parallel to the far field E
– vector. One defines the H – plane similarly. It is quire common to plot the pattern by normalizing
the field values with respect to the field strength in the direction of maximum radiation.
The radiation pattern of typical microwave antennas consists of a main lobe and a few
minor or side-lobes. Beam-width of an antenna is defined as the angular separation between 3 dB
points with respect to the maximum field strength. Side lobes represent a loss and leakage of
information in the transmit mode. In the receive mode, sidelobes may cause an uncertainty in
determining the angle of arrival of a signal. However, sidelobes are very sensitive to the
surroundings in which the radiation pattern is measured.
The wavefronts in the vicinity of an antenna have a small radius or curvature but after
traveling some distance the radius of curvature increases to such an extent as to make the wave
front practically a plane wave. A receiving antenna is considered to be in the far-field of the test
antenna if the wavefront across it is practically plane. Most measurements are carried out in the far
field region since; otherwise, when the receiving antenna is kept in the region of curved wavefornt,
there will be a phase difference across the receiving aperture. It can be shown that the phase
variation over the receiving aperture is less than one sixteenth of a wavelength if it is at a distance
R from the transmitting antenna, where
In which D = largest dimension of the larger of the receiver and transmitter antennas.
A horn antenna is a flared out waveguide at the end. If the flaring is done along both the
walls of the rectangular wave guide, then the pyramidal horn is obtained. Horn antennas are
extensively used at microwave frequencies. Theoretically the 3 dB beam width of the pyramidal
horn antenna is
0
0
53 where ' ' is the narrower dimension of the waveguide
80 where ' ' is the broader dimension of the waveguide
E
H
bb
aa
λθ
λθ
=
=
The directivity D can be calculated using the following approximate formula
32400 32400 or ( ) 10log
E H E H
D D dBθ θ θ θ
⎛ ⎞= = ⎜ ⎟
⎝ ⎠
Block diagram:
Procedure:
1. Set up the apparatus as shown in Figure. Again the antenna for maximum meter reading and mark this position of the receiver antenna as 0°. Use square- wave modulation if necessary, and tune the detector. Take care to kept the distance between the antennas sufficiently large so that they are in the far-field zone. 2. Rotate the receiving horn clockwise, in steps of 100, to cover the main lobe and atleast the first
sidelobe( till 900) . At each position, note the reading on the VSWR meter in dB scale. 3. Return to the position 0° and repeat the measurements by rotating the antenna in steps of 100 in the
anticlockwise direction till -900 . At each position, note the reading on the VSWR meter in dB scale.
4. Plot the radiation pattern in the above manner for both E- and H-plane. Determine the beam width and level of the first side lobe with respect to the main lobe.
5. Calculate the directivity and compare the result with the theoretical value. E - plane : H – plane :
Conclusions:
Out put power ( VSWR meter reading ) Angular
Position Clockwise Anti
clockwise
Out put power ( VSWR meter reading ) Angular
Position Clockwise Anti
clockwise
MIC Power Dividers
Objective : To measure the power division, isolation and return loss characteristics of Wilkinson power dividers and branch line coupler . Equipment & Components required :
Signal source Attenuator VSWR meter
Frequency meter Power divider Directional coupler, Detector Matched load Theory: The Wilkinson power divider is generally designed using microstrip lines as shown in
figure 2 and can be made with any number of ports with equal or unequal power divisions.
Wilkinson power divider has many advantages over other power dividers and has the following
properties
Expt. No. : Date :
1. Matched at all ports.
2. Large isolation between output ports
3. Reciprocal
4. Lossless when output ports are matched
The S-matrix of a 3-port Wilkinson power divider is given by
02 2
[ ] 0 02
0 02
j j
jS
j
− −⎛ ⎞⎜ ⎟⎜ ⎟
−⎜ ⎟= ⎜ ⎟⎜ ⎟
−⎜ ⎟⎜ ⎟⎝ ⎠
Theory : Branch line couplers are 3 dB directional couplers with a 900 phase difference in the
outputs of the through and coupled ports. This type of hybrid is often made in microstrip line form
as shown in figure 2. It is also known as Quadrature hybrid or 900 hybrid couplers. With all the
ports matched, power entering port 1 is eventually divided between ports 2 and 3 with a 900 phase
shift between these outputs. No power is coupled to port 4. Branch line coupler has a high degree
of symmetry, as any port can be used as the input port. The output ports will always be on the
opposite of the junction from the input port and the isolated port will be the remaining port on the
same side as the input port. The S-matrix will have the following form
Figure 1
0 1 00 0 11[ ]
1 0 020 1 0
jj
Sj
j
⎛ ⎞⎜ ⎟− ⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠
Attenuator (Optional)
Wilkinson power divider
Matched termination
Detector VSWR Meter
Microwave Source
Procedure: 1. Set the components as shown in figure 4 without Wilkinson power divider.
2. Energize the microwave source for particular frequency of operation.
3. Set any reference level of power on VSWR meter with the help of gain control knob of
VSWR meter, and note down the reading (P1 in dB).
4. Insert the Wilkinson power divider as shown in figure 4 with detector to port 2 and
matched termination to port 1, without changing the position of gain control knob of
VSWR meter.
5. Note down the reading of VSWR meter with the help of range-dB switch if required (P2
in dB).
6. Now carefully disconnect the detector from port 2 and matched termination from port 1
without disturbing the set-up.
7. Connect the matched termination to port 2 and detector to port 1 and measure the
reading on VSWR meter (P1 in dB).
8. Repeat the experiment by keeping port 2 and port 3 as input ports.
9. Scattering parameters of the Tee junction are calculated as follows
Port 1 as input port then, 221
1
PSP
= ; 331
1
PSP
=
Port 2 as input port then 112
2
PSP
= ; 332
2
PSP
=
Port 3 as input port then 113
3
PSP
= ; 223
3
PSP
=
10. Perform the experiment in a similar way using branch line coupler
Sample Observations:
I/P port
power(dB)
O/P port 1
power(dB)
O/P port 2
power(dB)
P3= -40 P1=-43 P2=-43
P2= -40 P3=-43 P1=-43
P1= -40 P2=-43 P3=-43
Practical Observations: (Wilkinson power divider) Practical Observations: (Branch Line Coupler)
Conclusions :
I/P port
power(dB)
O/P port 1
power(dB)
O/P port 2
power(dB)
I/P port
power(dB)
O/P port 1
power(dB)
O/P port 2
power(dB)
O/P port 3
power(dB)
Two Port Networks
Objective: To study the performance of different two port networks by determining their scattering parameters. Equipment required : AWR Microwave Office software Specifications : Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Metal thickness T = Dielectric constant εr = Loss tangent L = Theory : Microstrip lines: The simple microstrip line uses a single strip conductor on the dielectric that
rests on a single ground plane. Generally the ground plane made up of with good conductor like
silver or copper and the material used for the dielectric is Teflon or Aluminum or Silicon, etc.. It is
possible to use several independent strips with the same ground planes and dielectric. Microstrip
lines use quasi TEM mode of propagation. The ground plane of the microstrip line must be wide
compared with the top conductor, so it appears like a nearly infinite wide ground plane with only
very small electric field fringes at its edges. The characteristic impedance of a microstrip line
depends on the strip line width, thickness, the distance between microstrip line and ground plane
and the dielectric constant of the dielectric material.
Figure 1
Expt. No. : Date :
Design Equations: The effective dielectric constant is calculated by:
⎟⎠⎞
⎜⎝⎛+
−+
+=
WH
rre
1212
12
1 εεε
2
0
0
0
82
44 212 0.611 ln(2 1 ln( 1) 0.39
2
1 1 0.110.2360 2 1
3772
2
A
A
rr
r r
r r
r r
r
g
eeW forZ narrowstrip
H B B B
ZA
B forwidestripZ
l l
εε
π ε ε
ε εε ε
πε
φ πβ φ ββ λ
⎧ ⎫⎪ ⎪−⎪ ⎪= >⎨ ⎬⎡ ⎤⎧ ⎫−⎪ ⎪− − − + − + −⎨ ⎬⎢ ⎥⎪ ⎪⎩ ⎭⎣ ⎦⎩ ⎭
⎛ ⎞+ −= + +⎜ ⎟+ ⎝ ⎠
=
= = =
−
2gl
φλπ
=
W= Width of the microstrip line, l = Length of transmission line, H = Thickness of the substrate, A,B constants, Φ = Phase shift, λg=Guide wavelength.
Sample Observations: The behaviour of a two port network when matched with 50 ohm at both
input and output ports for a typical microstrip line with the following specifications is shown
below.
Z0 = 50 Ω, f = 3 GHz , H = 1.6 mm, T = 0.036 mm, εr = 4.4 , L = 0.001
Model graph: Practical Observations:
1 2 3 4 5Frequency (GHz)
Graph 1
-150
-100
-50
0
DB(|S(1,1)|)TWO PORT NETWORKDB(|S(2,1)|)TWO PORT NETWORK
6
Frequency S11 S12 S21 S22
Conclusions:
Wilkinson Power Divider
Objectives:
Expt. No. : Date :
1. To design and simulation of a Wilknson power divider for equal and unequal power divisions.
2. To determine the scattering parameters of Wilkinson power divider. Equipment required : AWR Microwave Office software Specifications : Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Metal thickness T = Dielectric constant εr = Loss tangent L = Figure (1) Theory: The Wilkinson power divider is generally designed using microstrip lines as shown in
figure 2 and can be made with any number of ports with equal or unequal power divisions.
Wilkinson power divider has many advantages over other power dividers and has the following
properties
5. Matched at all ports.
6. Large isolation between output ports
7. Reciprocal
8. Lossless when output ports are matched
The S-matrix of a 3-port Wilkinson power divider is given by
02 2
[ ] 0 02
0 02
j j
jS
j
− −⎛ ⎞⎜ ⎟⎜ ⎟
−⎜ ⎟= ⎜ ⎟⎜ ⎟
−⎜ ⎟⎜ ⎟⎝ ⎠
Figure (2)
Design Equations:
KZRKZR
KKZR
kKZKZZ
KKZZ
PPKionRatioPowerdivis
/
)1(
)1(
1
03
02
0
20
20302
3
2
003
2
32
==
+=
+==
+=
==
Sample Observations: For equal power division, sample results of a Wilkinson power divider
shown below
Z0 = 50 Ω, f = 3 GHz , H = 1.6 mm, T = 0.036 mm, εr = 4.4 , L = 0.001
Model graph:
Practical Observations:
1 2 3 4 5 6Frequency (GHz)
S parameters
-80
-60
-40
-20
0
DB(|S(1,1)|)Wilknson dividerDB(|S(2,1)|)Wilknson dividerDB(|S(3,1)|)Wilknson dividerDB(|S(3,2)|)Wilknson divider
Frequency S11 S21 S31 S32
Conclusions:
Branch Line Coupler
Objectives:
Expt. No. : Date :
3. To design and simulation of a branch line coupler. 4. To determine the scattering parameters of branch line coupler.
Equipment required : AWR Microwave Office software Specifications : Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Dielectric constant εr = Loss tangent L = Figure (1)
Theory : Branch line couplers are 3 dB directional couplers with a 900 phase difference in the
outputs of the through and coupled ports. This type of hybrid is often made in microstrip line form
as shown in figure 2. It is also known as Quadrature hybrid or 900 hybrid couplers. With all the
ports matched, power entering port 1 is eventually divided between ports 2 and 3 with a 900 phase
shift between these outputs. No power is coupled to port 4. Branch line coupler has a high degree
of symmetry, as any port can be used as the input port. The output ports will always be on the
opposite of the junction from the input port and the isolated port will be the remaining port on the
same side as the input port. The S-matrix will have the following form
0 1 00 0 11[ ]
1 0 020 1 0
jj
Sj
j
⎛ ⎞⎜ ⎟− ⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠
Figure (2)
Sample Observations:
Z0 = 50 Ω, f = 3 GHz , H = 1.6 mm, T = 0.036 mm, εr = 4.4 , L = 0.001
Model graph:
1 2 3 4 5 6Frequency (GHz)
S parameters
-60
-50
-40
-30
-20
-10
0
DB(|S(1,1)|)Branch line coupler
DB(|S(2,1)|)Branch line coupler
DB(|S(3,1)|)Branch line coupler
DB(|S(4,1)|)Branch line coupler
Practical Observations:
Frequency S11 S21 S31 S41
Conclusions:
1800 Hybrid Coupler
Objectives:
Expt. No. : Date :
5. To design and simulation of 1800 hybrid coupler. 6. To determine the scattering parameters of 1800 hybrid coupler.
Equipment required : AWR Microwave Office software Specifications : Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Dielectric constant εr = Loss tangent L = Figure (1) Theory : The 1800 hybrid junction is a four port network with a 1800 phase shift between the two
output ports. It can also be operated so that the outputs are in phase. With reference to the hybrid
coupler shown in figure 2, a signal applied to port 1 will be evenly split into two in-phase
components at ports 2 and 3, and port 4 will be isolated. If the input is applied to port 4, it will be
equallysplit into two compoents with a 1800 phase difference at ports 2 and 3, andport 1 will be
isolated. When operated as a combiner with input signals applied at ports 2 and 3, sum of the
inputs will be formed at port 1, while the difference will be formed at port 4. The 180 hybrid can be
fabricated in several forms. The ring hybrid or rat-race shown in figure 2 can be easily constructed
in microstrip form shown in figure 2. The scattering matrix for the ideal 3 dB 1800 hybrid thus has
the following form
0 1 1 01 0 0 1
[ ]1 0 0 120 1 1 0
jS
⎛ ⎞⎜ ⎟−− ⎜ ⎟=⎜ ⎟⎜ ⎟
−⎝ ⎠
Figure (2)
Sample Observations:
Z0 = 50 Ω, f = 3 GHz , H = 1.6 mm, T = 0.036 mm, εr = 4.4 , L = 0.001
Model graph:
1 2 3 4 5 6Frequency (GHz)
S parameters
-80
-60
-40
-20
0
DB(|S(1,1)|)180 Hybrid coupler
DB(|S(2,1)|)180 Hybrid coupler
DB(|S(3,1)|)180 Hybrid coupler
DB(|S(4,1)|)180 Hybrid coupler
Practical Observations:
Frequency S11 S21 S31 S41
Conclusions:
LPF – Richard’s Transformation Method Objectives: To design and simulation of low pass filter using Richard’s transformation method with parallel stubs. Equipment required : AWR Microwave Office software Filer specifications :
Filter type - Butterworth (or) Chebyshev Cutoff frequency(fc) - Insertion loss & - Frequency (w) - Ripple factor (δ) - Microstrip specifications :
Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Dielectric constant εr = Loss tangent L = Figure (1) Theory :
A microwave filter is a two port network used to control the frequency response at a certain
point in a microwave system by providing transmission at frequencies within the passband of the
filter and attenuation in the stopband of the filter. Most microwave filter design is done based on
the insertion loss method. The perfect filter would have zero insertion loss in the passband, infinite
attenuation in the stopband and a linear phase response in the pass band. Filter design at
microwave frequencies using lumped elements arise two problems. First, lumped elements such as
inductors and capacitors are generally available only for a limited range of values and are difficult
to implement at microwave frequencies, but must be approximated with distributed components. In
addition, at microwave frequencies the distance between filter components is not negligible.
Expt. No. : Date :
Richard’s transformation is used to convert lumped elements to transmission line sections,
while Kuroda’s identities can be used to separate filter elements by using transmission line
sections. Because such additional transmission line sections do not affect the filter response, this
type of filter design is called redundant filter synthesis. The Richard’s transformation is given by
Tan lβΩ =
By this equation, the inductors and capacitors of a lumped element filter design can be
replaced with short circuited and open circuited stubs as shown in figure 2, where the length of
each stub is λ/8 at cutoff frequency ωc. Three element filter design using parallel stubs in
microstrip form is shown in figure 3.
Figure 2 Figure 3
Design equations: (a) Maximally flat (or) Butterworth type:
Order of the filter: ( )
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
=
δ1010
1010
loglog2
110log
c
L
ww
N
L (in dB) is Insertion loss at w. δ is ripple factor.
Table of Element values for maximally flat LPF prototype (g0=1, gN+1=1)Order C1 L2 C3 L4 C5 L6 C7 L8 C9 L10
1 2.000 2 1.41421 1.41421 3 1.00000 2.00000 1.00000 4 0.76357 1.84776 1.84776 0.76537 5 0.61803 1.61803 2.00000 1.61803 0.61803 6 0.51764 1.41421 1.93185 1.93185 1.41421 0.51764 7 0.44504 1.24698 1.80194 2.00000 1.80194 1.24698 0.44504 8 0.39018 1.11114 1.66294 1.96157 1.96157 1.66294 1.11114 0.39018 9 0.34730 1.00000 1.53209 1.87938 2.00000 1.87938 1.53209 1.00000 0.34730 10 0.31287 0.90798 1.41421 1.78201 1.97538 1.97538 1.78201 1.41421 0.90798 0.31287 L1 C2 L3 C4 L5 C6 L7 C8 L9 C10
(b) Equal-ripple type:
Order of the filter
⎟⎟⎠
⎞⎜⎜⎝
⎛
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
−
=−
×
×−
c
G
L
ww
Mr
1
1.0
1.01
cosh
110110cosh
L (in dB) is the insertion loss at w. Gr is ripple amplitude in dB
Normalized Chebyshev element values, 0.01 dB ripple
Order C1 L2 C3 L4 C5 L6 C7 L8 C9
2 0.4489 0.4078 0.9085 3 0.6292 0.9703 0.6292 4 0.7129 1.2004 1.3213 0.6476 0.9085 5 0.7653 1.3049 1.5773 1.3049 0.7563 6 .07814 1.3600 1.6897 1.5350 1.4970 0.7098 0.9085 7 0.7970 1.3924 1.7481 1.6331 1.7481 1.3924 .07970 8 0.8073 1.4131 1.7824 1.6833 1.8529 1.6193 1.5555 0.7334 0.9085 9 0.8145 1.4271 1.8044 1.7125 1.9058 1.7125 1.8044 1.4271 0.8145
L1 C2 L3 C4 L5 C6 L7 C8 L9
Normalized Chebyshev element values, 0.1 dB ripple
Order C1 L2 C3 L4 C5 L6 C7 L8 C9
2 0.8431 0.6220 .07378 3 1.0316 1.1474 1.0316 4 1.1088 1.3062 1.7704 0.8181 0.7378 5 1.1468 1.3712 1.9750 1.3712 1.1468 6 1.1681 1.4040 2.0562 1.5171 1.9029 0.8618 .07378 7 1.1812 1.4228 2.0967 1.5374 2.0967 1.4228 1.1812 8 1.1898 1.4346 2.1199 1.6010 2.1700 1.5641 1.9445 0.8778 0.7378 9 1.1957 1.4426 2.1346 1.6167 2.2054 1.6167 2.1346 1.4426 1.1957
L1 C2 L3 C4 L5 C6 L7 C8 L9
Normalized Chebyshev element values, 0.20 dB ripple
Order C1 L2 C3 L4 C5 L6 C7 L8 C9
2 1.0379 .06746 0.6499 3 1.2276 1.1525 1.2276 4 1.3029 1.2844 1.9762 0.8468 0.6499 5 1.3395 1.3370 2.1661 1.3370 1.3395 6 1.3598 1.3632 2.2395 1.4556 2.0974 0.8838 0.6499 7 1.3723 1.3782 2.2757 1.5002 2.2757 1.3782 1.3723 8 1.3804 1.3876 2.2964 1.5218 2.3414 1.4925 2.1349 0.8972 0.6499 9 1.3861 1.3939 2.3094 1.5340 2.3728 1.5340 2.3094 1.3939 1.3861
L1 C2 L3 C4 L5 C6 L7 C8 L9
Normalized Chebyshev element values, 0.5 dB ripple
Order C1 L2 C3 L4 C5 L6 C7 L8 C9
2 1.4029 0.7071 0.5040 3 1.5963 1.0967 1.5963 4 1.6704 1.1926 2.3662 0.8419 .05040 5 1.7058 1.2296 2.5409 1.2296 1.7058 6 1.7254 1.2478 2.6064 1.3136 2.4759 0.8696 0.5040 7 1.7373 1.2582 2.6383 1.3443 2.6383 1.2582 1.7373 8 1.7451 1.2647 2.6565 1.3590 2.6965 1.3389 2.5093 0.8795 0.5040 9 1.7505 1.2690 2.6678 1.3673 2.7240 1.3673 2.6678 1.2690 1.7505
L1 C2 L3 C4 L5 C6 L7 C8 L9
Sample Observations: Specifications for a maximally flat low pass filter are
Cut off frequency is 1.5 GHz; insertion loss at 2.5 GHz is 10 dB .
With the given specifications, number of elements required is 3.
Z0 = 50 Ω, f = 1.5 GHz , H = 1.6 mm, T = 0.036 mm, εr = 4.4 , L = 0.001
Model graph:
Practical Observations:
0 1 2Frequency (GHz)
S parameters
-150
-100
-50
0
DB(|S(1,1)|)LPF RICHARDSDB(|S(2,1)|)LPF RICHARDS
3
Frequency S11 S21
Conclusions:
LPF – Stepped Impedance Method Objectives: To design and simulation of low pass filter using Stepped Impedance method. . Equipment required : AWR Microwave Office software Filer specifications :
Filter type - Butterworth (or) Chebyshev Cutoff frequency(fc) - Insertion loss & - Frequency (w) - Ripple factor (δ) - Microstrip specifications :
Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Dielectric constant εr = Loss tangent L = Figure (1) Theory :
A microwave filter is a two port network used to control the frequency response at a certain
point in a microwave system by providing transmission at frequencies within the passband of the
filter and attenuation in the stopband of the filter. Most microwave filter design is done based on
the insertion loss method. The perfect filter would have zero insertion loss in the passband, infinite
attenuation in the stopband and a linear phase response in the pass band. Filter design at
microwave frequencies using lumped elements arise two problems. First, lumped elements such as
inductors and capacitors are generally available only for a limited range of values and are difficult
to implement at microwave frequencies, but must be approximated with distributed components. In
addition, at microwave frequencies the distance between filter components is not negligible.
Expt. No. : Date :
One easy way to implement low pass filter in microstrip form is to use alternating sections
of very high and very low characteristic impedance lines. Such filters are usually referred to as
stepped impedance or hi-Z, low-Z filters. These filters are popular because they are easier to design
ad take up less space than a similar low pass filter using stubs. Because of the approximations
involved, however, their electrical performance is not as good, so the use of such filters is usually
limited to applications where a sharp cutoff is not required.
By using this method, the series inductors of a low pass prototype can be replaced with high
impedance line section (Z0=Zh) and the shunt capacitors can be replaced with low impedance line
sections (Z0=Zl). Stepped impedance filter implementation and its microstrip form is shown in
figure 2. With these approximations the electrical lengths of the inductor and capacitor sections are
calculated as follows
Inductor hZ
LRl 0=β and Capacitor
0RCZ
l l=β
R0 is the filter impedance; L, C are element values from the table.
Figure 2
Design equations: (a) Maximally flat (or) Butterworth type:
Order of the filter: ( )
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
=
δ1010
1010
loglog2
110log
c
L
ww
N
L (in dB) is Insertion loss at w. δ is ripple factor.
Table of Element values for maximally flat LPF prototype (g0=1, gN+1=1)Order C1 L2 C3 L4 C5 L6 C7 L8 C9 L10
1 2.000 2 1.41421 1.41421 3 1.00000 2.00000 1.00000 4 0.76357 1.84776 1.84776 0.76537 5 0.61803 1.61803 2.00000 1.61803 0.61803 6 0.51764 1.41421 1.93185 1.93185 1.41421 0.51764 7 0.44504 1.24698 1.80194 2.00000 1.80194 1.24698 0.44504 8 0.39018 1.11114 1.66294 1.96157 1.96157 1.66294 1.11114 0.39018 9 0.34730 1.00000 1.53209 1.87938 2.00000 1.87938 1.53209 1.00000 0.34730 10 0.31287 0.90798 1.41421 1.78201 1.97538 1.97538 1.78201 1.41421 0.90798 0.31287 L1 C2 L3 C4 L5 C6 L7 C8 L9 C10
(b) Equal-ripple type:
Order of the filter
⎟⎟⎠
⎞⎜⎜⎝
⎛
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
−
=−
×
×−
c
G
L
ww
Mr
1
1.0
1.01
cosh
110110cosh
L (in dB) is the insertion loss at w. Gr is ripple amplitude in dB
Normalized Chebyshev element values, 0.01 dB ripple
Order C1 L2 C3 L4 C5 L6 C7 L8 C9
2 0.4489 0.4078 0.9085 3 0.6292 0.9703 0.6292 4 0.7129 1.2004 1.3213 0.6476 0.9085 5 0.7653 1.3049 1.5773 1.3049 0.7563 6 .07814 1.3600 1.6897 1.5350 1.4970 0.7098 0.9085 7 0.7970 1.3924 1.7481 1.6331 1.7481 1.3924 .07970
8 0.8073 1.4131 1.7824 1.6833 1.8529 1.6193 1.5555 0.7334 0.9085 9 0.8145 1.4271 1.8044 1.7125 1.9058 1.7125 1.8044 1.4271 0.8145
L1 C2 L3 C4 L5 C6 L7 C8 L9
Normalized Chebyshev element values, 0.1 dB ripple
Order C1 L2 C3 L4 C5 L6 C7 L8 C9
2 0.8431 0.6220 .07378 3 1.0316 1.1474 1.0316 4 1.1088 1.3062 1.7704 0.8181 0.7378 5 1.1468 1.3712 1.9750 1.3712 1.1468 6 1.1681 1.4040 2.0562 1.5171 1.9029 0.8618 .07378 7 1.1812 1.4228 2.0967 1.5374 2.0967 1.4228 1.1812 8 1.1898 1.4346 2.1199 1.6010 2.1700 1.5641 1.9445 0.8778 0.7378 9 1.1957 1.4426 2.1346 1.6167 2.2054 1.6167 2.1346 1.4426 1.1957
L1 C2 L3 C4 L5 C6 L7 C8 L9
Normalized Chebyshev element values, 0.20 dB ripple
Order C1 L2 C3 L4 C5 L6 C7 L8 C9
2 1.0379 .06746 0.6499 3 1.2276 1.1525 1.2276 4 1.3029 1.2844 1.9762 0.8468 0.6499 5 1.3395 1.3370 2.1661 1.3370 1.3395 6 1.3598 1.3632 2.2395 1.4556 2.0974 0.8838 0.6499 7 1.3723 1.3782 2.2757 1.5002 2.2757 1.3782 1.3723 8 1.3804 1.3876 2.2964 1.5218 2.3414 1.4925 2.1349 0.8972 0.6499 9 1.3861 1.3939 2.3094 1.5340 2.3728 1.5340 2.3094 1.3939 1.3861
L1 C2 L3 C4 L5 C6 L7 C8 L9
Normalized Chebyshev element values, 0.5 dB ripple
Order C1 L2 C3 L4 C5 L6 C7 L8 C9
2 1.4029 0.7071 0.5040 3 1.5963 1.0967 1.5963 4 1.6704 1.1926 2.3662 0.8419 .05040 5 1.7058 1.2296 2.5409 1.2296 1.7058 6 1.7254 1.2478 2.6064 1.3136 2.4759 0.8696 0.5040 7 1.7373 1.2582 2.6383 1.3443 2.6383 1.2582 1.7373 8 1.7451 1.2647 2.6565 1.3590 2.6965 1.3389 2.5093 0.8795 0.5040 9 1.7505 1.2690 2.6678 1.3673 2.7240 1.3673 2.6678 1.2690 1.7505
L1 C2 L3 C4 L5 C6 L7 C8 L9
Sample Observations: Specifications for a maximally flat low pass filter are
Cut off frequency is 2.5 GHz; insertion loss at 4 GHz is 20 dB, highest practical line impedance is
120 Ω and the lowest is 20 Ω .
With the given specifications, number of elements required is 6.
Z0 = 50 Ω, f = 4 GHz , H = 1.58 mm, T = 0.0128 mm, εr = 4.2 , L = 0.02
Model graph:
1 2 3 4 5 6Frequency (GHz)
S parameters
-40
-30
-20
-10
0
DB(|S(1,1)|)LPF STEPPED IMPEDANCEDB(|S(2,1)|)LPF STEPPED IMPEDANCE
Practical Observations:
Frequency S11 S21
Conclusions: