Electronic Science
Electrodynamics and Microwaves 16. Matching networks and QWT
Module 16
Matching Networks and QWT
Index 1 Introduction
2. Input Impedance of a transmission line 3. Concept of Matching Networks
4. Insertion loss
5. Quarter Wave Transformer 6. Numerical Examples on QWT
7. Applications, Advantages and Limitations of QWT 8. Characteristic Impedance
9. Summary
Objectives: - After completing this module, you will be able to know about 1. The concept of matching networks.
2. Insertion loss.
3. Use of Smith chart in designing of QWT
4. Applications, advantages and limitations of QWT.
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Electrodynamics and Microwaves 16. Matching networks and QWT
1. Introduction
In the earlier module, we have studied how to use Smith Chart for determining the radially scaled parameters like reflection coefficient. Transmission coefficient, VSWR, Return loss etc. As we know, the main purpose of transmission line is to have nearly hundred percent transmission of the RF signal to the load without much loss of power. For this it is essential to achieve matching of input and output impedance of the transmission line to the source impedance and load impedance respectively. . We know that the conditions for matching a transmission line for 100% transmission and that for maximum power transfer are different. Generally, the source impedance is matched with the impedance at the input side .However; it may not be the case with the load impedance. It can be different in different applications and may not match with the impedance at the output terminals of the line. What to do in such a case? There are various ways to overcome such types of mismatches. In this module, let us discuss about the concept of matching networks comprising of reactive components and a techniques known as quarter wave impedance transformer or simply QWT making use of a piece of transmission line of length λ/4 for matching purpose. Smith Chart plays an important role as a graphical tool in the designing of both of these matching techniques.
2. Input Impedance of a transmission line
One of the important quantities of prominent importance is the input impedance of a transmission line generally denoted by Zin. Let us revise our knowledge about the terms input and output impedance of an electrical circuit. in brief.
Consider the circuit with generator across the input terminals and load impedance at the output terminals.
The impedance between the input terminals with load impedance ZL connected but generator removed is called as the input impedance of circuit and is given by
Zin = Z1 + [ (Z2 + ZL) // Z3 ]
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Electrodynamics and Microwaves 16. Matching networks and QWT
The impedance across the output terminals with generator having impedance Zg present but load impedance ZL removed is called as the output impedance of the circuit and is given by
Zout = Z2 + [ (Z1 + Zg) // Z3 ]
= Z2 +
Knowing the value of Z1, Z2, Z3 and ZL/Zg we can calculate Zin and Zout using the rules of complex algebra.
The choices of either Z1 , Z2 or Z3 equal to zero, we can get different types of filter network. For example, with Z2 = 0 we obtain L type filter. Such filters and combinations thereof, play an important role in what is known as matching networks. Let us try to understand the term
“impedance matching network “with the help of few simple examples.
3. Concept of Matching Networks
Now, consider a simple resistive network. Here we want to match the 10 Ω resistance ( RL )to the 6Ω resistance( RS . )This means, with Rs removed, the impedance i.e. resistance across the terminals A and B must be equal to 6 Ω. For this we cannot place a simple short circuit between terminals P and A and between terminals Q and B .We can easily understand that it will not serve the purpose of matching.
One of the acceptable solutions is to join terminals P and Q to terminals A and B respectively and connect a resistance R of 15 Ω between terminals A and B as shown in the following circuit.
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Electrodynamics and Microwaves 16. Matching networks and QWT
It can be easily verified that with RS removed, the resistance between terminals A and B, will be 6Ω.
RAB = R // RL = (R RL)/ ( R + RL ) = (15 x 10)/(15+10)= 150/25 = 6 Ω = RS.
Hence, we can say that R = 15 Ω in parallel with RL serves the purpose of the desired matching. Hence it is a matching network.
What will the matching network in this problem if the source resistance RS of 6 Ω is to be matched with the load impedance RL of 10 Ω ? The answer is simple. The matching network is a single resistance of 4 Ω connected between terminals P and A with a short circuit between terminals Q and B as shown.
Is it so easy for any given load? Definitely not. Can a resistor in parallel with 6 Ω will do the needful of matching the source resistance of 6Ω to the load impedance? Certainly NOT- because it leads to a negative value (- 15 Ω) of R which is not a practically acceptable solution
Now consider another circuit as shown involving ac source which is little bit complicated as compared to the earlier resistive circuit. It be noted that the choice of letters to denote input and out put terminals is arbitrary.
Z L = 20 + 10 j Ω , Z S = R S = 50 Ω , f = 400 MHz, Z L is to be matched with Z S
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Electrodynamics and Microwaves 16. Matching networks and QWT
In this circuit, it is expected to match the load impedance ZL=20 +10j Ω to the source impedance RS= 50 Ω at signal frequency of 400 MHz. In this case, what will be the network which can give the desired impedance? The calculations are not as easy as in the earlier problem with resistive network.
Matching networks of different types can be found as a solution. One of the solutions is as shown. N.B:- Z L is to be matched with Z S
Z L = 20 + 10 j Ω , Z S = R S = 50 Ω , f = 400 MHz
Answer :- X L ≈ j 14.50 Ω → inductor , X C ≈ - j 40.82 Ω →capacitor
We can verify numerically that with source removed, the impedance of ZPQ across the terminals P and Q has the desired value of 50 Ω. The calculations are as shown.
ZPQ= (ZL +XL) // XC = (ZL+XL) x XC / (ZL+XL+XC)
XL= j 2π f L ≈ j 14.50 Ω , L = 5.767 x10 -9 H , f = 400 x10 6 Hz XC= -j/ (2π fC ) ≈ -j 40.82 Ω , C =9.746 x10 -12 F.
ZL=20 +10 j Ω ZPQ = 50
0 0 Ω.We can have another solution for the same problem as a matching network as shown.
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Electrodynamics and Microwaves 16. Matching networks and QWT
X’ c = - 34.50 j Ω ( capacitor) , X’ L = 48.82 j Ω ( inductor ) , Z L = 20 + 10 j Ω Z S = R S = 50 Ω , f = 400 MHz
Note that in this case also, we have the value ZPQ=50 Ω as desired. Thus we have two matching networks for the same circuit.
ZPQ = ( ZL + XC’) // XL’ = ( ZL + XC’ ) XL’/ ( ZL+ XC’+ XL’) XC’ = - j 2 π f C’ = - j 34.50 Ω , C’= 11.53 x 10 -12 F , f = 400 x 10 6 Hz , XL’ = j 2 π f L’ = j 48.82 Ω , L’= 16.24 x 10 -9 H.
ZPQ = 50
0 0 ΩWe are familiar with the terms “star and delta networks” also known as “T and PI networks”.
Let us see the use of these networks as matching networks between source and load. It be noted that the two physical quantities namely source impedance and frequency of signal are of direct concern in designing of matching networks .Hence, many a times source symbol is not shown in the circuit diagram. See the circuit as an example of pi type of matching network. The designed values of components are as shown.
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Electrodynamics and Microwaves 16. Matching networks and QWT
The given and designed values of components are as shown.
Z L = 20 + 10 j Ω, Z S = R S = 50 Ω, f = 400 MHz, Q = 3 Zc = - 25 j Ω (capacitor), C = 15.915 pF
Za = 16.62 j Ω (inductor), La = 6.631 nH Zb = 10 j Ω (inductor), Lb = 3.979 nH
As an example of T type of matching network, see the circuit as shown. In the earlier module we have discussed about the computation of network impedance. It will be a good numerical computational exercise to verify the matching of the input and output impedances of these two circuits to the source and load impedance respectively.
The given and designed values of components are as shown.
Z L = 20 + 10 j Ω , Z S = R S = 50 Ω , f = 400 MHz , Q = 3 , Z 1 = - 42.27 j Ω ( capacitor) C = 9.414 pf , Z 2 = 86.60 j Ω ( inductor ) , L1 = 34.458 nH , Z 3 = 50 j Ω ( inductor ) L 2 = 19.89 nH
Thus, for a given load impedance ZL, we can obtain matching networks comprising of reactive components like capacitors and inductors. Note that inclusion of resistors is not recommended due their power dissipative nature. The designing of matching networks comprising of capacitors and inductors can be tedious and may not give the desired level of accuracy due to non-availability of components with exact values. Use of many on line sources available on the internet can be made effectively to design the desired type of matching network. We can study
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Electrodynamics and Microwaves 16. Matching networks and QWT
the effect of variation in circuit parameters such as signal frequency, source impedance, load impedance etc. on the values of the reactive components used in the matching network.
As an example, with Pi network discussed above, have a look at the effect on values of reactive components due to change in source and load impedance. Which values undergo a change under variation in source or load impedance?
Table: - Pi network
f = 1 GHz, Quality factor (Q) = 3, ZL = RL + j XL, ZS = R + j X
Sr no R X RL XL L nH C1 pF C2 pF
1 40 0 50 30 4.93 10.53 9.71
2 40 10 50 30 5.00 11.20 9.71
3 40 10 40 10 3.95 12.55 12.55
4 40 0 50 0 4.49 10.53 9.55
Also, as an additional example, in the case of T network, have a look at the effect on values of reactive components due to change in source and load impedance.
Table: - T network
f = 1 GHz, Quality factor (Q) = 3 ZL = RL+ j XL, ZS = R + j X
Sr no Rs Xs RL XL Ls nH C pF LL pF
1 40 0 50 30 19.10 2.25 16.28
2 40 10 50 30 17.51 2.25 16.28
3 40 10 40 10 19.51 2.38 17.51
4 40 0 50 0 19.10 2.25 21.05
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Electrodynamics and Microwaves 16. Matching networks and QWT
4. Insertion loss
Now consider a transmission line of length L having generator with impedance Zg at one end and the load impedance ZL at the other end as shown. Let Z0 be the characteristic impedance of the transmission line.
We know that for no reflection at the receiving end we must have, Z0 =ZL. In general ZL may not match with Z0.Especially with real Z0 and complex ZL, ZL Z0. Such mismatch will give rise to return loss and mismatch loss as discussed in one of the earlier modules. Also, use of matching network gives rise to what is known as “Insertion Loss” which mainly depends upon the composition of matching network and imperfection of components therein.
Insertion loss is the loss of signal power resulting from the insertion of a device in a transmission line or optical fiber. It is denoted by IL and is expressed in decibels (dB).
If the power transmitted to the load before insertion of the device is PT and the power received by the load after insertion is PR, then the insertion loss in dB is given by,
IL= 10 log 10 ( P T / P R ).
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Electrodynamics and Microwaves 16. Matching networks and QWT
The energy absorbed by the transmission line in the direction of the signal path is measured by Insertion loss in dB/meter or dB/ feet. Insertion loss of a cable varies with frequency; the higher the frequency, the greater is the loss
Advanced electronic instruments such as Network analyzer, have many attractive features of displaying the Smith chart, plot the measured data on it and showing the calculated impedance at the marked point in a several marker formats. Use of such instruments incorporating display of Smith charts and analyzing the data, is highly useful for computations of insertion loss. It be remembered that, Transmission coefficients are commonly referred to as gains or attenuations, while reflection coefficients relate to return losses and VSWRs.
Measurements of Insertion loss are useful in troubleshooting a given network. High insertion loss can contribute to poor system performance and loss of coverage.
The accurate and repeatable measurements of insertion loss can be made with the help of some advanced instruments - Site Master, for example.
5. Quarter Wave Transformer
Instead of using a matching filter networks, can we not have some other simple electrical system? The answer is “Yes, we do have “. Let us discuss about one of such systems. Consider the following system, Let λ be the wavelength of the signal transmitted along the transmission line.
To match the load ZL with Z0, the original length L of the given transmission line –also called as feed line in some other systems - is increased by inserting a piece of another transmission line of length λ/4 with characteristic impedance Z0 ‘between the output terminals of the receiving end of the original transmission line and the load impedance ZL. This technique involving the use of trans mission line of length λ/4 is known as QWT meaning Quarter Wave Impedance Transformer. With this the new system, becomes as shown.
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Electrodynamics and Microwaves 16. Matching networks and QWT
With such insertion of a small segment of transmission line of length λ/4, It can be shown that, or . For a given ZL, to achieve the matching condition Zin = Z0, we can calculate Z0’ and select the small segment of transmission line made up of appropriate material of the Line accordingly. The QWT is many a times referred in the literature as a /4 transformer.
The result , can be derived by finding the limiting value of Zin for a lossless transmission line as the electrical length βL → π/2.
= .
Note that, here, , and tan ( )
6. Numerical Examples on QWT
Let us see a simple numerical problem related with QWT. The problems read as shown.
Problem: - A loss less transmission line in air with characteristic impedance 50Ω is to be matched with a load of impedance 180Ω at a frequency of 6 GHz using a QWT. Determine the smallest length L and the characteristic impedance of the QWT.
Here , since the transmission line is loss less and is in air, we have
Phase velocity = c = 3 x 10 8 m/s. With frequency f= 6 GHz = 6 x 10 9 Hz, we obtain λ= c / f = 50 cm. Hence, L = λ / 4 = 12.5 cm.
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Electrodynamics and Microwaves 16. Matching networks and QWT
For perfect matching we must have Zin = Z0 = 50 Ω. Hence the desired characteristic impedance of the QWT can be obtained as
= 30 Ω.
Thus for matching we have to select a transmission line of length 12.5 cm with characteristic impedance 30 Ω. Any deviation from these values will give rise to a return loss, mismatch loss and insertion loss to some extent.
Generally, for a lossless transmission line, the characteristic impedance Z0 of the line is real.
While using QWT for impedance matching, the nature of load namely real or complex becomes another issue. Have a look at the formula for Characteristic impedance Z0’ of the QWT:
. Accordingly if the load impedance ZL is real then obviously the Characteristic impedance Z0’ of the QWT will also be real and can be realized easi ly. However, if ZL is complex, then will also be complex which will not match with real Z0 .In such a case QWT cannot be used.
To overcome this difficulty, another section of the transmission line with characteristic impedance Z0 of appropriate length L1 = t λ is connected between the QWT and the load as shown. The length L1 is so selected that its input impedance Z1 is real.
This real impedance Z1 is converted into a real input impedance Zin with the help of a QWT having real valued characteristic impedance Z0’. The wires having characteristic impedance Z0’
are used in QWT so that the matching condition Zin =Z0 is satisfied.
Let us see one example so as to have better understanding of this technique.
Problem:- In the diagram shown earlier, find
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Electrodynamics and Microwaves 16. Matching networks and QWT
i) the smallest length L1 of a lossless line of characteris tic impedance Z0 =50 Ω to be connected between QWT and the load and
ii) the characteristic impedance Z0’ of the QWT so that the load impedance ZL = 20 + 65 j Ω matches with the transmission line having characteristic impedance Z0 =50 Ω.
We will use Smith chart to find the value of normalized impedance z1 and the length L1 .For this follow the stepwise procedure as follows.
Step 1: Calculate and plot the normalized load impedance zl on the smith chart .Let point P represent the normalized load impedance zl.
Normalized load impedance zl = ZL/Z0 = (20 + 65 j )/ 50 = 0.4+1.3 j
Join points O and P. Extend the line OP towards P to meet the distance scale marked with
“Towards the Generator ”at point T. Note the reading “ k λ” at point T. From point T move on the distance scale to reach the point B on the s mith chart in the direction “Towards the Generator”. The total radial distance traversed in this way from T to reach B gives the value of required Length L1. Note that, L1 = (0.25-k) λ if the point T is on the upper half circumference, i.e. 0 < k ≤ 0.25 and L1 = (0.25+0.5-K) λ = (0.75-k) λ if if the point T is on the lower half circumference of the circle i.e. 0.25 < k ≤ 0.5.F
In the problem under consideration, we have k = .015. Hence L1= (0.25-0.15) λ = 0.1 λ.
To determine the real normalized impedance z1, draw a circle of radius OP with O as its center.
Note the reading at point of intersection W’ of the circle with radius OB of the smith chart. The reading at point W’ represents the value of real normalized impedance z1.
Use this value of real normalized impedance z1, to obtain the required input impedance Z1 using the formula: Z1 =Z0 x z1
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Electrodynamics and Microwaves 16. Matching networks and QWT
In the problem under consideration, we have z1 = 7.0. Z0 = 50 Ω. Hence, Z1= 50 x 7 = 350 Ω.
Thus knowing the value of Z1= 350 Ω, we can obtain the required value of the characteristic impedance Z0’ of the QWT using the relation derived earlier as shown.
Z0’= = = = 132.287Ω.
We can verify the fact that value of Z1 is real by using the analytical formula for calculating the impedance of a transmission line at a distance d from the load as shown.
L1= λ/10 , β L1 = (2π/λ ) ( λ/10) = π/5 , tan( βL1) = tan( π/5 ) ≈ 0.6283.
Z0 = 50 Ω, ZL = 20 + 65 j Ω. , Z1 = ≈ 350 0 0 Ω.
As an exercise, try to calculate and verify the values of L1, Z1 and Z0’ corresponding to the values of Z0 and ZL shown in the Table.
Sr No Z0 Ω ZL Ω L1 Z1 Ω Z0’ Ω
1 50 50 +50 j 0.088λ 131 81
2 50 100 -50 j ? ? ?
7. Applications, Advantages and Limitations of QWT
There are many applications of QWT. For example, many a times, we need to provide DC power to active devices such as switching transistor or varactor diode connected to a transmission line. We know that ideally DC voltage source has zero impedance. Hence , DC voltage source if connected directly will result in a transmission line short circuited at its input. Hence, the dc source is connected to the transmission line via a QWT. Due to this, the short circuit is transformed in to an open circuit and the signal transmitted on the line remains unaffected.
The QWT has a property of providing Zin as a dual of the load impedance. Hence it is used in inverters .Due to this property, QWT can also be used as a component in many types of filters.
What do we understand by the term dual of the load impedance? The dual of impedance is nothing but its reciprocal or algebraic inverse representing admittance. On similar line, we understand the term dual of a network as the network whose impedances are the duals of the
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Electrodynamics and Microwaves 16. Matching networks and QWT
original impedances. In the case of a black-box network with multiple ports, the impedance looking into each port must be the dual of the impedance of the corresponding port of the dual network.
Though simple and useful, QWT suffers from some drawbacks. For example, i) For a given load impedance ZL and the characteristic impedance Z0 of the feed line , if it is not possible to have a transmission line used as a QWT with desired characteristic impedance Zo’ having adequate level of precision , then the QWT matching technique cannot be used for impedance matching . ii) QWT can be used to match the load to the feed line only at one frequency. Any deviation from the original signal frequency causes changes in the load impedance ZL and characteristi c impedance Z0 of the transmission line. The frequency dependence of ZL and Z0 , in turn change the value of Z0’ . Thus, for matching the line at some other frequency, we have to select another transmission line with new value of Z0’. This fact is described by saying that QWT has low band width.
Here, in the case of QWT, the phrase low bandwidth indicates the fact that only little variation from the original or central frequency is tolerable so as not to allow much change in the component values. How to increase the bandwidth? To increase the bandwidth we may think of using many QWTs in series with the fed line. However, there are some disadvantages in this approach.
. As we know now, the major problem faced with QWT is its low band width. A single circuit matches only at a single frequency .Obtaining a good match over an extended frequency range may require many elements. The more the number of components, the more is the propagation of error in the calculations which can affect the reliability of the matching action.
Finding the precise values and their realization may become a challenging job.
We are familiar with the term “bandwidth“. It is a term which tells us roughly the range of frequency over which the response of the circuit is nearly the same as expected within the specified limit .The quality factor Q is another term which couples the central frequency and the bandwidth through the relation Q = bandwidth / central frequency. The desired value of Q depends upon the type of desired performance .For example, for amplifiers BW is expected to be large while for resonant circuits BW is expected to be small.
In principle , all complex loads can be matched with the help of networks comprising of reactive components like capacitors and inductors and sometimes a single transmission line, Still then why sometimes matching becomes so difficult? A little thought over this question, we understand that for loads with a large reflection coefficient, the element values may be practically difficult to realize. This is particularly there for distributed circuits.
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Electrodynamics and Microwaves 16. Matching networks and QWT
One has to think over an important challenging issue about designing aspects of QWT 8. Characteristic Impedance
From the discussion made so far, we note that, in the technique of impedance matching us ing QWT, characteristic impedance plays an important role. Let us note some points related with characteristic impedance.
1) The characteristic impedance is also called as surge impedance or natural impedance. It depends upon the geometry and materials of the transmission line.
2) For a uniform line, characteristic impedance is independent on its length.
3) A lossless line is defined as a transmission line that has no line resistance and no dielectric loss. The characteristic impedance of a lossless transmission l ine is purely real.
4) Underground cables normally have very low characteristic impedance.
Characteristic impedance of a coaxial cable mainly depends upon the size, spacing between the conductors and dielectric used between the conductors. At ordinary frequencies, Characteristic impedance of a coaxial cable depends in an exponential manner of upon the logarithm of the ratio of diameters of the outer and inner conductors. From the documented data we understand that most coaxial cables have a characteristic impedance of 50, 52, 75, or 93 Ω. The RF industries use standard type-names for coaxial cables. The characteristic impedance depends upon the standard. For example, in the case of USB standard the characteristic impedance is 90 ± 15%. Such technical data is very important for designers.
In electric power transmission, the characteristic impedance of a transmission line is expressed in terms of the surge impedance loading (SIL), or natural loading. It is the power loading at which reactive power is neither produced nor absorbed.
Improper loading of the transmission line , results in absorption or supply of reactive power.
When the line is loaded below its SIL, it supplies reactive power to the system which in turn tends to raise the system voltages.
When the line is loaded above SIL, the line absorbs reactive power, tending to depress the voltage.
This effect is known as The Ferranti effect. This effect describes the voltage gain towards the remote end of a very lightly loaded (or open ended) transmission line. Friends, so many points can be discussed regarding quantities like characteristic impedance and others related with transmission lines of different types. However we will stop here.
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Electrodynamics and Microwaves 16. Matching networks and QWT
9. Summary
Networks of different types comprising of reactive components can be used for matching a transmission line with a given load.
Use of matching networks or systems give rise to insertion loss.
The QWT has a property of providing Zin as a dual of the load impedance.
QWT has low band width.
DC source can be connected to the transmission line via a QWT.
Smith chart plays an important role in designing QWT and reactive matching networks.
Multiple choice Questions:
Q1:-In a resistive network ,a resistor (2.3Ω) is connected in series with a parallel combination of four resistors with resistances 20 Ω , 10Ω , 5Ω and 20 Ω .The effective resistance across the output terminals of the network will be equal to
a) 4.8 Ω b) 5.3 Ω c) 6.0 Ω d) 6.3 Ω Answer :- a)
Q2:-The effective resistance of a parallel combination of four resistances 10Ω , RΩ, 20Ω and 20Ω is 2.5 Ω. Then R =
a) 1 b) 1.5 c) 2 d) 5 Answer :- d)
Q3:- With conventional meanings of the symbols, the insertion loss (IL) in dB is given by the expression
a) IL = 10 Log10(PT/PR) b) IL = 10 Log10(PR/PT) c) IL = 20 Log10(PT/PR) d) IL = -20 Log10(PT/PR) Answer :- a)
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Electrodynamics and Microwaves 16. Matching networks and QWT
Q4:-If the power received by the load after insertion of a device is 10 % of the power transferred to the load before insertion of the device, then the insertion loss will be
a) 0.01dB b) 0.10 dB c) 1.00 dB d) 10 dB Answer:- d)
Q5:- A QWT transforms the real load impedance ZL (48 Ω) in to the characteristic impedance Z0 (75 Ω) of a lossless transmission line. Then the characteristic impedance Z0’ of the line used in QWT will be
a) 40 Ω b) 50 Ω c) 60 Ω d) 80 Ω Answer: - c)
Q6:-The electrical length of QWT is equal to
a) π / 8 rad b) π / 4 rad c) π / 2 rad d) 3π / 2 rad Answer: - c)
Q7:- A lossless transmission line in air can be matched with a load resistance of 100 Ω at frequency f GHz using a QWT of smallest length 12.5 cm .Then f =
a) 0.6 GHz b) 1.25 GHz c) 6 GHz d) 8 GHz Answer: - a)
Q8:- A section of a transmission line of the smallest length L1 and characteristic impedance Z0
(50 Ω) connected between QWT and the load transforms the complex load impedance ZL in to a real impedance Z1. If the smallest value of L1 is 0.3λ then ZL =
a) 20 -70 j Ω b) 70 + 20 j Ω c) 20 - 32.5 j Ω d) 32.5 +20 j Ω Answer: - c)
Q9:- A section of a transmission line of the smallest length L1 and characteristic impedance Z0
(50 Ω) connected between QWT and the load transforms the complex load impedance ZL (30 – 100 j Ω) in to a real impedance Z1 Ω. Then L1 =
a) 0.155λ b) 0.225λ c) 0.345λ d) 0.435λ Answer: - d)
Q10:- When a DC source is connected to a lossless transmission line via a QWT,
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Electrodynamics and Microwaves 16. Matching networks and QWT
a) The signal transmitted goes on decreasing exponentially along the line b) Power transferred at the input of the transmission line is increased c) Short circuit is transformed in to an open circuit
d) Open circuit is transformed in to a short circuit Answer: - c)
*************
Quadrant IV: Learn more Reference books
1.Microwave Devices and Circuits by Samuel Y. Liao, Prentice Ha
2.Microwave Engineering, by David M Pozar, 4ed Wiley, John Wiley & Sons, Inc.
http://www2.electron.frba.utn.edu.ar/~jcecconi/Bibliografia/Ocultos/Libros/Microwave_Engin eering_David_M_Pozar_4ed_Wiley_2012.pdf
3.Electromagnetics (Fourth edition )John D Kraus, McGraw-Hill International Editions
Useful web links
i) https://en.wikipedia.org/wiki/Quarter-wave_impedance_transformer ii) http://whites.sdsmt.edu/classes/ee481/notes/481Lecture9.pdf iii) http://wcchew.ece.illinois.edu/chew/ece350/ee350-10.pdf
iv) upcommons.upc.edu/.../DARFM Tapers++transformers and+ matching+...
v) www.priyadarshini.net.in/.../ece/V/.../PPT/Impedance%20matching.ppt
vi) https://www.svce.ac.in/.../EC6503%20Transmission%20Lines%20and%2..
vii) rfmwlab.kau.ac.kr/Data/Lecture/MW05.ppt
viii) higheredbcs.wiley.com/legacy/college/pozar/0471448788/ppt/ch05.ppt ix) https://en.wikipedia.org/wiki/Insertion_loss
x) https://www.microwaves101.com/calculators/872-vswr-calculator
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xi) https://www.microwaves101.com/encyclopedias/insertion-loss
xii) http://www.daycounter.com/Calculators/L-Matching-Network-Calculator.phtml xiii) http://www.allaboutcircuits.com/tools/tank-circuit-resonance-calculator/
xiv) https://home.sandiego.edu/~ekim/e194rfs01/jwmatcher/matcher2.html xv) http://circuitglobe.com/ferranti-effect.html
xvi) http://circuitglobe.com/ferranti-effect.html
xvii) http://electricalbaba.com/how-to-reduce-the-ferranti-effect-in-a-transmission-line/
