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Double stub matching eliminates standing waves on the source side of the left stub.
If Z_{sc} = 64Ω and Z_{oc} = 100 Ω, the characteristic impedance will be given by.
Characteristic impedance is given by
Consider a lossless line with characteristic impedance R_{0} and VSWR = S. Then, the impedance at the point of voltage maxima and voltage minima are respectively given by
Given,
Z_{0} = R_{0}
we have
and
If K is the reflection coefficient and S is the voltage standing wave ratio, then
Voltage standing wave ratio is given by
or,
(Using componendo and dividendo)
or,
In terms of R, L, G and C the propagation constant of a transmission line is given by
Propagation constant of a transmission line is given by
A line has Z_{0} = 300∠0º Ω, and Z_{L} = 150∠0º Ω Voltage standing wave ratio (S) is given by
Given
Z_{0} = 300∠0º
and Z_{L} =150∠0ºΩ
The characteristic impedance of a distortionless line is
Characteristic impedance,
or,
(Since L/R = C/G for a distortionless line)
Hence, characteristic impedance of a distortionless line is purely real.
A transmission line with a characteristic impedance Z_{0} is connected to a transmission line with characteristic impedance Z_{c}. if the systme is being driven by a generator connected to the first line, then the overall transmission coefficient of current will be
The overall transmission coefficient is
Which of the following statements related to a transmission line is/are correct?
1. Transmission line elements are integral parts of the antenna, in some antenna system.
2. A feeder is a particular case of a transmission Sine.
3. A lossless transmission line doesn’t has resistance but, has a nonzero value of leakage conductance.
4. At radio frequency (RF), R and G both are neglected.
Assertion (A): A finite transmission line terminated in its characteristic impedance Z_{0}, is equivalent to an infinite line.
Reason (R): The input impedance of an infinite line is the characteristic impedance of the line.
The input impedance of a finite line terminated in its characteristic impedance (Z_{0}), is equivalent to an infinite line because the input impedance of an infinite line is the characteristic impedance of the line (Z_{0}). Hence, both assertion and reason are true and reason is the correct explanation of assertion.
Consider the following statements:
1. Propagation constant is a dimensionless quantity.
2. When the line is lossless, propagation constant is directly proportional to the frequency.
3. Propagation constant when multiplied with the frequency gives the electrical length of the line.
Which of the above statements is/are true?
Assertion (A): The group velocity is usually more than the phase velocity.
Reason (R): If the transmission line or transmission medium is such that different frequencies travel with different velocities, then the line or the medium is said to be dispersive.
Group velocity is given by
Phase velocity or velocity of propagation is given by
The group velocity is usually less than the phase velocity. Hence, assertion is a false statement.
Assertion (A): A transmission line act as resonant circuit and is used in many applications at high frequencies in antenna design and other ratio circuitory
Reason (R): An open and shortcircuited lines behaves like resonant circuit when length of line is an integral multiple of λ/3.
Assertion is correct because when a transmission line is open or shortcircuited it behaves as resonant circuit. However, reason is false because this happens when length of the line is an integral multiple of λ/4.
We knnw that
Z_{oc} = j cot βl
and Z_{sc} = jZ_{0} tan βl
Thus, when βl = length of line = nλ/4 , then
cot βl = 0
and tan βl = ∞
∴ Z_{oc} = 0
and Z_{sc} = ∞
This means a quarter wave shortcircuit line represents an infinite impedance at inpul terminals, just like a parallel resonant (LC) circuil and a λ/4 open circuit line present zero impedance at input terminals just like a series resonant LC circuit.
Assertion (A): Sometimes a quarter wave line is called as impedance inverter.
Reason (R): The quarter wavelength line transforms a load impedance Z_{R} that is smaller than Z_{0} into a value Z_{s} that is larger than Z_{0} and viceversa.
ln an impedance smith chart, a clockwise movement along a constant resistance circle gives rise to
A transmission line whose characteristic impedance is purely resistive
The input impedance of a short circuited quarter wave long transmission line is
Input impedance of a shortcircuited quarter wave line depends on the nature of load impedance Z_{L}.
A rectangular air filled waveguide has cross section of 4 cm x 10 cm. The minimum frequency which can propagate in the waveguide is
Consider the transmission system shown below:
The input impedance Z_{in} is given by
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