In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmission must be taken into account. This applies especially to radio-frequency engineering because the short wavelengths mean that wave phenomena arise over very short distances (this can be as short as millimetres depending on frequency). However, the theory of transmission lines was historically developed to explain phenomena on very long telegraph lines, especially submarine telegraph cables.
Transmission lines are used for purposes such as connecting radio transmitters and receivers with their antennas (they are then called feed lines or feeders), distributing cable television signals, trunklines routing calls between telephone switching centres, computer network connections and high speed computer data buses. RF engineers commonly use short pieces of transmission line, usually in the form of printed planar transmission lines, arranged in certain patterns to build circuits such as filters. These circuits, known as distributed-element circuits, are an alternative to traditional circuits using discrete capacitors and inductors.
Ordinary electrical cables suffice to carry low frequency alternating current (AC) and audio signals. However, they cannot be used to carry currents in the radio frequency range above about 30 kHz, because the energy tends to radiate off the cable as radio waves, causing power losses. RF currents also tend to reflect from discontinuities in the cable such as connectors and joints, and travel back down the cable toward the source. These reflections act as bottlenecks, preventing the signal power from reaching the destination. Transmission lines use specialized construction, and impedance matching, to carry electromagnetic signals with minimal reflections and power losses. The distinguishing feature of most transmission lines is that they have uniform cross sectional dimensions along their length, giving them a uniform impedance, called the characteristic impedance, to prevent reflections. The higher the frequency of electromagnetic waves moving through a given cable or medium, the shorter the wavelength of the waves. Transmission lines become necessary when the transmitted frequency's wavelength is sufficiently short that the length of the cable becomes a significant part of a wavelength.
At microwave frequencies and above, power losses in transmission lines become excessive, and waveguides are used instead which function as "pipes" to confine and guide the electromagnetic waves. At even higher frequencies, in the terahertz, infrared and visible ranges, waveguides in turn become lossy, and optical methods, (such as lenses and mirrors), are used to guide electromagnetic waves.
Two very large parallel conducting plates of very large length l, and width w are separated by a distance d. A current I=Jw flows to the right in the lower plate and to the left in the upper plate. Each of the two currents produces a magnetic field \frac{B}{2} between the two plates.
(a)...
Two very large parallel conducting plates of very large length l, and width w are separated by a distance d. A current I=Jw flows to the right in the lower plate and to the left in the upper plate. Each of the two currents produces a magnetic field \frac{B}{2} between the two plates.
(a)...
Homework Statement
An ideal transmission line has a characteristic impedance of Z=50 Ohms and
v=200,000km/s propagation velocity. A sinusoidal signal with frequency f=1GHz and
A=10mV amplitude is traveling down the line.Its total duration is 10s.What total
energy is it carrying?
Homework...
Hi All,
I understand that if you have a lossless transmission line and a lossless antenna and there is a mismatch at the antenna/transmission line junction, no energy is lost. If the transmitter is delivering 100 watts into the line, 100 watts will be radiated from the antenna.
I'm...
Homework Statement
An annular sheet (i.e. a flattened ring) , of thickness t = 1mm and made of a material of resistivity 0.5 Ohm m connects the inner and outer conductors of an air spaced coaxial transmission line at a point on the line. A low frequency signal is fed into one end of the line...
Homework Statement
Prove that for a line having resistance R, and reactance X, and supplying load of P+jQ has an approximate voltage drop of:
Vr = [RP+XQ]/Vs
Homework Equations
none given.
The Attempt at a Solution
I made a diagram, with R, X, and P+jQ in series. Vr is the...
I was reading about transmission lines. I thought if the line and load are matched, then the voltage on the line will be equal to the voltage on the load. But fig 16.2 (page 1000) in the book here, the voltage at load is half the line voltage. I don't get it!
Book link-
(click the contents link...
In a transmission line, what makes the current flow?
I understand that the line is excited by an AC voltage at one end. This sets up a changing electric field between the conductors and therefore a changing magnetic field. However, there is no voltage along the line, so what makes the current...
Transmission line approximation
Homework Statement
In the derivation of the approximate formulas of \gamma and Z0 for low loss lines, all terms containing the second and higher order powers of R/wL and G/wC were neglected in comparison with unity. (R/wL<<1 and G/wC<<1)...
Dear All
I am hoping for some insight into a transmission line problem I have been experiencing. I am quite inexperienced and unqualified in this area so if I am not clear please let me know.
In wiring loom assemblies my employer offers there is a twisted transmission pair. The...
Hello,
As far as I understand, a transmission line is simply a wave-guide for TEM modes.
If the waves are propagating in the z direction so Hz=Ez=0. How does this fact leads to the conclusion that in any transverse plane (xy plane) the fields are conservative?
Thanks a lot.
Hi Guys,
I looked so hard on the net, trying to understand something that I am struggling with for the whole day, but I ended up frustrated.
I am working on my design project and was assigned a part conecnred with antennas, I am using the Antenna Theory Analysis and Design by Balanis to...
Homework Statement
A transmission line has the following properties:
L_{0} = 1 mHm^{-1}
C_{0} = 10 \mu F m^{-1}
R_{0} = 10 \Omega m^{-1}
G_{0} = 0 \Omega^{-1} m^{-1}
That is, inductance per meter, capacitance per metre etc. The line is 10m long.
The problem is to find the...
Asmall power plant produces a voltage of 6.0kV and a current of 150A. The voltage is stepped up to 240kV by a transformer before being sent to a substation. The resistance of the transmission line between the power plant and the substation is 75 ohm. How much is the current flowing in the...
I understand that reflected waves on a transmission line are a result of the constraints of Ohm's Law and Kirchhoff's Law at the transition points.
However, I'm having trouble visualizing the physical cause for this. What is actually causing the electrons to flow in the opposite direction...
Homework Statement
A transmission line consists of a cylindrical conductor of radius r at a distance d in air from a conducting plane (r >>d).
Derive the capacitance per unit length C and the inductance per unit length L and
check that 1/sqrt(LC) = c.
Homework Equations
The...
If a single conductor in a transmission line dissipates 6,000kWh of energy over a 24 hour period during which time the current in the conductor was 100 amps. What is the resistance in the conductor.
So could I just conver the kWh of energy to kW by dividing by 24 hours...than just use ohms...
Homework Statement
Design a dc transmission line that can transmit 225 MW of electricity 185 km with
only a 2.0% loss. The wires are to be made of aluminum and the voltage is 660 kV.
2. Homework Equations
P= IV = I^2 * R
R= p(L/A)
Power loss = Pf - Pi
Attempt at a solution
I worked through...
I am studying EM wave and transmission lines. I see both derive equations for propagation constant \gamma:
Plane wave velocity is 1/\sqrt{\mu\epsilon} and \eta = \sqrt{\mu/\epsilon}
Transmission line velocity is 1/\sqrt{LC} and Z0=\sqrt{L/C}.
From that the book just to say the velocity...
Hello everybody,
I have a question and I am wondering if you can help me find an answer. The problem I am trying to figure out is:
I have 400 miles of 345 kV transmission line. An outage happened twice in two different locations on the line caused by two different lightning strikes, a 35kA...
I have been trying to interpretating the voltage and current phasors in transmission line. I want to verify with you guys/gals here what my understanding. I am using only the voltage phasor as an example. I separate phasor V(z) into V(z)+ and V(z)-. I put the load at z=0 and V(z=0) at +r axis(...
I think pretty much everybody knows the length of the transmission line should be less than the wave length of the RF signal.
How do you explain it to some one who is not from engineering background.
I myself can't get it some times.
Say for example the wavelength of a wave is
2" =...
Z in =50-j10 Ohms
i in=2 amps
length = 2 meters
Z0=75 Ohms
u=2E8 meters per second
beta=.3 rad/m
How do I find I+ and I- at the input?
What is the voltage at the load?
Any help would be appreciated.
How is signal transmission speed determined in a transmission line? For example, what determines how long it takes a single pulse to go from one end of a line to the other end. I would assume it depends directly on the conductivity of the material from which the line is made but I'm not sure...
Hello everyone ,
I am still new to the protection field so i would appreciate if you can help me with analysis of the following,
A 13.8 Kv OHTL was cut and fell on ground , the cable was still live although being protected by Earth fault relays and Over current relays(Instantaneous and...
Hello All,
I have two PCBs, board A and board B. Board A has a 50MHz Crystal that I am making available through a high speed digital isolator (IL711-2E) to a chip that is on board B.
Here's the datasheet on the isolator IC http://www.nve.com/Downloads/il711-2.pdf".
Now, I was thinking about...
Is it true that lossless transmission lines don't distort signals?
to me, they seem like low pass filters.
i had this class a while ago, but I guess i forgot this, or never understood it
thanks
If I have a section of transmission line, with a characteristic impedance Z0, how does the standing wave ratio in that section change as a function of the frequency of operation?
Doesn't the stading wave ratio just depend on the characteristic impedance of the line, and the load impedance?
Can I first find the input impedance relative to the segment nearest to the load, then use the found input impedance as the load in next iteration? Or can I add the characteristic impedances, since they are sort of in series?
I'm looking at a lossless transmission line where the load is a resistor, and the input is a step. The source resistance is zero, and the system has reached steady state.
So in this case, what happens when the source is switched off? You'd have the resistor on the right, and to the left of...
In all the source I have read about, EM field analysis of Transmission Lines always assume the conductor is perfect (infinite conductivity), and that simplify a lot the analysis, since there can be no field inside the conductor and that gives much easier boundary condition, which allows us to...
-A transmission line has a resistance of 5 ohms. Calculate the power loss in the line when 10 000 kW are transmitted at 10 kV...
I don't know where to start, what formula am I supposed to use? I'm sure the second I find out its going to be soo easy, but any help would be apreciated.
Thanks...
Hi,
I want to clarify some notiona in an antenna. The major components of an antenna are a generator, transmission line and an antenna (dipole). Let's say the whole system has a perfect matche, i.e. the dipole is about 70 ohms as the transmission line. If my generator ,the output voltage, is...