# Transmission lines and waveguides pdf

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## Transmission lines and Waveguides notes

To learn more, view our Privacy Policy. Log In Sign Up. Download Free PDF. Transmission lines and Waveguides notes. Ranjit kumar. Download PDF. A short summary of this paper. Neper A neper Symbol: Np is a logarithmic unit of ratio. It is not an SI unit but is accepted for use alongside the SI. It is used to express ratios, such as gain and loss, and relative values.

The name is derived from John Napier, the inventor of logarithms. The value of a ratio in nepers, Np, is given by where x1 and x2 are the values of interest, and ln is the natural logarithm.

The neper is often used to express ratios of voltage and current amplitudes in electrical circuits or pressure in acoustics , whereas the decibel is used to express power ratios. One kind of ratio may be converted into the other. The voltage level is Like the decibel, the neper is a dimensionless unit. The ITU recognizes both units. Decibel The decibel dB is a logarithmic unit of measurement that expresses the magnitude of a physical quantity usually power or intensity relative to a specified or implied reference level.

Since it expresses a ratio of two quantities with the same unit, it is a dimensionless unit. A decibel is one tenth of a bel, a seldom-used unit. The decibel is widely known as a measure of sound pressure level, but is also used for a wide variety of other measurements in science and engineering particularly acoustics, electronics, and control theory and other disciplines.

It confers a number of advantages, such as the ability to conveniently represent very large or small numbers, a logarithmic scaling that roughly corresponds to the human perception of sound and light, and the ability to carry out multiplication of ratios by simple addition and subtraction. The decibel symbol is often qualified with a suffix, which indicates which reference quantity or frequency weighting function has been used. For a similar unit using natural logarithms to base e, see neper.

The bel B is the logarithm of the ratio of two power quantities of , and for two field quantities in the ratio [8]. A field quantity is a quantity such as voltage, current, sound pressure, electric field strength, velocity and charge density, the square of which in linear systems is proportional to power.

A power quantity is a power or a quantity directly proportional to power, e. The calculation of the ratio in decibels varies depending on whether the quantity being measured is a power quantity or a field quantity. Power quantities When referring to measurements of power or intensity, a ratio can be expressed in decibels by evaluating ten times the base logarithm of the ratio of the measured quantity to the reference level.

Thus, if L represents the ratio of a power value P1 to another power value P0, then LdB represents that ratio expressed in decibels and is calculated using the formula: P1 and P0 must have the same dimension, i. Since a bel is equal to ten decibels, the corresponding formulae for measurement in bels LB are. Field quantities When referring to measurements of field amplitude it is usual to consider the ratio of the squares of A1 measured amplitude and A0 reference amplitude.

This is because in most applications power is proportional to the square of amplitude, and it is desirable for the two decibel formulations to give the same result in such typical cases. Thus the following definition is used: This formula is sometimes called the 20 log rule, and similarly the formula for ratios of powers is the 10 log rule, and similarly for other factors.

The formula may be rearranged to give Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is held constant. A similar formula holds for current. An example scale showing x and 10 log x. It is easier to grasp and compare 2 or 3 digit numbers than to compare up to 10 digits. Note that all of these examples yield dimensionless answers in dB because they are relative ratios expressed in decibels. A change in power ratio by a factor of two is approximately a 3 dB change.

Similarly, an increase of 3 dB implies an increase in voltage by a factor of approximately , or about 1.

This allows one to clearly visualize huge changes of some quantity. See Bode Plot and half logarithm graph. The decibel's logarithmic scale, in which a doubling of power or intensity always causes an increase of approximately 3 dB, corresponds to this perception. Absolute and relative decibel measurements Although decibel measurements are always relative to a reference level, if the numerical value of that reference is explicitly and exactly stated, then the decibel measurement is called an "absolute" measurement, in the sense that the exact value of the measured quantity can be recovered using the formula given earlier.

Thus, 0 dBm is the power level corresponding to a power of exactly 1 mW. If the numerical value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel measurement is purely relative. Voltage Since the decibel is defined with respect to power, not amplitude, conversions of voltage ratios to decibels must square the amplitude, as discussed above.

Widely used in cable television networks, where the nominal strength of a single TV signal at the receiver terminals is about 0 dBmV. Widely used in television and aerial amplifier specifications. Properties of Symmetrical Networks and Characteristic impedance of Symmetrical Networks A two-port network a kind of four-terminal network or quadripole is an electrical circuit or device with two pairs of terminals connected together internally by an electrical network.

Two terminals constitute a port if they satisfy the essential requirement known as the port condition: the same current must enter and leave a port. Examples include small-signal models for transistors such as the hybrid-pi model , filters and matching networks. The analysis of passive two-port networks is an outgrowth of reciprocity theorems first derived by Lorentz[3]. A two-port network makes possible the isolation of either a complete circuit or part of it and replacing it by its characteristic parameters.

Once this is done, the isolated part of the circuit becomes a "black box" with a set of distinctive properties, enabling us to abstract away its specific physical buildup, thus simplifying analysis. Any linear circuit with four terminals can be transformed into a two-port network provided that it does not contain an independent source and satisfies the port conditions.

There are a number of alternative sets of parameters that can be used to describe a linear two-port network, the usual sets are respectively called z, y, h, g, and ABCD parameters, each described individually below. These are all limited to linear networks since an underlying assumption of their derivation is that any given circuit condition is a linear superposition of various short-circuit and open circuit conditions. At high frequencies e. The terms four-terminal network and quadripole not to be confused with quadrupole are also used, the latter particularly in more mathematical treatments although the term is becoming archaic.

However, a pair of terminals can be called a port only if the current entering one terminal is equal to the current leaving the other; this definition is called the port condition.

A four-terminal network can only be properly called a two-port when the terminals are connected to the external circuitry in two pairs both meeting the port condition. Validity of complex representation This representation using complex exponentials may be justified by noting that by Euler's formula : i.

By the principle of superposition, we may analyse the behaviour of the sinusoid on the left-hand side by analysing the behaviour of the two complex terms on the right-hand side. Given the symmetry, we only need to perform the analysis for one right-hand term; the results will be identical for the other. At the end of any calculation, we may return to real-valued sinusoids by further noting that In other words, we simply take the real part of the result.

Phasors A phasor is a constant complex number, usually expressed in exponential form, representing the complex amplitude magnitude and phase of a sinusoidal function of time. Phasors are used by electrical engineers to simplify computations involving sinusoids, where they can often reduce a differential equation problem to an algebraic one. The impedance of a circuit element can be defined as the ratio of the phasor voltage across the element to the phasor current through the element, as determined by the relative amplitudes and phases of the voltage and current.

This is identical to the definition from Ohm's law given above, recognising that the factors of cancel 5. Propagation constant The propagation constant of an electromagnetic wave is a measure of the change undergone by the amplitude of the wave as it propagates in a given direction.

The propagation constant itself measures change per metre but is otherwise dimensionless. The propagation constant is expressed logarithmically, almost universally to the base e, rather than the more usual base 10 used in telecommunications in other situations. The quantity measured, such as voltage, is expressed as a sinusiodal phasor. The phase of the sinusoid varies with distance which results in the propagation constant being a complex number, the imaginary part being caused by the phase change.

It is probably the most widely used term but there are a large variety of alternative names used by various authors for this quantity. These include, transmission parameter, transmission function, propagation parameter, propagation coefficient and transmission constant.

This last occurs in transmission line theory, the term secondary being used to contrast to the primary line coefficients. The primary coefficients being the physical properties of the line; R,C,L and G, from which the secondary coefficients may be derived using the telegrapher's equation. Note that, at least in the field of transmission lines, the term transmission coefficient has a different meaning despite the similarity of name. Here it is the corollary of reflection coefficient.

Angles measured in radians require base e, so the attenuation is likewise in base e. For a copper transmission line, the propagation constant can be calculated from the primary line coefficients by means of the relationship; where; , the series impedance of the line per metre and, , the shunt admittance of the line per metre.

Attenuation constant In telecommunications, the term attenuation constant, also called attenuation parameter or coefficient, is the attenuation of an electromagnetic wave propagating through a medium per unit distance from the source.

It is the real part of the propagation constant and is measured in nepers per metre. A neper is approximately 8. Copper lines The attenuation constant for copper or any other conductor lines can be calculated from the primary line coefficients as shown above. For a line meeting the distortionless condition, with a conductance G in the insulator, the attenuation constant is given by; however, a real line is unlikely to meet this condition without the addition of loading coils and, furthermore, there are some decidedly non-linear effects operating on the primary "constants" which cause a frequency dependence of the loss.

There are two main components to these losses, the metal loss and the dielectric loss. The loss of most transmission lines are dominated by the metal loss, which causes a frequency dependency due to finite conductivity of metals, and the skin effect inside a conductor. The skin effect causes R along the conductor to be approximately dependent on frequency according to; Losses in the dielectric depend on the loss tangent tan of the material, which depends inversely on the wavelength of the signal and is directly proportional to the frequency.

Phase constant In electromagnetic theory, the phase constant, also called phase change constant, parameter or coefficient is the imaginary component of the propagation constant for a plane wave.

It represents the change in phase per metre along the path travelled by the wave at any instant and is equal to the angular wavenumber of the wave. It is represented by the symbol and is measured in units of radians per metre. From the definition of angular wavenumber; This quantity is often strictly speaking incorrectly abbreviated to wavenumber.

For a transmission line, the Heaviside condition of the telegrapher's equation tells us that the wavenumber must be proportional to frequency for the transmission of the wave to be undistorted in the time domain.

## Transmission line

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.

## Transmission Lines and Wave Guides - TLWG Study Materials

Antenna Handbook pp Cite as.

### Transmission Lines and Waveguides

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