Transmission Losses & Parameters Part 2 PDF

Transmission Losses & Parameters Part 2  Transmission Losses For analysis purposes, metallic transmission lines are often considered to be totally lossless. However, in reality, there are several ways in which signal power is lost in a transmission line....

Transmission Losses & Parameters Part 2  Transmission Losses For analysis purposes, metallic transmission lines are often considered to be totally lossless. However, in reality, there are several ways in which signal power is lost in a transmission line. These losses are as follows: conductor loss, radiation loss, dielectric heating loss, coupling loss and corona.  Conductor Loss It is also known as conductor heating loss is simply an I2 R power loss. This loss is directly proportional to the square of the transmission line length and is also inversely proportional to characteristic impedance. To reduce conductor loss, simply shorten the transmission line or use a larger-diameter wire, but this will affect the characteristic impedance of the transmission line and, consequently, the current. Conductor loss somewhat depends on frequency because of a phenomenon called the skin effect.  Conductor Loss Skin effect At high frequency, most of the current flows along the surface (outer skin) of the conductor rather than near its center. This is equivalent to reducing the cross-sectional area of the conductor and increasing the opposition to current flow (i.e., resistance). Therefore, the ac resistance of the conductor is proportional to the square of the frequency. The ratio of the ac resistance to the dc resistance of a conductors is called the resistance ratio. Above 100 MHz, the center of a conductor can be completely removed and have absolutely no effect on the total conductor loss or EM wave propagation. 𝐼2 𝑅 losses and dielectric losses are proportional to length, hence they are generally lumped together and expressed in decibels of loss per unit length (i.e., dB/m).  Dielectric A difference of potential between two conductors of a metallic transmission line causes dielectric heating. Heat is a form of energy and must be taken from the energy propagating down the line. For air dielectric transmission lines, the heating loss is negligible. However, for solid-core transmission line, dielectric heating loss increases with frequency.  Radiation Loss If the separation between conductors in a metallic transmission line is an appreciable fraction of a wavelength, the electrostatic and electromagnetic fields that surround the conductor cause the line to act as if it were an antenna and transfer energy to any nearby conductive material. The energy radiated is called radiation loss and depends on dielectric material, conductor spacing, and length of the transmission line. Radiation losses are reduced by properly shielding the cable, therefore, shielded cables such as STP and coaxial cable have less radiation loss than unshielded cables. Radiation loss is also directly proportional to frequency.  Coupling Loss Coupling loss occurs whenever a connection is made to or from a transmission line or when two sections of transmission line are connected together. Mechanical connections are discontinuities where dissimilar materials meet. Discontinuities tend to heat up, radiate energy and dissipate power.  Corona It is the luminous discharge that occurs between the two conductors of a transmission line when the difference of potential between them exceeds the breakdown voltage of the dielectric insulator. When corona occurs, the transmission line is destroyed.  Incident and Reflected Waves An ordinary transmission line is bidirectional; power can propagate well in both directions. Voltage the propagates from the source toward the load is called incident voltage, and voltage that propagates from the load towards the source is called reflected voltage. Incident voltage and current are always in phase for a resistive characteristics impedance. For an infinitely long line, all the incident power is stored by the line, and there is no reflected power. If the line is terminated in a purely resistive load equal to the characteristic impedance of the line, the load absorbs all the incident power (assuming a lossless line). Reflection power is the portion of the incident power that was not absorbed by the load. Therefore, the reflected power can never exceed the incident power.  Resonant and Non-Resonant Lines A transmission line with no reflected power is called a flat , matched line or non-resonant line. A transmission line is non-resonant if it is of infinite length or if it is terminated with a resistive load equal in ohmic value to the characteristic impedance of the transmission line. When the load is not equal to the characteristic impedance of the line, some of the incident power is reflected back toward the source. If the load is either a short or an open circuit, all the incident power is reflected back toward the source.  Resonant and Non-Resonant Lines If the source were replaced with an open or short and the line were lossless, energy present on the line would reflect back and forth (oscillate) between the source and load ends similar to the way energy is transferred back and forth between the capacitor and inductor in an LC tank circuit. This is called a resonant transmission line. It is also known as a mismatched line, in which the load impedance does not equal to characteristic impedance of the transmission line (Zo ≠ ZL). In a resonant line, energy is alternately transferred between the magnetic and electric fields of the distributed inductance and capacitance of the line.  Resonant and Non-Resonant Lines Such a mismatch produces standing waves, but the amplitude of these waves is lower than that of the standing waves resulting from short or open circuits. The distribution of these standing waves looks like that shown in the figure. Note that the voltage or current never goes to zero, as it does with an open or shorted line.  Resonant and Non-Resonant Lines Note that the voltage or current never goes to zero, as it does with an open or shorted line.  Disadvantages Of Not Having A Matched (Flat) Line One hundred percent of the source incident power is not absorbed by the load. The dielectric separating the two conductors can break down and cause corona as a result of the high-voltage standing-wave ratio. Reflections and re-reflections cause more power loss. Reflections cause ghost images. Mismatches cause noise interference.  Reflection Coefficient It is also called the coefficient of reflection, is a vector quantity that represents the ratio of reflected voltage to incident voltage (or reflected current to the incident current) that measures the mismatch between the line and the load. Denoted by symbol gamma (Γ). Reflection Coefficient  Sample Problems What proportion of incident power is reflected back from the load for a 75-ohm line terminated with 50-j25 ohms? Ans. 7.69%  Standing Waves With mismatched line, there are two electromagnetic waves, travelling in opposite directions, present on the line at the same time. These waves are in fact called travelling waves. The two travelling waves set up an interference pattern known as a standing wave. These stationary waves are called standing waves because they appear to remain in a fixed position on the line, varying only in amplitude. The standing wave has minima (nodes) separated by a half wavelength of the travelling waves and maxima (antinodes) also separated by a half wavelength.  Standing Waves For a TL with shorted load, incident voltage is reflected 180 degrees from how it would have continued while its incident current is reflected as if it were to continue down the line. For a TL with open-circuited load, incident current is reflected 180 degrees from how it would have continued while its incident voltage is reflected as if it were to continue down the line.  Standing Wave Ratio (SWR) It is defined as the ratio of the maximum voltage (or current) to the minimum voltage (or current) of a standing wave in a transmission. It is a scalar quantity and is also a measure of mismatch between the load impedance and the characteristic impedance of a transmission line. Standing Wave Ratio (SWR)  Sample Problems A transmission line has a reflection coefficient of -0.35, what is its SWR? Ans. 2.07  Sample Problems An SWR meter is used to measure the degree of mismatch on the line. The SWR meter records 1.6 when the line is terminated with 50 ohms and 2.2 when the load is changed to 176 ohms. What is the characteristic impedance of the line? Ans. Zo = 80 ohms  Sample Problems For a transmission line with incident voltage 𝐸𝑖 = 5 𝑉 and reflected voltage 𝐸𝑟 = 3 𝑉, determine a) Reflection coefficient b) SWR 𝐸𝑟 𝐸𝑖 +𝐸𝑟 Γ= 𝑆𝑊𝑅 = 𝐸𝑖 𝐸𝑖 −𝐸𝑟 Ans. a) 0.6 b) 4 Matched Line (𝑍𝑜 = 𝑍𝐿 )  Open & Shorted Load Transmission Line with Open Load An open element has max voltage across it with zero current flowing through it. The same is also true for a TL with an open load. All the energy is reflected, setting up the stationary pattern of voltage and current standing waves shown.  Open & Shorted Load Transmission Line with Open Load  Open & Shorted Load Transmission Line with Open Load  Open & Shorted Load Transmission Line with Shorted Load A shorted element has zero voltage and has maximum current flowing into it. The same is true for a TL with a shorted load, the voltage is zero when the current is maximum and all the power is reflected back toward the generator. The fixed pattern, which is the result of a composite (combination) of the forward and reflected signals, repeats every half wavelength. The voltage and current levels at the generator are dependent on signal wavelength and the line length.  Open & Shorted Load Transmission Line with Shorted Load  Open & Shorted Load Transmission Line with Shorted Load Absorbed Power by the Load Return Loss and Mismatch Loss  Sample Problems Calculate the SWR and the reflection coefficient of the line if the forward power is 250 W and the reversed power is 45W. Ans. Γ = 0.424 SWR = 2.47  Sample Problems What is the actual length in meters of 2 wavelength of a coax with a velocity factor of.71 at 37 MHz? Ans. 11.51 m