Chapter 14 transmission lines presentation.ppt
- 2. Introduction • Signals can be delivered from the transmitter to the receiver using a variety of means: – Metallic cable – Optical fiber – Radio transmission
- 3. Coaxial Lines • Two conductors are concentric, separated by an insulating dielectric • Coaxial cables are unbalanced because of their lack of symmetry with regard to ground
- 4. Parallel Lines • Parallel lines are typically balanced lines, the impedance to ground from each of the wires being equal • Balanced refers to the signals being the same level but opposite in polarity
- 5. Electrical Model of a Transmission Line • The electrical characteristics of a transmission line become increasingly critical as the frequency of transmission increases • Factors influencing transmission lines: – Resistance – “Skin effect” – Conductance of the dielectric – Impedance – Capacitance – Inductance • These factors are distributed rather than lumped
- 7. Step and Pulse Response of Lines • In a line of infinite length, a stepped input signal will surge forever because of the capacitance of the line • The characteristic impedance of the line is also know as the surge impedance • The impedance is a real number for a line with no losses; for example, a 50-ohm line does not refer to the resistance of the wire in the line, but the voltage/current ratio as seen by the source
- 8. C j G L j R Z ω ω 0 Characteristic Impedance of a Line • A terminated transmission line that is matched in its characteristic impedance is called a matched line • The characteristic impedance depends upon the electrical properties of the line, according to the formula:
- 9. Characteristic Impedance • The characteristic impedance for any type of transmission line can be calculated by calculating the inductance and impedance per unit length – For a parallel line with an air dielectric the impedance is: – For a coaxial cable: d D Z r log 138 0 r D Z log 276 0
- 10. Coaxial Cable Applications • In practice, it is usually unnecessary to find the impedance of coaxial cable since the impedance is part of the cable specification • As indicated in the table, there are standard impedances for coaxial cable Impedance (ohms) Application Typical type numbers 50 Radio Transmitters Communications Receivers RG-8/U RG-58/U 75 Cable Television TV Antenna feedlines RG-59/U 93 Computer networks RG-62/U
- 11. Velocity Factor • A signal moves down a transmission line at a finite rate, i.e. somewhat less than the speed of light • The propagation velocity of a signal, compared to the speed of light, varies as follows: – Coaxial cable with polyethylene dielectric: 66% – Coaxial cable with polyethylene foam dielectric: 78% – Air-dielectric cable: 95% • Rather than specify the actual velocity, manufacturers specify the velocity factor • The velocity factor for a transmission line depends almost entirely upon the dielectric
- 12. Reflections • In a line where the termination is equal to the impedance of the line, the reflections are zero • A line that is terminated other than Z0 is said to be mismatched and will have reflections • The reflection coefficient is found by: i r V V
- 13. Wave Propagation on Lines • If a sine wave is applied to a transmission line, the signal moves down the line and disappears into the load • Such a signal is called a traveling wave • This process also takes time • A time delay of one period causes a phase shift of 360º, which is indistinguishable from the original • The length of a line L that causes a delay of one period is known as a wavelength
- 14. Traveling Waves
- 15. Standing Waves • The interaction of incident and reflected waves in a transmission line results in standing waves • When a reflected wave is present but has lower amplitude than the incident, there will be no point on the line where the voltage or current remains zero over the whole cycle
- 16. Variation of Impedance Along a Line • A matched line presents its impedance to a source located any distance from the load • An unmatched line impedance can vary greatly with its distance from the load • At some points mismatched lines may look inductive, other points may look capacitive, at still other points it may look resistive
- 17. Impedance on a Lossless Line • The impedance on a lossless transmission line is given by the formula: θ sin θ cos θ sin θ cos 0 0 0 L L jZ Z jZ Z Z Z
- 18. Characteristics of Open and Shorted Lines • An open or shorted line can be used as an inductive, capacitive, or even a resonant circuit • In practice, short-circuited sections are more common because open-circuited lines radiate energy from the open end • The impedance of a short-circuited line is: θ tan 0 jZ Z
- 20. Transmission Line Losses • No real transmission line is completely lossless • However, approximation is often valid assuming lossless lines
- 21. Loss Mechanisms • The most obvious loss in a transmission line is due to the resistance of the line, called I2 R loss • The dielectric can also cause loss, with the conductance becoming higher with increasing frequency • Open-wire systems can radiate energy – Loss becomes more significant as the frequency increases – Loss becomes worse as spacing between conductors increases
- 22. Loss in Decibels • Transmission line losses are usually given in decibels per 100 feet or 100 meters • When selecting a transmission line, attention must be paid to the losses • A 3-dB loss equates to 1/2 the power being delivered to the antenna • Losses are also important in receivers where low noise depends upon minimizing the losses before the first stage of amplification
- 23. Mismatched Lossy Lines • When a transmission line is lossy, the Standing- Wave Ratio (SWR) at the source is lower than that at the load • The reflection coefficient and standing-wave ratio both have larger magnitudes at the load • Computer programs and Smith Charts are available to calculate losses and mismatches in transmission lines
- 24. Power Ratings • The maximum power that can be applied to a transmission line is limited by one of two things: – Power dissipation in the line – A maximum voltage, which can break down the dielectric when exceeded • A compromise is often achieved in power lines between voltage and line impedance
- 25. Impedance Matching • Impedance mismatches are deleterious in transmission lines • Mismatches result in power being reflected back to the source and in higher-than-normal voltages and currents that can stress the line • Best results are obtained when the load is matched to the characteristic impedance of the transmission line • Impedance matching can be accomplished by matching networks using: – Lumped constants (inductors, capacitors, transformers) – Waveguide components – Transmission line sections
- 26. The Smith Chart • The Smith Chart has been used since 1944 to indicate complex impedances and admittances and the way in which they vary along a line • Computer programs are now available that make use of the functions formerly relegated to the Smith Chart
- 27. Matching Using a Transformer • A transformer can be used for impedance matching provided the load impedance is real at the point where the transformer is inserted • Transformers are also used for connecting balanced and unbalanced lines. These transformers are called balun transformers
- 28. Series Capacitance and Inductance • When the resistive part of the load is correct, the reactive part of the load impedance can be corrected by adding a series of reactances of the opposite type • Stub Matching – Shorted transmission line stubs are often used instead of capacitors or inductors at VHF and above – In these cases, admittance is calculated for, rather than impedance
- 29. Transmission-Line Measurements • Specialized test equipment is available to measure and evaluate transmission lines using these techniques: – Time-Domain Reflectometry – The Slotted Line – Standing-Wave-Ratio Meters and Directional Wattmeters