9/5/2007 Transmission Lines 1/2 Jim Stiles The Univ. of Kansas Dept. of EECS 3 Microwave Components Let’s carefully examine each of the microwave devices that are useful for radio design: A. Transmission Lines B. Amplifiers C. Mixers D. Oscillators E. Isolators/Circulators F. Switches and Attenuators G. Power Dividers/Couplers H. Filters A. Transmission Lines Perhaps the most common transmission line structure is coaxial transmission line. HO:Coaxial Transmission Lines Coaxial transmission lines are used with connectorized devices. HO: Coax Connectors We can also construct transmission lines on printed circuit boards. HO: Printed Circuit Board Transmission Lines9/5/2007 Coaxial Transmission Lines 1/4 Jim Stiles The Univ. of Kansas Dept. of EECS Coaxial Transmission Lines The most common type of transmission line! The electric field ( )points in the direction ˆaρ . The magnetic field ( )points in the direction ˆaφ. E. M. Power flows in the direction ˆza. A TEM wave! ε b a + V0 - Outer Conductor Inner Conductor Coax Cross-Section9/5/2007 Coaxial Transmission Lines 2/4 Jim Stiles The Univ. of Kansas Dept. of EECS Recall from EECS 220 that the capacitance per/unit length of a coaxial transmission line is: 2 farads ln b/a meterCπ⎡⎤=⎢⎥⎡⎤⎣⎦⎣⎦ε And that the inductance per unit length is : 0Henriesln 2mbLaµπ⎡⎤⎡⎤=⎢⎥⎢⎥⎣⎦⎣⎦ Where of course the characteristic impedance is: 01ln 2 oLZCbaµπ=⎡⎤=⎢⎥⎣⎦ε and: 0LCβωωµε== Therefore the propagation velocity of each TEM wave within a coaxial transmission line is: 0001111prrvcωβµεµεε ε== = = where 0rεεε= is the relative dielectric constant, and c is the “speed of light” (8310cm/s=× ).9/5/2007 Coaxial Transmission Lines 3/4 Jim Stiles The Univ. of Kansas Dept. of EECS Note then that we can likewise express β in terms rε: 000rrcωβωµε ωµε ε ε== = Now, the size of the coaxial line (a and b) determines more than simply 0Z and β (L and C) of the transmission line. Additionally, the line radius determines the weight and bulk of the line, as well as its power handling capabilities. Unfortunately, these two characteristics conflict with each other! 1. Obviously, to minimize the weight and bulk of a coaxial transmission line, we should make a and b as small as possible. 2. However, for a given line voltage, reducing a and b causes the electric field within the coaxial line to increase (recall the units of electric field are V/m). A higher electric field causes two problems: first, it results in greater line attenuation (larger α); second, it can result in dielectric breakdown. Dielectric breakdown results when the electric field within the transmission line becomes so large that the dielectric material is ionized. Suddenly, the dielectric becomes a conductor, and the value G gets very large!9/5/2007 Coaxial Transmission Lines 4/4 Jim Stiles The Univ. of Kansas Dept. of EECS This generally results in the destruction of the coax line, and thus must be avoided. Thus, large coaxial lines are required when extremely low-loss is required (i.e., line length A is large), or the delivered power is large. Otherwise, we try to keep our coax lines as small as possible!9/5/2007 Coaxial Connectors 1/2 Jim Stiles The Univ. of Kansas Dept. of EECS Coaxial Connectors There are many types of connectors that are used to connect coaxial lines to RF/microwave devices. They include: SMA The workhorse microwave connector. Small size, but works well to > 20 GHz. By microwave standards, moderately priced. BNC The workhorse RF connector. Relatively small and cheap, and easy to connect. Don’t use this connector past 2 GHz! F A poorman’s BNC. The RF connector used on most consumer products such as TVs. Cheap, but difficult to connect and not reliable.9/5/2007 Coaxial Connectors 2/2 Jim Stiles The Univ. of Kansas Dept. of EECS N The original microwave connector. Good performance (up to 18GHz), and moderate cost, but large (about 2 cm in diameter) ! However, can handle greater power than SMA. UHF The poorman’s N. About the same size, although reduced reliability and performance. RCA Not really an RF connector. Used primarily in consumer application for video and audio signals (i.e., <20 MHz). Cheap and easy to connect. APC-7 and APC-3.5 The top of the line connector. Best performance, but cost big $$$. Used primarily in test equipment (e.g., network analyzers). 3.5 can work to nearly 40 GHz.9/5/2007 Printed Circuit Board Transmission Lines 1/3 Jim Stiles The Univ. of Kansas Dept. of EECS ε Printed Circuit Board Transmission Lines Recall that a transmission line must consist of two separate conductors. Typically, the volume between these conductors is filled with a very low-loss dielectric. For example, a coaxial line has an inner conductor (conductor #1) and an outer conductor (conductor #2), with the cylindrical space between filled with dielectric. However, we can likewise construct a transmission line using printed circuit board technology. The substrate of the circuit board is the dielectric that separates two conductors. The first conductor is typically a narrow etch that provides the connection between two components, while the second conductor is typically a ground plane. Below are some of the most popular types of printed circuit board transmission lines:9/5/2007 Printed Circuit Board Transmission Lines 2/3 Jim Stiles The Univ. of Kansas Dept. of EECS Microstrip Probably most popular PCB transmission line. Easy fabrication and connection, yet is slightly dispersive, lossy, and difficult to analyze. Stripline Better than microstrip in that it is not dispersive, and is more easily analyzed. However, fabrication and connection is more difficult. Coplanar Waveguide The newest technology. Perhaps easiest to fabricate and connect components, as both ground and conductor are on one side of the board. Slotline Essentially, a dual wire tranmission line. Best for “balanced” applications. Not used much. εr εr εr εr εr9/5/2007 Printed Circuit Board Transmission Lines 3/3 Jim Stiles The Univ. of Kansas Dept. of EECS An antenna array feed, constructed using microstrip transmission lines and circuits. A wideband microstrip coupler.