If Zs = Rs + jXs is given, we could solve for X and B by equating the real and imaginary parts of the above expression: Single Lumped Element Transformation Network (2)ĭual Lumped Elements Transformation Network (1) jXġ 1 Ys = jB + Zs RL + j ( X L + X ) RL + jXL Single Lumped Element Transformation Network (1) jX Zs = ZL + jX Low resistance Shunt Multi-Loop Spiral Inductor
Interdigital Capacitor Series Single-Loop Spiral Inductor High εr dielectric Passive Lumped Components for Incorporation into PCB and other Substrates Add the corresponding schematics for these Microstrip Line Medium Frequency Passive Components (up to 250MHz)Ĭoil inductor with air core Carbon/metal film resistor Nowadays there are also 025 Coil inductor (0805) Thick film resistor Other sizes from (1210) JEDEC Solid State Technology Association - 0402, even smaller than 0603. Multilayer ceramic capacitor (0603), NPO dielectricĠ805 (0805) (0603), (1210), NPO dielectric Y5V dielectric Self-resonance frequency ranges from 200MHz to greater than 5GHz for L250MHz) Multilayer electrolytic capacitor (1812) Aluminium oxide The inductors come in a variety of form, from coil-type, thin-film, to spiral inductors mounted in SMD package. With tolerance from ± 2% to± 10%, operating temperature from -40oC to 125oC and Q factor from a minimum of 15 to greater than 45. SMD inductors have a range from 1.0nH to greater than 4000nH.
With tolerance less than ± 5% and operating temperature between 55oC to 125oC. SMD capacitors have a range from 0.47pF to greater than 10000pF. Lumped components such as surface mounted device (SMD) inductor and capacitor can be easily purchased nowadays. Impedance Transformation Using Lumped Elements Hybrid - Consists of both Tline and lumped elements Triple lumped elements (Pi or T impedance matching network)ĭistributed elements (consists of section of Tlines)
August 2007ĭual lumped elements (L impedance matching network) ~ Standardizing to a fixed impedance simplifies system design, as each module can be replaced with module of similar functions and we can be assured the power flow along the path is not affected. To maximize power transfer to the load impedance, ZL must be the complex conjugate of Zs, a notion known as Conjugate Matched.Īn example of a RF system where every modules are internally matched to 50Ω RS Zo We find that the value for RL and XL that would maximize PL is RL = Rs, XL = -Xs. The Theory of Maximum Power Transfer Time averaged power dissipated across load ZL: * 1Ģ * V Z Vs 1 Vs Z L PL = 1 Re s L ⋅ = Re 2 Zs +Z L Zs +Z L 2 Z s + Z L 2 2 Vs R L 2 (R + R )2 + ( X + X )2 s L s L Impedance matching in a power distribution network (such as antenna array feed network) will reduce amplitude and phase errors. Impedance matching on sensitive receiver components (antenna, lownoise amplifier etc.) improves the signal-to-noise ratio of the system.
Maximum power is delivered when load is matched to the Tline (assuming generator is matched). We immediately notice that the transformation network is a 2-port network. Zs is known as the image impedance of ZL. ZL is usually not equal to Zs (otherwise there will be no need for transformation). Collin, “Foundation for microwave engineering”, 2nd edition, 1992, McGraw-Hill.ġ.0 Lumped Impedance Transformation NetworkĪn impedance transformation network is a two-port network that when connected in series with an impedance ZL at one port, will result in Zs being seen on another port. Pozar, “Microwave engineering”, 2nd edition, 1998 JohnWiley & Sons (3rd edition, 2005 by John-Wiley & Sons is also available). Bretchko, “RF circuit design - Theory and applications”, 2000 Prentice-Hall. The author does not guarantee the accuracy or completeness of any information presented herein, and shall not be responsible for any errors, omissions or damages as a result of the use of this information. The information in this work has been obtained from sources believed to be reliable. Impedance Transformation and Impedance Matching