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ENE 490 Applied Communication Systems

Learn about transmission lines, Smith charts, impedance matching, power transmission, & more for high-frequency applications in communication systems. Gain insights on transmission coefficients, standing wave ratios, and Smith chart applications in impedance transformations.

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ENE 490 Applied Communication Systems

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  1. ENE 490Applied Communication Systems Lecture 1 Backgrounds on Transmission lines and matching on Smith chart

  2. Introduction • How does information transfer?

  3. High frequency operation • Microwave frequency range (300 MHz – 300 GHz) • Microwave components are distributed components. • Lumped circuit elements approximations are invalid. • Maxwell’s equations are used to explain circuit behaviors( and)

  4. Applications of high frequency communications • Antenna gain • More bandwidth • Satellite and terrestrial communication links • Radar communication • Remote sensing, medical diagnostics, and heating methods

  5. Frequency behavior of passive components At 60 Hz An equivalent circuit representation of high frequency resistor

  6. Transmission lines (TLs) analysis (1) • At higher frequencies, voltage and current are not spatially uniform, must be treated in terms of propagating waves. The distributed-parameter model including instantaneous voltage and current

  7. Transmission lines (TLs) analysis (2) • Kirchhoff’s circuit laws fail to explain circuit behaviors at high frequency • The transmission line must be viewed in terms of distributed parameters, R, L, C, and G. • A transmission line theory is applied when (lA is the average size of the discrete component) Example of transmission lines

  8. General transmission line equation (1) • Kirchhoff voltage and current law representations

  9. General transmission line equation (2)

  10. Lossless case • Special case: Lossless line R = 0  and G = 0

  11. Terminated lossless transmission line • Convenient representation of source and load ends for some T.L. problems

  12. Voltage reflection coefficient • Define load reflection coefficient: • Load reflection coefficient in terms of impedance: Definition: Note:ZL is a load impedance.

  13. Impedance along the transmission line • Impedance anywhere on the transmission line

  14. Ex1 Determine the input impedance Zin when • l = /4 • l = /2 • ZL = Z0

  15. Voltage standing wave ratio VSWR (1)

  16. Voltage standing wave ratio VSWR (2)

  17. Ex2 Determine VSWR and the locations of maximum and minimum voltages for • matched load • ZL = 100 , Z0 = 50 

  18. c) short circuit d) open circuit

  19. Source and loaded transmission lines Transmission coefficient:

  20. Power transmission of a transmission line • Average power: • For lossless line: • For lossless and matched condition: we have Pavs, maximum available power provided by the source. • Power in decibel:

  21. Ex3For the circuit shown above, assume a lossless line with Z0= 50, ZS = 75, and ZL = 100. Determine the input power and power delivered to the load. Assume the length of the line to be /2 with a source voltage of VS = 10 V.

  22. Input impedance matching • Optimal power transfer requires conjugate complex matching of the T.L. to the source impedance: Zin = ZS* • Similarly for output matching: Zout = ZL*

  23. The Smith Chart • a graphical tool to analyze circuit impedance • design of matching networks • computations of noise figures, gain, and stability circles.

  24. Using of the Smith Chart • Impedance transformation Step 1 – Normalize the load impedance ZL with respect to the line impedance Z0 to determine zL. Step 2 – Locate zL in the Smith Chart Step 3 – Identify the corresponding load reflection coefficient 0 in the Smith Chart both in terms of its magnitude and phase. Step 4 – Rotate 0 by the length in terms of wavelength  or twice its electrical length d to obtain in(d). Step 5 – Record the normalized input impedance zin at this spatial location d. Step 6 – Convert zininto actual impedance Zin.

  25. Ex4 Given the load impedance ZL to be 30+j60, Determine the input impedance if the T.L. is 2 cm long and is operated at 2 GHz.

  26. Standing wave ratio in Smith chart • The numerical value of SWR can be found from the Smith chart by finding the intersection of the circle of radius with the right hand side of the real axis. • Ex5 Three different load impedances: • ZL = 50 , • b) ZL = 25+j75 , and • c) ZL = 40 + j20 , • are sequentially connected to a 50  transmission line. • Find the reflection coefficients and the SWR circles.

  27. Admittance transformation • Rotations by 180 degrees convert the impedance to the admittance representation. • Y-Smith chart • ZY-Smith chart

  28. Parallel and Series Connections(1) • Parallel connection of R and L elements

  29. Parallel and Series Connections(2) • Parallel connection of R and C elements

  30. Parallel and Series Connections(3) • Series connection of R and L elements

  31. Parallel and Series Connections(4) • Series connection of R and C elements

  32. Ex6 of a T-network (operated at 2 GHz)

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