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TELECOMMUNICATIONS

TELECOMMUNICATIONS. Dr. Hugh Blanton ENTC 4307/ENTC 5307. Properties of transmission lines. Inductance (L) and Capacitance (C ) per unit length. Characteristic Impedance Propagation coefficient Phase Velocity Effective dielectric constant. RF.

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TELECOMMUNICATIONS

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  1. TELECOMMUNICATIONS Dr. Hugh Blanton ENTC 4307/ENTC 5307

  2. Properties of transmission lines Inductance (L) and Capacitance (C ) per unit length • Characteristic Impedance • Propagation coefficient • Phase Velocity • Effective dielectric constant Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)2

  3. RF • When a capacitor is created by two parallel conductors, the dimensions of the conductors compared to the actual wavelength (lG) affects the RF performance of the component. • For example: • If l<< lG ,the capacitance of the parallel plates may be treated as a single (“lumped”) capacitance C between points x1 and x2. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)3

  4. If l > 0.05lG, the capacitance of the parallel plates must be treated in “distributed” form as C1, C2, ... Cn, including the effects of the incremental inductances L1, L2, ..., Ln-1,etc. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)4

  5. The physical dimensions of conductors and components, relative to the effective signal wavelength, determines the method required for accurate modeling. • When conductors are realized on FR-4 type PC-boards, the effective wavelength at 1 GHz is about 10 cm (~ 4”). • Five percent of that length is 5 mm (~ 200 mils); therefore if the conductors exceed this length, they should be analyzed in distributed form at frequencies above 1 GHz. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)5

  6. The 5% “border” is just an approximation, not an absolute rule. • It is generally used as an upper limit to which the tangent of an angle changes in a near linear fashion Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)6

  7. Transmission lines • At high frequencies wires become transmission lines • Coaxial • Microstrip • Coplanar • Input and Output needs to be matched. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)7

  8. Types of Transmission Lines • RF transmission lines generally consist of two conductors, one of which may be a ground plane or a shield. • The most commonly used forms are: • twin-leads, • coaxial, • stripline, and • microstrip Twin leads Coaxial Strip line Microstrip line Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)8

  9. Coaxial • Coax is the most common form of a transmission line. • Note that: • Stripline is essentially square coax and • Microstrip is open top coax. • Most of the magnetic field terminated in the ground strip. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)9

  10. Transmission lines may be defined two ways: • by physical dimensions (conductor size and spacing) or • by electrical parameters (characteristic impedance and electrical length). • At higher microwave frequencies single conductor transmission lines, such as waveguides may also be used Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)10

  11. If the dielectric is non-homogeneous, er, is replaced with the dielectric constant, eeff, which is an average of the dielectric layers. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)11

  12. Characteristic Impedance • Characteristic impedance (Zo) of a uniform, lossy transmission line is a complex number; • it is defined by the ratio of the series impedance and shunt admittance of an incremental line segment. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)12

  13. R and G represent dissipative losses while L and C are the incremental inductance and capacitance in the equivalent series and parallel circuits. • Characteristic impedance is given by: • If the line is lossless (R = 0, G = 0) the impedance definition is simplified to a real quantity: Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)13

  14. Characteristic impedance is what the signal “sees” while traveling through the transmission line. • Electrically, it is the ratio of the instantaneous voltage and current. • a quantity that is constant throughout a homogeneous line. • If high-impedance lines the incremental inductance is the dominant term of the impedance expression. • In low-impedance lines the capacitance term is relatively large, while inductance is low. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)14

  15. Thus in high-impedance lines the incremental inductance is the dominant term of the impedance expression. • In low-impedance lines the capacitance term is the dominant term in the impedance expression. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)15

  16. If the transmission line is lossless (R = 0, G = 0) and the impedance definition is simplified to a real quantity: Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)16

  17. Example • A uniform transmission line has the following incremental lumped equivalent circuit parameters: • R = 0.2W/m • G = 2  10-5 S/m • L = 2.51  10-7 H/m • C = 10  10-12 F/m • Find the characteristic impedance of the line at 1000 Hz and 1 GHz. • Comment about the nature of the impedance at different frequencies. • That is, at 1 KHz, is the circuit a transmission line? • Is the circuit a transmission line at 1 GHz? R L G C Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)17

  18. Electrical Length of Transmission Lines • The term electrical length refers to the ratio of the physical length (l) of the transmission line to the wavelength (lG) in the applicable dielectric. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)18

  19. Example • If a 15 cm long coaxial line is filled with dielectric of er = 4, what is E at 2 GHz? • We could also compute the effective wavelength first Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)19

  20. Physical Forms • A transmission line may have various physical forms: • The electrical schematic • The real physical circuit equivalent in • coaxial form or • microstrip form Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)20

  21. Characteristics • If an ideal transmission line of characteristic impedance Zo is terminated with a complex impedance ZL, the new input impedance is ⅛l ¼l Impedance Inverter Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)21

  22. Lossy Transmission Lines • For lossy transmission lines the input impedance is a more complicated function: • where • g is the propagation constant (a + jb) • l is the physical length of the transmission line. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)22

  23. If ZL = Zo, the input impedance of the transmission line is always equal to ZL and is not a function of the line length. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)23

  24. In a uniform transmission line the current flow is determined by the ratio of the instantaneous voltage and characteristic impedance. • Load current depends on the voltage and load impedance. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)24

  25. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)25

  26. When a uniform transmission line is terminated with a load impedance other than its characteristic impedance, reflected waves are created. • The ratio of the reflected and forward voltages is called the reflection coefficient and is denoted by G. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)26

  27. RF Parameters • As frequencies reach 100 MHz, the voltages and currents are difficult to measure. • A more practical set of parameters can be defined in terms of traveling waves. • Four such parameters are: • Reflection Coefficient • Return Loss • Voltage Standing Wave Ratio • Mismatch Loss Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)27

  28. Reflection Coefficient • The Reflection Coefficient (G) shows what fraction of an applied signal is reflected when a Zo source drives a load of ZL. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)28

  29. Return Loss • The Return Loss (RL) shows the level of reflected wave referenced to the incident wave, expressed in dB. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)29

  30. Reflection Coefficient () • If the load impedance differs from the characteristic impedance of the line then part of the wave is reflected. • The ratio of the incident voltage to the reflected voltage is  Sometimes specified by the return loss = 20 log () Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)30

  31. VSWR • The Voltage Standing Wave Ratio (VSWR) compares the maximum and minimum values of a “standing wave” pattern, caused by wave reflection. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)31

  32. Mismatch Loss • The Mismatch Loss (ML) is the power lost between two interconnected ports, due to mismatch. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)32

  33. The four circuit parameters (G, RL, VSWR, and ML) are interrelated. • Knowing one, the magnitudes of the others can be computed. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)33

  34. When EM waves propagate in two directions inside a transmission line, a “standing wave” pattern is formed. Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)34

  35. Voltage Standing Wave Ratio (VSWR) is by definition the ratio of maximum (Vmax) and minimum (Vmin) voltages of the standing wave function.  Dr. Blanton - ENTC 4307 - Transmission Lines (cont.)35

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