# INTRODUCTION TO TRANSMISSION LINES DR. FARID FARAHMAND FALL 2012

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1 INTRODUCTION TO TRANSMISSION LINES DR. FARID FARAHMAND FALL 2012

2

3 RF Design In RF circuits RF energy has to be transported Transmission lines Connectors As we transport energy energy gets lost Resistance of the wire à lossy cable Radiation (the energy radiates out of the wire à the wire is acting as an antenna We look at transmission lines and their characteristics

4 Transmission Lines A transmission line connects a generator to a load a two port network Transmission lines include (physical construction): Two parallel wires Coaxial cable Microstrip line Optical fiber Waveguide (very high frequencies, very low loss, expensive) etc.

5 Types of Transmission Modes TEM (Transverse Electromagnetic): Electric and magnetic fields are orthogonal to one another, and both are orthogonal to direction of propagation

6 Example of TEM Mode Electric Field E is radial Magnetic Field H is azimuthal Propagation is into the page

7 Examples of Connectors Connectors include (physical construction): BNC UHF Type N Etc. Connectors and TLs must match!

8 Transmission Line Effects Delayed by l/c At t = 0, and for f = 1 khz, if: (1) l = 5 cm: (2) But if l = 20 km:

9 Properties of Materials (constructive parameters) Electric Permittivity ε (F/m) The higher it is, less E is induced, lower polarization For air: 8.85xE-12 F/m; ε = εo εr Remember: Homogenous medium is medium with constant properties Magnetic Permeability µ (H/m) For air: 4piE-7 H/m Relative permittivity and permeability (for air they are 1) Higher value à more retention of magnetic property can be experienced in the material after removing B field n For ferromagnetic materials (Nickel, Cobalt) If diamagnetic (gold) and paramagnetic (air) µ ~1 Conductivity (S/m = Siemens/meter) σ = INF à perfect conductor σ = 0 à perfect dielectric

10 Properties of Materials Ferromagnetic materials (Nickel, Cobalt, pure Iron) magnetic material n Retain magnetic property n Higher µrà more retention n Electrons are unpaired orbiting around Diamagnetic materials (Gold, Copper) non-magnetic material n Composed of atoms which have no net magnetic moments (i.e., all the orbital shells are filled and there are no unpaired electrons) - no net magnetic moment n When exposed to a field, a negative magnetization is produced n µr=1 (slightly less than 1) Paramagnetic materials (Air, Aluminum) non-magnetic material n some of the atoms or ions in the material have a net magnetic moment due to unpaired electrons in partially filled orbitals n Magnetization is zero when the B field is removed n In the presence of a B field, there is a partial alignment of the atomic magnetic moments in the direction of the field, resulting in a net positive magnetization n µr=1 (slightly more than 1)

11 Transmission Line Model

12 Transmission Line Model Three Basic Properties: Resistance: impacts the flow of current; controlled by the cross section area Inductance: due to magnetic field; thus impacted by magnetic object Capacitance: generally impacted by the grounding Note that these parameters are very low when the input voltage is DC or operating at low frequency, thus they can be ignored!

13 Perfect Conductor and Perfect Dielectric (notes)

14 TEM Transmission Line For all TEMs: Perfect _Conductor :! =!;Rs " 0 Perfect _ Dielectric :! = 0;G ' " 0 L ' C ' =!µ G ' / C ' = " /! If the TL is lossless: c =1/! o µ o Z o = L ' / C ' v p = ". f =1/ L ' C ' = c /! r µ r = # / \$ V(t, x) = Acos(#t! \$x +% o ) V(t, x) = Ae!&x cos(#t! \$x +% o ) Sinusoidal traveling wave representation Lossless medium Lossy medium; a is the attenuation constant (Neper/m)

15 Wave Propagations Propagation Velocity Assuming lossless line Velocity Factor VF = vp/c (less than one) Where C = 3x10E-8 m/s v p =!. f =1/ Dispersion effect is due to Vp variations due to frequency differences L ' C ' Remember any composite signal is made up of many difference frequency components (cf., Fourier Analysis) The result is a narrowed pulse! The speed of light = m / s Example 1 See Notes

16 Energy Loss As the wave propagates it may looses energy Ohmic Loss: Due to resistance of the wire; at high frequency current flows outside the surface of the conductor à Skin Effect (thus circumference is critical) Dielectric Loss: Energy is lost in dielectric à converted to heat! The best dielectric is air! How much energy is lost Measured in db/unit_of_length db gain =10log(P out / P in ) Example 2 See Notes

17 ADS LineCalc Tutorial (1) ADS has many other tools built into it. A popular one is LineCalc. This tool calculates impedances and dimensions for the much different geometry of wave-guides and microstrip lines. To start the tool, there must already be a schematic open. Use the quarter-wave circuit just built. From the schematic at the top choose Tools à LineCalc à Start LineCalc. A window such as that below will appear.

18 ADS LineCalc Tutorial (2) At the top is the Type of structure to be analyzed. The program defaults to microstrip. Take a look at some of the other available such as COAX and CPW. The ID is the name of the defaults being viewed. This has initial parameter values and an initial Type. You can make your own ID if you wish. For the microstrip the parameters stand for: Er relative permitivity Mur relative permeability H height of the substrate Hu if the design was covered by a metal box, this would be its height T conductor thickness Cond conductivity of the conductor TanD dielectric loss tangent Rough RMS surface roughness of the dielectric W width of conductor L length of line Z0 characteristic impedance of line E_Eff effective electrical length K_Eff effective dielectric permitivity of the system A_DB total attenuation of the system

19 ADS LineCalc Tutorial (3) Let s go through an example. Set all but the Physical parameters (W and L) to those as in the Fig. Notice there are two arrows. Clicking the arrow pointing up will calculate W and L of the microstrip while clicking the down arrow will calculate Z0 and E_Eff. Push the up arrow. The simulator will run and the W and L will be calculated as in the Fig. Let s go the other way. Set W = 50 mil and click the down arrow. Now Z0 = and E_Eff = A wider conductor gives lower impedance as would be expected. LineCalc Example

20 Refer to :

21 Practice: Estimate the impedance of a coaxial cable assuming the relative permeability of the conductor is 1;this is actually the simplified form for calculating the lossless coaxial TL. You must simplify the expression as much as possible. The expression must be a function dimensions and relative permittivity of the line. Assuming E(x,t) = 2cos(3x10^15t 10^7x) V/m, calculate the wave velocity. Assume we have a transmission line in which air separated the two perfect conductors. Assume the impedance of the line is 50 ohm, phase constant is 20 (rad/m) and the operating frequency is 700MHz. Calculate the line inductance/meter and capacitance/ meter Refer to the Microstrip Transmission Line Applet and design a 33 ohm microstrip. Assume h=0.635 mm; t=0.005 mm; f=1.794 GHz; relative permittivity of the substrate is 9.8 with perfect conductor. What happens to the impedance if the with of the trace changes by 10 percent? Show a snapshot of your results. Learn about EEsof LineCalc. Repeat the LineCalc Example in the previous slides. Show what happens if the conductor s width is increased by 10 percent. Show a snapshot of your results.

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