Question

a) A parallel plate transmission line has a plate width 3 mm, plate separation 0.3 mm and is filled with a dielectric of relative permittivity 2.2. The dielectric breakdown field is 180kV/cm. Find the maximum peak power that can be transmitted down it and the corresponding peak values of the transmission line voltages and currents when the transmission line is matched to a terminating load. (5 marks) b) A 1 GHz signal of voltage amplitude 0.1 Vis propagated without reflection along the transmission line in question 4(a) above. Find the values of 1. velocity of signal propagation wavelength along the transmission line ill. capacitance per unit length iv. inductance per unit length characteristic impedance (5 marks) V.

Answer 1

(0 ) W= 3 mm - -W d d ay Given 3x10-3m d = 0.3 mm = 0.3x103m 3x10-4 m Relative permitivity Ex= 2.2 Dielectric Break down Eb = 180 kvlem 180x10 3 vim 1 kV = 103V 1 cm 10-2m 10-2 E6 = 180X105 V/m) - P Now Power Power in a transmission is P. Led Power densidy (Power box unit Area) = Pd Then P = Pa x Area of Cross sechen of te line Pd x Wd Power density of ware in terms of E-field is given as L1E012 2 a Pd 3 gn where Eo: Peak Eleche field intrinić impedonce of medium 10 = 1207 R intrinsic impedance n? TER An of 1207 12.2 254.16 RI- Pulting value of (inlo (Eol²x (Wd) - ② =an 5 CS Scanned with CamScanner

To Calculate Pmax E should be marm | Eomax 1² xwd) 1.0 Pmax 6 loc Monem volue of (Eomax ) is nothing but Eb Eb = 180x10 1 80 X 10Vlm Eomax 7 © Now Pulting Pmax all the values into eq? (180X105)2 x 3 x103 x 3x104 ã 254.16 co 5 Pmax 5. 74 x 10 Walt And - - Now we know the helahon blu Polenhal (v) and Electric field E = V V = Exd E - Eomok Max Elechne field, then corresponding V max z Eomar xd Let Polenhal vz Vimax So Putting the value of Vmax Vmax Eomox and d 180 x105x 3x10-4 5 400 V 5.4 KV Ans. 9 1) ds Scanned witam CamScanner

To Calcul alz Cument, we know on for sene (3 V = I zo I V Zo Vmax (10) Imax= zo when Zo: Charecen'she impedance of Te line geven as all Zoo 2 wo where Mod 12 L = W L in du chance of Paralled Plebe Te line per unit length (hlm) 40 = 46x1077 Permeability of Air (Him) EW 13 and C = d € = to GR : Permittivity of medium (fm) Go = 8.854 x10-12 permittivity of Air (flm) C: Cabaukonce Per a unit length of the line (flmi L and C inlo eqn Leone Go GR w Pulling 2 d Mo GOER X lod w Zo Х Mo Zo X da Go GR cs faling rate values of Paramete

zo 4k X16 8.854x10-12 X 3x10-4 3x103 x 2.2 254 x To 10 Zo 25.4 14 Putting Vmax 10 Imax and zo inlo ean 5.4x103 25.4 Iman 212.6 A Ana 6 1 GHZ = HZ frequency 1x109 V- O. IV 15 1) Velocity of Signad propogahom va C VER 3x108 mla 8 when C: Velocity of light in Ant GR 2 2.2 Relative permittivity C and GR mlo equahm 5 Puldin 3X108 V V22 2.02 X108 m/secl Ans 8 v ii) Wavelength and frequency are related as cs Scanned with 4.2 = C CamScanner

when = ) 2= elt 16 5) Where 7. Wavelength Co 3x108 ms f = 1x10 9 Hz Puting values of C and into done een 7= 3x108 1x109 1) 3 10 3 10 X100 cm 7= 30cm And (ni from eq? 13 Capaci lonce bes unit length Сpeg 40 8.854x10 3x10-4 -12 x 2.2% 3x10-3 ca d 9 flm 2 0.195 X10 C An - 0.195 n fim -6 - Inductance per unit length can be Celovaled from egn ® 47x10-7 x 3810-4 3x10-3 = 0.126 X10 0.126 X10-6 HIM = 0.126 4H Im L. Am @ Charodenshi impedance Zo we have already Calculated c Scanned with 70 = 25.4 And CamScanned