Question

3. (20 points) (a) Design an LC matching network for a load with an impedance of 100+ j60 ohm at 2 GHz. (b) Design an LC matching network for a load with an impedance of 20-j20 ohm at 2 GHz. Assume ideal inductors and capacitors, and that you can choose any value you wish. This is not true in real life. oh smith clads

Answer 1

ANSWER ::

  An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together.

Given that

a) 100+j60 ohm at 2 GHz

  b) 20-j20 ohm at 2 GHz

  
network for a load LC matching with an of impedance 100+J6o ich at 2 GHZ a) ...c- matching Network is i- 00000 ZL = 100 tj 60 jul + Juc = 100 tj 60 jul - I = 100 + 360 Lic j w ²LC - j - 100 tj 6o we je w ² Lc - j - 100 t660 [:32 - 1] jwc - w LC-1-1) - 100tj 60 juc - We LC C = 100+560 ا لمال 1-12x109) ².c = 100 tj 60 j (2x109) c

1-4x1018 Lc E = 100+; 60 j (2x109) C - 1-4X108 Lc = 100 (jwc)+ j (j WC) to 100jwc + J WC GO 1-4X108 LC = 1-4X108 LC = loojwc-wc6o 1+ Gowe - 4X108 LC = 100jwc & ( + 60w-4X1082) = 100jwe + 60w-4X108 L = 100jw Ź = 100jw-600 + 4x108 L 2 = 100jw + w²2-bow ca 100kw twa l-bow ich = = L +loow) 2 + 16ow) 2 I= IMH w=9x109 Jl 2x103) 31 +100 12x103)2 + (60x2x103)2 14x10'8 + 2x101)2+(1.44 X1622) 9919

::C=3.294*10 NIW Lc -matching b) - ma Z2 = 20-j 20 at a GHZ wett = 20-320 (match case) jul - = 20 - 320 (2 w LC t1 = 20 -j 20 jwc - w²LC - - 20-jao Jwc in (2x109) ²2.C . - - 20-j 20 j (9x109) C 1-4X108 Lc = 20 (j WC ) -j zo (jWC) = 20jWC + 20 wc 1 - 2owc - 4x1018Lc = 2cjwo -row-w²L = rojwa

b = rojw tw² L + row c=- rojw twll + row cl = 5(W²L+ 2ow)² + (20w)? let. L=1mH 12x 109 x1 +20x109)2+(20x109)2 ✓ 122*107) 2 + (20 x 109) 2 V (H4 Xp0!8) + ( 40x1018) √ 84 X1018 - 2.499 x 10-16 Ich = 0.2499 ff