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lectures on RF and Microwave Engineering
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97 views6 pagesSheet 2 - Solution
lectures on RF and Microwave Engineering
Uploaded by
Sajjad AhmadCopyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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/ 6
Benha University
Faculty of Engineering at Shoubra
Electrical Engineering Department
(2013-2014)
Microwave fundamentals
3" Year Communications
Sheet 2 - solution
A lossless transmission line is terminated with a 100 Q load. If the SWR on the line is
1.5, find the two possible values for the characteristic impedance of the line.
+ Sloss,
Whe Sop = SE 20.2
P| ef BeBe] = | 00
Ie fSS| = eke] al)
So itn, yeas.
oe
oe 100-2.
aa 22,0 ape/t2) =
Teer OZ BRL ayoe/ id) = 1502
Let Z,. be the input impedance of a length of coaxial line when one end is
circuited and let Zj. be the input impedance of the line when one end is
terms of Z,, and Z,.
| 2s =f 2 Tin pl 1 Zoe = ~/ oct pl
BeBe <2 > > [Bec Bee
short-
open-
circuited. Derive an expression for the characteristic impedance of the cable in
pF at 2.5 GHz. Repeat for an inductance of 5 nH.
"Cl Boe = fue = -j 273A Ske ot pL CF pF
Com BL = 100/273 => Le 82.77% ¥
Aczo.tlwe , B= amV€e/ro = 3854%m => LBM Tem ¥
Lt Bop ej = +] 72.52 = ~j2o cot ph Lesyh
Tim BL = l0o/re.5 => Ph i281°/ 42 3.324 omY
These reeubte were erupt with Strerode
A 100 Q transmission line has an effective dielectric constant of 1.65. Find the
shortest open-circuited length of this line that appears at its input as a capacitor of 5 4] A radio transmitter is connected to an antenna having an impedance 80 + j40 Q with
a 50 O coaxial cable. If the 50 Q transmitter can deliver 30 W when connected to a
50 Q load, how much power is delivered to the antenna?
B04;40 . 50 12R
“1304s 36172
Row > BueRer = Poue (I-irl*) * 30[}-6367)"] = ase w
. we
= = 6.367136.
5] The transmission line circuit shown below has V,= 15 V rms, Z,=75 Q, Z, =75 O, Zi=
60- j40Q, and f = 0.7A. Compute the power delivered to the load using three different
techniques:
(a) find f and compute
Ve)" 1 2).
a=(%) Zz, ( ITP);
Vg riSv Rms, By 752, Be7Sn, B66; Hn, LGTA
5540 _ ya rpctos®
BE S4e ye ces
0.303 [299" = -e.0a/-j 0-308
Re CB a (rire) = acer w «
This rmuthed ia actiath tosol om A= Fone I-III), LA na.
the asneplst muted, nck only, elite ty realise Lect .
(b) find Z,, and compute
Ys
2
sa| ReZua);
Rare (Zin); and
y=
>) ain g, Bet) to tan Pe = 7p bOHil¥% 96 2oolta
24) tam pt (asia ier”? a708 7
= 55 yl 2 48.24j973 0
R- [es R@a)= |i “(yn2) = 2.68w v
Vapeaa
T23.anja75
Thin mabe commpaartec, PL= Pin =|Ec.|* Pain » Anol alee cgebete
only, te eveleaee bowie (c) find V: and compute
vp
P= |=] Re(Z,).
VCR) = vt(et®? pr eify
Vs veo) = VtCitr) vt Bers,
> 7.5 (|-veal ~s.302)
= 7.68 £12°
(60) = 0.68lw
(d) Discuss the rationale for each of these methods. Which of these methods can be
used if the line is not lossless?
24 <—— 1 ——
>
3 @ a> ns n3 =
Tie cthed Computic PL= ITU RL , ancl agetiea &
at swell 04 Lewelere Leta. We che Comrecpt that Vt=Y4/a
Aegite a Good Lmolerstimdling of the tamemustin Lat
egrations, Ourok onby apilte hun Heoauet ZyoZo.
6] For a purely reactive load impedance of the form Z,= jX, show that the reflection
coefficient magnitude If IT lis always unity. Assume the characteristic impedance Z, is
real.
Bejx
Pe Zecde , UX -2e
Bree fxr zo
In}t= 7D pee 7
Consider the transmission line circuit shown below. Compute the incident power, the
reflected power, and the power transmitted into the infinite 75 Q line. Show that power
conservation is satisfied.
$00 +—_sn—_+
Pat —> —> Pram
i
See BO
7 Gee bm ae a; em
c= Et soyoow ¥
Powsk vavveeed BY serge = £ oe
fower Dssirmey WW Ban Lot = ECM) = Olow S
2
Power. TRAMSM rTrED DOWN LIN 078) (seezz) O.avow vo
Encwenr power ~ (50) f 12
Bim) ~carow Vv
REFLECTED Power = Prve iF]* =
Bene ~ Peep * -2607.010-70.240 = Praws 7
Poiss+ Prrgus = 604-240 = 2.400 = Poouece
8] A generator is connected to a transmission line as shown below. Find the voltage as a
function of z along the transmission line. Plot the magnitude of this voltage for
-¢sz