Exam text content

ELT-47206 Basics of RF Engineering — May 9, 2017, 13-16, Festia iso sali 10f4

 

Exam

Examiner: Olli-Pekka Lunden

Students are allowed to use any types of calculators and any written material. Use
of mobile phones, laptops, or other communication devices is prohibited. Students
may keep the problem sheet. Evaluation shall be based on the evidence student
demonstrates about the learning outcome statements of this course.

To solve the problems students may also need: a compass and either a ruler or a
set sguare.

Problem 1: The following claims may contain inaccuracies or falsities that you must iden-
tify and explain what is wrong. In addition, you have to provide a fully cor-
rected sentence, corrected with minimum editing. The actual claim is in bold-
font. The normal-font text should always be correct. If the claim is com-
pletely correct you must state this to be the case and not comment or edit
10.

(a) Transmission lines are homogeneous conductor constructions that
are comparatively long; in practice, at least 5 mm long.

(b) Consider a transmission line and a load. Reflection coefficient corre-
sponding to load impedance of Z; = 75 2 isT/ = 0.2, in all cases.

(c) The amplitude of a voltage wave reflected from a 75-ohm load is 50%
of the incident wave. In this case the characteristic impedance of the
transmission line is 25 2 or 250 0.

(d) An impedance inverter made of microstrip line on FR4 (€, = 4) is 30
mm long. The freguency of interest is 1.25 GHz.

(e) The transducer power gain of a two-port is defined as Gr = Pi] Pave:
where P7 is the power delivered to a load and Pyyg is the power available
form a generator. The voltage gain of a two-port Ay = V1/Vin = V/Gr,
where V7 is the voltage across the load and V;,, is the voltage across
the two-port's input.

(£) Consider a (theoretical) two-port with S1> = 0. Such a two-port is nec-
essarily unconditionally stable, or, in other words, it cannot possibly
show negative input or output resistance.

Each subproblem yields ] point at max.
ELT-47206 Basics of RF Engineering — May 9, 2017, 13-16, Festia iso sali 20f4

 

1k

 

   

Characteristic impedance Zy, 2

 

0.3 10
Line width to dielectric thickness ratio, w/h

Figure 1: Microstrip characteristic impedance for several relative permittivities €,.
Source: Reinhold Ludwig and Gene Bogdanov, RF Circuit Design, Theory and
Applications, 2nd ed. Prentice Hall, 2009.

Problem 2:

Problem 3:

Certain rules-of-thumb say there is always x nanohenries of parasitic series
inductance for every millimeter of (thin) wire, while x varies between 0.5 and
1. In this problem, you are studying the grounds for this rule-of-thumb using
transmission line theory:

(a) First estimate the characteristic impedance of a 1-mm wide microstrip
line printed on 1.6-mm thick FR4 (€, = 4). You may use Figure 1.

(b) Assume you have a 5-mm long segment of this microstrip line (/=5
mm) and that the line is ideally shorted at its end. Calculate its input
impedance Z at some freguency, such as 450 MHz.

(c) Find the inductance L that gives the same impedance Z at the same fre-
guency according to Z = XK. Z=)Wh <7l- Eur

(d) Calculate L/7 in nH/mm and compare your result to the x of the rule-of-
thumb mentioned above.

(e) Contemplate the limitations of the rule-of-thumb, such as what comes
to the physical dimensions and freguency.

Subproblems (a) through (d) yield 1 point at max, but (e) can yield 2 points.

Under certain conditions, transistor BFG520 should *see” generator and load
reflection coefficients I'yc = 0.67/40? and I'vz = 0.38/55", respectively, in
order to provide maximum gain at 450 MHz.

(a) Choose the topologies for input and output impedance matching. Moti-
vate your choice with good reasons.
ELT-47206 Basics of RF Engineering — May 9, 2017, 13-16, Festia iso sali 3 of 4

(b) Design the input impedance matching network for an external generator
having 50-ohm internal impedance. Give all the needed the transmission

line dimensions or discrete component values.
Subproblems (a) and (b) may yield 2 and 4 points, respectively.

Problem 4: Figure 2 shows the measured Sj] of an amplifier. Determine the 70-dB input
return loss-bandwidth' of that amplifier.

 

S(1,1)

 

freg (100.0MHz to 700.0MHz)

Figure 2: Measured Sjj. The 10-dB input return loss-bandwidth should be deter-
mined from this graph. Markers are at 100 MHz, 200 MHz....700 MHz. Note that
the curve is not completely smooth but is uses straight-line extrapolation between

data points. Freguency step is 10 MHz.

1 Over this bandwidth, the return loss of the amplifier is 10 dB or more.
 

 

RADIALLY SCALED PARAMETERS

 

 

 

 

 

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» 15 w 8 6 s TIT ah 11712 1314 16 1872 3 453 0» -
Id ASS T S I 2 4 20, 30-10 O) 02 — 04 06 08.1.15. 2 3.4, 36, , 10 15
07 06 05 04 03 —02 MIA 00 = ojo 11 512 13 14 15 16 17 18192 253 15 T0-
081107 0,08 05 04 103 02 01 0 0|1 099 095 = 09 08 , 07 — 06 05 04 03 02 01. 0
= x
CENTER
02,03, 04 1,08 |. 108,07 008 009, 1 [R 12,13 14 1 1889 2