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NF(Mstages)
=10*log[nf1
+(nf2-1)/(gain1)+(nf3-1)/(gain1*gain2)+...+(nfM-1)/(gain1*gain2*...*gainM-1)];
whereeach"
nf"
and"
gain"
valueisexpressedasaratioratherthanindB,andMisthetotalnumberofstages.
Thenoisefigureofanattenuatorisequaltoitsinsertionloss(10dBinthiscase).Notethatpertheequationthatthenoisefigureofthefirstelementinthechainisnotmodifiedbythegainofprecedingstages-asarethesubsequentstages'
noisefigures.Therefore,anynoisefigureaddedtothefrontendaddsdirectlytotheoverallsystemnoisefigure-inthiscaseanincreaseof10dB.
3.
An
system
has
linear
throughput
gain
+10
and
an
output
3rd-order
intercept
point
(OIP3)
+30
dBm.
input
(IIP3)?
+20
dBm
+40
4.
Which
filter
type
greatest
selectivity
for
given
order
(i.e.,
N=5)?
Bessel
Chebychev
(ripple=0.1
dB)
Butterworth
5.
mixer
spurious
product
5th-order
product?
1*LO
+
5*RF
6*LO
-
1*RF
3*LO
2*IF
6.
A
2.8
GHz
oscillator
phase-locked
MHz
reference
that
single-sided
phase
-100
dBc
1
kHz
offset.
singlesided
offset?
-48.6
dBc
-51.1
Whenanoscillator(2.8GHzinthiscase)isphase-locked(PLO)toareferencesource(10MHzinthiscase),thephasenoiseisincreasedinamplitudebyanamountequalto20*log(fPLO/fRef)+2.5dB,wheretheadditional2.5dB(ruleofthumb)isduetophasenoiseaddedbythephaselockingcircuitry.ThisexplainswhyanextremelylowphasenoisereferenceoscillatorisrequiredwhenbeingusedwithamicrowavefrequencyPLO.
-100dBc+[20*log(2800/10)+2.5]dB=-48.6dBc
7.
power
2
Vpk-pk
sine
wave
across
50
ohm
load?
-20.0
+10.0
+19.0
8.
2-port
S-parameter
commonly
referred
as
"
reverse
isolation"
in
amplifier?
S21
S22
S12
Commonnamesforeachofthefour2-port
S-parametersare:
S11:
inputreturnloss
S21:
forwardgain
S12:
reverseisolation(orreversegain)
S22:
outputreturnloss
9.
are
minimum
maximum
combined
VSWR
limits
interface
characterized
1.25:
2.00:
VSWR?
1.75:
(min),
2.25:
(max)
1.60:
2.50:
0.75:
3.25:
VSWR(max)=[VSWR1*VSWR2]:
1
VSWR(min)=[VSWR1/VSWR2]:
1,whereVSWR1>
VSWR2.
10.
ideal
directional
coupler
directivity
25
isolation
40
dB.
its
coupling
value?
65
15
Adirectionalcouplerischaracterizedbyfivemainparametersasfollows:
Frequencybandofoperation.
PowercouplingexpressedasdBdownfromtheinputpowerlevel.
Isolationofthecoupledportfromtheoutputport(essentiallycouplingfactorfromtheoutputporttothecoupledport)
Directivity,which
ismathematicallythedifferencebetweenthemagnitudesoftheisolationandthecoupling.Ifthecouplerinthiscasehad0dBmsignalsappliedtoboththeinputandoutputports,thecoupledportwouldsee-15dBmfromtheinputportand-40dBfromtheoutputport,hence,anisolationof25dB.
Coupling=40dB-25dB=15dB
#2
On
Smith
chart,
what
does
bottom
half
chart
represent?
inductive
impedance
capacitive
Power
saturation
While
we'
re
on
subject
charts,
far
left
edge
center
horizontal
line?
Infinite
ohms
(open
circuit)
Zero
(short
match
single-conversion
downconverter
uses
high-side
local
(LO)
translate
radio
frequency
(RF)
intermediate
(IF).
Will
spectral
inversion
occur
IF?
Yes,
always
No,
never
Sometimes
Spectralinversionoccurswhenhighfrequencieswithintheinputsignalbandwidtharetranslatedtolowfrequenciesintheoutputbandwidth,andviceversa.Sinceadownconversionisbeingperformed,thelowersidebandofthemixingprocessisextracted,hencethedifferencebetweentheLOfrequencyandtheRFfrequencyisdesired.Considerthefollowingparametersandhowspectralinversionoccurs.
RFinputfrequencyband:
fc=1250MHz,BW=100MHz(1200-1300MHz).
LOfrequency:
1600MHz.
IFoutputfrequencyband:
fc=350MHz,BW=100MHz(300-400MHz).
WhenthelowerfrequencyoftheinputbandissubtractedfromtheLOfrequency(1600MHz-1200MHz=400MHz)alargerfrequencyisobtainedthanwhenthehigherfrequencyoftheinputbandissubtractedfromtheLOfrequency(1600MHz-1300MHz=300MHz).Thismeansthattheoutputspectrumisthemirrorimageoftheinputspectrum.
Howtoavoidspectralinversion?
Alwaysusealow-sideLO(LOfrequencybelowRFinputfrequencyband)formixing,orensurethatanevennumberofspectralinversionsareperformedintheconverter(i.e.,twostagesofconversionwithhigh-sideLO'
s).
floor
spectrum
analyzer
resolution
bandwidth
decreased
two
decades?
20
increase
decrease
Theinputfilterbandwidthdeterminestheamountofpowerthatwillbepresentatthedetectorcircuitry.Sincethedetectorperformsapowerintegrationfunction,itsumsalloftheincidentpoweracrosstheband.Decreasingthebandwidthbyafactorof100(twodecades)allowsoneone-hundredthoftheamountofpowertoreachthedetector,whichintermofdecibelsis:
10*log(1/100)=-20dB.
primary
advantage
quadrature
modulator?
Low
LO
required
Four
separate
outputs
Single-sideband
output
meant
dBi
applied
antennas?
Isolation
decibels
Physical
size
relative
intrinsic
antennas
Gain
isotropic
radiator
dynamic
range
12-bit
analog-to-digital
converter
(ADC)?
36.12
120
72.25
Anideal12-bitADCcanassume212
(4,096)uniquevoltagelevels.Sincepowerisproportionaltothesquareofthevoltage,themaximumpowersamplevalueis40962
(16,777,216)timestheminimumpowersamplevalue.Thereforethedynamicrangeis10*log(16,777,216)=72.25dB.
Aruleofthumbis6dBperbit.
front
load
VSWR.
resulting
attenuator?
1.07:
1
2.10:
12.0:
VSWRisrelatedtoreturnloss(RL)accordingtoVSWR=[10^(RL/20)+1]/[10^(RL/20)-1].ItfollowsthatincreasingthereturnlosswillresultinalowerVSWR.TheRLofa2.00:
1VSWRis9.542dB.Addthe10dBattenuatorforatotalRLof2*10dB+9.542dB=29.542dB.ConvertbacktoVSWRusingthegivenformulaforavalueof1.07:
1.
Whyaddtwicetheattenuatorvaluetothereturnloss?
Returnlossisthetotaldecreaseinsignalstrengthinpassingthroughtheattenuatorandbeingreflectedbackthroughtheattenuator.Hence,thesignalisdecreasedbytwicetheattenuatorvalue.
thermal
temperature
degrees
Celsius
(assume
0
dB)?
-114.0
dBm
(in
bandwidth)
dBm/Hz
Thermalnoisepowerdensityisgovernedbytheequation10*log(k*T*B*1000)dBm,wherekistheBoltzmannconstant.TisthetemperatureindegreesKelvin,andBisthebandwidthinHertz.Multiplicationby1000istoconvertwattstomilliwatts.Aruleofthumbfortemperaturesnear15°
Cistobeginwithathermalnoisedensityof-174dBm/Hz,andscaleaccordingly(add10dBperdecadeofincreasedbandwidth).
Two
equal
amplitude
tones
have
dBm,
generate
pair
intermodulation
products
-20
2-tone,
3rdorder
system?
+25
2-tone,3rd-orderintermodproductsincrease3dBinpowerforevery1dBincreaseintonesthatproducethem.Thatmeanstheintermodsincreaseinpoweratarateof2dBper1dBrelativetothetonepower.The2-tone,3rd-orderinterceptpointisdefinedasthetheoreticalpointwherethetwooriginaltonesandthetwo3-rd-orderproductswouldhaveequalpower(notpossibleinrealsystemsduetosaturationlimits).
Ifthetwooriginaltoneshaveapowerof+10dBmandthe3rd-orderproductshaveapowerof-20dBm,thentheinterceptpointwillbeat+10dBm+[(+10)-(-20)]/2dB=+10dBm+15dB=+25dBm.
#3
using
90
degree
(quadrature)
hybrid
couplers
amplifier
designs?
Wider
possible
figure
Input/output
not
dependent
devices
long
device
impedances
equal
Duetothephysicalconstructionofthequadraturecoupler,aslongasthetwodevicesbetweenthecouplersexhibitidenticalimpedancestheinputandoutputimpedanceswillexhibittheintrinsiccouplerimpedance.Forexample,ifmatchedtransistorswithinputimpedancesof12-j5Ωareconnectedbetweentoquadraturecouplersthathaveanintrinsicimpedanceof50+j0Ω,thena50+j0Ωimpedancewouldbeexhibitedatthecircuitinput(similarfortheoutput).
Why
there
term
equation
free-space
path
loss?
There
no
term
Atmospheric
absorptio