''
racte
Cha
ristiss'
andApplications
of DiodeDetectors
Ron Pran
Rf & Mlcrowave
fYleasurement
Symposlum
ancl
Exhlbltlon
ftE FF&TJJ
Applicationsof Detectors
AbsolutePowerMeasurements
RelativePowerMeasurements
LevelingLoops
Systems
Monitoring
PulsedRFMeasurements
The diode detectoris a very common elementin microwave
measurement
setupsand findswide
applicationin systems.
semiconduoordiodesare usedfor measuringabsotutepower.
Networkcharacterizationoften employsdiodesto measurerelativepower,
aiJteuet;ng loops,systemmonitors,and
pulsedRFmeasurements
are other applications
which rreq*nily employdiode detecrors.
The systemperformanceone obtainsis a funoion
or trrl aeteaor d;ode,its associared
RFmatching
circuit'the circuitrywhich processes
the dereoed signal,and the environmentalconditions
over which
the systemmust operate.Tireparameterswhich
.;;rJ
i;;;"rtor,,.,.n.u of a deteoor are presentin atl
isimportant
fr?[tj||lT:j."
to understand
howrtey inrliaa sothartr'eaes;lalfrt". p"rrormance
Diodesfor microwavedetectotr
semiconductor
"rnffi
interface
Theyare majorig carrierdeviceswhich minimize
storedcharge
Pointcontactand schottky(hot carrier)diodesare
the mostcommon typesof detectori
r
E\
PSi
Pointcontact
'7g
MFTAL
N EPI
N+si
High BarrierSchottky
METAL
A@
P IPI
P+Si
LowBarrierSchonky
conventional PN junaion diodes exhibit storedchargeeffeos which limit
their operaringfrequency.
Currentflow in a metal-semiconducror
junoion is due irimarily to maiorirycarriers,so the
effeo of
chargestorageis minimized.Thismakei devicessuchasthe poinr contao
diode o, the Schonky
junction performasefficientreoifiersat microwave
frequencies.
For manyyears,the only way to fabricatethe requiredmetalsemiconductor
interfacewasto employa
point contactsystem.Thistype of constructionyieldeddiodeswith
a wide variationin unit to unir
performanceand the delicateassemblyis subjea to damagefrom
excessive
power, mechanicalshock,
or temperaturecycling. -ut
more rugged strucrureevolvedby depositingthe 6ariier meral
dlreJv
on an epitaxiallygrown Ilayer'ordinary schottkydiodeshavea hijh potenri.iu.rii.i.na
r.quir. ---ui"i
currentto achievesensitivities
eguivalentto point contactdiodes.Ttremost recentdevelopmeniii
"
detectordiodesis the formationof a Schonkybarrieron P type siliconwhich
hasa barrierheighrabout
% that of ordinary schonky diodes.The low barrier height resultsin delecrors
which are electrically
similarto point contact devicesbur much more ruggedl
Allthree typesof diodes are found in current xF-produas. The K and R 4224
derectorsuse poinr
contactdiodes,and achievea sensitivity
at 40 GHz tuhichis quite similarto lower tr.lr"n.y point
contactdetectors.The 11664AAmplitude Analyzerdetectorsuse biased
Schonkydejces ln
conjunclion with an AM modulated sourceto achievea -50 dBm sensitivity,
and the g4s4Apower
sensoremploysa low barrier Schottkydetector and providesCW power measurement
..p.'bility to
-70 dBm.
Diode Equation
-)
lr
le- vi J
-U
| = ts[exp(Vilvr)
I = diode current
Vj : junctionvoftage
Vt: "thermalvoltage,,
Vt : nKT/q
ls: reverse
saturationcurrent
=
K Boltzmann
constant
Determinedby,
T = Absolutetemperature
Junctionarea
g = Electroncharge
materials
n = idealityfactor
temperature
( 1< n < 2 )
ls changesby 2:1 for temperaturechangeof about
20 degreesc
At low signallevels,all.threetypesof
diodes.closely
obey the equationfor the idealdiode, and rhis
will be the startingpoint for rne Jiscuision
of deteoor aoion. ihe equationrelaresrhe currenr
through
the diode to the vohagea.ppearing
acrossthe junoion. ri" fr,.r.oerisricsof the diode
are reffeoed in
the so-called"thermal voliage",vi."Jii"
reversesarurationcurrenrrs.At a giventemperature
Vt wirl
be differentfor varioustypei of diodes,
and this.is,"trua"Juv t-heuarueof the idealityfactor
n which has
a valuein the rangeof 1 io 2. The predominanr
faoor which ierer,',,ines;";;;;;;istics
of the diode
is the valueof the reversesaturation
currentls.Thiscurrent is a function of devicearea,
materialsusedto
form the iunoion' and temper.rrt".
iiu i",np.r.,rr" dependenceis very importantbecause
mostof
p"'io'',n."
;liJI:?i"#:rTH
..i u" related
to vaiiations
in rs,which.l,r"i", Lyapp,ori,,.'arery
a
Effectof Reverse
SaturationCurrent
I in microamps
V in millivohs
A-low
barrierSchortky
ls = 25 microamps
B-Point contao diode
ls = 5 microamps
C-High barrierSchottky
ls = 2.5nanoamp
D-High barrierSchonky
wirh 25 microampbias
By examiningthe lV curvesfor the varioustypesof detector
diodes,rhe influenceof the reverse
saturationcurrenl can be seen.curve A is typiialof a low
barrierschonkywith is = x microamps.This
is contrastedagainsta point contactdevice(curve
B) whosels = 5 microamps.curuet i, to..a rypical
high.barrierschottkyhavingan ls = 2.5nanoamps.The
diodesdescribedby curvesA and B show
significantcurrent flow.atviry fow junctionvoltagesand
this is the type of tv charaaeristicwhich is
desirablefor a low levefdeleoor. Similarbehavioican be
obtainedwitn the hif;;;;",
schonkyby
applyinga biascurrentto.shiftthe operatingpoint to a region
similarro that .f?; 1o."barrieror poinr
contact device' The penaltyfor doing this ,itie dc offserit
i.n is produced. g;asedderedors are either
usedfor detectingsignallevelsaboui -s d?-- in dc coupled
systemsor are usedin ac coupled
systemswhich eliminaresthe effea of rhe offset.
Squarelaw Detection
SimplifiedAnalysis
Vp COS(coT)
| = ls[exp(vjNtl-1J = ls[VjA/t+ t/2(yjNt)2+ . . . . 1
Assume:Vj = Vp cos(<oT);
Vo << Vp; Vp < Vt
I =#
+ f Unnrt),[1+ cos(2a,T)]
cos(a,T)
tdc=|{vnru,t'
O.neof the major applications
of diode detectorsis to measureeither absoluteor relativepower
.
levels'Al low power levels(<-20 dBm),the diode respondsro the sguareof the voltage
appearing
acrossthe junction so the deteoed signalbecomesa iunoion of power.An approximlte
but accurate
analysisrevealsthe reasonfor the squarelaw response.The diode currentcan be estimated
by a series
expansionof the diode equation.Upon substitutionof a sinusoidaldescriptionfor the signal
voltage,
restrictingthe analysis
to signallevelslessthan vl, and assumingthat the iereoed signalisnegligib-le
with respeo to the input voltage,one findsthat three domin.ni t"r-, appearin rhe
expression.
Two of
thesedescribethe fundamentaland secondharmonicof the inpur signjl which are
bypassedby a
capacitor.A dc term which is proportionalto the sguareof the'input-vokag.r,"prer"nr,rhe
detected
signal.Experimental
evidenceon a wide varietyof detectorsconfirmstt e Jatiaiiyof the analysis.
lr
nol be surprising.that
significantdepariurefrom squarelaw is nored for signallevelsexceeding
:P,f.a26 millivolts(about -22 d8,min a 50-ohmsystem)and the dereaed outpur level is-about157o
of the
peak RF inpur voltageat this power level.
Equivafent
Circuitof Diode Output
Detectedcurrentgivenby:
ls
ldc = q NONt)'z
Define"originresistance"
Ro = Yt/ls
Substitution
yields
, - V -p '
IDC
ARM
Whichsuggests
the followingcircuits:
Vp'
aRoV
]
Ro
oR
Vp'
4Vt
Biaseddetectorsaresimilarexceptthat
=I
Ro
"le
19= Biascurrent
and fixedcurrenror voltagesourceshaveto be addedto account
for
the biassignal.
lf a new term "origin resistance"
is introduced,the analysis
can be extendedto obtain a usefulmodet
for the deteaed orriur. The origin resistance
of rhe diode is simplyrhe slopeof rhe diode lV curveat
the point of zero signal.
RFcomponentsof rhe diode currentare bypassed,
j]l*:L:
the outpur of the diode is a dc voltage
..
when a cw signalis applied.The analysis
suggesrs
tharii,e diode output is in the form of a current
sourcedrivinga shuntresistorwith a valueei-ualto
the origin resisrance.
Thiscan be transformedto an
equivalentvoltagesourceand seriesresistance.
The RFbyplsscapaciloris includedin the modelto
accountfor the transientresponseof the detector.
An analysis
of a biaseddetectorwill leadro a simitar
resultexcept fixed sourceshaveto be added
and the origin resisrancebecomesa function of Vt and the
biascurrent lo.
DetectorCircuitConsiderations
Matching
Network
Thematchingnetworkdetermines
thesespecs
BANDWIDTH
swR
opEN
ItrT'ft Bl[?l?l$r',
r,v,w
The diode and the matchingnetworkdeterminethe tangentiat
signalsensitivity
TSS
The specifications
which are obtainedfor a deteoor are governedprimarill,
by the microwavecircuit
in which the diode is imbedded.The diode impedance
is raiely equalro the zo or tr," sysremso a
matchingnetwork is necessary.
The designor t-hiscircuitdererminesoperaringbandwidth,
SwR,
frequencyresponse'and open-circuitvoitage.sensirivity.
A systemsrelated,pJ.iii.riion, tangentialsignal
sensitivity(TSS),
is governedboth by the malchingnerworkand the charaoerisrics
of the diode.
MatchingCircuits
Resistive
Matching
RT
Input
ReactiveMatching
RF
Input
l*nv'rl
-T-att-1'--
i
I
=
I n=
Pointcontact,low barrierSchoftky
or biasedSchottky
BiasedSchottky(fowRs,tow e)
Broadbandwidrh(.Ol- 26.5CHz)
L o w S W R( < 1 . 3r o t 8 C H z )
Moderare sensitivity(500pVlp watr)
Freq.response:.35 dB .m - 1gGHz (8494)
Narrowbandwidrh(ocraveor less)
H i g h S W R( 2 : 1t y p i c a l )
High sensitiviry(2000pY/y wan or higher)
Freq.response:.5 dB./ocrave
Sensitivityspecson chips and packageddiodes almosruniversallyrefer to
a reactively
matched circuit.
Thereare two approaches
to the designof the matchingnetwork,either resisliveor reacrive.The
resistivenelwork is usedin broadbanddesigns(.01ro 25.5-CHz;and
can yield low SWRand flar
frequencyresPonse.
The sensitivity
of resistively
marcheddeleclorsis almosrindependentof rhe diode
characteristics.
The reaoivelymatcheddereaoiswork over only modesrbandwidihs,lenerallyhaue
relativelyhigh SWR,and the sensitivity
obtainedis a strongfunoion of the diode characteristics.
The
advantageof reactivematchingis a markedincreasein sensitivity.
Thisis due to the fao that the
matchingnetworkactsasa transformerso the voltageappliedto the diode junoion is increased
by the
tquare root of the ratio of origin resistance
to Zo. Toobtain a reasonable
bandwidrh,biaseddiodei wirh
an origin resistance
of about 4 timesZo areoften usedin reactivelymatcheddesigns.Thisresuls in a
faoor of 4 increasein sensitivity
over the resisrive
matchingn"t*oik. lt shouldbe-menrionedthar the
sensitivityspecifications.Jor
diodesin chip or packagedform almostuniversallyassumea reactively
matchedcircuit.Regardless
of the sensitivity
specon a reaoivelymatcheddiode,rhey will all yielj very
similarperformancein a resistively
matchedcircuitbecausethe transformerpropertiesare nor present.
Departurefrom ldealDiode
3 Key Elementsto took for are:
R6 SpreadingResistance
Ro Origin Resistance
G5 ShuntConductance
I
=
Ro Yt/ls
R;
I
R;
Non linear Model
linear Model
(SquareLaw Region)
Theslopethroughthe originisreallythe parafrer
combination
of
Roand G,
Theseadditionalelementsreducethe sensitivity
of the detectorfrom
itstheoreticalvafueof
Vdet = Vp,
4V
The actualdiode will showsomedeparturefrom
the idealdevice.Theoretically,
the origin resisrance
is givenby vt/ls, but a conductance
Gsshuntsthe iunoion or tle aoual diode,so rhe slope
ar zero
signalis definedby the parallelcombination
of Ro and Gs.All diodeserhibira spreading
resisrance
Rb
which is in serieswith the nonlinearportion
of the diode-Rb,cr, .na rhe parallelcombinarion
of Gs
and Ro may be dererminedfrom the devicelV
curve,and contriburero a Lar.tloiin sensitivity.
Low BarrierSchottkyDetectorCircuit
r-R FI n p u t
'vi-i
-T
-'l
v,;
I
I
L
JDiode
circuit wasoptimizedto minimizechangein V; with frequencyand
arsoprovidea
good marchar the RFinput
Ro = origin ResistanceRb = spreadingResistancecj =
Junctioncapacitance
[p = Leadlnductance Zo = RFLoadResistor c = RFBypass
capacitor
Rc= Compensation
for LpCjResonance
Lengthand impedance
of stuboptimizedto minimizeSWR
A completemodelof the HP low barrierschotrkydeteclorshowslhe
elementswhich haveto be
consideredduring the designof a broadbandresisrively
marcheddereoor. tt e capacirance
of the diode
Cj and its feadinductanceLp effea the matchand frequencyresponse.A
resisrorRc dampsthe
resonance
of LpCj,and a stubis placedin serieswith the RFload to minimizeSWR.
The various
elementsin the circuirwork togetherto keep rhe voltageacrossthe junction
constanrwith frequency.
10
The Sensitivity_
of the Det".to
Diode and the MatchingCircuit
r --
l-Y*l
:-r--[-'r
i*'
I
I
I
I
I
L--
JDiode
Vi2
ldealfy Vo=If
1. ldeafity factor increasesVt:
, brr
Vt=nKT/q 1 <n<2
2. Shuntconductanceof diode:
A.
Lowers
originresistanceR6=
'=fu;
g. Self-loadingu t =
-
uo
1+GrRo
3. Matching circuit loss:
tv/ -r : 6 V R d
A finiteoutPut loadresistorwill havea dramatic
effeo on the derectorperformance
The sensitivity
of the resistively
matcheddeteoor is not a srrongfunction of the diode
characterisrics,
but the actualsensitivitywill be iomewhatlower tnan
thai pr.oo"a by rhe analysis.
The idealiryfa.or n
causesan increasein the valueof Vt. The shuntconduorniu
cs lowersrhu orilin ,iriir.n." and also
actsasa built-infoadfor the videooutput.Finally,
there is a rJu.oion in the junoion volrageVj relative
to.the appliedsignalV.du.eto.the lossesproducedby
the RFload, Rc and Rb. The combinationo{ rhese
effeos causesthe sensitivity
of actualdeieoorsro be 30 to soo/;lower
rhan ideal.
11
Loadingthe DetectorOutput
Vdet
R;
i*o
I
I
I
I
Rr
I
L--
--J
Diode
Circuitfor Output
Equivalent
RV
vd
Rr
von
I
I
Vdet=ffiuo
Video resistance
Rv=Rd +Ru*R. *74/2
Rv is a functionof power level,temperatureand R1
The mostdramaticchangein sensitivity
is producedwhen the outputof the derecloris loaded.The
finitevideo resistance
Rv formsa voltagedividerwhich cansignificantl;,decrease
lhe outputvoltage.ln
the squarelaw region,Rv is governedmainlyby the originresistance
of the diodeRo,but asthe diode is
driven out of squarelaw, Rv becomesa complicatedfunctionof power level,temperature,and R,.
12
low BarrierSchoftkyDetector
Typica
I TransferCharacteristics.
At 250C
Rr=1ko
lfi) mV
Rr = 50kO -:;,
Vo,rt
1mV
-lo
o
fnputPower(dBm)
examiningthe transfercharacteristics
of a typicalfow barrierschottkydetector,one can seelhe
,.By
effea of load resistance
on lhe output voltage.Notethat in the range of -30 to -20
dBm the outpur
voltagechangesby 10to i, th-usiniicatingsqu"relaw
operarion.
Ar higherpower levels,the slopeof rhe
'linear
transferfuncrionis cur in half,which is an-indication
of
ofer.tion.
13
Comparisonof Low and High LevefSignals
linear
-..-l
P < 10 microwansinto 50 ohms
Detected voltageproportional to
the squareof appliedsignal.
F
Von
Power levelstrearer than 10 milliwans
Detected voltageproponional to
the peak RFvoltage.
Video loadingwill lower the detectedyoltage
In the squarelaw region,the waveformof the diodecurrentis almostidenticalto that of the input
signal.Underlargesignaloperation,the diodecurrentwaveformbecomesa functionof input signal
leveland video output voltage.The output voltagebecomesa complicaredfunctionof load resisiance,
power level,and diodecharacteristics.
The key point is thatthe derectionlaw will undergoa rransilion
from squarelaw to linear.Thisoccurswhen the junoion voltageexceedsVt. In the linearmode rhe
diode is actinglike the familiarpeakdetector.
14
Video Resistance
Rv Varieswith power, Rr and
Y
ts
Y
E
d,
-10
P d8m
when the diode is in squarelaw,the video resistance
is essentially
constant,but at higherpower
levelsthe currentthrough the diode exceedsts
and the video resistance
becomesa complicared
funoion of power, load resistance,
and ls. For low barrierdiodes,fs determinesRv ai low
fevels.At high
levelsthe vafueof Rv is d.eterminedby rhe actualdiode
currentand rhe orher ,"rirro* in rhe detector
circuit'The percentagechangein Rv and rhe actual
transitionfrom squarelaw to linearis governed
by ls
and R, and the decreasingvalueof Rv can be used
to extendthe squareraw range.
15
Transitionfrom SquareLawto Linearts
Governedby RatiosRv/Ro and Rr-/Ro
a
Diodeorigin
resistance:
co2
--RO=10k
Ro = 1'5k t
---Ro=100rl
-50
o
ag
tt)
\\.
9-r
Detector
Video Resistance
c
.9 -6
.E
o
50K
.5K
.5K
50K
50K
Rv=Ro+100fl
-10
0
P;n(dBm)
TypicalSquareLaw Deviation
T h e s q u a r e l a w d e v i a t i o n i s a m e a s u r eo f t h e e r r o r b e t w e e n t h e d i o d e o u t p u t v o l t a g e r e l a t i v et o r h a t
p r o d u c e d b y a t r u e p o w e r s e n s i n gd e v i c e .T h e d a t a p r e s e n l e ds h o w st h a t t h e t r a n s i t i o nf r o m s q u a r e l a w
t o l i n e a r i s a s t r o n g f u n c t i o n o f v i d e o l o a d . T h i s c a n b e u n d e r s t o o d b y o b s e r v i n gt h a t a t h i g h l e v e l st h e
o u t p u t i m p e d a n c e o f t h e d e t e o o r i s d e c r e a s i n gt,h u s t h e v o l t a g ed i v i d e r a c t i o n i s r e d u c e d a n d t e n d s t o
c o m p e n s a t ef o r t h e c o m p r e s s i o ni n t h e d i o d e o u t p u t . T h i s e f { e o c a n b e u s e d t o e x t e n d t h e s q u a r e l a w
r e g i o n a b o u t 1 0 d B . T h e e f f e o o f l o a d r e s i s t a n c eo n d i o d e l a w i s d e t e r m i n e d b y t h e r a t i o so f R v / R o a n d
R , / R o . l f R o i s l a r g e ,t h e v i d e o r e s i s t a n c eR v i s a b o u t e q u a l t o R o a n d t h e d i o d e l a n ' i n t h e l r a n s i t i o n
r e g i o n o I - 2 0 t o 0 d B m w i l l b e a s t r o n gf u n c l i o n o f R , . l f t h e R o o f t h e d i o d e i s l o w e r , l o a d i n g w i l l n o r
haveas much effeo.
16
TemperatureEffects
With proper biascircuit design,temperatureeffectson high barrierdetectorscan be minimized
Performanceof low barrierschonky is governedby variationin 15
(Ro=f,t lsaorUles
for2O.CAT
Videoresistance
is alsoa functionof powerand R,'.lf diode is in
linearregion,temperaturesensitivity
decreases.
rmK
;
10k
= 200Oro 50k0
5=n,
E
.9
Sr-
u,
<-20dBm
ilk
{0
-20
60
rypicatvideo,.o"ol",ll"iijlo",,'.1'*,,nremperature.
effectsis the variationin ls.Forthe derectorthistranslates
. The biggestcontributorto temperature
to a
changein video resistance.
As can be seen,rhischangecan span a6out2t/zdecadesover a -60 to 100.c
temperaturerange.At higherpower levels,the changein ls is maskedby the large
currentsflowingin
the diode,so the high levelresisrance
mayonrychangeby a factorof 3 or less.
17
Due to variationin Rg the temperaturecoefficient
of low barrierSchottkydetectorsis a strong
functionof load resistance
and power level
rd8
.,q9,,-.,=Tt)
0
I
-t,
/
'
,
:
.,'i/
-./
/
/
- /.t
R, = tO[
-\
i.
<
I
0
-q
.l -
r-Ri<:
orr
rd8
0d8=Ourpur@25'C
P - == --20
! ) dd'h.
8m
P'"
.
P
-2 dE
-\
dBm
-l d8
.-r.rtll
<d8
-60
-20
{r
.,:r'
Lttlr.r.rtrrrr
ao
( ,
High Power
Sincethe squarelaw deviationis governedby
Rv --, RL
tno
Ro
G
the squarelaw,deviationwill alsobe a temperaturesensitiveparameterwhen Rr. Ro
Theeffeo of ls variations,
power level,and videoloadmakesthe changein sensirivity
with
temperaturea rathercomplicatedfunction.The datapresentedhere coversan extremerange.Over a
narrowertemperaturerange,sensitivity
changescanbe minimizedby seleoionof an optimumvideo
load,or by designinga lemperaturecompensating
amplifier.Sincethe ratioof Ro/R,determines
the
squarelaw deviation,thisparameter
will alsoshowa temperature
dependence.
Thedatapresented
earlierwasactuallyobtainedfrom the samediode measured
at -25,25and 100oC.
One canconclude
from thisthat an optimumdesignexistsfor a specificapplication,
but no optimumexistsfor all
applications.
18
Risetimeof Detector
Rv
c
Voc
Rr
-
R1= 25f)
F2o ns
Rr = flX)
Rr= 100(!
Rr'= 300o
Video loadingis an importantconsideration
during the measuremenr
of pulsedRFsignals.lf one is
.
dealingwith fastrisetimepu.lses
severalprecautionshaveto be exercised.The outpur of the deteoor is
takenacrossa capacitorso the RC time constantof the detectorand toad
hasto be small.The data
presentedshowsthe envelopeof a 10 mw pulseoverlayedon the
detectedor,prt. iin." tr," diode is
actingasa peakdeteoor, the video impedanceof the iereoor is low so rhe rise
time is quite fasr.The
decaytime is governedonly by the toadresisrance
and can be appreciablylonger.
19
Effectof Cable
3 f tET_q
r!
R Fl nPUt
Scope
4 = sott
Rr
*l
l'-zo ns
R, = 50O
R, = 100O
R1= 3dX)
often a cableis usedbetweenthe deteoor and the scope.Thiscable
shouldbe rerminatedin irsZo
to minimizethe effeo of multiplereflectionsbouncingbei*een rhe
scopeand the deteoor. lf the rise
timesare long with respectto the time delayin the ca6le,an accurate
estimateof cableeffeos can be
obtainedby simplyaddingthe capacitance
of rhe cableto the output capacirance
of the dere.or.
20
Tangential
SignalSensitivity
(TSS)
N
J/lfl/]/L
[lUUU
VVMCASUICd
Signallnput
I
'tor"sff
=4dB
€
TSSis acceptedto be the signallevelrequiredto producean 8 dB S/N ar rhe svstem
output.Thisis equivalent
to a 4 dB S/N ar the detecrorinput.
A very common systemsspecification
for a deteoor is its tangentialsignalsensitivity(TSS).
The TSS
point is generallyregardedasthe amountof RFpower requireJto producean 8 dB S7Nratio
ar the
systemoutput' Sometimesthis is referredbackto the input of the squarelaw device,and the ratio is
thar
of power and is 4 dB. The derivationof the TSSlevelis interesringbecauseit pointsout the paramerers
one can work with to maximizethe sensitivityof a system.
n
TSSDerivation
For marimum powet lransfer Rr = Rv
Signalinput power
Equivalentinpul noisepowel
Pr.r= KTBF
(YPtr'r)t
P.- =
t0Rv
= RFpower
P16..
7= Opencircuitvoltagesensitiviry
R,= Videoresistance
of diode
K = Boltzmannconsrant
T = Absolute temperature
t = Amplifier noisefigure
B = Amplifier bandwidrh
Ps=
UsingI dB S/N ar ourpur
PN
Prss= 3.23x m-m\@
l1s/lo-
(YPrss)2
4RvKTBF
watts:at 3ooK
Sincethe diode is operatedin squarelaw,itssmallsignalmodelcan be used.Toextractmaximum
powerfrom the diode it mustbe loadedby with R,= Rv.The videoamplifier hasa noisefigure
F so the
equivalentinput noisecan be found.By findingthi rarioof signalpowerro noisepower and applying
the appropriate
ratioof S/N,the powerat the tangential
signailevelcan be compured.Norethatthe
diode relatedparameters
do not offer much helpin obtaininghighersensiriviriei.
In resisrively
marched
detectors,
the sensitivity
is diode independentuntil Rv is reducedto ratherlow levels.In reaciively
matcheddeteclors,high sensitivity
can be obrainedat the expenseof RFbandwidrhbunhe high trv
increases
the noise,and biaseddiodesmustbe usedto minimizethe effeo of ls variarionswirl-r
erature.The offsetvoltageproducedby the biasmakesit difficultto measurelow levelsignals
unlessAC couplingis.used.
The biggestimprovements
in sensitivity
areobtainedby reduilngrhe system
noisefigure and bandwidth.Note that the noiseproducedby the diode is the sameasrhe noise
producedby a resistorof valueRv.Thisdiscussion
appliesdirecrlyro zero biaseddiodes.For biased
detectorsthe presenceof excessnoise(espectally'l/1y
produced'bythe biascurrenrcan placeanorher
limitationon their ulrimatesensitivity.
22
Non SinusoidalSignals
Vd"r = KVt2
The analysis
predicts,and experimental
evidenceconfirms,that the output of a square
law detectorwill be:
Vder=K1Vr2+Vr2+VrJ
SignalPower
Prie=* 1v.,2+vr2*Vrr)
As we haveseen,the output of a squarelaw derectormay
be expressedby a constantmultipliedby
the squareof the RFinput voltage.lf ihe signalis nor sinusoidal,
it can be describedby a numberof
frequencycomponentssuchas6armonics
or modulationsidebands.
lt can be determinedanalytically
a.ndverifiedexperime.nta.lly
rhar the ourput of the squarelaw,diode will be proportional
ro the sum of
the squaresof the individualfrequencycomponents.Except
for a constanr,this is idenricalto the
expressionfor the power conlent of rhe signal.Probablythe
mosrdramaticdemonstrarionof the ability
of the diode to measuretolal power is rhe-application
where the squarelaw diode is usedto accuralely
measurebroadbandnoisepower.
when the diode is operatedout of sguarelaw its responsetransforms
to a peakdetectorand rhe
direo indicationof power is not obtained.circuitswhich compensate
or',shape',the diode output will
onfy correctfor the diode'sresponseto a parricularsignal,gen'eralty
a sinusoij.ir the signatis not
sinusoidal,the relationshipof peakto RM3 vohage
lp6*"rt"ir dlfferentand resultsin an error for rhe
power measurement.
23
SimplifiedNon LinearDetectorModel
DEFINE
CONSTANTS
GUTSSV2
=Vp(ttn.!l+Xco6
u;=V-V2
l=;o1guj/ul-11
l._ , _{
Vr=Vr+f t
f*-uii
I
v
{=*,',,,
introducedby the presence
the error in powermeasurements
!t is difficultto experimentally
evaluate
of harmonicsbecausethe diodeoutputat high levelsis a functionof the precisephaserelationship
of
procedureprovidesa methodof
the fundamental
to the harmonic.A verysimplenonlinearanalysis
studyingthiseffect.
procedureis a numericalsolutionfor the integralequationthat describes
the voltage
The analysis
sourcevoltageV is calculated,
the juncrionvoltage
appearingon the bypasscapacitor.
The instantaneous
the currentl. Thiscurrentis integrated
is determined,and the diodeequationis appliedto calculate
over a completecycle.After eachcyclethe capacitorvohageis testedto seeif it changedappreciably.lf
is made;if not, the resultsare printed.
a changeis notedanothercalculation
24
Error Producedby 2ndHarmonic
Predictedby SimpleModel
10log
rr* (3)2r
"'-I
'=f)
f s t i m a t e dm a x i m u me r r o r l i m i l s ,
for harmonic20 dB below fundamenral
Thisanalysisprocedurewasused to predio the worst
caseerror a secondharmonic20 dB below the
fundamentalcould producewhen measuringpower
with a diode. At row power levels,the diode output
is found to be '04 dB high which correspondiio the 17o
additionarpower added by the harmonic.At
high levelsthe deteoor outpul is seento vary by the
directsum of the two volrages,which is an
uncenaintyrangeof 0.83to -0.92dB, or roughly+20%when
relatedback to an Jqriuatenrpower input.
The precisetransitionfrom squarelaw to linearis a function
of detectorand load,and experimental
evidenceshowsthat actualdiodesshowsomewharlessdeviation
than rhe simpleanalysis
predicts.
25
More RefinedModelsCan predict
TemperatureEffects
Temperature
Sensitiveparameters
ReverseSaturationCurrent t5
= 2:1for 20"C JT
to
ShuntConductanceG5
Tracksl5
z
s;
"ThermalVohage"
nKT
vr=T
SpreadingResisrance
Rs
Rs = k T^s5
=
E F F E COTT T I M P E R A T U ROEN
SENSITIVIT
OYF I E S DD T T E C T O R
COMPARED
TO NONLINEAR
MODEL
PWR-20 dBm
VIDEOI-OAD NOTED
F
a
z
UJU6O
T E M P ,D E C R E E S
C
while we are on the su.bjeoof modeling,it might be inreresring
ro seerhe resultsobrainedfrom a
more detailedstudywhich wasperformedio verifythe resulrs
obriined from a i"ifurr,rr"
resrof rhe
low barrierschottkydeteoor- T-heonly paramerers
which were variedin the model to accountfor a
temperaturerangeof -60 to 1000cwere ls, Gs,Vt, and Rb.The f it
betweenmodel and actualresultsis
fairlygood over from -60 to 55oc, but someerror is nored ar 1(x)oc.
Mosr fikely,rhe simple,,rhumb
rule" eslimales
for the diode parameters
are breakingdown and directmeasurements
of theseasa
functionof temperaruremighr yield a bener fir.
26
Summary
Squarelaw detection
Circuitrealizations
Performa
nce characteristics
Temperature
effects
Pulsemeasurements
Effea of signalwaveforms
variousaspedsof diode detectorshave
been discussed.
squarelaw deteoion, circuil realizations,
loadingeffects,temDeraturecharacteristics,
rangentialsensirivity,
riserime,and effecs of harmonicsare
allfaoorswhich effectthe performancu
oi. u"teaor in a particura,
application.
As with manydevices,
the multitudeof interacting
parameters
makesir impossibl!ioJ"tin" a universal
solutionfor all
measurementproblems'Hopefully,this
work will aid in makinjthe proper rradeoffsnecessary
to
achievethe desiredlevelof performance
ii a glvensystem.
t
The contributionsand.helpful discussions
provided.byRusseflRiley,Luiz
- - -peregrino,
-'-D""-r Nick Kuhn,
pereszenteare gratefullyacknowledg6i.
Stevesparks,and in parricular
,
Bibliography
Riley,R. B', A New CrystalDeteclorwith ErtremelyFlel FrequencyResponseHp
fournal, Nov. 1963
P A. Szente,5. F.Adam, R. B. Riley,l-ow BarrierSchottly Diode DelectorsMicrowave
lournal,
Feb.1976
R. I Pratt very tow Lcvel Microwavepower MeesurementsHp fournat, oct. 1975
E K. Davirl,Evolutionof a Diode Detector Hp fournal, Nov. 1972
M' M' Atalfa,Melal SemiconduclorSchottkyBarrierDevicesand Appticationsproceedings
of rhe
Microelecrronics
Symposium,
pp 123-iS7Munich, 1966
M' J. lazarus,[. K. Mak, Diode RFRectificationPredictit More ClosetyMicrowaves,teb.
197g
C' A' Hoer, K. C' Roe,C. M. Allred,Measudngand MinimizingDiode NonlinearitytEEE
Transa6ions
on Instrumentation
and Measurements
Vbl.lM_25,No.4, Dec.l97G
F K' Weinert,B. O' Weinschel,D. D. Woodruff, Earretlerand Diode Comparisonfor
InsertionLoss
Measurements
Microwavefournal,March 1975
A' Uhlir' Characlerizationof CryslatDiodesfor Low tevel Microwave Delection Microwave
fournal,
luly, 1953
H. C. Torrey,C. A. Whirmer,CrystalRectifiersMcGrawHill, t94g
28
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