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racte ''
Cha ristiss'
andApplications
of DiodeDetectors
Ron Pran
Rf & Mlcrowave
fYleasurement
Symposlum
ancl
Exhlbltlon
ftE FF&TJJ
Applications Detectors
of
AbsolutePowerMeasurements
Relative
PowerMeasurements
Leveling
Loops
Systems
Monitoring
Pulsed Measurements
RF
The diode detectoris a very common elementin microwave
measurement setupsand findswide
application systems.
in semiconduoordiodesare usedfor measuring absotutepower. Networkcharac-
terizationoften employsdiodesto measure relativepower,aiJteuet;ng loops,system
pulsedRFmeasurements other applications monitors,and
are which rreq*nily employdiode detecrors.
The system performance one obtainsis a funoion or trrl aeteaor d;ode,its associared
circuit'the circuitrywhich processes dereoed signal, RFmatching
the and the environmental conditionsover which
the system must operate.Tireparameters which .;;rJ i;;;"rtor,,.,.n.u of a deteoor are presentin atl
isimportant
to understand rtey inrliaa sothartr'eaes;lalfrt". p"rrormance
how
fr?[tj||lT:j."
Diodes microwave
for detectotr
semiconductor
interface "rnffi
Theyare majorig carrierdeviceswhich minimize
storedcharge
Pointcontactand schottky(hot carrier)
diodesare
the mostcommon typesof detectori
r
E-
\
PSi
Pointcontact
MFTAL
'7g High Barrier
Schottky
N EPI
N+si
METAL
P IPI
A@ LowBarrier
Schonky
P+Si
conventional PN junaion diodes exhibit storedchargeeffeos which limit
their operaringfrequency.
Currentflow in a metal-semiconducror junoion is due irimarily to maiorirycarriers, the
so effeo of
chargestorage minimized.Thismakei devices
is suchasthe poinr contao diode o, the Schonky
junction performasefficientreoifiersat microwave
frequencies.
For manyyears, only way to fabricate requiredmetalsemiconductor
the the interface wasto employa
point contactsystem. Thistype of constructionyieldeddiodeswith a wide variation unit to unir
in
performance and the delicateassembly subjea to damage
is from excessive power, mechanicalshock,
or temperaturecycling. -ut more rugged strucrureevolvedby depositingthe 6ariier meral
on an epitaxially I dlreJv
grown layer'ordinary schottkydiodeshavea hijh potenri.iu.rii.i.na
r.quir. ui"i----
currentto achieve sensitivities
eguivalent point contactdiodes.
to Ttremost recentdevelopmeniii "
detectordiodesis the formationof a Schonky barrieron 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 achieve sensitivity 40 GHz tuhichis quite similarto lower
a at tr.lr"n.y point
contactdetectors.The 11664A Amplitude Analyzerdetectorsuse biasedSchonkydejces ln
conjunclion with an AM modulated sourceto achievea -50 dBm sensitivity,
and the g4s4Apower
sensoremploysa low barrier Schottkydetector and providesCW power measurement
-70 dBm. ..p.'bility to
Diode Equation
-)
lr
le- vi J
| = ts[exp(Vilvr)
-U
I = diode current
Vj : junctionvoftage
Vt: "thermal voltage,,
Vt : nKT/q ls: reverse
saturationcurrent
K = Boltzmann constant Determined by,
T = Absolute temperature
g = Electron Junctionarea
charge materials
n = idealityfactor
temperature
( 1< n < 2 )
ls changesby 2:1 for temperaturechangeof about
20 degreesc
At low signallevels,
all.three typesof diodes.closely obey the equationfor the idealdiode, and rhis
will be the startingpoint for rne Jiscuision deteoor aoion.
of ihe equationrelares currenrthrough
rhe
the diode to the vohagea.ppearing across junoion. ri" fr,.r.oerisricsof the diode
the
the so-called "thermal voliage",vi."Jii" are reffeoed in
reverse sarurationcurrenrrs.At a giventemperature wirl
be differentfor varioustypei of diodes, Vt
and this.is
,"trua"Juv t-he uarueof the idealityfactorn which has
a valuein the rangeof 1 io 2. The predominanr
faoor which ierer,',,ines;";;;;;;istics
is the valueof the reverse saturation of the diode
currentls.Thiscurrent is a function of devicearea,
form the iunoion' and temper.rrt". materialsusedto
iiu i",np.r.,rr" dependence very importantbecause
is
p"'io'',n." mostof
..i u" related vaiiationsrs,
to in which
.l,r"i", Lyapp,ori,,.'arery
;liJI:?i"#:rTH a
Effect Reverse
of Saturation
Current
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 examining the lV curvesfor the varioustypesof detectordiodes,rhe influenceof the reverse
saturation currenl can be seen.curve A is typiialof a low barrierschonky
is contrasted with is = x microamps. This
against point contactdevice(curveB) whosels = 5 microamps.
a
high.barrier curuet i, to..a rypical
schottkyhavingan ls = 2.5nanoamps. diodesdescribed
The by curves and B show
A
significant current flow.atviry fow junctionvoltages and this is the type of tv charaaeristic
desirable a low levefdeleoor. Similar
for which is
behavioican be obtainedwitn the hif;;;;", schonkyby
applyinga biascurrentto.shiftthe operating point to a regionsimilarro that .f?; 1o."barrier
contact device' The penaltyfor doing this ,itie dc offserit or poinr
i.n is produced. g;asedderedors are either
usedfor detectingsignallevels aboui -s d?-- in dc coupledsystems are usedin ac
or coupled
systems which eliminares effea of rhe offset.
the
Squarelaw Detection
Simplified
Analysis
Vp COS(coT)
-1J
| = ls[exp(vjNtl = ls[VjA/t t/2(yjNt)2 . . . . 1
+ +
Assume: = Vp cos( Vj Vo
I =# +f
cos(a,T) Unnrt), + cos(2a,T)]
[1
tdc=|{vnru,t'
O.neof the major applications diode detectors to measure
of is either absolute relativepower
or
.
levels' low power levels
Al (<-20 dBm),the diode responds the sguareof the voltageappearing
ro
across junction so the deteoed signalbecomes iunoion of power.An approximlte
the a but accurate
analysis reveals reason the squarelaw response.
the for The diode currentcan be estimated a series
by
expansion the diode equation.Upon substitution a sinusoidal
of of description the signalvoltage,
for
restricting analysis signallevelsless
the to than vl, and assuming that the iereoed signalisnegligib-le
with respeo to the input voltage, one findsthat three domin.ni t"r-, appearin rhe expression. Two of
thesedescribe fundamental
the and secondharmonicof the inpur signjl which are bypassed a by
capacitor. dc term which is proportionalto the sguareof the'input-vokag.r,"prer"nr,rhe
A detected
signal.Experimental evidenceon a wide varietyof detectors confirmstt e Jatiaiiyof the analysis.
lr
nol be surprising.thatsignificant
depariurefrom squarelaw is nored for signallevels exceeding
:P,f.a-
26 millivolts (about -22 d8,m a 50-ohmsystem)
in and the dereaed outpur level is-about 157o the
of
peak RF inpur voltageat this power level.
Equivafent
Circuitof Diode Output
ls
Detected
currentgivenby: ldc = q NONt)'z
Define"originresistance" Ro = Yt/ls
Substitution
yields IDC '
,-V-
p
ARM
Whichsuggests following
the circuits:
Vp' Vp'
Ro oR
aRoV ]
4Vt
Biased
detectors similar
are exceptthat
Ro=I
"le
=
19 Bias
current
and fixedcurrenror voltage
sources
haveto be addedto account
for
the biassignal.
lf a new term "origin resistance" introduced,
is the analysis be extendedto obtain a usefulmodet
can
for the deteaed orriur. The origin resistance
of rhe diode is simplyrhe slopeof rhe diode lV curveat
the point of zero signal.
j]l*:L: RFcomponents rhe diode currentare bypassed, outpur
of the
..
when a cw signalis applied.The analysis of the diode is a dc voltage
suggesrs ii,e diode output is in the form of a current
thar
sourcedrivinga shuntresistor with a valueei-ualto the origin resisrance. can be transformed
This to an
equivalent voltagesourceand series resistance. RFbyplsscapacilor includedin the modelto
The is
accountfor the transient response the detector.An analysis a biased
of of detectorwill leadro a simitar
resultexcept fixed sourceshaveto be added
and the origin resisrancebecomesa function of Vt and the
biascurrent lo.
DetectorCircuitConsiderations
Matching
Network
Thematching
networkdetermines
thesespecs
BANDWIDTH
swR
opEN t Bl[?l?l$r',
ItrT'f r,
v,w
The diode and the matchingnetworkdetermine tangentiat
the
signal
sensitivity
TSS
The specificationswhich are obtainedfor a deteoor are governedprimarill,
in which the diode is imbedded.The diode impedance by the microwave circuit
is raiely equalro the zo or tr," sysrem a
so
matchingnetwork is necessary. designor t-his
The circuitderermines operaringbandwidth,SwR,
frequencyresponse' and open-circuit voitage.sensirivity.
A systems related,pJ.iii.riion, tangentialsignal
sensitivity
(TSS), governedboth by the malchingnerwork
is and the charaoerisrics the diode.
of
MatchingCircuits
Resistive
Matching Reactive
Matching
RT RF l*nv'rl
Input Input -T-att-1'--
i I
=
I n=
Pointcontact,low barrierSchoftky Biased
Schottky
(fowRs,tow e)
or biasedSchottky
Broadbandwidrh(.Ol- 26.5 CHz) Narrowbandwidrh(ocrave less) or
L o w S W R( < 1 . 3 o t 8 C H z )
r H i g h S W R( 2 : 1 y p i c a l )
t
Moderare sensitivity (500pVlp watr) High sensitiviry (2000 pY/y wan or higher)
Freq.response :.35 dB .m - 1gGHz (8494) :.5
Freq.response dB./ocrave
Sensitivity
specson chips and packageddiodes almosruniversally
refer to a reactively
matched circuit.
Thereare two approaches the designof the matchingnetwork,either resislive reacrive.
to or The
resistive
nelwork is usedin broadband (.01
designs ro 25.5-CHz;and yield low SWRand flar
can
frequencyresPonse. sensitivity resistively
The of marched deleclorsis almosrindependent rhe diode
of
characteristics. reaoivelymatcheddereaoiswork over only modesrbandwidihs,lenerally
The haue
relatively high SWR,and the sensitivity obtainedis a strongfunoion of the diode characteristics. The
advantage reactive
of matchingis a markedincrease sensitivity. is due to the fao that the
in This
matchingnetworkactsasa transformer the voltage
so appliedto the diode junoion is increased the
by
tquare root of the ratio of origin resistance Zo. Toobtain a reasonable
to bandwidrh, biaseddiodei wirh
an origin resistance about 4 timesZo areoften usedin reactively
of matcheddesigns. Thisresuls in a
faoor of 4 increase sensitivity
in over the resisrive
matchingn"t*oik. lt shouldbe-menrioned thar the
sensitivityspecifications.Jordiodesin chip or packaged form almostuniversallyassume reactively
a
matchedcircuit.Regardless the sensitivity
of specon a reaoivelymatcheddiode,rhey will all yielj very
similarperformance a resistively
in matchedcircuitbecause transformer
the properties nor present.
are
Departurefrom ldealDiode
3 Key Elements took for are:
to
R6 Spreading
Resistance
Ro Origin Resistance G5 ShuntConductance
I
Ro = Yt/ls R;
I
R;
Non linear Model
linear Model
(SquareLaw Region)
Theslopethrough originisreally parafrer
the the combination
of
Roand G,
These additionalelements
reducethe sensitivity the detector
of
itstheoretical from
vafueof
Vdet = Vp,
4V
The actualdiode will showsomedeparture from the idealdevice.Theoretically, origin
is givenby vt/ls, but a conductance shunts the resisrance
Gs the iunoion or tle aoual diode,so rhe slope
signal definedby the parallel
is ar zero
combination Ro and Gs.All diodes
of erhibira spreading
which is in serieswith the nonlinear resisranceRb
portionof the diode-Rb,cr, .na rhe parallel
and Ro may be dererminedfrom the devicelV combinarion Gs
of
curve,and contriburero a Lar.tloiin sensitivity.
Low BarrierSchottkyDetectorCircuit
'vi-i
r-- -T -'l
v,;
R FI n p u t
I
I
L JDiode
circuit wasoptimized minimizechange V; with frequency
to in and arsoprovidea
good march the RFinput
ar
Ro = origin ResistanceRb = spreading
Resistancecj = Junctioncapacitance
[p = Leadlnductance Zo = RFLoadResistor c = RFBypass
capacitor
Rc= Compensation LpCjResonance
for
Lengthand impedance stuboptimized minimize
of to SWR
A complete modelof the HP low barrier schotrkydeteclor shows elements
lhe which haveto be
considered during the designof a broadbandresisrively
marched dereoor. tt e capacirance the diode
Cj and its feadinductance effea the matchand frequency of
Lp response. resisror dampsthe
A Rc
resonance LpCj,and a stubis placed series
of in with the RFload to minimize SWR. The various
elementsin the circuirwork togetherto keep rhe voltageacross junction
the constanrwith frequency.
10
The Sensitivity_ the Det".to
of
Diode and the MatchingCircuit r --
l-Y*l
:-r--[-'r
i*' I
I I
I I
L-- JDiode
Vi2
ldealfy Vo=If , brr
1. ldeafity factor increases
Vt: Vt=nKT/q 1
2. Shuntconductance diode:
of
A. Lowers resistanceR6=
origin g. Self-loadingu t = uo
'=fu; -
1+GrRo
3. Matching circuit loss:
t/- :6V Rd
vr
A finiteoutPut loadresistor havea dramatic
will effeo on the derector
performance
The sensitivity the resistively
of matcheddeteoor is not a srrongfunction of the diode
but the actualsensitivity be iomewhatlower tnan characterisrics,
will thai pr.oo"a by rhe analysis. idealiry
causes increase the valueof Vt. The shuntconduorniu The fa.or n
an in cs lowersrhu orilin ,iriir.n." and also
acts a built-infoadfor the videooutput.Finally,
as there is a rJu.oion in the junoion volrage relative
Vj
to.the appliedsignalV.du.eto.the losses
producedby the RFload, Rc and Rb. The combination
effeos causes sensitivity actualdeieoorsro be
the o{ rhese
of 30 to soo/;lowerrhan ideal.
11
Loading DetectorOutput
the
Vdet
R;
i*o I Rr
I I
I 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,temperature R1
and
The mostdramatic change sensitivity produced
in is when the outputof the dereclor loaded.
is The
finitevideo resistance formsa voltage
Rv dividerwhich cansignificantl;,decrease outputvoltage.
lhe ln
the square law region,Rv is governed
mainlyby the originresistance the diodeRo,but asthe diode is
of
driven out of squarelaw, Rv becomes complicated
a functionof power level,temperature,
and R,.
12
low BarrierSchoftkyDetector
TypicaTra
I nsferCharacteristics.
At 250C
Rr=1ko
lfi) mV
Rr = 50kO -:;,
Vo,rt
1mV
-lo o
fnputPower
(dBm)
examiningthe transfer characteristics a typicalfow barrierschottkydetector,one
of
,.By can seelhe
effea of load resistance lhe output voltage.
on Notethat in the range of -30 to -20 dBm the outpur
voltage changes 10to i, th-us
by iniicatingsqu"relaw operarion. higherpower levels,
transfer 'linear Ar the slopeof rhe
funcrionis cur in half,which is an-indication
of ofer.tion.
13
Comparison Low and High LevefSignals
of
linear
-..-l F Von
P < 10 microwansinto 50 ohms Power levelstrearer than 10 milliwans
Detected voltageproportional to Detected voltageproponional to
the squareof appliedsignal. the peak RFvoltage.
Video loadingwill lower the detectedyoltage
In the square law region, waveform the diodecurrentis almost
the of identical that of the input
to
signal. Underlargesignal operation, diodecurrentwaveform
the becomes functionof input signal
a
leveland video output voltage. The output voltagebecomes complicared
a functionof load resisiance,
power level, and diodecharacteristics. key point is thatthe derection will undergoa rransilion
The law
from squarelaw to linear.Thisoccurswhen the junoion voltageexceeds In the linearmode rhe
Vt.
diode is actinglike the familiar
peakdetector.
14
Video Resistance Varies
Rv with power, Rr and ts
Y
Y
E
d,
-10
P d8m
when the diode is in squarelaw,the video resistance
is essentially
constant, at higherpower
but
levelsthe currentthrough the diode exceeds and the video
ts resistance
becomes complicared
a
funoion of power, load resistance, ls. For low
and barrierdiodes,fs determines ai low fevels.
Rv At high
levelsthe vafueof Rv is d.etermined rhe actualdiode
by currentand rhe orher ,"rirro* in rhe detector
circuit'The percentage changein Rv and rhe actualtransitionfrom squarelaw to linearis governedby ls
and R, and the decreasing valueof Rv can be usedto extendthe squareraw range.
15
Transition Lawto Linearts
a
from Square
Governed Ratios
by Rv/Ro and Rr-/Ro
Diodeorigin
resistance:
co2
--RO=10k
- Ro = 1'5k t -50
---Ro=100rl o
ag
tt)
9-r \\. 50K
c .5K
.9 -6 .5K
.E
Detector o 50K
Video Resistance 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 e 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
o
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 e 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
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
Temperature
Effects
With proper biascircuit design,temperatureeffectson high barrierdetectorscan be minimized
Performance low barrierschonky is governedby variationin 15
of
(Ro=f,t lsaorUles 2O.CAT
for
Videoresistance alsoa functionof powerand R,'. diode is in
is lf
linearregion,temperaturesensitivity
decreases.
rmK
; 10k
E
5=n, = 200O 50k0
ro
.9
Sr- <-20dBm
u,
ilk
{0 -20
60
rypicatvideo,.o"ol",ll"iijlo",,'.1'*,,nremperature.
. The biggestcontributor temperature
to is
effects the variation ls.Forthe derector
in thistranslates a
to
changein video resistance. can be seen,rhischangecan span a6out2t/zdecades
As over a -60 to 100.c
temperature range. higherpower levels, change ls is masked the largecurrents
At the in by flowingin
the diode,so the high levelresisrance onrychange a factorof 3 or less.
may by
17
Due to variation Rg the temperature
in coefficient
of low barrierSchottkydetectorsis a strong
functionof load resistance power level
and
rd8
.,q9,,-.,=Tt) R, = tO[
I
0
0
I
.,'i/ -\ -q
orr
r-Ri<:
-t, -./ i. < .l - rd8
/ / 0d8=Ourpur@25'C
, ' / P - = --20 d'h.
P'" = ! ) d 8 m P dBm
-\
: - /.t . -2 dE
-l d8
.-r.rtll
-60 -20 {r .,:r' ao
Lttlr.r.rtrrrr ( ,
High Power
Sincethe squarelaw deviationis governedby
Rv --, RL
tno
G Ro
the squarelaw,deviation
will alsobe a temperaturesensitive
parameterwhen Rr. Ro
Theeffeo of ls variations,
power level, and videoloadmakes change sensirivity
the in with
temperature rathercomplicated
a function.The datapresented here coversan extremerange.Over a
narrower temperature range, changes be minimized seleoionof an optimumvideo
sensitivity can by
load,or by designing lemperature
a compensating Since ratioof Ro/R,determines
amplifier. the the
square deviation, parameter alsoshowa temperature
law this will dependence. datapresented
The
wasactually
earlier obtainedfrom the same diode measured -25,25and 100oC.
at One canconclude
from thisthat an optimumdesign exists a specific
for application, no optimumexists all
but for
applications.
18
Risetime Detector
of
Rv
Voc c Rr
- F2o ns
R1= 25f) Rr = flX)
Rr= 100(! Rr'= 300o
Video loadingis an importantconsideration
during the measuremenr pulsedRFsignals. one is
. of lf
dealingwith fastrisetimepu.lses
severalprecautions haveto be exercised. outpur of the deteoor is
The
takenacross capacitor the RC time constant the detectorand toad
a so of hasto be small.The data
presented shows the envelopeof a 10 mw pulseoverlayed the detectedor,prt. iin."
on tr," diode is
actingasa peakdeteoor, the video impedance the iereoor is low so rhe rise
of time is quite fasr.The
decaytime is governedonly by the toadresisrance can be appreciably
and longer.
19
Effectof Cable
3 f tET_q
r! Scope
R Fl nPUt 4 = sott Rr
*l l'-zo ns
R, = 50O
R, = 100O R1= 3dX)
often a cableis usedbetweenthe deteoor and the scope. Thiscableshouldbe rerminated irsZo
to minimizethe effeo of multiplereflections in
bouncingbei*een rhe scopeand the deteoor. lf the rise
timesare long with respect the time delayin the ca6le,an accurate
to estimate cableeffeos can be
of
obtainedby simplyaddingthe capacitance rhe cableto the output
of capacirance the dere.or.
of
20
Tangential
Signal
Sensitivity
(TSS)
J/lfl/]/L N
[lUUU VVMCASUICd
Signallnput
I
'tor"sff
=4dB
TSS accepted be the signal
is to levelrequiredto producean 8 dB S/N ar rhe svstem
output.Thisis equivalent a 4 dB S/N ar the detecror
to input.
A very common systems specification a deteoor is its tangential
for signalsensitivity
(TSS). TSS
The
point is generallyregardedasthe amountof RFpower requireJto producean 8 dB S7Nratio ar the
system output' Sometimes is referredbackto the input of the squarelaw device,and the ratio is thar
this
of power and is 4 dB. The derivation the TSS
of levelis interesringbecause pointsout the paramerers
it
one can work with to maximize sensitivity a system.
the of
n
TSSDerivation
For marimum powet lransfer Rr = Rv
Signalinput power Equivalent
inpul noisepowel
(YPtr'r)t
=
Pr.r KTBF
P. =
- t0Rv
= RF
P16.. power K = Boltzmann consrant
7= Opencircuitvoltage
sensitiviry T = Absolute temperature
R,= Videoresistance diode
of t = Amplifier noisefigure
B = Amplifier bandwidrh
Ps (YPrss)2
Using dB S/N ar ourpur
I = l1s/lo-
PN 4RvKTBF
Prss 3.23 m-m\@
= x watts: 3ooK
at
Since diode is operated square
the in law,itssmall signal modelcan be used. extract
To maximum
powerfrom the diode it mustbe loadedby with R,= Rv.The videoamplif hasa noisefigure
ier F so the
equivalent input noisecan be found.By findingthi rarioof signal powerro noisepower and applying
the appropriate ratioof S/N,the powerat the tangential signailevelcan be compured. Norethatthe
diode related parameters not offer much helpin obtaining
do highersensiriviriei. resisrively
In marched
detectors, sensitivity diode independent
the is until Rv is reduced ratherlow levels. reaciively
to In
matched deteclors,high sensitivity be obrained the expense RFbandwidrh
can at of bunhe high trv
increases noise,and biased
the diodesmustbe usedto minimizethe effeo of ls variarions wirl-r
erature.The offsetvoltageproducedby the biasmakesit difficultto measure low levelsignals
unless couplingis.used. biggest
AC The improvements sensitivity obtained reduilngrhe system
in are by
noisefigure and bandwidth.Note that the noiseproducedby the diode is the sameasrhe noise
producedby a resistor valueRv.Thisdiscussion
of applies direcrlyro zero biased diodes.For biased
detectors presence excess
the of noise(espectally'l/1y produced'by the biascurrenrcan placeanorher
limitation their ulrimate
on sensitivity.
22
Non Sinusoidal
Signals
Vd"r = KVt2
The analysis
predicts, experimental
and evidence
confirms,
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 expressed a constant
by multipliedby
the square the RFinput voltage. ihe signal nor sinusoidal,
of lf is it can be described a numberof
by
frequency components suchas6armonics modulation
or sidebands. can be determined
lt analytically
a.nd verifiedexperime.nta.lly the ourput of the squarelaw,
rhar diode will be proportionalro the sum of
the squares the individualfrequencycomponents.
of Except a constanr, is idenrical the
for this to
expression the power conlent of rhe signal.
for Probably mosrdramaticdemonstrarion the ability
the
of the diode to measure of
tolal power is rhe-applicationwhere the squarelaw diode is usedto accuralely
measure broadbandnoisepower.
when the diode is operatedout of sguarelaw its response transforms a peakdetectorand rhe
to
direo indicationof power is not obtained.circuitswhich compensate
or',shape',the diode output will
onfy correctfor the diode'sresponse a parricular
to signal,
gen'eralty sinusoij.ir the signatis not
a
sinusoidal, relationship peakto RM3 vohage
the of lp6*"rt"ir dlfferentand results an error for rhe
in
power measurement.
23
Non LinearDetectorModel
Simplified
DEFINE
CONSTANTS
GUTSS V2
=Vp(ttn.!l+Xco6
u;=V-V2
l._ , _{ l=;o1guj/ul-11
Vr=Vr+f t
f*-uii
I
v
{=*,',,,
evaluate error in powermeasurements
!t is difficultto experimentally the introduced the presence
by
of harmonics because diodeoutputat high levels a functionof the precise
the is phaserelationship
of
the fundamental the harmonic. verysimplenonlinear
to A analysis procedure provides methodof
a
studying effect.
this
The analysis procedure a numerical
is solution the integral
for equationthat describes voltage
the
appearing the bypass
on capacitor. instantaneous
The sourcevoltage is calculated, juncrionvoltage
V the
is determined, and the diodeequation applied calculate currentl. Thiscurrentis integrated
is to the
over a completecycle.After eachcyclethe capacitor vohageis testedto seeif it changedappreciably.lf
a change notedanothercalculation made;if not, the results printed.
is is are
24
Error Producedby 2ndHarmonic
Predicted SimpleModel
by
10log rr* (3)2r
"'-I '=f)
f s t i m a t e d a x i m u m r r o rl i m i l s ,
m e
for harmonic20 dB below fundamenral
Thisanalysis procedurewasused to predio the worst caseerror
a secondharmonic20 dB below the
fundamental could producewhen measuring power with a diode. At row power levels, diode
is found to be '04 dB high which correspondiio the 17o the output
additionar power added by the harmonic.At
high levels the 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 precise transitionfrom squarelaw to linearis a functionof detectorand load,
evidence and experimental
shows that actual
diodesshowsomewhar deviation
less than rhe simpleanalysis predicts.
25
More RefinedModelsCan predict
Temperature
Effects
Temperature parameters
Sensitive
Reverse
SaturationCurrent t5
= 2:1for 20"C JT to
s;
ShuntConductanceG5
Tracks
l5 z
"ThermalVohage"
nKT =
vr=T E F F E C TT T I M P E R A T U R E
O ON
F S E N S I T I V I T Y I E S DD T T E C T O R
OF
a
z COMPARED O NONLINEAR ODEL
T M
SpreadingResisrance
Rs PWR-20 dBm
Rs = k T^s5 VIDEOI-OAD NOTED
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 results obrainedfrom a
more detailedstudywhich wasperformedio verifythe resulrs
obriined from a i"ifurr,rr" resrof rhe
low barrierschottkydeteoor- T-he only paramerers which were variedin the model to accountfor a
temperature rangeof -60 to 1000cwere ls, Gs,Vt, and Rb.The f it between
model and actualresults is
fairlygood over from -60 to 55oc, but someerror is nored ar 1(x)oc.
Mosr fikely,rhe simple,,rhumb
rule" eslimales the diode parameters breaking
for are down and directmeasurements theseasa
functionof temperarure of
mighr yield a bener fir.
26
Summary