Fluctuations in IMPATT-diode oscillators wi th low Q-factors. Dr
IMPATT 05CILLRTORS(U) I/i I MICHIGAN UNIV ANN ET … · 2014. 9. 27. · 71d-ai4i 378 dynamic...
Transcript of IMPATT 05CILLRTORS(U) I/i I MICHIGAN UNIV ANN ET … · 2014. 9. 27. · 71d-ai4i 378 dynamic...
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71D-Ai4i 378 DYNAMIC BEHAV'IOR OF PULSED IMPATT 05CILLRTORS(U) I/iI MICHIGAN UNIV ANN ARBOR DEPT OF ELECTRICAL AND COMPUTERIENGINEERING R K MAINS ET AL. 198± N6@53e-8i-C-0364
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NATIONAL BUREAU OF STANDARDS-1963-A
IA
111
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E-eot-rc. -s~2 Iab:ra:-:
-,~~A -:'r, *.
nowiz~rg an' er: Afe i kW
Naa Wea-.onsz Cent-ern ~a 1 al, 9A 3 2 c
,Lt' o,-:'o o f s imulai ing t 11e dvnarn'. ea'- c ir c 2e a
MP.2l oS c .lators it-re sen~te. :t is as~ed t*-at the iiac.
vari alez change slowi-',, with respect. to the RF perifod so ta: te
cu'as-Static approximatior. may be used. A cormoarison of _4_u a-, - n
eei:i:~ exr.er fient a- r e Suts focr an X-b anc eir c,)i S
4-V
approv
13.,ut4tbsOe prv
-4 ulcr~es rd ae !
.4.'ok.a z r.c~t dN v '-C -- a -,l.- :
-KAM~ 2 %.
-
as::--, a -ry ma::r man vefezt--elx use- to,
*ec S fz. n- f-. r- e,. -r rl*~n n a leoc-Iczoked I
oc_-aot rZ -- F an a'l rn'a-ive --c 11..e t--cns
mezdcrr~u acr:-.ete Ae-vi ce-circ-u::- -rteractior, simulatio
the tim oma-n using- a small ti1me ster due to stability restric-
tiorns on, the device simulatifon. The ouasi-stat4 C metnonreo~re a
comn -Iete sleady-Fseate characteriz:ation of the U-A'Ae-. 4 C e over
the r-an:Je -nprature, bias current denz:-,v an';~
a--,", e na wi. be encountered in i ransient, 7iuain t
is then ass, ed trha-, ts'e simulation uaramet ers hnescw7-: w-t-
-4 es-nect to the --- nerioa so that the- 7A- appears to be ina
I.stead.--staz-e condit.ion at, ani- -,art a-cular i nst.ant of time ts
manner -tn-e z ransfer-L can readily be simulated over the entire Ios e
w ith.
-gure - srL-ws t 'e QoO-:n7 ncro:e -cf th-e GaAs or .:d- 2
C4A? code used 4-.te snulati-n-. '7nar- -ia srctr
1 w~~-as fatri4ca-te-.*:rwv so;ts* ann' vas P'sc uce-
U'in t-e exr---" -n f fett~ w~ o an
!r.aunrnS an,: s-ca,-:, &I- 1W:C:ac~' arsa
wnereln E sz -:~L ta' t- .tC>C Currents ccrsst Cf a d rrusC C aiFui7cs ter, : tol>te and diffusio ncefiiet
U' ~~ex-mrecsec as Iu: :. fte1ca: electric field. Smain
;1c/ orDist"a
- - ~ ~~ ~. . .. 4 .. .j .. . . . .~ %
-
were carrie- zu-, &Ite-:~e ~ ~ a'K
At each te-cerature, simulations were 4erformed a: iaz curren
densities of -. = h0C, 650 and 100C A/c. For -
combination, a sinusoidal R: voltage at I3 3Hz was a-r!-ed and the
amDlitude was varied from zero tc tne pcin: wher :::e diode efficienc.
dropped si r-nificantly. The information thus obtained s Y f = IC z;
M d % ), the diode admittance in mhno/c=-, and z= H;
J V ) the diode large-signal operatinc voltage. At C.= 0, thedc' F dc
diode is modeled as a depletion capacitance, C = (E '/ ' "F, in series
with a small resistor, Ro=(wu/cA)C, to account for the .Lnde-leted region
(d is the derletion region width and w is the width of the undepleted
region). To obtain the diode characteristics at operating points
other than those simulated, a linear interpolation scheme is used [2].
It is assumed that the circuit admittance Y (s) varies morec
rapidly with frequency than the diode admittance so that YD may be
assumned constant with frequency over the frequency range of interest.
However, the diode cold caDacitance C = (C/w) F/cm 2 (where w = w, + w =D a u
6.95 om' is lumoed into Y (s) sc that the component of the diode
susceptance does vary with frequency. The device area was assumed
to be A = 1.- x 0- 3 cm2 which is the measured value for the diode.
Figure 2 shows the circui- used to model the actual oscillator
circuit, which consists of a 5-x transmission line (represented by
F.) and a low-impedance tran:sfcrner adjacent to the diode package
(represented by Z , £, and E,. The capacitance C is the discontin-
c ruity capacitance between the %-2q transmission line and the
[ .'. ...... _ .... ...... . . . - ... . . -... ... ..-.-. -.- ... . . ..-... . .. ... . , . ... ._ . .. .*.
-
Pr T -- -m -
-was a-:: e-'ted tc measure e~z roae-c tno cou-v a ent
c ircuit e-,emen- s Land_ C h=,;ever s :n .. ne- _n- rema~re
ccncerning -these vaus etca-l:: 'r the ser-'tS rtac
Thne rorocedure 'was :o use the exrcerimen-.ally dietermined v~~
0.32 cF for and- to det.ermine L. as follows. Thie diode admittance
resulting from the simulatio-n at T = 500'K, do = _5c ~~ bias cr
rent dens-it- use-d experinentallv and V,,, .7 -'ma7xmumefr
-Dcir.-t for thiS rartio_'ular c com.bnatior.' was iranS~'--.-
th r c ur t -; a ca g.-e -7,cn zng e rui va en-t ci4-r cuit 1 to tane r :n
2.L was ~nnchosen so ha this transformed dfitnc was e~ual.
to the exrerircental large-signal ad-mittance measurements a:- T-a
C, is the d~c,7e co.!d canacitance, wh~hi uodf.otec_'r2-uh
rirure T~n~ae a v;era.> pr e,.r
s4 -I a t on . in..'. -a, .I s th a I t a: E c7 eY
frequen~cy the circuit" '--z, 2 a-, 4lar
~s t h e d ce P a :tn ce e er7--*.:: from: ah IaC---
s 1uaao r. , 4;.- e. C. -Urrel.- uSf E. a 'E
e-*ctiOr.--- :r-.e ca2e . tr,~k - ue of :h v 0oa
a- tnE- di*:oe termnals, an os te ~ *'ti ~
to ,.z:.. ant d are r ,..:-.~>.:n
The- c:mp!x freueny .. cI er ene rt r 7 E T~ Cz~ 7- oxr,~
the eouaocn:
P ,
-
%7
'
+=
and are uT ec ac-crd 4= to
9, - U : .. =...
-"-an!
deC
7,:e diode temrerature : is updated from-P.h p
7 -- - A
dt T T
..... "s the diode thermal resistance in °K/;, _. is the power
dissf-_a- ed in the diode in W, TA is the a=,bient temperature inK
and :'s the therm..al relaxazicn time in seconds.
Tig 3(b], the bias current J_ s assic to r-secc
l-near' from zero to a constant value at turn on, tc maintain this
cornstant va7lue :hrou.hou7 the pulse width, and then to fall l near
to zero at turn off. In principle, the bias circuit co'uld be modeed
and a secornd device-circuit interaction could be solved tc determine
the evo.ut:. of J. with time, however, this was nct done in the
simuatins resente_ here.
For the inlecticn-locked case, it is assumred that 1 is on long
before the bias currnt density J. is switched on at t = 0. Therefore,ac
at t = a substantial -.. voltage existZ across :he diode terminais
ever. thour*, the device is passive at this time.
°,LI. • . . .
-
. . .'. -.
Figure ;.resents the turn-on and turn-cf-f characteristics
observed for the free-riunning case and rig. (a) shows the behavior over
the entire I.5-us .1se. The diode was f Cd o oscillate at 9.7 G;iz,
the peak outrut -ower was 15.S W, and the diode orerating voltage was
approximately 1C V. Figure 5(b) shows that, for the injecticn-locked
case, the diode turns on faster than for the free-r'nning case. (In
Figs. 4 and 5, an additional 6 ns delay is introduced in the detected EF
waveform relative tc the bias current waveform due to the measurement
setur.)
Table I shows the experimental results for the injection-locked
case as the injection signal power is varied. The injection frequency
vas 10 GH: and the (-eak) bias current was I = C.8L A, or d = 646.~~~ -e. anda doe notr '
A/cm 2 ". F is the (peak) EF power generated by the I1'T_ and does not
include the t, ower delivered by the inection source Fn is the
average junction temrerature calculated from the exper i -entally deter-
mined thermal resistance. It was found exnerimentallv that if the
injecticr. power was reduced below 2 W, the I.FAT did not lock w .th the
injection source.
The thermal resistance was experimentally determined to be R. -tn
5O:/W for the diode and 101:W for the cun,. Sdnce the temiperature in
the mount changes more z~owly than the diode temerature r61, the
10K/W contribution was assumed tc increase the ambient temperature, -.
in (h), from rcom temrerature as follws:
T1 = 30C°K + 6L.7 W x C.24r x 10*:,W = 29oK , (5)
where 64.7 W is thIe peak dissirated power 4!. the d;!de and C.L5 is the
• ' . . , . • - -. . . . -. . -* . -- - .. " .- . " *.- . -W .,'., ' . ...." ' . % " .- '- ",' W.",,'.-""" ."""""%-.- -
-
%ut? factr. ..e _-.T dicoes were fabr4caied :r. a ud mesa structure;
a. at-rozriate -.herma: relaxaticn ime -.cr tnis arran ement is T = 8 "s
iT (L). Using these values, 1 ilies ,a-., in order for the average
diode temoerature to -e LT 0 w ,see Tatle i, the diode temerature at
the beginninz c' the bias current 'use must le a..rcxima-,ely .. in the
steady state.
'Figure 6(a) shows the start-up behavior obtained from the quasi-
static simulation for the free-running case. For comparison, the corres-
ponding portion of the experimentally observed FF -,ower from FiL. L(a)
is alsc shown. The amplitude of the experimental curve is ncrr'alioed sc
that both the experimental and theoretical curves reach the same maximur.
RF power level. The bias current increases linearly from zero at t = 0
to do 646 A/cm2 at t = 60 ns in Fig. 6 (a). The starting temperature
at t = 0 is 4600K. From Fig. 4(a), the detected F power turns on approxi-
mately 32 ns after the bias current begins to increase (recall the
additional 6-ns delay in the measurement system;; this exre...i.e.tal de'ay
is very close to the delay resulting from the simulation in Fig. 6(a,.
Figure 6(b) shows a plot of the circuit admittance vs. real frequency
(o = G) and srall-signal device ad;ittanc vs. at the start -.-
temperature T = h..K. From I2), v4R_ will nct increase until () is
satisfied for a value c f s su1. that -e{s = > r. :. To. 6(b), the
re:cn tc the right cf th- 4' curve '.,e..v e
such that ReEs ) < C, and the area tc the Ieft t c he -Y f carve co.-
ccTa ins (s' valu es s., ;,_. -ha -.rer.s) ? :. . er: tc
23C . -/c he. a , , vh = es >r,, ,. c r..I..
in~crease. As J.creases further, tlhe > cur'-,,_- .e- trLe
and. . ((,,,ti osee that tVe ou;c 'eicr.an
-
* - - - - - -_ . . . . . , . _ . •. . ....-r~ ------ *- - - , --,,
._ ." . .. --. - . .
LZ
frequenc:, w- ' ar' a, a.rcx:.-,aty 9. , w:.,c:. -s tre experamentallvo
observed freauency for the free-running case.
Figure 7 shows the R. power simulated during the oscillator
turncf w"ere -t is a5s'med - 7 decreases linearlydc
A/cm 2 at t = C to zero at t = 9c n .. 7 iF result should be
compared with Fig. 4(b), although in the experimen. J departs from thedoc
linear waveform.
Figure 8 shows the start-up transient for the injection-locked
case, with I, = 0.557 A see (1) and Fig. 3(a)] so that the incident power
from the locking source is 2 /8G = L W at 10 GHz. Comparison of Fig.
8 with Fig. 6(a) shows that the RF power turns on faster for the injection-
locked case than for the free-running case. This is in agreement with
the experimental result shown in Fig. 5(b). This is because there is a
5' substantial RF voltage across the diode at t = 0 due tc the injection
source.
-able 2 presents the simulation results as the injection power
is varied from 2.0 to 6.0 W. Comparison with Table I shows that the
same general RF power variation as observed experimentally is predicted
by the simulation, although the simulation predicts a _wer maxim, at
P.n = h.C W instead of 3.5 W, and the maximum Dower rredicted by the
simulation is 16.56 W instead of 11.6'_ W.
The behavior fndocated in-.abe 2 can be understood Ity ex-a.ininr
the curves in Fig. 9. S nc oe, for in ecion-locking, _ rus- be satis-
fied, the magnitude of the irnjection current source i. mu.t -atisfy
the following relation at the start of the pulse 'af-er -he bia: cur-
rent has reached its maximum value):
IL = V IY (f=10 GHz) + Y (T=L6o°%,j. =6( A/cn2;VRF) (6)F.F c D RF'
5% ~4.5
-
mani evotare a: .e di de terzEnas a:- Zhe
corresponding ' 2>_ were previously; obtained by the dicie character-
ization process, using the steady-state I-._T simulatio-. rro-'am.
Ecuation (6) matches each V value with a corresponding 7 for
t stead'v-state locking. Also, for each V.7 the r power generated by
the diode is
BF 2 DE 7
where G = Re{Y (V,,)). The exTressions in (6) and (7) are olotted in
Fig. 9. it is see that as i- is varied from 300 A/cm2 .... -L
800 A/cm (1.0k A), the RF power first increases, reaches a maximunm
for L = 450 A/cm2 (0.58" A), and then decreases. (F in Fig. 0 isRF '
the R rower at the start of the pulse, whereas the RF power in Table
2 is the average over the 1.5-s pulse width). Below IL - 285 A/cm2
(0.370 A, F. = 1.76 W), it is anticipated from Fig. 9 that locking
cannot occur except perhaps at very low F__ values. (It must also be 4n_
vestigated whether the operating points in Fig. 9 are stable. -ns
expectation is borne out by the simulation in Fig. 10 for which
. = 1.5 W ( IT = 0.341 A). The diode does not lock untaJ"t !n as
heated up to L7 0K, so that the curves in Tio. 9 are no cnrer aprlicable.
As the diode continues to heat ur the generated RF power gradually
increases to 1l.9 W. This behavior is consistent with the exz.ri...+al
results, since for F. much below 2 W the locking at IC GHz was nc-an
found to be stable.
u.':.T dijo de E J at c... .
it has been shown that a large-sirnal _MT= da 1 ... c ,
program employing the drift-diffusion armrcximation Jn ccn-unc-o.n
LIZ,.
-
W_ 7. a 77767. ~ .. - - 7 77
w- t a c -c::. f-~h S rarurn C
ex-.er~merta__- c bserveC bePhavicr a-,fee- u-r
andia ~rec:-I _ ockecd cases. 7,ie E!e r c,- ra-. s ma sedefe diode andc
c ircuit des 4. i at '-igfcr e 2~ e- nauee!--ce ..- r
d ff f-4 -1u 1 c-wever, f t-,.,,- e ne _essar-: :: :xxuce n
effects d4Cn; tae 47A Cid inIa n 4-ce~ has been sc.tha-,
-- these effects becom~e Si~n4 ficant at 7low ir7-eter-wave -freouernc-es[7
.
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7-rwaesc 's.a
-4.-, s r
::uoka-a,'ln arcio of'cr~ mirwvolid-stat
P. 1tulsed n TMPT ocilatrs art cn- o--ocke marlfn, icc
- The Un~of iveity ofr Michign,AnAroFb19.
.. R. . -. z.ainas art G. . addad, "IM-wpATTf~ dvce imulatio'c~ ncan
rropber - -ice, !E- Elcton aeics, vl ol. D2vicpe.s, L
Orc, =-2ne 1?"?.Fe.15C
7. R. K. Mains and G. . :'Haddad, "Properlties of high -ffT diodc s
z275%c5n Labraryan TheUnvrity ofnsr eqichian," nn98o, WOCSE ll.:
volf. San7 "itnic L3- "eb.-ar 19 .
4g 5%
-
'iN . C.& *7 OW ' w VI'V -2X% 4r nu w w rw E7 ey f r. a-t ,is .- -- -. -- - .
op N
_-267cm = 0.1 r an-R 5
Fig. 3 >(aZ'RF circuite o:d !'b ba c ci used in t he theore, tia 44o
beavorfo nv restratznsz c e are 7. 6 t /'c.c--
wiopt 1.5 -,s an ru~ -yc fl
Fig. 6e usaSarti eavior fr e sintatior is simuatio
) = 0.13 n , C _ (t =3 6B, n = 6Q, q/m ,
cc CII
ad T .5 ;s and duty cycltae zlo of5YCvl
4%4
tu rn-onf cnaracteristicfo 'hiect fre qun aeny=T
Fig. 6 (a erStaruph behavior foed reerrning tsiuain
C' C) = 0 I J tH 6c ns: 6L46 A/cm 2 r% - i
a.±~ A 4T W and f 1ita 0 rio o Y (R 0
-mltd and je-nandd RVpowr v
Big.dii. T and C chrcersi for the, re-unic case1./cF2
1.d3K x C = m 6 n6 A/ T2 J.(t= 0 s)= ad =8
Big. RB owerfortheinjetio-loced tar-u; ranien
-
'it-.
I F~ig. 10 -- ;cwer for th e iz~jectior-oz'ke5 case -= ,=,
i-cc2-. . . =0.L . : n n =
-, %''
i-.°o
..-.:.,
#v4°,
w* .
- o-4
'p-."So
• --
.4-- p
-' . -, . - • , . . ' " • . . . .,, - ! " I . . ,, - , , " , ,t 4 " -
'4,. ,.4 ,. ,,-'". ,' ," -. " ." " " -" ".' " "" " '.-" / "- "'- ,, " ,," ,,- ''" e . . ., ,", ,- " - '
l4
-
ELI
.1,_i able I inljecticn-locked resultIs bserved expDeri mentally as a funct'on
o.f ,4e -ea'e (f 10 GHz, J,=6 A/cr.2, -us widt
5 -s and d, - factor= .
A, Table 2 Results f the uasi-static simulation for "he inecicn-
. locked case. (j- = 646 A/cm, = 8 vs, f = 10 GHz,GC 05ulse width 1!5 Vs and duty factor =4,"'. P is averaged
- " " EF
over the tulse width.)
.. ,[
."
'4.'
,..
".4'..
i. .4.4. 4." -"-' -. _,'._ 'v -" "" .-. . " % :,, ', , ' . .% . % . . - . - . . . - . ' . .. ,
-
-is
.-.%
Table i
Injection-locked results observed experimentally
as a function cf in.ected nower
f_0- ...6 2, w,. = I us and duty factor = 1,55)
1D Added Average T,. Efficiency V"in "F " dV(w, peak) (W, -peaK) (OV)() v
2.00 14.77 49. 17.9 98.0
2.50 16.28 472.8 20.0 97.0
3.00 17.4 1472.0 21.2 98. 0
3.50 17.63 471.4 21.4 98.0
3.75 17.39 472.1 21.1 98.0
4.00 16.51 474.5 20.1 98.C
4.50 16.12 1475.6 19.6 98.0
5.00 15.88 476.2 19.3 98.0
-u
ios:
4°...
-4-.. , " "-;4. v ~ - . .$: .,
-
.* .]
Resultz of t*-e mias-static S 41-,; a-tic. for -the ireto-o'~case
(Ja C. .... , - = c .s, C = !GHz, pulse w dth 1.5 . andCc -c--
duty factcr = -- S. F s averazea over the pulse width."
(W) Pr (W, poeak)
C- .39-' 2.0 15.50
So L6 2.5 16.30
3.0 16.41
0.521 3.5 16.53
C. 557 4.o 16.56
0.59-1 . C3
C.C2: 5.0 16.11
. 5.15.87
c. o.6,_ 6 .0 15.56
V.;'..
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