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LUMPED MODEL TRANSISTOR NOISE Á2ALÏSIS
DOXAN ILRAH.Li KKYA
 THESIS
su4nitted to
OREGON STATE IJNIVE:RSITY
in rti1 fulfillment of the reçiirenients for the
deree of
akSTLR OF SCIENCE
June 1962
PFEO VED ¡
Profsor of E1ectric1 Engineering
In Charge of Major
Head of Lepartient of Electrical Engineering
Chirmn of School Graduate Comniitto.
Dean of Graduate School
Date thesis i resented 7
Typed by Mary Jd&Lfl$
ACKNOVLEDOE4ENT
The work reported in this thesis was performed under
tÎie direction of J. C. Looney, Professor of Eìectrical
n4neering at Oregon State University. The author wishes
to xress his appreciation to Professor Looney for his
suggestions, constructive criticism and advice, and also
extend.s his appreciation to Professor L. N. Stone,
Professor h. J. Oorth.iys of Electrical Yngineerin, and
Professor A. '1. Lonseth of' the athematics Department for
their valu bie encouragement; and of course to his wife.
TAULE OF CONT±TS
P
IN2RODUCTION . . . . . e . . . . . . . . . . . . . . i
LiJI'4P;D 4Qtij,S . e e e e e s e e e e e e e e L
NOISE THEO! ;ITH LUMPiiD MOLiEL PARAMETERS , . . . . . 7
TRANSISTOhNOISEi'iODr.L,,...a..e....e..... 14
CORRELATION bETWEEN LUNPED MODEL PARAMETERS WITHNEASURLBLE UANTITIES , . . . . . . . , . . . . . . . 16
LtJPEJ) MODEL SM.LL SIuNAL PAFJETEBS , , 19
THE NOISE FIuURE e s s e s e a e e s s e e i i s a e 2i
XPERIMENTAL INVESTIGATION . . . e . . . . . . . . . 30
COi4PARISON OF CALCULATED AND MEASURED DATA e e e a a e i a 32
CO11PARISON WITH THE RESULTS OF CTHiRS . . . . . . . . . 34
CONCLUSION s s I e s a a a s e a s a s s s s e a a s e e 38
BIBLIOGRAPHY s e s a s s e s a a a e a s s e s e s s e s s 39
APPFDIX . . . a . . . . . . . . . . . . . . . . ho
LIST OF FIGEThÌ5
Figure Pge
is Lumped noae1 of a pnp oifí'usion transistor . . . . . . 4.
Genrtion nd recombixiatlon currents . . . . . . . . 9
:3. TAie noise gener&tor and kir e . . . . . . . . 12
4. d' T1eChaniSß for p type aterta1 betweentwojunetions ................ 12
5. Lumped pnp transistor itioúel wlth rbb 15
6. Lumped pup trnsitor model with noise gonertors . . 15
7. Small sin1 y parbmeterB . . . . 20
L Equivalent ciicuit forai of Figure 7 . a . . . . a e 20
9 Transistor p1ifier nOise iaociel . . . . s . e a e a e 23
loe Correlation of noise ouree of an am1tfjer into V and I voltage and current genemtore . . . . 23
i1. F vs. log f a e . s e a e a a e a e e s e e e e a s 28
i2. vS. log f . . . . . . a . a e e e a . e e e a a e 28
i3. Pn vs. log f . . . . . . . . a . . . . . . . . . 28
:I4e 1ocy :igra.n of instruiìenttiou . . . 31
15. Trpic1 spectrwn level ehractristic for G. Ft. Type 1390-B Randor oie Generttor . . . . . . . . . 31.
16. Calculated and reasured noise figire function of R, for I ot. condition e e . a a a . a 35
17. Ca1cu1ted mesured noise fiure as a function of R8 * . * a . . . . . . . . 36
18, Cd.cu1ated nd neasured noise figure s function of 'E' for R5 opt. condition . . a . 37
NOISES Any undesired sound. by extension, noise is
any unwanted disturbance within & useful fre-
quency band, such as undesired electric waves
in eny transmission channel or device. Such
disturbances when produced by other services
are called interference.
The Interntion'l Lictiorxry
of Physics and Electronics
LUNPED MODEL TIi3SISTOR NOISE MLYSIS
IÏIIkOLJCTION
The rocesses of electron-uiole-pair cretion, iotion, and
recombination form the ba8is of tr.nsistor ction. Noise unavoidably
accompanies these processes. These rocsses are random, so related
noise is randoni in nature.
At room temperature there is a continual formation of hole-
electron pairs and on the averae an equa]. rete of recombination of
electrons with holes. Forma tion of a hole-electron ir is dependent upon the chance acquisition of energy by a valence electron and
recombination is in dyninio equilibrium with the population of
conduction electrons and holes per unit of volume fluctuating about
the average value.
It is desirable to use s lumped transstr model to investigate
transistor noise because of its inherent simplicity with regard to
physics of tne transistor. The object of this work is to study the
cnaracter of noise in transistors tr laboratory measurements and to comare the results with those predicted by a simple lumped noise model.
2
LJ4PD ìOIELS
Serniconäuctor having two kthd of carriere, holes and electrons,
exhibit a more complicated mode of behavior th.n vacuum tubes.
The processes of ionization of atoms to provide holes and
electrons as well as the rocesses by which holes and electron
rcouìbine, ieducin, both carrier .opulation with each event re
new,
Luniped models due to J. G. Linvill (8, 9, p, 47) bear a one-
to-one correspondence to the physic&l 'rocesses encountered in the
semiconductor, the lumped nodels apøroximatin the distributed
devices, The models used ordinarily exhibit relationshiis between
current and excess density of carriers. A síngle aoiel is then
applicable both for snall signals and large sigials.
The behavior of a transistor is simply described in tenas of
the behmvior of the two junctions, since the tranlstor is essentially
two diodes sharing a common region. Lut a transistor Lekmaves quite
differently from the two diodes placed in the sa'e enveloLe.
Fire i is a simplified lumped model developed Ìy J. G.
Lirmvill (8, 9, p. 47) for transistors. In the model, each junction
is represented y a rectangular box snd serves to transform the
voltage V applied across it to an excess ainority carrier density
just inside the base re4on. The property of the junction can be
expressed by Ecuations (i) snd (2).
Fee = Pn g V - (1) /
qV ec
= P (exp kT
- i)
Wkaere
?ee xce8s censity at e;iitter.
Excess density at collector.
Pn Minority carrier density in 4 type base.
q Electron charge.
T Junction tenperture in ¿bolute degrees in K°.
k oltzman Constant.
V ApplIed forward voltae across the junction.
(2)
3
As can be seen, the iodeI has synaaetry about the axis of the
bas leed. The symbols hei, kTee r . preeent to a first-order approx-
imtion the distributed generation-recombinatlon echanisa of ±iinority
carriera near the collector and emitter junction respectively. They
are cllcd coìibinance e1eenta which ha"e the analogy of conductance,
Ve can define cobinance as
p as conductances C I
V
This analo is true if the reference for expressing excess
density is selected in &ccordnee with the Equation (lb).
11d represents to a first order p;iroximation the diffusion
nechanism of iInority carriers between the two junctions.
Sc end S0 are the symbols which represent, to a first order
approximation, the storage iaechanisn of ninority carriers near the
collector and emitter jiuiction, respectively. They are analogous
to the capacitors of an electric circuit. We can see that
V
p r°
Fec
SCI j
I Tc
(r C
Fisura (i) Lumpd modJ.of . PNP di-Fu3ion tTJni.sor.
I S jÇ! ct The corbin.nce elernent cn be expressed in ieasurable qUiXti-
ties by connecting the coflector to the bse tLrouh a low ïnpedce current rneasuring device (, 9). Since VC = O, Ecuation (2) shows
that O. y forward biasing the eniitter with a current
short circuit collector current can be rnesured, so
(3a) e
It will be ahown later that
= ee
(3b)
sii:irí a explained in Ejuation (h2) 1eg.. y;Hd kid f' I i:- (lid 1d + 1ec
In the case where ec ?n in EQuations (i) nd (2), I col-
lector leakage current can be found by esurin the reverse- biased
collector current with the íaitter o'en and will Le eu1 to ( , 9) P 4 H +- h li 4- k:i j
I = (-ci ee d cc ee ec) co (1ee ±
Sidlarly - Pn (ilci Hee + 11d '1ec + Hee k) () leo ± Hi.)
These equations were derived ±rorn E;qutions (37) and (33).
The storance elements are deteriineá froi the alpha cutoff
frequencies and f1 as followsz When collector volte is constant, ec constant, so
i s. (7) 2TTfN Hec± 11d
_________ Sc 211 f0(1 - H+ Hd (8)
We can solve Equations (3), (4), (5), (6), (7), () to get for
a np transistor
(leo (i - N5) (9) H ee Pfl(i_o(NcXI)
H = - (i -0i) (io) ec Pn (1 - 0NiXI)
EcoO(I 'eo'N (u)
n
= - 'eo (12)
P 217 o(N (i -°N oi)
Sc leo
P 27f ixI (i <N 0<i) (13)
7
itOISE THEORY WITH LUMPED MODEL PÁFAMETERS
In a lump of n material the net recombination currerLt is the difference of the aeneration and recombination currents. In eiil-
ibriun no net current flows, which means that genertion current mist be eual to and in the opposite direction from the recoinbination
current. The average recombination nd generation currents, (1, 3,
10, p. 46-47)
qPV /7.
(14) q P
q electron charge
V Volume
Pn equilibrium hole density in n :c terial
p mean hole life ti:e in n materi1
'g almost independent of hole density (P s
e bUt 'r
depends on hole concentration, so it can be modified to the fox
where
T .q(P+ 1e) V
excess hole censity.
(15)
We can rapresent these two currents as current generEtors
connected between minority ¿d majority carrìer lines. They re
ìndeendent, random, ipu1sive in n turc and exhibit full shot
effect (Van aer Ziel) (Lt, p 47),
Since fluctution current due to th coruculir structure
of electric charges passes through th seilconductor materid, an
equilibriura condition can be restored by supplying a noise current
generator to each of thei in parallel with 'r a 'g generators. This additional noise current is noniially eral cornpared with
the d-c current I and so the superposition rinciple of noise cui'-
rents can :.e applied to this case. Now 'r and I can &e rgarded
as an exact d-c current without any acconipaxying randoni part at
the terninaïs (see Fiure 2).
'r -F- nr
ig = 'g ± iflg
(16)
Two theorems from the theory of fluctuation in temperature-lImited
tube currents Ll1 be useful. tiere.
The first theorem concerns a curreiit I consisting of many short
current pulses of ecual charge content Q istributed randomly in
tiaie.+ It states; At frequencies low compared to the reciprocal of
the time durtion of one pulse, f1uctuation in the current I &re
described by
U-n:) : 2 Q2 Li f (17)
where
* complex conjugate
(____) mean value averaged o7er a time auch longer than -
+ The chrgn content is equal to fi dt integrated over one pulse.
Lr- ]lr+ L
Lg
gun. ) Gnrrion cgnd Rcornbrìafion curr-1n1s.
I',
* average nuniber of pulses or unit tiie.
If the pulses are unidirectional Ç, N0 is equal to the direct current
I so EQution (17) cn he written as
(i j*) 2 . I f (]3)
The secon theDre st tes wuen several currents I are flowing
into a coxnon terilhinal x, but fron several circuit branches XL
(n = 1, 2, .....), the totd current I consists of many short
unidirectioni1 current ?uìses of eaual charge content q distrii'uted
randomly in time. If a given pulse is to pass throuch but one of
tne circuit brncììes xn, nd the prob..bility of passage throuh a
given branch aì is to be the sane for all pulses, then, at frequen-
cies low coiip&red to time reci. focal of time duration of ono puise,
fluctuation in the currents I i described by,
(j j *) = 2 q . (19) 'V X
Then we can express our noise generators in the form,
(i i* = 2 q tr (20) ' nr nr'
(i 1* '2qIgLf. (21) ng ng'
These equations are derived for "spot" or narrow-bad noise currente
where f is the incremental bandwith. e can combine Fcuatioz ( 2))
and (21) into one equation
(i ) = nr jr (ing j) 2 q (Ir + 1g) A f (22)
ana from E. nations (14) and (15)
( i i) = 2 q
(
y q ± e)v) A f (23)
c. q ! P) A f p
2q1(2P-- (64)
trom the 1uped ioui (°, n. h7)
(25)
so
(in i) = 2 q r (2 P-i- e) (26)
u
This noise generator nd H. are shown in Figure 3.
There re two kinds of carriers resent in seiniconth.ictors, holes
and electrons, aìd there are two rnechanisms of current flow, drïft of
carriers and diffusion of carriers, The holes and electrons in the
seniconcuctor rnbterLl re in rndoni tìotiorx virtue of their thermal
velocities. In a region in which their ensity ts uniform we can
place an iraaginary plane inside an count the holes or electrons
passing through it per unit tie in each of the directions. e
would find on the average tht the net current .s zero , the currents passing in one direction being equal to the currents assing in the
other for either holes or electrons, Now if we consider two regions in which tne censit3r of carriers are not equal, there i certainly a
net flow of carriers from the region of hih density to the region of low density. The net flo is :roportional to the gr&dient of
density
Therefore, as in Figure 4, the hole current b.twen the (i)th and the (i l)th region due to diffusion is
.1
Figur. (3) Th Noise Gnrator and Hr
p___ ___
1gur (4-) Dif-fusion mzchanisni
°F p±ypmi1 bczFwan +VVO jund-ìon5.
13
[p(i) -p(i± i)] Âqt i (i, i -j-- 1) = A - (27) pd
&d (9, p. 47),
A q D0 hpd=
L\x
then
(26)
pd (i, i -j- i) Hpd {2(i) - p(i + 1) (29a)
= 'pd(i) - 1pd(i -j-- i) (29b)
pd consista of -wo rardom indpendent impulse currents as can be
seen from Equation (2%,b) and should exhibIt full shot effect
(12, p. 47). Giving the same resonind as Equation (16) we can
express the diffusion current as
then
'd -F- 1nd (30)
i (i, I ± i) = 'dt -ndi - 1d(t + i') - + 1)
(31)
Using the vacuu tube theory used in the derivation of
Equations (23 (1) we can express the diffusion current noise
generator as,
(-a ici) 2 q (ia(i)± 1d' + :i)
2 q (lid P(j) ± e(i -i- i)) L f (32)
1h.
TRANSISTOR NOISE MODE.
Fiure 5 shows the intrinsic, lumped, pnp trnsistor nìodel
(3, 9, p. 47) to which the extrinsic base resistance has been added
to inprove the accuracy of the nodel. All the noise iray be accounted
for L associating a noise current generator with each of the con-
ductces &pearing in the lwiiped iiocel and associating a thermal
noise voltage generator with the extrinsic resistive eieiient as
shown in Fiure 6.
as
e on write the corresponing equations for the n3ise generators
(me e) = 2 q Lïr Hee (2 P + see) (33)
) = 2 q Lf 1ec (2 eec) (4.)
(d ') 2 q 11d (2 Pn 4 ee + fec) (5)
(Cflb eb) s 4 T Af rbb S (3ö)
fv D Hd rvcC
Figur(5) Lumd pnp +ransÌsÖr rnodczl if1-ì rbb.
¿nd
çv C
Rd I
H H
gur- () Lunip4 modal wi-h noi rìar or-s.
16
CORRELATION BETWEEN LU4PTD NODEL Pi\RAMETERS
WITH MEASURkI4E QUANTITIES
In the lumped model of Figure 5 we can write the following
relationshi3a between the d-c values of the excess carrier density
and current vrt les s (, 9, p. 47),
'E = (Hee ± lid) ee - hd ec (37)
IC = - Hd ee + (rLec# lid) ec (33)
The above equations express the f&ct that for the lurnped model shm,
the f1oT of carriers ecross the bese region is a linear function of
carrier ensity near the junctions. Unuer the conditions that the
collector volt&.ge is held zero, Ecuations (i) and (2) show that ec
becomes zero, and we can rite the ratio of the currents coming out
the collector I to th&t injected into the emitter I as in quation
(39),
C VE 1'ee (exp.
IÇT i) (i)
qV eC (txp.
iT i) (2)
lE_________ - .; (V0 - 3) : dee Hd cXN . (39)
The transistor car. be ooerated in the reverse direction with
current injectea at the collector holding V O. We can define,
- .- (Vj, = o) = kki
: c'K (40) IC Heo+ d
In the saine manner we can evaluate I collector ie!ae ctrreit and
'CO eraitter leakage currenta,
r7
- ± Ha)
= - p.S, (Hee 1ec ± H He -i-- Hd H)
(41) ee + Ha
(eec H2 e ± Re c -- 11d ll
'EO = - + H s (4')
By insoection of EcuLtion (39), (40), (41), (2) we can find the
saze equation founo by Moll (4,), cx i
= () it_o
From the above ecuations we can derive
C) r
1E0 .a__ H ? (1 - 1) - -Pn (î - O( oc1)
= - Pn (i o - i] .
"ee
: - ' o(i) °<N (44)
- - ri (1 - O(: %f)
(1 - oc i) (45)
o( O( I H----- LI1À, leo u - P (1 - O(N °( i) - P (1 -°N (46)
Accoring to Shock1ey' theory (1g) for th low injection
levels (under noriia]. oprating condition8) in a pnp transistor
VC < O then,
I qV0j » kT s (47)
Therefore it will he a good ap3roxiniation to write,
'ec -
which will be used 1ter,
(4e)
18
i»
LUNPED MODEL &4ALL SIGNLL PiRiiiETiLFS
In oraer to derive noise figure foiiu1as in texs of lixaped
model parameters, it is necessary to evelor a sml1 sia1 euiva- lent circuit for the lumped iodel. The y prieters for the common-
e!nitter orientation are used s shown in Figure 7. ¡s e conse:uence of Equations (I7) and (4), l2 and y would be practically zero
under nonul operatin conditions. But vrious experiments showed
they re not zero. Early (3) tried to explain this by the modula-
tion of the thickness of the bese layer due to the collector ac
voltu'e. Stili l2 and Y22 are of a smaller order of maiitude
than ii and y an9 my Le neglected in practical eases. Their
contribution to noise is thus negligible. Lxpressin the ecuivalent circuit variables in te1ns of the variables in the lumped model,
neglecting the noise generators, as shown in Figure 8, we find,
Il - 1'ee (Hee + j 1JS)
=-P ___ kT
hence,
vi = _ Ve
so
(Hee j Ve (49)
( 50)
Il = F exp (c Ve
(hee j WSe) Vl T \kT
( T y11 a = exp
q Ve ee Se) ( 51)
12 - ee 'd (52)
)
(7) Small c'nal y Framars. I1V1 +IaVa 1 +Y22
Ii
p r
1
vi I
-
ylvI
Figure (8) Euivaln crcuÌt o urz(7).
21
so, q (qV"\
y,'
1 eed ICT ) -" .1
Ve
- (qv' LT
exp T I
.
22
THE NOIgE FIGURE
The re8ultin.-; nodei shown in Figure 9 represents e common
eriitter pnp transistor amplifier with resistive source and 1od
with three independent stiot noise current generators nd one therrnal
noise voltage generator. The genera]. noïse equation '. a function
of source resistance R for a narrow-band is,
N. B F i -t- - C ..... ()
s
This is a :enerl ecuation escribing any amplifier. If tue
re.ctive coiraonent of the source is held constant and the resistive
coxnonent is varied, the variEtion of noise factor should follow
this law. The noise performance of the .iii4ifier can therefore be
characterized by the parameters a B and C if the source is resistive
which is our case. If the source is partly reictive, another texìi is
necessary which is beyond the scope of this paper.
This representation is advantageous because the amplification
properties of the aïnclifiers do not appear in the noise factor
calculation.
Over an incremental frequency band f, a noisy amplifier can
be represented by a noise free arnalifier with a noise voltage
genertor and a noise current generator at the input, V and
as shown in Figure 10. Figure 9 shows a source resistance con-
nected at the input of the amplifier. The forraula for the noise
factor is (2),
ur(S) Tran5Isfor rnplifr NÖì5cz mocZI
-r
-4- __ I
NO5
_1i' FIERJVa
-
1-REE y In MPLÌÌE
(k)
4igur(iC) CorrczLhcn oj rioì öurcs an
rnpli1uzr nfrû Vn and 1En /oa nid c.urriznt noIscL g(Zfl(ZrâFÖrS.
23
24
F=1+ (vv) ± Il) r
I) + (v () For frequencies at which O is a» roximateiy constant, I is
usually negligible (see Equation ) so that
(V v*)
= ± 4 T R Af
De fining
(v v) neq 4 kT Af (57)
Eu&tion (45) becomes
F i *
Assuming no correlation between the noise genertors, we cn find V aIt I frozu Fip.ire lOb with the transistor in »rounded
emitter orientation as suggested tr Becing (2) . The derivtion
is shown in the appendix. V aiid I in terras of measurable
quantities are, 2
(v v) = 2 q Af {
I rhb+ re
Z'bb4 IeJ (5:)
(I I) = 2 c; 1f f _ 'e (c)
( 1l ej
(v In) 2 1 2 f C
21 (Tbb + re)
-qi.fIerbb (ti)
1e can assume that the collector contribution to the collector-
cutoff current I is ìuch greater than the emitter contribution
25
nd I is larg' £nough to allow the aìroxim'tion re T
e e cl cx'
For our soec:Lfic purposes, - ° f ; DK2 and 1+
CO
inäeende;t of current o that l 1e 'co Y putting
- = :i. + L and treating -- ¿nd ±.2 &s tka11 quantities. Now by
C, p (3 le
putting the values of 1quation ( 59) , (6o) , ( i) into Equation ( 55),
e C8fl write the noie fEetor :ith mesur:b1e civantities as,
F
[ J
2] (rbb + re) _ 'e r
q [ rbb+re I
2} 4
2 kT h8 L
O( e rbb J
qR0 I +2kT
j
(<12'ej or
F+0+
/ ___ s f' 2 re \ (3 fCO2)
For our purposes, there is negligIble error in using Equations (62)
and (64).
If we put the values of 1;uation (51) into Lutions (80), (1),
(82), (83) and rewrite Eauations (84), (5), (86), use iquation (55)
for the noise factor F, and assume the source impedance is complex
Z5R5-- ji5, we canget,
F 2 q I rbb ±
l \
2
2 q 'e rbb s I
4 kT
Equation ( 65) is the same ss that obtained by Guggenbuhi and
Strut ( 6) whIch checks our results with the other investigators.
Now it is necessar- ic develop m1nimu noise figure for our
secific case in order to find the optimum oper&tion Qoints. First
we will find tie ootimurn R5.
Taking the partial ceriv tive of Lquation ( 55) with rspect to
R8 and equating to zero we get,
d' :1. _____ (T T* o = - - (y v}- '
a h h. kT 2 n n iT
1/2
IC rb re
(
2
rbb4 IC
(66) ICT:
'e ic(V And by putting Equation (66) into Eouation (2) we get,
=
{ [(
j
'e) b 112_
'e rbb6J 1/2
(
C
( r re) - 'e rbb
J . (67)
cuatian (7) is used to calculate the lowest part of the curve
which is shown below for specific pnp transistor (2N1128).
The derived noise figures were for snot noise fiure and the
re1tion between Lverage noise fiure and spot noise figure is (7),
.;= F(f)G(f)df (68)
J(f)af
where G(f) rnsicer am of he amplifier
F(f) Soot Noise Factor
Average noise Factor,
In our region it can be seen from Figures 11 j2 and 13, and
Equations (o5), (66) that F(f) is independent of frequency so can be
reoved from the integral aL. n nd
-- f_ç_ JG553(f
Figures 11, 11 and 1, show that transistor noise is 1ndeendent
of frecuency. Lower tbn f1 (around a few kca. region) the flicker
( i/i) noise L coin&nt which is ut cicusea in this paper. Tk
origin of this low freo;ency noise is related to the surface pro-
orties of the device (12).
Above f (aprrodxnte region of f cutoff frequency), noise
currents generated near the collector junction ure collected und
1gu ni F
Corn mon zmiftr currznI
Nbs Pwr- oufptJ
-Pn
Figur(() vs. LogÇ
Furci2) (3 vs. LóÇ
J-
(t3) Pn vs. LoÇ.
29
ubeuent1y conducted to the collector termin1. Since th noise
currents sources re 3.istributed throughout the bse region and the
signì is injected t tAie mitter-hse junction, the rtio of the
collected noise currents to the collected signal currents increases
with frequency above f. In other worts, the power gain of tr.nsistor falls off more
raidly with frequency then does the noiEe outut power jenerated
in the transistor base region.
30
EXPERL'IENThJJ INVESTIGATION
There are v&riou methods available to determine noise fctor,
the one usine a noise generator for reference is selected for its
sirni.icity. This method makes it ossib1e to ueasure noise with
resonab1e eccuracy using common ibortory equipnent. Noise
generator, VTVM, 20 keps. lowoass filter, re1ted block digria are shown in Figure 14.
In the experiment, the average noise figure is detenined by
using a G. . Tyoe 1393-B Rindoui-Noie Generator with a band-width
of 20 keos. which has a constant noise spectrum in te s;ecific
region of our interest as shown in Figure 15.
The low pass filter is utilized to exclude the noise ;;enerated
in the unwanted band. of the trxisistor mp1ifier and at the same time
to narrow the VrVM's pass band.
The transistor under test is bi&ed from a battery power supply
in common emitter node, and operEted for small-sidn&1s current gain
in the common emitter mode. Ail the connections nade in shielded
and coaxial cables &re used to prevent pickups. Tecktronix type
503 Scooe is used to control the noise wave shapes.
____ TOR Ñ O i S E VO LTA(
HTRJNS S -I
I LOW PA DÌYDE UÑDE
I i iLTER TO T3TI I
SC-OPE
VTVM
Ft'gur. (14) Nock digr-im o +hz fnsfHiman-
rrê
I a io 20K. IOOK
gJral5) Typical spach-um !cva/ airc- -çt-ishc -sor 6.ryp IO-B Randorn NJd Gn.ratör.
32
COMPARISON OF CLCTJLJTED ND ME.SURED DATA
For a particular trnsitor, certain paraietera rbb, 1co3 saust be measured for substitution into Equation (ô2).
The bse spreaöing resistance rbb was eaaured with G.R. Typ*
916 A Radio frequency bridge using the circuitry suggested tr Terwn (ii). rbb detezined by ¡rieasiring the h1h frequency
input impedance ¿md tking the real pirt as rbb which is the part
that gives rise to therm1 noise. For the auecific transistor used
an avere value of 375 Q. was found.
For ech tranaistor, O was ieasured usine the setup in Corn.
Lab. O.S.U. 70523, and I and! vere ueasured using the 8etup
Corn. Lab. O.S.U. 70553.
Figures 16 and 17 show that good agreeuent with aeasurement wa
obtained arounc the inimuxa noise figure. The source resistance F5
is the independent variable with a-c bies current held constant
at 0,995 xna for a 2N1128 PN? Gemaniurn Alloy Junction Transistor.
when R5 is incresed, the cifference between Ftheo and Fep also
increased.
An R opt. of 500Q. is obtained for specific c&se shown in
Fiure 16. Fj .92, which is ver close to c.icu1ated values
obtained.
Frora Equation (66) R8 opt. was found to be 517 Il , which la
again very close.
The iffer'mce between calculated and measured values shown in
3,
Figure 17 is due to the change in for the specific tr&nsistor
which c&ued R opt. to he around 600 -Q The for a specific
eniitter current is (Ex) = 3.52 whicn is reason&tly close to
the theoretical value,
Figure 18 shows good agreement between calcule ted nd mee sured
noise fiEures in the neighborhood of it not at other values of
F. This is unfortunute but not surprising because the elements of
the nichel aire not considered functions of 1L' t can be seen from
Figure 18 tht the elements have soue deendence on I and the model
should be modified to reflect this deoendence if better &greement is desired over a broader imnge.
3h.
coMPrISoN WITH THE RESULTS OF OTHERS
(iuggenbuhl and Strutt ((a) have noted experimental datE. similar
to iiure 18. Their ueasured data show a similar departure f rom the
theoretical as a function of bias current and frequency.
W. H. Fonger (5) uses another ap.roach to the problem and
virtually arrives &t the same noise-fi,ure exresdon as shown in
Ecuation (ó2). He inicates that any one of the four uncorrelated
noise ;enerators may be mtäe dominant as a function of bias point
and source termination.
s noted before, Equation (62) can be written as Equation (ò)
which is the same equation Guggenlb1 and Strutt ( ) used.
Equation ( 62) is :lso in agreement with the theoretical resulta
of Beattie (1).
L 15 Figur.(6) CALCULATED AND MEA'3URED NOI5E I
flSURE OF N PNP '4- AU_Cri' TRANSS-TOR. NO.1,AS A
I RUNCTON O S 'E 0FF. I_13
vc. _Io.c
ia
ir
¡O
\ \
S
\ 8 \
¡'lEA 7
ft
/ N 5
'N
Z'N 4
- 3 uLAyD
a
30 200
Ql
r
/I/
.-1R5 (ahrn,$) .1000 aoôo 3000 5O 700 7oOSOQ9
.1 i i i i i i I I i i iii'ii I
II
EI1
Figur. (iT) I
CALCULJ\TED AND MEASURED NOISE j
c'&URE OF 2N 1128 PNP JUNCTION j
ALLOY TRAN.SSTOI NOII, AS A FUNCTION OF R-s, FOR 'E O.77Om. I0
V=-IO.ov /
\ /
/0
II \ /
\ o
-Io \ /
/ \ /
s \
4
<I
/ /
z1z
7+ MEAUQD
/' /
\ / GLL
/ /.
/
/N 4 I ULTEi O -.5--
-O- -!)-- 3
a
s- R5 (ohms) 11000 a000
I °
1100 aoo 10 -° i I i
1.3000 oc
r
s r:gur() CALCULIATEE AiJD MEASUZD NOi.sE F(GURE OF 2N 1128 PÑP JUNCTION
¡4 ALLOY TP,AN.S1STOR NO.1, AS A RUHCT(ÖN oc r , 500.Q.
'v'c -10.0v
I-12
I-II
lo
\ \ s \
8
<V 'e
o
z z \\ A5URED T \/'
r r
r ¡I
O r /0
4
lL
3
ZCALCULATP a
- 'E (microampws)
I
1100 i400 «oo oc 2000 3OOO 14-0001
I i i I I I
CONCLUSION
Ce.lculation of noise figure for PN? Gernniu Alloy junction
transistor 1sed on the lumped noise ioel shown in Figure 6 agrees
well with the eperiinentally nesurod vdues shown in Figures 16 :nd
17. The theoretical reu1ts of Foncer (5), Ee&ttie (i), nd the
experimental results of Guggenl*ih]. nd Strutt () arc Liso th good
greemct with this ode1. ?e can conclude that the 1uxped noice
tr&nsistors aoie1's vLiidity hïs been ste.biished.
39
131 xLIOGíAPk
1. k3eattie, R. N. A luniped uode1 &na1yis of noise in seiii-
conductors. IRE Transactions on Electronic Leviceß 6i13- 140. 1959.
2. t3ecking, A. u. T, i. Groeidi2k &nd K. S. Knol. The noie factor of four tenninEl networks. Phillips Pesearch Teport lo, 1955, p. 349.
3. Early, J. 1. îffcLs of space-charge layer widening in junction transistors. Proceedings IRE 40:1401-1406. Noveìiber 1952.
4. Ebers, J. J. nä J. . ioll. Lare-signEJ. behavior of junction trnsitors. Proceedings IRE 42:17i1-1772. 1954.
5. Fon:er, . ii. Noise in trnsistors. In: L. L. Siu1iin and 1-i. Â. klaus. Noise in electron devices. New York, i1ey, 1959.
p. 34J-405.
6. uuggentuihl, nd 4. J. 0. trutt. Theory anQ experlzftenta
on shot noise in serniconäuctor junction diodes cnd transistors. 2roceedinks IRE 45:839-43. 1957.
7. IRE Standards on 4ethods of i4easuring NoiEe in Linear Twoorts. ?roceedins IRE 48:b0-6. 19&D.
8. Linvill, J. u. Models of transistors &nd diodes, C18ß Notea 1960 of Stanford University.
9. Linvill, J. u. Luiiped .nociels of tr5istors ana diodes. Proceedins IPE, 46:1L41-1152. 1958.
10. Shockley, i1ectrons .nd holes in semíconJxctors. New Ior, D. Van Nostrand, 1950. 55]. p.
U. Ternn, F. E. lectronic and rado en:ineering. .4th Ed. New York, McGraw-lili, 1955. 1078 p.
12. Ziel, A. Van lier. Theory of shot noise in junction iiodea and junction transistors. Proceedins IRE 4:l9-1646. 1955.
APPENDIX
Lrivation of the equations of nd
Assuming no correlation between the noise generators, we can
find V end. from Figure lOb, with the transistor in grounded
emitter orientation as suggested by ieoking (2).
Putting V2 = O and i2 = O
we can solve,
v=-v1 111=_Il (70)
hence,
V2 VC (1 - Ve (71)
12 - 1nc Yce Ve - (72a)
- Ii-I-- I+ - - (72b) Ve y,
Putting Equations (72a) and (72b) into Ecuation (71) and for
from,
V2 = O , i2 = O
u1e Yc L \Yc I] Ye
e 1nc I1__i,-f YO (73)
+ Y0,
VlVnb+ Ilrbb_VC+ V2 forV2O , 12_O (7i,a)
Vl_Vnb_l'V. +Ilrbb ( 74b)
Inc Vl _ Vflb4
Yc (i -i-- r Ye) me rbb
(1 -) f - ceJ
(74c)
hi
Putting !2!. - - V - V I - I - 1 n i n Ye
and p 4. 1 80 ce
= 1e which are
reasonable approximations,
nc - V + -- (r 4
i-ne rbb (75)
Iflmne± . (76)
Then we csn find,
(v V) (Vnb V) 4 (ne i8) 'bh2 2
i0) __________ i
< I
2 rbb + e
kT ee
q
+
+ 2 Re [ifld (rbb+
i
q (q_V\ (H + j Se) kT kT
(i I) = ne t8) rbb 1_ (i + Re [mj (7e)
(v n) (ne j8) "bb4 (inc
(rbb +
q fqV8\ Pn exp.
icT J (Hee _ j u) e)
f2 R8 {(ind d)
J
42
'-na 1d
(* ex ee -
(79)
Using Equations çi), (2), (:), (4o (.i), (42), (43), (4), (5),
(46) nci pproximtions in Ecuations (47) (4e) , we can rcwrite
Th-uatjons (33) , ( :4) , ( ? 5) (6) i.r the form
ne 2 q L f "ee ( n
2kTfe[ (h1ee
-2qfI (so)
(i = 2 q J f ec (2 F + eec) 2 q Af I (u)
(d 14i) = ;: q Ar (2 P± Pee±
s 2 kT Ar o [p exp (kìeet JSe
(Vl.b i.T ¿f rbb L3)
Pitt1ng tne iauation$ (so), (si), (2), and (33) into JL:uation
(79) we can get,
(v v) 4 T f rbb ± rbb2 T f Re Fn ep (ve)
(Ree + j Se) - 2 q f I r.b J
J
4 1
exp ee L)Se)
'.3
2 kT f rbb2 q fqV
(H + kT
)
ee i W Se)]
+2kT/1frbb 2
I rbb+ q /q_Ve' Pu e
kT J
(H ee i 8) a2qf I
o
_rbb2I
I
(34)
Hence,
____ r q (qV\
- 2 qLf 'e 2 q f ( _ ' 2) \tcd
- 2 Re 2 T f exp (q Ve
(H ea + T)
2qAf 'C J2 e] (85)
I) : rbb A f Re n e (e)
(Hee + i 5e)]
i -qL1fI -- 2qf C
q fqV\ 2kTAfrbb exp
T i
ea j W
I q íqV ie -2kTAf
-2kT Ar+ 2qíf 1
1o2
44
Çr+ ___ exp )
(ll, i Se) q IqV\
-2qLfIr (86)
Using the Ecuations (1.4), (45) and (46) and approximating in
our range of interest
ii 1/re (1 -t- j 1/re (8'7)
rbb+ rei r2Ie = 2 q ______ 2
(88)
IC (II)2qf (of2 1ej (89)
I i
-2 qf 'e rbb l2 (rbb4 re)
(90)
