Idea Transcript
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MTT-33, NO. 3, MARCH 1985
181
Theoretical and Experimental Studies of Gain Compression of Millimeter-Wave Self-Oscillating Mixers FERNANDO
Abstract
—A general theory for a heterodyne
is developed output
to explain
the experimentally
power compression,”
a decrease
of millimeter
conditions.
This
equation
power. Adter’s
of the self-oscillating
of the irtjeeted
owing
to the
mixer,
bias
of the
theory GaAs
is modotate~ obtained
“induced”
agrees
quite
Gunn diodes
well with
I
(SOM)
mainly
a perturbational
to
equa-
aflow
the
of the new
teehnique,
where the the locking
has been based on the fact that, (voltage
both
tunable)
in amplitude
experiments
and in angle.
This
performed
range 75-100
self-oscillating The
on the order of magni-
of modulation.
in the frequency
IN
modified The solution
depends, primarily,
frequency
I. NTEREST
has been
of the
gain with
and proper boundary
mixer is assumed to be outside
perturbation
dependence
of “beat
generstf differential
modulated.
signal. The theory
the oscillator
functional tude
through
AND
mixer
phenomenon
modifications
equation
to be frequency
has been obtained
frequency range
differerrthd
mixer
Gunn self-oscillating
observed
i.e., an increase of down conversion
injected
tion has been used, with some pertinent self-oseillathtg
R. PANTOJA
semi-quantitative
with
both
GHz.
self-oscillating
because of the high bum-out
power in the beat frequency is related to the millimeter-wave received power, and it is shown that the conversion improves with decreasing millimeter-wave received power. The
theoretical
Adler’s
equation
mixers
power
limit,
rugged-
simple circuitry for sigmixer has the advantage
and mixer diode. It acts simultaneously and a mixing element. range
are several potential
radars,
etc., especially widths ticularly
those applications
are required.
Moreover,
advantageous
as a local oscillator
is important
such as short-
electronic
seekers,
where broad
band-
millimeter
waves are par-
if uses in smoke, dust, fog, or other
adverse environments are contemplated where infrared would be absorbed and scattered. In the present article, results from detailed investigations of heterodyne InP and GaAs SOMS are reported. A semiquantitative theory for the experimentally observed phenomenon of gain compression is also presented. This phenomenon down-conversion injected
power
manifests
itself
gain with
through
cerned with
out using
the pertinent
the
increase
words,
the behavior
that the theory
as a semi-quantitative
the general pattern
0018 -9480/85
con-
diodes used in the experiments
were rated for
maximum output powers around 94 GHz, and the tests were carried out in the frequency range 75–100 GHz. The
diodes used were of then ‘-n-n+ of the experimental
sandwich
results presented
diodes were carried out at 94 GHz, of a comparative study. II.
THEORETICAL
sandwich, The GaAs
structure.
Some
for the types of Gunn thus providing
means
ANALYSIS
A. RF Voltage Across the Gunn Diode 1 presents
the experimental
basis of the subsequent of an externally to avoid
injected
driven-oscillator
setup used and is the
theoretical
analysis, In the presence
signal, which instability
of the beatjrsg millimeter-wave be analyzed
is sufficiently
small
spectra [9], the effect
signals across the device can
in terms of an amplitude-modulated
voltage
signal together with a frequency-modulated voltage signal owing to the bias perturbation of the (voltage tunable] Gunn self-oscillating mixer ( SOM). Therefore, disregarding absolute phase differences (e.g., between the modulating signals), the actual RF voltage across the Gunn v=
Manuscript received January 17, 1984; revised September 30, 1984. This work was supported in part by SERC (United Kingdom) under Grant GR/A93525, and in part by the Brazilian Navy Research Institute under Contract FO1/1094. The authors are with the Brazilian Navy Research Institute-IPqM, Praia da Bica, Rua Ipiru s/no., Rio de Janeiro, Brazil.
here develtheory
of response of self-oscillat-
diode can be written
of of
the basic
assumptions
ing mixers.
a decrease of millimeter-wave
[1], [7]. In other
is carried
to note, however,
oped is to be regarded
Fig.
applications,
secure communications, for
analysis
[8] in which
and boundary conditions are introduced. Such conditions and assumptions are going to be discussed in due course. It
of large instantaneous bandwidth of operation [6] and the fact that it does not need a separate local oscillator (LO)
There
JR.
InP diodes were of two types: either a n+-n-n+ or n-n+ with a current-limiting cathode contact.
has been on the increase in recent years [1]-[5],
ness, low cost, and comparatively nal processing. The self-oscillating
T. CALAZANS,
The Gunn
IrrP aud
INTRODUCTION
millimeter-wave
EUTIQUIO
A(l+mcosti~t)
where A is the amplitude ter-wave signal, is the” induced”
sin
A(J coot+ ;sinamt m
(
of the free-running
(1) )
SOM millime-
m is the amplitude modulation index, ti~ modulation frequency,l aO is the free-run-
1 i,e,
mixing frequency, , fundamental Ulnj is the angular frequency of the free-running SOM frequency.
/0300-0181 $01.00
as
@1985 IEEE
defined injected
by U,nj – coo-~n,, where signal and o+ is the
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHN1@ES, VOL. MTT-33, NO. 3, MARCH 1985
182 EXPERIMENTAL
SET-UP
FOR METEROOYNE
EXPERIMENTS
the device
(SOM)
terminals.
However,
the bias choke
of
the SOM “prevents” high-frequency radiation leaking out via the bias port and, therefore, only the lower frequency components develop a substantial voltage drop across the load (input
-%=4 El 1
-
m,”
-w.
,..,
,qw,
PowER
SWPLV q
The
— Fig.
—
1.
Experimental
1
impedance
of the IF amplifier,
in our case). By
“substantial” we mean a signal greater than the input noise signal to the amplifier, regardless of the nature of the noise, and a signal which lies within the overall bandwidth of the IF system. time
varying
representation
of the IF
current
is
given by [13]
1
test system,
i(t)
=~gnu”,
n=0,1,2,.
... m
(3)
g. is the n th order conductance.
Although
a higher
n
ning
SOM
ulation
frequency,
frequency
not difficult,
and Au/u~
index.
algebraic
After
is the “induced”
a somewhat
manipulation
mod-
laborious,
we can expand
but (1) in
terms of a combination of Bessel functions and trigonometric functions according to [10] and reach an expression which gives the total RF voltage across the device in terms of each frequency
()
U= AJO &
component
sinoot
~ n =1,2,3,
1
sin(uOt
Au/u~
‘[l+m
+
individually, AJ~
i.e.,
...
order power series can describe more precisely the phenomenon [14], it is sufficient to take the first three terms of the power series given by (3) to achieve a good compromise between simplicity and accuracy for small signal nonlirtearity. The first two terms (n = O,1) only yield the average dc term and high-frequency of m). Therefore,
~ ()
where
for smallest
m
signal
ulation products nents at 6J~, are
+ namt)
components
it follows
nonlinearity, from
(even for high values
that for simple
multiplication
the first-order
(2), which
yield
iOmaAJo(~)~+AJO(~)~+n=
cross-mod-
frequency
compo-
l~,,EE+l
‘n=,~jAJn(~)[=-l]sin(aot-n@mt) +
+
~
Wnzn+,
+
~
Wn+lzn
.=:i6,...AJn(5)[=lsin(QoQ”@~t)~t)
(4)
~=2,4(j .,
?I =1,3,5,
where
(2) where
the J~’s, k = 0,1,2,0 ... n, are the first-kind
functions
of order
The right-hand
k and argument
Bessel
Ati/ti~.
side term of (2) could be put together
as ~=
A.l(~)[&-1],
forn=l,3,5,-
Z=A.1(~][1-*], Rearranging
However,
for future
use, it is better to preserve (2) as it has
been presented previously. Therefore, (2) represents the instantaneous RF voltage across the Gunn device in terms of each frequency component (provided that the relaxation frequency of the SOM is much higher than ti~ ). B. Derivation
of the Intermediate
Frequency
Output Power
It has been accepted so far (e.g., [11], [12]) that the main nonlinearity in the Gunn diode is its differential negative resistance, and, of course, by the very nature of a nonlinear element, a complete set of terms derived from the mixing between the components (or any other higher order crossmodulation product) are obviously going to be present at
forn=2,4,6,
(4) we have
‘@m’A2Jt3J&)* +2 A’n=1;3
.,, Jn(:)Jn+,(&j[m&/;:)].
(5)
,,, Since
converges very quickly for simplicity (without
for small arguments Ao/a~, and losing any essential feature of the
process) approximating the Bessel functions by the asymptotical expression for very small arguments [10]
PAN’IVJA
AND
Equation
CALAZANS,
JR: MH,LIMETJ?R-WAVE
(5) is simplified
SELF-OSCILLATING
183
MI~Rs
re-write
to
intermediate
frequency
equation
Q..,
where @ is the outgoing signals, ference,
a
K3m2+
z
(ia~)2
Kdm2
power, (5r+K5m2(ti)4
Under
the small-signal
shall now establish ude index
modulation Au/a~
index
analogy dependence
Modulation
For modulation
(e.g., [15]) we
J;(E)+2
representation.
amplitude
can be regarded
of angle modulation,
the finite
of
the modulation
m with
modulation
as limited
frequency
frequency
sin@-<
(lo)
{
pout >
r
ext
out
C = A(,oO as compared tion
with
Adler’s
in the latter
general
form
differential
equa-
we have AuO
In other words,
>1
the —— ;:t r
in favor frequen-
cies the effect of the phase delay actually enhances the FM sensitivity [16]. Therefore, it is reasonable to assume that m is a fairly insensitive function of the injected power. The dependence
(9) is then
Piw
—. ;:t
time
When
so that at high-modulation
constant
output
with
A=
z Y:(&)=l ~=1,’2, . .
in the Bessel function
and
equation
Asin@–l?sin(u.t)
modulation
tion, which in turn synthesizes the angle modulation. This synthesis, being essentially a phase shift of the AM sidebands, is adding energy to the carrier (cf., fundamental angle modulation) which satisfies
for
d~ —=– dt
B=-& j~ >10 MHz,
POU, are the
frequency
of the differential
power Pinj.
of energy storage in the self-oscillating mixer leads to a phase delay of the amplitude modula-
modulation
form
Index
frequencies
Q, and LOOand
free-running
i.e., the injection closed-form
frequency
solution
Pinj pout is outside the locking
range, the
is given by [8]
is nearly
range of our con-
cern and it will be neglected. Hence,
we can say that for high-modulation M=
M+6(Pinj)
=MfOr
which
Pinj>t~
(8)
where M is a small constant, 8( Pin,) is a “zero order” function of the injected power, and t ~, is a lower limit for injected power such that (8) is still va~d.
Within
Modulation
a fairly
Index
wide range of high-modulation
frequen-
cies & the peak frequency deviation Ati can be regarded as independent of ~~, but not independent of Pi,j. Actually,
Aco is only a strong function
(11)
frequencies mj
D. Frequency
and dif-
of the amplit-
m and the frequency
with respect to the injected
C. Amplitude
constant resonator
injection
the functional
phase difference between injected AuO is the free-running frequencies
mixer
The general
n = 3,4,5, being constants.
the Kn’s,
(9)
respectively.
(7) with
Pinj — sin+ - Au, P out
r
QeXt is the external
self-oscillating ‘IF
as
(WO + A~ sinti~t)
e=. @
(6) where KI and Kz are constants. Therefore, the power at the w~, P1~ is
Adler’s
of ~~ as the modulation
frequency approaches the relaxation frequency of RF energy in the self-oscillating mixer, which normally lies around 1 GHz for J-band devices [17]. One would expect the relaxation frequency to increase for higher frequency devices, as has been already reported for Q-band devices [6]. Adler’s equation [8] can be extended such as to allow the self-oscillating mixer to be frequency modulated by Aa by the small injected signal. Under this assumption, we can
shows
that
@ undergoes
does not converge
a periodic
to a constant
differential equation ward, but since
value.
(10), the solution
variation
However, is not
and
for our
straightfor-
iaE