1109
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MTT-30, NO. 7, JULY 1982
[5]
L, A, Weinstein, “The Theory of Diffraction Metiod~ in Generalized WzenerHopf Technique.
and the Factorization
Boulder, CO: Golem, 1969. S. W. Lee, W. R. Jones, and J. J. Campbell, “Convergence of numericrd solutions of iris-type discontinuity problems,” IEEE Trans. Microwaoe Theory Tech., vol. MTT- 19, pp. 528–536, June 1971.
[6]
(a)
(b)
Exact Derivation of the Nonlinear Negative-Resistance Oscillator Pulling Figure J. OBREGON Abstract figure
— Only approximate
of an oscillator.
AND A. P. S. KHANNA relations
are so far available
An exact derivation
of the pnlling
here, tafdng fufly into account the nonlinearity Effect
of the oscillator
nonlinearity
for the pufling
of the oscillator
on the asymmetry
(c)
figure is presented Fig,
admittance.
of the pulling
1.
Simulation
is presented.
and I.
INTRODUCTION
dBTo
ABL+ Oscillator
frequency
represented been
either
with
the
approximately the oscillator
taking
voltage
into
derivation
the nonlinear
relation
between Pulling
The pulling
the transferred perturbation figure
admittance
particular
calculated
by
admittance
in
fully
admittance.
of the oscillator
certain
has so far
AYL=AGL+ABL and
pulling
Y~o = G~o + BTO.
into The
From
cases are also pre-
FREQUENCY VARIATION WITH THE LOAD
The oscillation
condition
any load perturbation
at the oscillator-output
is represented
AGL% Au=
dGTo dBTo _ dGTO dBTo —. —— — dV do do “ dV
Y~ is the oscillator
nonlinear
dG ABL. ~
CHANGES
—
plane without
dGTo dBTo dGTo dBTo —— .— .— dv da dw dV
by
YTO=YT+YO=O where
(4) and (5)
range
has been de-
sented. 11.
(1)
output
admittance
and YO is
If the oscillations output
ing frequency
dG ABL. ~ exist with
and RF voltage
of A YL in the
Au and A~ as the correspond-
changes,
the oscillation
condition
Av=
do
Au
+
dY -#
AGL. ~
Av=o.
—
(2)
real and imaginary
dGTo
AGL + ~Aco+
III. From
parts
LOAD VARIATION
(4)
tion of AG by suitably line between
the oscillator
of the exact derivation Manuscript received November 18, 198 1; revised February 9, 1982. The authors are with Laboratoire d%fectronique des Microndes, E.R.A. au C.N.R.S., U.E.R. des Sciences, 123 rue Albert-Thomas, 87060 Limoges, Cedex, France.
0018-9480/82/0700-1
selecting
the reference figure,
For the purposes
we simulate
the load
the transmission-line
For any value of b’ = I?l, the transferred
IEEE
load perturba-
plane in the output
and the perturbation.
perturbation by AG (Fig. 1(b)) with variable between O and ~ /2.
109$00.7501982
load perturbation
by a nonreactive
of the pulling
(7)
SIMULATION
Fig. 1 it can be noted that any reactive
of value jA B cm be represented
dGTo ~Av=O
dGTo _dBTo “
dGTo dBTo dV”dudm”dV
(1) and (2)
into
dV dBTo
“~o
(3) separating
dGTo . _dBTo
dGTo — dBr-o —. dV do
by
Y~o+AYL+z. From
a load perturbation
plane and writing
can be represented
(6)
and
the load admittance. oscillator
(5)
where
admittance
taking
dBTO ~v=o
~Au+
is often
[2]. We present
of the oscillator
of the oscillator for
figure
the oscillator
of the pulling
the asymmetry
figures
changes
[1] or has been
account
behavior
the nonlinearity
the load
neglecting
for a small-load
account
rived.
with
figure.
by
RF
plane
here an exact
and
variation
by its pulling
calculated
variation
of load variation.
range
load admittance
length
1
YL at