n this letter, the global stability analysis of an L-band push-pull power amplifier is presented. The analysis is carried out for the amplifier operating in different modes, such as Class AB, Class B, and Class E/F, considering variations in the bias voltages, the input power and the input frequency. After determination of the oscillation mode, three different stabilization techniques are applied and compared: feedback resistors, neutralization capacitors, and odd-mode stabilization resistor. The element values of each stabilization network, ensuring a stable behavior for all the operating conditions, are calculated with a bifurcation-analysis technique. Good agreement is found between measured and simulated results

Rutledge, David B.

Suárez, Almudena

Wang, Feiyu

English

Caltech Authors - Main

Bifurcation analysis of stabilization circuits in an L-band LDMOS 60-W power amplifier

712 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 15, NO. 10, OCTOBER 2005
Bifurcation Analysis of Stabilization Circuits in an
L-Band LDMOS 60-W Power Amplifier
Feiyu Wang, Student Member, IEEE, Almudena Suárez, Senior Member, IEEE, and David B. Rutledge, Fellow, IEEE
Abstract—In this letter, the global stability analysis of an L–band
push-pull power amplifier is presented. The analysis is carried out
for the amplifier operating in different modes, such as Class AB,
Class B, and Class E/F, considering variations in the bias volt-
ages, the input power and the input frequency. After determina-
tion of the oscillation mode, three different stabilization techniques
are applied and compared: feedback resistors, neutralization ca-
pacitors, and odd-mode stabilization resistor. The element values
of each stabilization network, ensuring a stable behavior for all
the operating conditions, are calculated with a bifurcation-analysis
technique. Good agreement is found between measured and simu-
lated results.
Index Terms—Bifurcation, push-pull power amplifier, stability
analysis, stabilization.
I. INTRODUCTION
POWER amplifiers are likely to exhibit instabilities, leadingto oscillations at sub-harmonic or incommensurate fre-
quencies [1]–[5]. The oscillations can be associated with
negative resistance exhibited by the nonlinear capacitances,
and also to gain increase versus the input power and undesired
feedback. These oscillations, occurring from a certain level of
input power, cannot be detected with conventional techniques,
based on the -factor. Their prediction requires a large-signal
stability analysis of the steady-state solution. Different tech-
niques [1]–[5], based on harmonic balance (HB), have been
proposed for this analysis. In case of variation of circuit pa-
rameters, the boundary between stable and unstable operation
can be efficiently determined through bifurcation detection
on HB [1], [5]. In general, the amplifier will operate under
different values of bias voltages and different input frequency
and power, so the bifurcation analysis should be carried out
in terms of all significant operation parameters. This global
analysis will be applied here to a push-pull power amplifier,
in the band from 1.1 to 1.3 GHz. The actual design goal will
be the stabilization of the amplifier, and the knowledge of the
instability regions in the parameter space, together with the
analysis of the oscillation mode, will be helpful to devise a
proper stabilization technique. Three different techniques will
be considered here, based on the use of odd-mode stabilization
resistor, neutralization capacitors, and feedback resistors. The
Manuscript received May 18, 2005; revised July 6, 2005. This work was sup-
ported in part by the Jet Propulsion Laboratory and the Lee Center for Advanced
Networking.
F. Wang and D. B. Rutledge are with the Department of Electrical Engi-
neering, California Institute of Technology, Pasadena, CA 91125 USA (e-mail:
feiyu@caltech.edu; rutledge@caltech.edu).
A. Suárez is with the Communications Engineering Department, University
of Cantabria, Santander 39005, Spain (e-mail: suareza@unican.es).
Digital Object Identifier 10.1109/LMWC.2005.856830
Fig. 1. Simplified schematic of the Class E=F amplifier.
use of bifurcation analysis enables efficient determination of
the element values of each stabilization network. The perfor-
mances of the resulting stabilized amplifiers will be compared,
in terms of output power and efficiency.
II. STABILITY ANALYSIS OF THE PUSH-PULL AMPLIFIER
Fig. 1 shows the simplified schematic of our push-pull ampli-
fier. The amplifier is optimized for a Class- operation
[6], [7]. When backing off from deep nonlinear regions, it can
also be operated in other modes, such as Class AB, and Class
B. When operating in the Class- mode, this amplifier
has zero-voltage switching like a Class-E amplifier, while the
odd harmonics and the second harmonic are terminated like a
Class- amplifier.
The amplifier contains four parameters that can be varied:
gate-bias voltage , drain-bias voltage , input power ,
and input frequency . For some operation conditions, the
pole-zero identification technique [2] predicts an oscillation at
about 200 MHz. For a global determination of the unstable op-
eration ranges on HB, a bifurcation-analysis technique will be
used, providing the oscillation boundaries in terms of , ,
, and . A small-signal current generator at the frequency
, nonharmonically related with the input-drive frequency ,
is introduced into the circuit at the gate terminal of one of the
transistors. The generator enables the definition of an admit-
tance function , given by the current-voltage ratio, which is
calculated with the conversion-matrix approach [4]. Then, the
bifurcation condition is given by 0. First, the plane defined
by and is considered. For a given and the oscil-
lation boundary is obtained from
(1)
1531-1309/$20.00 © 2005 IEEE
WANG et al.: BIFURCATION ANALYSIS OF STABILIZATION CIRCUITS 713
Fig. 2. Boundaries between the stable and unstable regions based on global-
stability analysis of the amplifier, for different operation conditions. Lines
indicate simulation results, and markers indicate measurement points. (a) In
the plane defined by f and P . (b) In the plane defined by V and V .
The above system is solved through error-minimization or opti-
mization procedures, combining HB and the conversion-matrix
approach. The analysis is performed for different and con-
stant 3 V, obtaining the loci of Fig. 2(a). The frequency
is swept, calculating, at each step, and the oscillation
frequency , which varies along the locus. As confirmed by
pole-zero identification, the instability occurs at medium input
power, where the gain is the highest. As the drain-bias voltage
increases, the instability region shrinks due to reduced feedback
through the gate-drain capacitance ( ). For 1.14 GHz,
no instability is obtained at any of the considered bias voltages.
Measurements are superimposed.
The second analysis is carried out in the plane defined by
and [see Fig. 2(b)] solving
(2)
Constant 1.03 GHz and two typical operation values
have been considered, with the results of Fig. 2(b). In agree-
ment with the pole-zero identification technique, the amplifier
is unstable inside the different loci. The unstable behavior is
observed in different operating modes: Class AB, Class B,
and Class C. However, the instability region is smaller for the
Class-C operation, which corresponds to lower . At higher
, oscillation vanishes due to smaller feedback capacitance.
TABLE I
PHASES OF VOLTAGES AT THE GATE AND DRAIN TERMINALS
Fig. 3. (a) Stabilization with an odd-mode stabilization resistor. Typical
operation conditions have been considered in these simulations. (b) Stabilization
with neutralization capacitors using bifurcation loci.
III. STABILIZATION TECHNIQUES
The nature of the oscillation has been investigated obtaining
the steady-state solution within the unstable regions, where the
amplifier behaves as a self-oscillating mixer, at the two fun-
damental frequencies and . An auxiliary generator (AG)
has been used, in order to avoid the HB convergence to the
unstable periodic solution at [1]. The transistor harmonic
voltages at the input-drive and oscillation frequencies are com-
pared in Table I, for 3.5 V, 7 V, 3 W,
1030 MHz. The voltages exhibit a phase difference close to
180 at both and . Thus, there is an odd-mode oscilla-
tion. In the following, three different stabilization techniques
will be considered.
A. Stabilization With an Odd-Mode Stabilization Resistor
The odd-mode oscillation can be eliminated through the con-
nection of a resistor between the gate terminals of the two tran-
sistors. The maximum allowed value for the stabilization re-
sistor is obtained by tracing the oscillation boundary in the
plane defined by and one of the four circuit parameters. In
714 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 15, NO. 10, OCTOBER 2005
Fig. 4. (a) Simulated amplifier performance after applying three different
stabilization techniques. (b) Measured amplifier performance before and after
applying odd-mode stabilization resistor of 150 
.
the analysis of Fig. 3(a), the considered parameter is and
the oscillation boundary is determined for different and bias
values. The amplifier is unstable on the right-hand side of the
represented loci. Note that the selected bias values correspond
to the edges of the operation intervals. Due to the continuity
of the system, this provides information about the required re-
sistance for a general stabilization of the amplifier, for all the
operation conditions. In order to avoid the instability, the am-
plifier must operate outside the instability regions for all the
values. Thus, the maximum allowed value for the stabilization
resistance is 200 .
B. Stabilization With Neutralization Capacitors
In push-pull configurations, neutralization capacitors can be
connected between the gate and drain terminals of the oppo-
site transistors to cancel undesired feedback through . Effec-
tively, a negative capacitance is added in parallel. To determine
the minimum capacitance value required for stable operation,
the oscillation boundary will be traced on the plane defined by
and , considering different values and bias conditions.
For clarity, only two loci have been represented in Fig. 3(b). To
ensure stable behavior for all the operating conditions, the en-
tire set of bifurcation loci must be taken into account. From this
global analysis, the neutralization capacitance should be larger
than 25 pF.
C. Stabilization With Feedback Resistors
In order to reduce the positive feedback, a resistor and a
dc-blocking capacitor are connected between the gate and the
drain terminals of the same transistor. Only limited power is
dissipated, as parasitic inductances of the two elements provide
high impedance at , which is about five times the oscillation
frequency. These parasitic inductances do not have a significant
effect on the feedback resistance at . The bifurcation-anal-
ysis technique indicates the maximum value of stabilization
resistance of 90 .
D. Comparison of Performance
Fig. 4(a) shows the comparison of the stabilized-amplifier
performance for the three different stabilization techniques. The
resistive stabilization techniques show little change in perfor-
mance. The neutralization capacitors improve the gain of the
amplifier by about 2 dB, but the PAE is reduced by 6%. In this
particular amplifier, neutralization is not easy to implement due
to layout constraints. The odd-mode resistor is implemented in
the amplifier. Fig. 4(b) shows the gain and the PAE at 1210 MHz
before and after applying the odd-mode stabilization. The mea-
sured performances are almost identical.
IV. CONCLUSION
In this letter, the global stability analysis of an LDMOS am-
plifier has been presented. Four parameters–two bias voltages,
the input power and the input frequency–have been considered.
After determination of the oscillation mode, three different sta-
bilization techniques have been compared. For each approach,
the values of the stabilization elements ensuring stable behavior
for all the operation conditions have been determined through
bifurcation analysis.
ACKNOWLEDGMENT
The authors would like to thank S. Weinreb, C. Andricos,
W. Edelstein, A. Moussessian, Jet Propulsion Laboratory,
K. Potter and S. Jeon, California Institute of Technology, and
J.-M. Collantes, University of the Basque Country (Spain), for
their advice and discussions.
REFERENCES
[1] A. Suárez and R. Queré, Global Stability Analysis of Microwave Cir-
cuits. Boston, MA: Artech House, 2003.
[2] A. Anakabe, J. M. Collantes, J. Portilla, J. Jugo, S. Mons, A. Mallet,
and L. Lapierre, “Analysis of odd-mode parametric oscillations in HBT
multi-stage power amplifiers,” in Proc. EuMW 11th GAAS Symp., Mu-
nich, Germany, Oct. 2003, pp. .533–536.
[3] A. Collado, F. Ramírez, and A. Suárez, “Analysis and stabilization tools
for microwave amplifiers,” in IEEE MTT-S Int. Dig., Fort Worth, TX,
Jun. 2004, pp. .945–948.
[4] S. Jeon, A. Suárez, and D. B. Rutledge, “Global stability analysis and
stabilization of a class-E/F amplifier,” IEEE Trans. Microw. Theory
Tech., to be published.
[5] , “Analysis and elimination of hysteresis and noisy precursors in
power amplifiers,” IEEE Trans. Microw. Theory Tech., to be published.
[6] S. Kee, I. Aoki, A. Hajimiri, and D. B. Rutledge, “The class-E/F family
of ZVS switching amplifiers,” IEEE Trans. Microw. Theory Tech., vol.
51, no. 6, pp. 1677–1690, Jun. 2003.
[7] F. Wang and D. B. Rutledge, “A 60-W L-band class-E=F LDMOS
power amplifier using compact multilayered baluns,” in Proc. IEEE
Topical Workshop Power Amplifiers for Wireless Communications, San
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Bifurcation analysis of stabilization circuits in an L-band LDMOS 60-W power amplifier

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