Gain–Bandwidth Limitations of Microwave
Transistor
Filiz Güneş1 Cemal Tepe2
1
Department of Electronic and Communication Engineering, Yıldız Technical University, Beşiktaş
80750, Istanbul, Turkey
2
Alcatel, 5501 Reunion Point, #304, Raleigh, North Carolina 27609
Received 14 June 2001; accepted 28 February 2002
ABSTRACT: This work enables one to obtain the potential gain (GT) characteristics with the
associated source (ZS) and load (ZL) termination functions, depending upon the input mismatching (Vi), noise (F), and the device operation parameters, which are the configuration
type (CT), bias conditions (VDS, IDS), and operation frequency (f). All these functions can
straightforwardly provide the following main properties of the device for use in the design of
microwave amplifiers with optimum performance: the extremum gain functions (GT max,
GT min) and their associated ZS, ZL terminations for the Vi and F couple and the CT, VDS, IDS,
and f operation parameters of the device point by point; all the compatible performance (F,
voltage–standing wave ratio Vi, GT) triplets within the physical limits of the device, which are
F > Fmin, Vi > 1, GT min < GT < GT max, together with their ZS, ZL termination functions; and
the potential operation frequency bandwidth for a selected performance (F, Vi , GT) triplet.
The selected performance triplet and termination functions can be realized together with their
potential operation bandwidth using the novel amplifier design techniques. Many examples
are presented for the potential gain characteristics of the chosen low-noise or ordinary types
of transistor. © 2002 Wiley Periodicals, Inc. Int J RF and Microwave CAE 12: 483– 495, 2002. Published
online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mmce.10049
Keywords: transducer power gain; input voltage–standing wave ratio; noise figure; source
termination; load termination
I. INTRODUCTION
The characterization of active microwave devices and
design of the wide-band microwave amplifiers are
among major interests in communication engineering.
Especially in designing microwave amplifiers, many
sophisticated numerical methods are utilized to optimize system performance. Generally, the optimization
is focused on the transducer power gain (G T ) over the
frequency band of operation without controlling the
other performance criteria such as the noise (F), the
input voltage–standing wave ratio (VSWR, V i ), and
the output VSWR (V o ). It should also be mentioned
Correspondence to: Dr. F. Güneş; e-mail: gunes@yildiz.edu.tr.
that the optimization process of the performance is
highly nonlinear in terms of the descriptive parameters of the system. Certainly, within the optimization
process, one can easily embed the desired performance goals without knowing the physical limits
and/or compromise relations among F, V i , and G T
appropriately. Unfortunately, this process often fails
to attain the desired goals. However, the complete
performance characterization of a microwave transistor overcomes all the above-mentioned handicaps.
In this work the upper (G T max) and lower (G T min)
gain bounds are easily obtained for the chosen noise
F ⱖ F min and V i ⱖ 1 pairs point by point in the
operation domain of the transistor. Furthermore, one
can have all the interrelations among the performance
© 2002 Wiley Periodicals, Inc.
483
484
Güneş and Tepe
Figure 1. A neural block diagram of the gain– bandwidth limitations of a microwave transistor.
measure components F, V i , G T for determined bias
conditions (V DS, I DS) and operation frequency ( f )
condition set. These can give all the necessary information to design a microwave amplifier with optimum
performance because the F, V i , and G T can be determined only by the active devices in the amplifier
circuits with the lossless and reciprocal matching circuits.
Two approaches can be followed in the utilization
of the (F, V i , G T ) triplet and the Z L, Z S functions in
the design of the microwave amplifier circuits:
1. Only the (F, V i , G T ) triplet function can be
employed to provide the reference values over
the predetermined bandwidth to the optimization process of the element parameters of the
front- and back-end matching networks that was
recently applied and completed by Aliyev [1].
2. In the second approach only the Z S, Z L termination functions can be employed in the design
of the front- and back-end matching networks,
respectively, to obtain the corresponding performance (F, V i , G T ) triplet over the predetermined bandwidth. Yarman and Aksen [2] recently completed an immitance-based tool to
model passive one-port devices by means of
Darlington equivalents.
On the other hand, it is well known that modeling
problems of the behaviors of linear and nonlinear
elements and circuits in RF and microwave systems
are very complicated and large scale. Therefore, in the
last few years artificial neural network techniques
have been developed and applied to the RF and microwave areas as the solution methods for these types
of problems [3–5].
This work can be described in three main stages
(Fig. 1): In the first stage the signal and noise behaviors of the small-signal transistor are modeled by a
multiple bias and configuration, signal–noise neural
network so that the scattering (S) and noise (N)
parameters can result from the output of this neutral
network as the functions of the configuration type
(CT), the V DS, I DS, and the f. This part of the work
can be considered as the function approximation
through the neural network technique, and it includes
highly accurate approximations of the eight scattering
and four noise functions [6, 7].
The second stage consists of determining the compatible performance (F req, V i req, G T req) triplets and
their associated source (Z S req) and load (Z L req) terminations. In this part of the work the performance
characterization theory of the transistor is employed,
the details of which are given in [8] and [9] using,
respectively, the impedance [8] and scattering parameter [9] approaches. The input of the second block is
the S and N parameters resulting from the signal–
noise neural network, and the free variables of F req ⱖ
F min, V i req ⱖ 1, and G T min ⱕ G T req ⱕ G T max. The
second block results in the following triplet and termination data in the operation domain of the device:
共Freq, Vi req, GT max兲 N ZS max ⫽ RS max ⫹ jXS max;
ZL max ⫽ RL max ⫹ jXL max;
Gain–Bandwidth Limitations
485
Figure 2. A two-port model of a small-signal microwave transistor.
共F req, Vi req, GT min兲 N ZS min ⫽ RS min ⫹ jXS min;
ZL min ⫽ RL min ⫹ jXL min;
共F req, Vi req, GT req兲 N ZS req ⫽ RS req ⫹ jXS req;
ZL req ⫽ RL req ⫹ jXL req.
equations in the operation domain of the active device:
F⫽
RN 兩ZS ⫺ Zopt兩2
共S/N兲 i
⫽ F兵R S, XS其 ⫽ Fmin ⫹
;
共S/N兲 O
兩Zopt兩2
RS
(1)
The third stage of the work is to obtain the gain–
bandwidth limitations of a small-signal microwave
transistor, depending on the other performance components F, V i in the operation domain (CT, V DS, I DS).
The originality of the work presented in this article is
essentially based upon this final stage of the work.
The motivation underlying this is mainly to put forward new design methods based upon active device
characterization for microwave amplifiers. These
methods can employ the resulting (F, V i , G T ) triplet
or Z L, Z S termination functions in the design of microwave amplifiers in narrow, medium, or broad
bands, so that the optimization processes can be applied in a more deterministic and analytical manner
[10].
In the next section the performance characterization of the device is briefly considered as the center of
the gain– bandwidth limitations.
II. COMPATIBLE PERFORMANCE (F, Vi,
GT) TRIPLETS AND (ZS, ZL)
TERMINATIONS
A. Two-Port Representation of
Microwave Transistor and Performance
Measure Functions
All the performance (F, V i , G T ) triplets and their
source Z S ⫽ R S ⫹ jX S and load Z L ⫽ R L ⫹ jX L
terminations can be obtained from simultaneously
solving the following three nonlinear performance
1 ⫹ 兩␳i 兩2
input VSWR ⫽ Vi ⫽ Vi 兵RS, XS, RL, XL其 ⫽
,
1 ⫺ 兩␳i 兩2
␳i ⫽
GT ⫽
⫽
ZS ⫺ Z*i
;
ZS ⫹ Zi
(2)
PL
⫽ G兵R S, X S, R L, X L其
PAVS
4R SRL
.
兩共z11 ⫹ ZS兲共 z22 ⫹ ZL兲 ⫺ z12 z21 兩2
(3)
The solution subsets {Z S, Z L/R S ⬎ 0, R L ⬎ 0} in
which we are interested are the sets that ensure stable
working of the transistor within its physical limitations:
Re兵Zi 其 ⬎ 0,
G T min ⱕ GT ⱕ GT max,
Re兵ZO 其 ⬎ 0;
(4a)
Vi ⱖ 1,
(4b)
F ⱖ Fmin.
Figure 2 presents a two-port representation for a transistor with its impedance ( z) and noise parameters.
The V ⫺ I equations of the transistor can be written
in the form
冋 VV 册 ⫽ 冋 zz
1
11
2
21
z 12
z 22
册冋 II 册 .
1
2
(5)
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Güneş and Tepe
Furthermore, the termination equations and the Z i and
Z o impedances of the transistor can be given as
V 2 ⫽ ⫺I2 ZL,
V1 ⫽ VS ⫺ I1 ZS;
(6)
兩Z S ⫺ Zcv 兩 ⫽ rv ,
Zi ⫽
V1
z 12z 21
⫽ z 11 ⫺
;
I1
z 22 ⫹ Z L
(7a)
Zo ⫽
V2
z 12z 21
⫽ z 22 ⫺
.
I2
z 11 ⫹ Z S
(7b)
The problem of the physical limitations can be described as a mathematically constrained extremum
problem, which is to find the extremum stable values
of the function G{R S, X S, R L, X L} subject to ␾ 1 ⫽
F req ⫺ F(R S, X S) ⫽ 0, ␾ 2 ⫽ V i req ⫺ V i (R S, X S, R L,
X L) ⫽ 0, and the corresponding values of the source
and load terminations Z S ⫽ R S ⫹ jX S, Z L ⫽ R L ⫹
jX L, where F req ⱕ F min, V i req ⱖ 1 are the required
noise figure and the input VSWR, respectively. Here
an analysis based on a geometrical method [8, 9] is
employed to solve this constrained extremum problem. The fundamentals of this geometrical method are
given in the following subsection.
B. Performance Characterization
Here all the possible (F req, V i req, G T ) triplets and
their (Z S, Z L) terminations are determined using z
parameters in the Z S and Z i planes.
Noise Figure, Input VSWR, and Gain in ZS Plane.
The variations of the noise figure, input VSWR, and
gain in the Z S plane can be briefly described. All the
source Z S ⫽ R S ⫹ jX S terminations that satisfy
F{R S, X S} ⫽ F req take place on the circle of
兩Z S ⫺ Zcn 兩 ⫽ rn ,
(8a)
where Z cn is the center phasor and r n is the radius,
which can be given as
Z cn ⫽ R opt ⫹ N ⫹ jXopt,
rn ⫽ 冑N共N ⫹ 2Ropt兲,
(8b)
where
N⫽
F req ⫺ Fmin
兩Zopt兩2 .
2RN
All the source Z S ⫽ R S ⫹ jX S terminations that
satisfy V i (R S, X S, R L, X L) ⫽ V i req for a fixed passive
load Z L take place on the circle of
(8c)
So all the Z s values satisfying the other required
components of performance, V i req and G T req, must be
chosen among the Z s values on the F ⫽ F req noise
circle.
where Z cv is the center phasor and r v is the radius of
Z cv ⫽
1 ⫹ 兩 ␳ i兩 2
R ⫺ jX i,
1 ⫺ 兩 ␳ i兩 2 i
rv ⫽ 2
兩 ␳ i兩
R.
1 ⫺ 兩 ␳ i兩 2 i
(9)
A V i ⫽ V i req circle corresponds to a constant gain
circle for a fixed load Z L, which can be expressed
using eqs. (2) and (3) as
G T ⫽ 共1 ⫺ 兩 ␳ i兩 2兲
R L 兩z21 兩2
.
Ri 兩z22 ⫹ ZL兩2
(10)
Therefore, only the required noise and the input
VSWR circles are sufficient to be taken into account
in the Z S plane. As already shown, while the required
noise circle is fixed in the Z S plane the required input
VSWR circle can travel, depending on the load impedance Z L, via the input impedance Z i in a manner
given by the center and radius relations in eq. (9).
Thus, the following situations are possible: these circles may not touch, they become tangential, or they
cut each other (Fig. 3). In the following section, each
of these positions is controlled from the Z i plane.
Solution Regions and Control Parameter Zi. The
solution regions in the Z i plane are now briefly summarized (Fig. 4). Because both the external and internal tangential positions are the transition positions
between the solution and no-solution positions, these
positions must first be controlled from the Z i plane via
the following general equation in the Z S plane:
兩Z cn ⫺ Z cv兩 2 ⫽ 共r n ⫾ r v兲 2.
(11)
Substituting the Z cn , r n , Z cv , r v expressions in eqs.
(8a), (8b), and (9) into the above equation, another
couple of circle equations that represent the two different tangent positions of the noise and the input
VSWR circles in the Z S plane can be obtained in the
Z i plane.
The center phasors Z ct1 , Z ct2 and radii r t1 and r t2
of the circles, which are the mappings of the external
and internal tangent positions in the Z S plane, respectively, can be given as follows:
Z ct1 ⫽ R cnU ⫹ r nV ⫺ jX opt,
rt1 ⫽ 冑兩Zct1 兩2 ⫺ 兩Zopt兩2 N T1 circle
共region 2兲;
(12)
Gain–Bandwidth Limitations
487
Figure 3. The positions of the input VSWR circles with respect to the noise circle in the Z S plane
controlled by the regions in Figure 4.
Z ct2 ⫽ R cnU ⫺ r nV ⫺ jX opt,
rt2 ⫽ 冑兩Zct2 兩2 ⫺ 兩Zopt兩2 N T2 circle
共region 4兲
(13)
where U and V are given by
U⫽
1 ⫹ 兩 ␳ i兩 2
,
1 ⫺ 兩 ␳ i兩 2
V⫽
兩 ␳ i兩
.
1 ⫺ 兩 ␳ i兩 2
(14)
As seen from eqs. (12) and (13), the centers of the T 1
and T 2 circles lie on the same imaginary axis, (X opt),
and it can also be proved that circle T 2 is always
situated inside circle T 1 without touching as shown in
Figure 4.
All the Z i values ensuring intersection positions of
both the noise and input VSWR circles in the Z S plane
are situated in region 3 between the T 1 and T 2 circles
in the Z i plane, which is shown in Figures 3 and 4.
The remaining regions numbered 1 and 5, which
are the outermost and innermost regions, respectively,
are impossible solution regions that include Z i values
controlling all the nontouching positions in the Z S
plane (Figs. 3, 4).
In order to find physically realizable solutions, the
unconditionally stable working area (USWA) and the
gain circles constrained by the V i req must also be
constructed in the Z i plane, so the design configuration will have been formed in the Z i plane.
Gain Circles in Zi Plane Constrained by Input
VSWR. The constant gain circles constrained by the
V i req can be formed using eq. (10), which is different
for the two stability cases. In the unconditional stability case, the necessary and sufficient conditions can
be given as
r 11 ⬎ 0,
r 22 ⬎ 0,
2r11 r22 ⫺ r ⬎ 兩z兩;
(15a)
i ⫽ 1, 2; z ⫽ z12 z21 ⫽ r ⫹ jx.
(15b)
and
where
r ii ⫽ Re兵 zii 其,
In the absolute stability case, all the passive impedances can be employed as either source or load terminations and the USWA is the area inside the G T ⫽
0 circle. The center phasors Z cg ⫽ R cg ⫹ jX cg and
488
Güneş and Tepe
Figure 4. The solution geometry of the constrained maximum gain for the unconditional stability
case.
radii r g of the gain circles in this stability case can be
expressed in terms of z parameters, G T , and 兩 ␳ i 兩 2 as
follows:
Z cg ⫽
1
1
共Q ⫺ P兲 ⫹ j
共2x 11r 22 ⫺ x兲;
r 22
r 22
(16a)
1
冑P 2 ⫺ 2QP ⫹ 兩z兩 2;
r 22
(16b)
rg ⫽
P⫽
兩z 12兩 2G T
,
1 ⫺ 兩 ␳ i兩 2
Q ⫽ 2r 11r 22 ⫺ r.
(16c)
It can be seen from eqs. (16a)–(16c) that R cg
decreases with the increase of G T req ⱕ G T max when
X cg remains constant (Fig. 4) and the G T max is only
achieved at the point where the r g equals zero. Setting
r g to zero in eq. (16b) gives
G T max ⫽ 兵Q ⫺ 冑Q2 ⫺ 兩z兩2 其
1 ⫺ 兩␳i 兩2
,
兩z12 兩2
(17)
which is only achieved when the device is absolutely
stable; otherwise the square root in (17) becomes
negative because conditions are given by (15a) and
(15b). The Z i max input impedance providing G T max
can be found by substituting (17) into (16a) as follows:
Z i max ⫽ Zcg max ⫽ Rcg max ⫹ jXcg ,
Rcg max ⫽
1
共Q2 ⫺ 兩z兩2 兲.
r22
(18)
The minimum gain limit circle is the G T ⫽ 0 circle N
input stability circle whose center phasor Z cg min ⫽
R cg min ⫹ jX cg min and r g min can be given as follows:
Gain–Bandwidth Limitations
489
Figure 5. Constant gain circles in the Z i plane for a conditionally stable transistor.
R cg min ⫽
Q
,
2r22
Xcg min ⫽ Xcg ,
rg min ⫽
兩z兩
.
2r22
where
(19)
Because Q is greater than 兩z兩 for the absolutely stable
device, R cg min is greater than r g min, which results in
the G T ⫽ 0 circle being entirely in the right half of the
Z i plane with the positive real part and enclosing all
the circles for G T ⬎ 0 (Fig. 4).
In the case of the gain circles of the conditionally
stable transistor, the USWA is the region between the
input and conjugate source stability circles. The constrained gain formula eq. (10) can be rearranged in
terms of the radius and center of the source plane
stability circle as
兩Z i兩 2 ⫹ 2共R cs ⫹ S兲 R i ⫹ 2X csX i ⫹ 兩Z cs兩 2 ⫺ r 2s ⫽ 0,
(20)
S⫽
兩z 12兩 2G T
,
2r 22共1 ⫺ 兩 ␳ i兩 2兲
(21)
where Z cs ⫽ R cs ⫹ jX cs and r s are the center and
radius of the source plane stability circle, respectively,
which can be written as follows:
R cs ⫽ ⫺
2r11 r22 ⫺ r
,
2r22
Xcs ⫽ ⫺
2x11 r22 ⫺ r
,
2r22
rs ⫽
兩Z兩
.
2r22
(22)
Thus, the center Z cg ⫽ R cg ⫹ jX cg and the r g of the
gain circle family will be
490
Güneş and Tepe
plane (shaded area in Fig. 5), and the center phasors of
these circles are always on the line X i ⫽ ⫺X cs . It
should be noted that in the case of unconditional
stability, all the G T circles are situated entirely in the
right half of the Z i plane. In the conditionally stable
case, the maximum gain will be obtained on the arc of
the conjugate stability circle remaining in the positive
real Z i plane. It can be found by substituting R cg ⫽
R cs in eq. (23). Referring to eq. (22), the maximum
gain subject to the V i can be expressed for the conditional stability case as
GT ⫽ 2
1 ⫺ 兩 ␳ i兩 2
共2r 11r 22 ⫺ r兲;
兩z 12兩 2
(24)
and, setting 兩 ␳ i 兩 ⫽ 0, eq. (24) yields the maximum
stable gain (MSG),
MSG ⫽ 2
冏 冏
z21
␩,
z12
(25)
where ␩ is the stability factor,
␩⫽
2r 11r 12 ⫺ r
.
兩z兩
(26)
For conditionally stable cases, it has values between
zero and unity (0 ⬍ ␩ ⬍ 1).
C. Design Configuration and
Performance (Freq, Vi req, GT req) Triplets
Figure 6. The G T max variations for the NE38018 transistor. [Color figure can be viewed in the online issue, which
is available at www.interscience.wiley.com.]
R cg ⫽ ⫺共Rcs ⫹ S兲,
Xcg ⫽ ⫺Xcs ,
rg ⫽ 共S2 ⫹ 2SRcs ⫹ r2s 兲.
(23)
The features of the G T circles, which can be derived from eqs. (20)–(23), can be ordered (Fig. 5). All
G T circles cut the imaginary axis at the same points,
which are the intersection points of the conjugate of
the source plane stability circle with the same axis.
The G T ⫽ 0 circle, whose center is Z cg min ⫽
⫺R cs ⫺ jX cs with r g min ⫽ r s , is symmetrical with
the conjugate of the stability circle with respect to the
imaginary axis. The G T max ⬎ G T ⬎ 0 circles always
take place in the area bounded by the G T ⫽ 0 circle
and the arc of the conjugate of the stability circle
remaining in the right half of the input impedance
Using the performance theory given briefly above, for
a small-signal transistor with the given operation conditions and the required noise F req and V i req, the basic
performance measure function given by eqs. (1)–(3)
can be represented in a geometrical configuration in
the Z i plane. This configuration may be called the
design configuration, which consists of the USWR,
the T 1 and T 2 circles, and the constrained gain family.
In this design configuration all the physically possible
(F req, V i req, G T ) triplets of the microwave transistor
must take place in the intersection areas of possible
solution regions 2, 3, and 4 with the USWA of the
transistor. Therefore, no physical solution can exist
for the G T constrained by the F req and V i req when the
USWA takes place completely in region 1 or 5.
The determination processes for the required (F req,
V i req, G T ) triplets with G T min ⱕ G T ⱕ G T max
among the infinite number of possible triplets are
again based on the geometrical analyses [8, 9], depending on the type of design configuration.
Gain–Bandwidth Limitations
491
Figure 7. The G T max ⫺ f curves for the NE02135 transistor. [Color figure can be viewed in the
online issue, which is available at www.interscience.wiley.com.]
A compact computer program was completed in
[11] to obtain all the physically possible (F req, V i req,
G T ) triplets and the (Z S, Z L) terminations as functions
of the device operation parameters CT, V DS, I DS, and
f. These functions can be employed in the manufacturer’s data sheets of the transistor to give full information to the designer of the active microwave circuits. The next section focuses on the constrained gain
characteristics. Then the gain– bandwidth limitations
are determined, depending on the other performance
components (F req, V i req), operation conditions (CT,
V DS, I DS, f ), and the magnitude of the gain itself.
of I D ⫽ 10 mA and the same values of the other
performance components (V i req, F req).
In the second step the effect of noise on the gain
performance is given by the G T max ⫺ f curves at
III. POTENTIAL GAIN
CHARACTERISTICS
For the potential gain characteristics, three typical
microwave transistors are employed. Two of them are
low-noise application transistors (NE38018 and
NE329S01); the other is an ordinary transistor
(NE02135). Thus, the characteristics can be discussed
in three steps.
In the first step the effect of the bias condition on
the gain performance is given by G T max (dB) ⫺ I D
(mA) characteristics at F req ⫽ 0.5 dB; V i req ⫽ 1, 1.5,
and 2; f ⫽ 1 GHz for NE38018 [Fig. 6(a)]. Concerning these curves, for an efficient gain performance the
transistor must have a bias current (I D ) that is greater
than a certain I DT value, and the effect of change in
the input mismatching is around 1 dB at most. In
Figure 6(b) the G T max (dB) ⫺ f(GHz) characteristic
is given for the same transistor at a reasonable value
Figure 8. The [Fmin( f ), 1.2, GT max( f )] triplets for the
NE329S01 transistor. [Color figure can be viewed in the online
issue, which is available at www.interscience.wiley.com.]
492
Güneş and Tepe
Figure 9. The termination functions of the [F min( f ), 1.2, G T max( f )] triplets for the NE329S01
transistor. [Color figure can be viewed in the online issue, which is available at www.interscience.
wiley.com.]
V i req ⫽ 1.5, V CE ⫽ 10 V, and I C ⫽ 5 mA and various
noise levels from 2 to 4.5 dB for the NE02135 transistor (Fig. 7). From these curves it can be concluded
that the noise acts essentially as a band-limiting factor
on the gain performance of the transistor.
In the third step the characteristics in Figures 8 –13
are basically gain–frequency characteristics belonging
to the various (F, V i , G T ) triplets for the low-noise,
high quality NE329S01 transistor biased at V CE ⫽ 2 V
and I C ⫽ 10 mA and with an operation bandwidth of
2–18 GHz.
Figure 8(a,b) gives variations of the minimum
noise figure and the maximum gain with respect to the
frequency, and Figure 9(a,b) gives the corresponding
source and load terminations. The constraints for the
gain are that F req is equal to the minimum noise figure
F min at each f and V i req is 1.2. It should be noted that
there are no stable gain solutions at the first three
frequencies of 2, 3, and 4 GHz; the stable gain performance starts at the operating frequency of 5 GHz.
The source Z S(␻) and load Z L(␻) terminations for the
constant gain level of 10 dB for the same constraints
are given in Figure 10(a,b). Again in this case, unstable gain performances are met at the frequencies of 2,
3, 4, and 18 GHz, so the operation band is between 6
and 17 GHz. Figures 11 and 23 provide graphics of
the triplets [0.46 dB, 1, G T max( f )] and Z S(␻) and
Z L(␻) termination functions, respectively. In this case
the input port is completely matched and F req is taken
as a constant 0.46 dB; various bands of operation can
be considered as the design applications of the narrow-, medium-, and broad-band circuits.
The final curves in Figure 13(a,b) give the Z S(␻)
and Z L(␻) functions for the (0.46 dB, 1, 12 dB)
triplets. As seen from Figure 13(a,b), the Z S(␻) and
Z L(␻) functions provide an operation with the parameters of G T ⫽ 12 dB, V i ⫽ 1, F ⫽ 0.46 dB over the
band of 2–11 GHz and cannot go further because of
the unstable operation.
IV. CONCLUSIONS
The contributions of the theory for the performance
characterization of an active device to circuit theory
are given in detail in [8] and [9]. The importance of
this work is particularly focused on the design aspects
of active microwave circuits. In fact, the core of the
work can essentially be briefly given as the neural
block diagram in Figure 1. As seen from this diagram,
the output is the possible performance (F req, V i req,
G T ) triplets with G T min ⱕ G T ⱕ G T max and their
Gain–Bandwidth Limitations
493
Figure 10. The termination functions of the [Fmin( f ), 1.2, 10 dB] triplets for the NE329S01 transistor.
[Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]
associated source (Z S req) and load (Z L req) terminations as the functions of the device operation conditions, which are sufficient to completely characterize
the potential performance features of the active device
Figure 11. The [0.46 dB, 1, G T max( f )] triplets for the
NE329S01 transistor. [Color figure can be viewed in the online
issue, which is available at www.interscience.wiley.com.]
for linear amplification. These output functions can
provide the straightforward fundamental information
necessary for the design of a microwave amplifier
with optimum performance, which can be ordered as
follows: the extremum gain functions G T max, G T min
and their associated Z S, Z L terminations for the V i and
F couple and the CT, V DS, I DS, and f operation
parameters of the device point by point; all the compatible performance (F, V i , G T ) triplets within the
physical limits of the device, which are F ⱕ F min,
V i ⱖ 1, G T min ⱕ G T ⱕ G T max, together with their
Z S, Z L termination functions; and the potential operation frequency bandwidth for a selected performance
(F, V i , G T ) triplet. Thus, the designer is able to
instantly know: the optimum bias conditions V DS,
I DS; the available stable gain dynamic between G T min
and G T max for the required F req, V i req couple, depending on the f; the compromise relations among the
F, V i , and G T ; the selection of the performance (F,
V i , G T ) triplet using the compromise relations; the
operation frequency bandwidth that the device is capable of giving for the selected (F, V i , G T ) triplet;
494
Güneş and Tepe
Figure 12. The termination functions of the [0.46 dB, 1, G T max( f )] triplets for the NE329S01
transistor. [Color figure can be viewed in the online issue, which is available at www.interscience.
wiley.com.]
Figure 13. The termination functions of the [0.46 dB, 1, 12 dB] triplets for the NE329S01
transistor. [Color figure can be viewed in the online issue, which is available at www.interscience.
wiley.com.]
Gain–Bandwidth Limitations
and the Z S, Z L termination functions over this potential frequency bandwidth.
Finally, this work gives the potential gain performance of a microwave transistor, which depends on
the input mismatching, noise, and device operation
parameters. In other words, these are the limitations
for the gain performance that the designers can reach
by realizing the source Z S(␻) and load Z L(␻) terminations. In this respect, by combining the novel optimization processes and termination data modeling
with this work, new design techniques can be generated for microwave amplifiers. The most important
feature of these new techniques is expected to be that
the optimization will be processed on deterministic
and analytical bases so that efficient and high speed
communication systems can be realized.
REFERENCES
1. I. Aliyev, Design of the microwave amplifier using the
performance (F, V i , G T ) triplets, M.S. thesis, Yıldız
Technical University, Science Research Institute, Istanbul, November 2001.
2. B.S. Yarman and A. Aksen, An immitance based tool
for modelling passive one-port devices by means of
Darlington equivalents, Int J Electron Commun 55
(2001), 443– 451.
3. Q.J. Zhang and K.C. Gupta, Neural networks for RF and
microwave design, Artech House, Norwood, MA, 2000.
495
4. M. Vai, S. Vu, B. Li, and S. Prasad, Creating neural
network based microwave circuit models for analysis
and synthesis, Proc Asia Pacific Microwave Conf,
Hong Kong, December 1997, pp. 853– 856.
5. Y. Harkouss, J. Rousset, H. Chehade, E. Ngoya, D.
Barataud, and J.P. Teyssier, The use of artificial neural
networks in nonlinear microwave devices and circuits
modeling: An application to telecommunication system
design, Int J RF Microwave CAE 9 (1999), 198 –215.
6. F. Güneş, F. Gürgen, and H. Torpi, Signal–noise neutral
network model for active microwave device, IEE Proc
Circuits Devices Syst 143 (1996), 1– 8.
7. F. Güneş, H. Torpi, and F. Gürgen, A multidimensional
signal–noise neural model for microwave transistor,
IEE Proc Circuits Devices Syst 145 (1998), 111–117.
8. F. Güneş, M. Güneş, and M. Fidan, Performance characterisation of a microwave transistor, IEE Proc Circuits Devices Syst 141 (1994), 337–344.
9. F. Güneş and B.A. Çetiner, A novel Smith chart formulation of performance characterisation for a microwave transistor, IEE Proc Circuits Devices Syst 145
(1998), 1–10.
10. F. Güneş and B.S. Yarman, Potential broadband characteristics of a microwave transistor and realization
conditions, 2000 PIERS Progress in Electromagnetics
Research Symposium, Cambridge, MA, July 5–14,
2000, pp. 8 –15.
11. C. Tepe, Modelling and performance analysis of a
microwave transistor using neural network, Ph.D. Thesis, Yıldız Technical University, Science Institute,
Istanbul, 2000.
BIOGRAPHIES
Filiz Güneş received her M.S. degree in
electronic and communication engineering
from Istanbul Technical University in 1972.
She attained her Ph.D. degree in communication engineering from Bradford University, London, in 1979. She worked as a Research Fellow at the same university between
1979 and 1983 with contracts from the European Space Agency and British Defence
Minister in the areas of the propagation and electromagnetic compatibility. Since 1983 Dr. Güneş has been with Yıldız Technical
University, where she is currently a full Professor and head of the
Electromagnetic Fields and Microwave Technology Group. Her
current research interests are in the areas of multivariable network
theory, device modeling, computer-aided circuit design, microwave
amplifiers, microwave filters, broad-band matching circuits, mono-
lithic microwave integrated circuits, and electromagnetic compatibility.
Cemal Tepe received the B.S. and M.S. degrees in electronics and communication engineering from Istanbul Technical University
in 1991 and 1994, respectively. He acquired
his Ph.D. degree in communication at Yıldız
Technical University in 2000 in Istanbul. Dr.
Tepe is currently working as a Software Designer for Alcatel, a telecommunication
company in Raleigh, NC. His research interests include microwave device and circuit modeling and analysis,
neural networks, and computer-aided design of telecommunication
networks.