Performance characterisation of a microwave
transistor
F. GuneS
M. Guneq
M. Fidan
Indexing t e r m : Microwave transistor, Transistor performance characterisation
Here, zll, z I 2 , zzl and zz2 are the small-signal opencircuit z-parameters of the two-port and pi is the input
reflection coefficient.
The transducer power gain of the same two-port is a
function of source and load impedances and the zparameters are as follows [ 3 , 4 ] :
Abstract: The maximum transducer power gain
GTmx of a bilateral microwave transistor is analytically expressed in terms of only noise figure F,
input VSWR % and the open-circuit parameters
IzJ. The analysis is based on a geometrical
approach using the constant noise, input VSWR
and gain circles in the source and input impedance
planes keeping the solution within the physical
bounds. The corresponding source Z, and load Z,
terminations are also obtained analytically. Crossrelations among the possible (F, &, GTmnx)triplets
have been utilised in obtaining the performance
contours of a microwave transistor at an operating frequency and bias condition. This type of
representation of performance promises to be used
in data sheets of microwave transistors by manufacturers in forthcoming years.
1
(5)
+
Description of the problem
The noise figure of a linear noisy two-port with an arbitrary source impedance (2,= R , j X J , shown in Fig. 1,
can be expressed in terms of equivalent noise resistance
( R J , minimum noise figure as ratio ( F A , and the
optimum source impedance (Z,,, = R,,,
j X o p , ) of the
two-port as follows [ 3 , 4 ] :
+
+
Input VSWR of the two-port is a function of the
source (Z, = R , j X J and load (Z, = R , j X J impedances via input impedance (Zi = Ri + j X J of the twoport, as follows [ 3 , 4 ] .
+
The problem can be described as a mathematically constrained maximisation to find the maximum value of
G A R , , X , , R L , X J subject to m1 = F,eq - F(R,, X $ = 0
and m2 = &,eq - K(Rs, X , , R, , X , ) = 0 and the corresponding values of Z, = R , + j X , , Z , = R , j X , where
F,,, and Vbeqare the required noise and input VSWR,
respectively.
The method can be summarised step by step as
follows:
(a) First, for a given transistor, the circles belonging to
F(R,, XJ = constant, K(Rs, X , , R , , X J = constant and
G A R , , X , , R , , X,) = constant are considered in the 2,
plane. In this step, it is shown that only noise and VSWR
circles are sufficient to be considered in the Z,-plane.
(b) For all passive loads relative positions of the performance circles are analysed and all the possible situations are mapped into the solution regions bounded by
the two circles in the Zi plane, one of which (7”)always
takes place inside the other (Tl).
(c) In this step, the gain circle constrained by the given
q are formed in the Zi plane.
(d) In the final step, comparing the positions of the
gain circles with the solution circles TI and T 2 , the constrained maximum gain GTmx and its corresponding Z i ,
Z, and Z, are determined. As the result, the possible triplets (F, &, GT-) are calculated; using these triplets the
performance contours of a microwave transistor can be
obtained.
+
where
I
z, - z:
z, + zi
I
lPil = -
zi=zll--
z12z21
222
+ ZL
(3)
2
(4)
A general circle equation in the Z, plane, whose centre
and radius are Z, = R, j X , and r, respectively, may be
expressed as
+
lZ, - Z, I = r
0IEE, 1994
Paper lllOG (E3, E12), received 18th October 1993
The authors are at h l d i i Technical University, Electronic and Communication Engineering, Maslak, Istanbul, Turkey, 80670
I E E Proc.-Circuits Deuices Syst., Vol. 141, No. 5, October 1994
Constant noise, input VSWR and gain circles in
t h e 2 plane
or
1 Z, 1’
- ZR,
R, - ZX, X ,
+ I Z, 1’
- r’ =
O
(6)
331
2.1 Constant noise circles
Using eqn. 1, the equation of the constant noise circle
in the 2, plane can be expressed in the following form
(Fig. 2 ) :
I z,
l2 - 2(R,,, + N ) R , - 2x,,, x, + I z,,l2,= 0
where the centre Z,, = R,, + j X , ,
found, with the help of eqn. 6, as
(7)
As is clearly seen from eqns. 10 and 11 2," = 2: and
ro = 0 when I piI = 0 which means the required input
VSWR is unity (complex conjugate matching at the input
port). The radius and only the real part of the centre
increase with the increase of lpil although X,, is constant.
and radius r, are
2.3 Constant transducer gain circles
Rearranging eqn. 5 with respect to Z,, gives an equation
of the constant transducer gain circle family:
(G", )
IZ,I2 - 2 - - Ri R,
+ 2 X i X , + IZiJ2= 0
(12)
where the constant C is
F , , R,, R,,, , X,,, are as previously defined for eqn. 1.
zs
z,
I
I
z,
ZL
I 1
and the centre Z,, = R,, + j X , , , the radius r, can be
expressed in the following form:
R =--R.
cp
GC
T
X
"
=-Xi,r
'e
=
'
- -/[:T(:T
2Ri)]
(14)
1
,
P,"
POVS
pout
The two-port under consideration and its port impedances
Fig. 1
required noise figure circle
@
. .......
r e q u i r r input VSWR circle
constant gain
circles
I
Fig. 2 Representation of the constant noisefigure, input V S W R md
gain circles in the Z , plane
2.2 Constant input VSWR circles
Using eqn. 3, the equation of the constant input VSWR
or reflection coefficient modulus circles in the 2, plane
can be obtained as follows (Fig. 2 ) :
+ 2 X i X , + IZi12 = 0 (10)
where, using eqn. 6, the centre 2," = R,, + j X , , and the
IZ,I2 - 2Ri l+lp,12R,
l--lP,I2
radius r , are found as
338
For a given load the maximum gain is only obtained
when the input is complex-conjugate matched; using
eqns. 12-14, r, = 0 is obtained.
As can be seen from eqn. 11 and eqn. 14, the centres of
the input VSWR and transducer gain circles lie on the
same imaginary axis, i.e. - X i . At the same time, by
having R,, = R,, , it can be proved that r , = r v . This
means that only a source impedance chosen on the
required input VSWR circle will always make gain
maximum under the constraint of the required input
VSWR. In this case, the gain G, and the radius r , are,
respectively, equal to
which is r, in eqn. 11.
The result is that only the required noise and the input
VSWR circles need to be taken into account in the Z ,
plane, because any mutual points of these two circles not
only satisfies both the noise and input VSWR requirements, but also makes the transducer power gsin
maximum in the 2, plane.
As has already been shown, while the required noise
circle is fixed in the Z , plane, the required input VSWR
circle can travel, depending on load impedance, via the
input impedance Zi. Therefore, 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 possibilities is discussed.
3
Control of the positions of constant input
VSWR circles with respect t o the noise circle in
the.?, plane from the.?, plane
First, two types of tangent position (external and internal
positions) between the noise and input VSWR circles in
the 2, plane will be investigated; these positions are
transition stages between non-touching and intersection
positions (Fig. 3). A general equation can be written for
both of the tangent positions in the 2, plane as follows:
IEE Proc.-Circuits Devices Sysf., Vol. 141,No. 5, October I994
Substituting Z,, ,r,, Z,, , and r, from eqns. 8 and 11 into
eqn. 16, another couple of circle equations which represents two different tangent positions of the noise and
the input VSWR circles in the 2, plane, can be obtained
in the Ziplane (Fig. 4) as follows:
With a positive sign in eqn. 17, the centre Z,, = R
j X m l and the radius rtl of the circle TI which corresponds to the external tangent position are found as
+
R,,, = R,, U
+ r+, V ,
x,,,= -x
1 + I Pi l2
I zi I2 - 2 (R,,, + N ) 1 - I Pi l2
0”
{
rt1 = JCC I Zrll IZ - I z,,,
12)1
(18)
where
+
XS
t
jXd2
With a negative sign in eqn. 17, the centre Z,,
and the radius rI2 of the circle T2 which corresponds to
the internal tangent position are, respectively, found as
XS
t
Noise
Mise
Ret2 = R, U - r, V ,
Xn2 =
-x,,>
rI2 = JCC 1 zn21’ - I Z,,,
b
a
RS
e
Fig. 3 The positions of V S W R circles with respect to noise circles in
the Z,plane controlled by the regions in Fig. 4
maximum gain circle which satisfies
(20)
where U,V are defined by eqn. 19.
The centre of the T, and T2 circles lie on the same
imaginary axis, -X,,, ,and it can also be proved that the
circle Tz is always situated inside the circle Tl without
touching, as shown in Fig. 4. This can be provided
showing the existence of the following inequality in all
cases:
‘11
input VSWR or Noise
Region 5
12)1
3 R,tl - Rd2
+ r12
(21)
The equality only can be obtained when lpil = 0; as a
result, V in eqn. 19 becomes zero and RcIl and rIl
become equal to Rnz and rt2, respectively. This means
only one circle exists in the Zi plane and the VSWR circle
is not a circle, but a point in the Z , plane.
Five different regions in the Ziplane bounded by the
TI and T2 circles in Fig. 4 cause different interactions of
the required input VSWR circle with the noise circle in
the Z, plane (Fig. 3). As can be seen from Figs. 3a and 3e,
no input impedance Zi chosen in regions 1 or 5 will cause
a mutual point of both noise and input VSWR circles in
the Z , plane; these cases will therefore give no solution
for maximum gain constrained by the required noise and
input VSWR.
In order to find exact geometrical and analytical solutions in the other regions, the constant gain circles
satisfying the required input VSWR will be constructed
in the Z , plane and values of these gain circles in the
solution regions will be investigated: the maximum one
satisfying all the constraints will be then determined as
the solution.
4
Constant gain circles in the.?, plane constrained
by the input VSWR
Expressing load impedance in terms of input impedance.,
eqn. 15 can be rewritten in the following form:
reglcns
The solution of the constrained maximum gain and corresponding terminations
Fig. 4
I E E Proc.-Circuits Devices Syst., Vol. 141, No. 5, October 1994
1
- - (rrll
r22
+
XXll)
+ lZll
12
=0
(22)
339
where
rij = Real {zij}, x i j = Imag {zij}, z = zI2zz1= r + j x
(23)
Let the centre and the radius of the circle family given by
eqn. 22 be Z,, = R,, + j X , , and r,, respectively, which
can be found as
r,
1
= -J[(P’
2r22
- 2QP
+ 1 z l’)]
(24)
where
maximum gain will have the value of a constant gain
circle, tangential to the circle TI. Similarly, when Z,,,, is
in region 5, the maximum gain will have the value of a
tangential constant gain circle with the circle Tz . By the
same reasoning, two possibilities are understood to exist,
for which there are no physical solutions. These are the
cases for the G, = 0 limit circle being completely outside
the circle TI or completely inside the circle T z . All the
other possibilities are discussed separately for the derivation of analytical solutions below.
5.1 Z,,,,, in region 1
Writing the tangent conditions for one of the gain circles
and the circle TI as
I z,, - z,,, IZ = @,I + r,)’
or
It can be seen from eqns. 24 and 25 that R,, decreases
with the increase of G, when X,, remains constant, (Fig.
4) and the maximum gain is only achieved at the point
where the radius r, equals to zero. Setting r, to zero in
eqn. 24 gives
which is only achieved when the device is absolutely
stable: otherwise the square root in eqn. 26 becomes
negative since conditions for absolute stability are rI1
0, r22 z 0 and 2rI1r,, - r > IzI. Substituting eqn. 26
into eqn. 24, the solution with R,, > 0 is obtained as
follows:
I z,,
1’ + I z,,, 1’
- 2R,,
R,1 - 2x,,x,,,
+ r: + 2rf1rg
=
(32)
and letting
+
D = IZ,, I’ - r: 1ZcflI2gives the following equation for G,:
P’(1 - F’)
- 2(Q
+ EF)P + I z l2 - E’
(33)
=0
(34)
where
E = Dr22 - Rc11(2r11r22 - r) - 2XC‘,x,, 1 2 2
rfl
F=%
1
where
and Xc4 is given by eqn. 24; the maximum transducer
gain satisfying the required input VSWR is
when p i = 0. The maximum available power gain, MAG,
can be obtained from eqn. 29 which is the gain of the
device when both ports are complex-conjugate matched :
The limit circle of the circle family expressed by eqn. 22
can also be found substituting G, = 0 in eqn. 25; then,
= Rrsmin+ jXceminand the radius (rgmin)
the centre ZCgmim
of the GT = 0 circle from eqn. 24, are, respectively
since Q is greater than IzI for the absolute by stable
device, Rcgminis greater than rgminwhich results in the
G, = 0 circle being entirely in the positive real plane, and
enclosing all the circles for GT > 0 (Fig. 4).
5
Geometrical and analytical solutions of the
constrained maximum gain in theZ, plane;
determination of correspondingterminations
In the circumstances of the absolute stability the solution
appears geometrically depending on the position of
Z,,,,
(Fig. 4). For example, if Z,,,, is in region 1, the
340
where D can be expressed in terms of two-port parameters as
D=
r221z111z-rrll
r22
-=I1
+ I z,,, I2
(35)
and P and Q are given by eqn. 25. Solving eqn. 34 yields
+
k JC(Q
En’ - (1 - F’X I z 1’ - E’)]}
(36)
Since F > 0 and 1 - F’ < 0, the negative sign in eqn. 36
will provide the greater gain. It can be. seen that the
maximum gain is not a direct function of source or load
terminations but of the required input VSWR, noise
figure and z-parameters only.
From Fig. 4, it is easy to find the input impedance Zi
where the constant gain circle is tangent to the circle Tl
as
and the corresponding load impedance can be found in
terms of input impedance as
The proper source impedance Z, will be the impedance at
the tangent point of the both circles of the noise and
input VSWR in the Z, plane (Fig. 36):
(39)
IEE Proc.-Circuits Devices Syst., Vol. 141, No. 5, October 1994
5.2 Z,,,,, in region 2
Since region 2 is the circle TI, i.e. the geometrical location
of all the input impedances that make the input VSWR
circle tangent to the noise circle in the Z , plane, the
maximum gain will be Grmxas given by eqn. 29 and the
corresponding input impedance will be Z,,,
in eqns. 27
and 28. The load and source impedances can be
obtained, respectively, from eqns. 38 and 39.
5.3 Z,,,,, in region 3
In this case there are two source impedances which both
satisfy the required input VSWR and noise (Fig. 3). Since
2,is inside region 3 the maximum gain will be G,,
as given by eqn. 29 and Z , equals to Z,,,
as derived in
eqns. 27 and 28.
The source impedances Z,, and Z,, can be derived
from the intersection points of the two circles in Fig. 5
t
The corresponding source impedance can also be found
depending on which circle is the larger: if rn > rv
TI#
I"
z,= Z," - -Z,"
'n - T"
r. -
otherwise,
5.5 Z,,,,, in region 4
In this case the maximum gain and the corresponding
input impedance will be, respectively, G,,,
and Z,,,
which are as defined previously. The source impedance is
derived from either eqns. 45 or 46,depending on the radii
of the noise and the VSWR circles.
6
x5
(45)
Tu
Considerationsfor a conditionally stable
microwave transistor
The constrained gain formula, eqn. 22, can be rearranged
in terms of the radius and centre of the source plane stability circle as:
IZiI2
+ 2(R, + S)Ri + 2 X , Xi + I Z ,
1'
- I,' = 0
(47)
where
+
With Z , = R,, j X , and r, being, respectively, the
centre and radius of the source plane, the stability circle
can be written as follows [3,4]
Rs
Fig. 5
Source impedance when Zc-
is in region 3
The centre Z , = R,
circle family will be
R, = -(Res
+jX,,
+ S), X ,
(49)
and the radii re of the gain
= - X _ , rg = (Sz
+ 2SR + r Z )
cs
s
(50)
The features of the G, circles, which can be derived from
eqns. 47-50, are as follows (Fig. 6).
C=
5.4
R,,
+ AX,
Z,,,,,
- AB
1+A2
B2
3D=
t
+ IZ,,12
l+AZ
xi
R
in region 5
stant gain circles
In this case the maximum gain will be obtained at the
point where a constant gain circle and the circle T, are
internal tangents to each other. This situation also
corresponds to the internally tangential situation of the
noise and input VSWR circles in the Z , plane. An equality can be written for the condition of tangent position of
the two circles as
This is very similar to eqn. 32, so all the expressions
derived for the case of 5.1 will be valid, substituting Z,,,
and -rfZ for Z,, and r,,, respectively. Hence the input
impedance where the two circles are tangential is
I E E Proc-Circuits Devices Syst., Vol. 141, No. 5, October 1994
conjugate of the source
plane stability circle
GT=O circle
(a) All G , 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.
(b) The GT = 0 circle whose centre is Z,,,, = -Res
- J X , with radius rgrnin
= rs, is symmetric of the conjugate of the stability circle with respect to the imaginary
axis.
(c) G,
> G , > 0 circles always take places in the
area bounded by the G, = 0 circle and the arc of the
conjugate of the stability circle remaining in the positive
real input impedance plane (shaded area in Fig. 6), and
centre phasors of these circles are always on the line
x i =-x c s . It should be noted that in the case of the
unconditional stability, all the G, circles are situated
entirely in the right half of the Z,-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 2,-plane. It can be found by substituting
R , = R , in eqn. 50 and, referring to eqn. 49, the
maximum gain is subject to the input VSWR as
1
GT=2-
I Pi l2
(2r11r22- r)
I 2 1 2 l2
-
(a) No physical solution exists for G , if G, = 0 is completely in region 1. This case can be described by the
inequality
I Zcgmin - Zct~I > rs + rtl
(53)
(b) One possible maximum gain is available when
region 2 (circle Tl) cuts the constant gain circle area.
The maximum gain and its corresponding input
impedance can be calculated from the tangential relation
between a constant gain circle and the circle Tl which is
The maximum gain can be derived by just substituting in
eqn. 57 the quantities from eqns. 33-35, 51 as shown
above. The corresponding input impedance is then
derived as
(55)
After finding 2, the source impedance Z, can also be calculated from eqn. 39 where noise and input VSWR circles
are outer tangents in the Z, plane. The existence of this
case may be verified by the following inequalities :
and, setting I pil = 0, eqn. 51 yields the maximum stable
gain, M S G :
where q is the stability factor [3,4]
and, for conditionally stable cases, has values between
zero and unity (0 q < 1).
-=
(c) When the circle Tl cuts the conjugate source plane
stability circle, some portion of this conjugate stability
circle stays in region 3, so input impedances on this
portion will provide the same maximum gain given by
eqn. 51. In this case there will be two source impedances
that satisfy the requirements, because of the intersection
of both noise and input VSWR circles in the Z, plane,
which are calculated from eqns. 40-42. This case is also
described by the following inequalities:
I Zegmnr- z,t2 I > rs + rt2
I zcgmnx
- z,,
I,
-= rs + rt1
6.1 Maximum gain subject to the noise and input
VSWR for a conditionally stable transistor
Since five regions have been defined in the Zi plane,
which control the locations of the input VSWR circle
with respect to the noise circle in the 2, plane, the constant gain circles subject to input VSWR with respect to
these regions for conditionally stable case (Fig. 7) can
now be considered.
t
(d) When the circle T2 cuts the conjugate source plane
stability circle, the portion of this circle in region 5 gives
no solution, while the portion in region 3 provides the
maximum gain and the terminations, as explained in case
(b)(Fig. 7).
7
maximurn gain circle which
Mtisfias the required noise
(57)
Computer simulation and conclusions
The flow chart of the performance simulation program is
given in Fig. 8. For the GaAs transistor NE72089A, the
given small-signal parameters at the bias conditions
V,, = 3 V, I,, = 10 mA and operation frequency 4 GHz,
the numerical output is given in Table 1, the gain and
solution circles and performance contours are given by
Figs. 9-12. The following published performance data
are also given: minimum noise, F,, , input termination,
ZOpt: the associated maximum gain G,,,,,
and the
maximum gain G,,,. As far as performance analysis is
concerned, this data is insufticient to characterise the
transistor performance. The present work gives not only
the possible performance triplets ( F ,
GTmx), but also
the termination couples (Zs, ZL). Furthermore, the performance contours not only show what is available, but
let the designer trim the requirement at the expense or
benefit of each other. For example, if a designer requires
1.20 dB noise with matched input at 4GHz, he has
2.60 dB gain; however, from Table 1 and at the same frequency, a slight increase in noise of 0.04 dB (to 1.24 dB),
would give 4.9 dB gain with the matched input. The conditional formulation of the maximum gain subject to
v,
0
Fig. 7 Determination of the constrained maximum gain and corresponding input impedancefor a conditionally stable transistor
342
I E E Proc.-Circuits Devices Syst., Vol. 141, No. 5, October 1994
noise and input VSWR may be used on data sheets of
microwave transistors in the future. Because the constrained maximum gain contours cannot be bettered, the
performance of low noise microwave transistors with the
corresponding terminations will facilitate rapid design. It
will also inform designers of some incompatibility
between gain, noise and VSWR for narrow and medium
band amplifier design.
To date, the usual design method a low noise amplifier
is to get the noise figure as lower as possible while letting
the input VSWR 'go free', and to use a circular or a balanced configuration to meet the input match requirement. If a circulator is used, its loss is added to the
system noise figure. Also, use of a circulator or coupler
with the MMICs cancels the benefits of a small MMIC
amplifier. This analysis is also aimed at providing a
higher level tool for the design of MMIC amplifiers with
which to overview possible designs.
Table 1 : Performance data
NE7-A
Rn.rOpt
4
=l.Av,l<V,<B
F:F,,(dB)t
AF
Fm,,<FsFmlnt2 2
V,
S parameters
Mag. Ang.
.I
TI and 12 solution circles for the performonce
couple (F,VI) are formed in the Z, -plone
S,,: 0.76
1
S z , : 2.34
The gain circle constrained by the current V,
IS also formed In the 2, plane
GaAs transistor
S , z : 0.11
SZ2: 0.59
-95
90
26
-66
Noise parameters
Mag.
Ang.
roo,: 0.65
f,,,,": 1.00
R5
/,.0:
0.42 n
VSWR
Noise Gain
R,
X,
R,
X,
1.32
1.36
1.40
1.44
1.48
1.52
1.56
1.60
1.64
1.68
1.72
1.76
1.80
1.84
1.E8
1.92
1.96
2.00
2.04
2.08
2.1 2
2.16
2.20
2.24
2.28
2.32
2.36
2.40
2.44
2.48
2.52
2.56
2.60
2.64
2.68
2.72
2.76
2.80
2.84
2.88
2.92
2.96
3.00
3.04
3.08
25.47
41.92
54.24
62.83
68.39
71.65
73.24
73.66
73.27
72.35
71.08
69.60
68.00
66.35
64.68
63.03
61.42
59.85
58.34
56.89
55.50
54.16
52.89
51.67
50.51
49.41
48.35
47.34
46.38
45.46
44.58
43.74
42.94
42.17
41.43
40.72
40.04
39.39
38.77
38.17
37.59
37.03
36.50
36.50
36.50
36.50
36.50
36.50
-99.48
-90.93
-80.20
-68.81
-57.72
-47.44
-38.18
-29.99
-22.80
-16.52
-11.04
-6.24
-2.05
1.64
4.88
7.76
10.31
12.58
14.61
26.44
18.08
19.57
20.91
22.14
23.26
24.28
25.22
26.08
26.87
27.60
28.28
28.91
29.50
30.04
30.55
31.03
31.47
31.89
32.28
32.65
32.99
33.32
33.63
33.63
33.63
33.63
33.63
33.63
22.30
21.31
20.40
19.58
18.81
18.10
17.45
16.83
16.26
15.72
15.21
14.73
14.28
13.85
13.44
13.06
12.69
12.34
12.01
11.69
11.39
11.10
10.82
10.55
10.29
10.05
9.81
9.58
9.36
9.15
8.95
8.75
8.56
8.38
8.20
8.03
7.87
7.71
7.55
7.40
7.26
7.12
6.98
6.98
6.98
6.98
6.98
6.98
48.67
47.72
46.92
46.24
45.66
45.15
44.70
44.30
43.95
43.63
43.35
43.09
42.85
42.64
42.45
42.27
42.10
41.95
41.81
41.68
41.56
41.45
41.35
41.25
41.16
41.08
41.00
40.93
40.86
40.79
40.73
40.68
40.62
40.57
40.52
40.48
40.43
40.39
40.36
40.32
40.28
40.25
40.22
40.22
40.22
40.22
40.22
40.22
1.20
2.60
1.oo
4.90
1.24
1.oo
1.28
6.20
1.oo
ma%gain and the (Z,.ZL)aredeterrnined
by following the simdliar vmy to the
unconditionally stable cose
I
store the performance triplets (F,V, . G T ~ ~ )
The simulation program chnrt
noise(dB) 144
gain (dB) 11 40
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
1
1
1
1
1
1 .oo
1
1.oo
1
1
1.oo
1.oo
1.oo
1.oo
1
1
1
1
1.oo
1 .oo
1
1
1.oo
1
1
1
1
1
1
1
1.oo
1.oo
1.oo
1
1
1
1
1
1.oo
1.oo
1
1
1
1
1.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
.oo
Fig. 9 Gain circles constrained by V, = 1.55 and solution circles T,
and T2for F = 1.44, = 1.55 of NE72089A nt the bias condition V,, =
3 V , I , = I O mA nnd opernting frequency 4 GHz
IEE Proc-Circuits Devices Syst., Vol. 141, No. 5, October 1994
.oo
.oo
.oo
.oo
68
dB
Z, P R.+X.
Z. R . + X .
Fig. 8
the
Version: 2.0
Date: 12/87
Text name: N72089AA. S2P
NEC Serial number: NE72089A
Bias condition: ,V
,
= 3 V. I
, = 10 mA
Transistor type: Gaas
Operating frequency: 4 GHz
Give [S1.Fm,n,
1
for
7.20
7.90
8.40
8.90
9.30
9.60
10.00
10.20
10.50
10.70
10.90
11.10
11.30
11.40
11.60
11.80
11.90
12.00
12.20
12.30
12.40
12.50
12.60
12.70
12.80
12.90
13.00
13.10
13.20
13.30
13.40
13.50
13.50
13.60
13.70
13.80
13.80
13.90
14.00
14.10
14.10
14.10
14.10
14.10
14.10
343
2 502 352 20-
:I /
21
'1 21 0590760455,
,
,
,
,
,
,
,
,
\ \ \\ \
1 30-
3 8
26
104 126 1 4 8 170 192 2 14 2 36 2 58 2 80 3 02 3 24
notse,dB
1 15
l o o
'
1
'
\
'
'
'
"
Fig. 10 Gain against noise with respect io VSWR at 4 GHr for the
iransistor NE72089A
....... VSWR = 3
VSWR = 2
______ V S W R = I
~~~~
13.9r
91.;
8 5:
344
8
References
1 FUKUI, H. (Ed.): 'Low-noise microwave transistors and amplifiers'
(IEEE, 1981)
2 YONG-SHI, WU, and CARLIN, H.J.: 'The design of low-noise,
broad-band microwave FET amplifiers'. IEEE MTT-S International
Microwave Symposium Digest, N20, 1983
3 LIAO, S.Y.: 'Microwave circuit analysis and amplifier design'
(Prentice-Hall, Englewood Cliffs, NJ, 1987)
4 GENTILI, C.: 'Microwave amplifiers and oscillators' (Academic,
North Oxford, 1986)
5 GONE$, M., and GONE$, F.: 'A new design method for maximum
gain formulation of a microwave amplifier subject to noise figure and
input VSWR. ECCTD-91, 10th European Conference on circuit
Theory-Design
IEE Proc.-Circuits Devices Sysr., Vol. 141, N o . 5, October 1994