一种宽带微波放大器设计方法, A BROADBAND MICROWAVE AMPLIFIER DESIGN BY MEANS OF IMMllTANCE BASED DATA MODELLING TOOL
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IEEE Africon 2002 535 A BROADBAND MICROWAVE AMPLIFIER DESIGN BY MEANS OF IMMllTANCE BASED DATA MODELLING TOOL A Impt H Pinarbqi1M engiiP BS Yarmanll Isik University Kadir Has University Istanbul Turkey f i i the optimum ABSTRACT In this paper a practical broadband microwave amplifier design algorithm is introduced utilizing the tool In the course of immittance datamodelling design input and output terminations for the active device are produced employing the real frequency techn......
IEEE
Africon
2002
535
A BROADBAND MICROWAVE AMPLIFIER DESIGN
BY
MEANS
OF
IMMllTANCE
BASED DATA MODELLING TOOL
A
&Impt)
H
Pinarbqi('1M
$engiiP'
BS
Yarman~ll
"'Isik University, "'Kadir Has University, Istanbul, Turkey
ABSTRACT
In
this
paper
a
practical broadband microwave
amplifier design algorithm
is
introduced utilizing the
immittance data-modelling tool.
In
the course
of
design,
f i i ,
the optimum input and output
terminations for the active device are produced
employing the real frequency technique. Then, these
terminations are modelled utilizing the new
immittance-modelling tool t o synthesize the front-end
and back-end matching networks.
An
example is
included to exhibit the implementation
of
the proposed
design algorithm to construct a single stage
BJT
amplifier over a wide frequency band. It is expected
that the proposed design algorithm will find
applications to realize widehand microwave amplifiers
put
on
MMIC
for
mobile communication.
1.
realize microwave amplifiers on MMIC for mobile
communication.
2.
THE
IMMI'ITANCE
MODELLING
TOOL
[l]
BASED
DATA
Any positive real rational immittance function
F(s)
can
be written in terms of
its
minimum and the Foster parts;
F ( s )
=
F,
( s )
+
F/
( s )
(1)
where
s
=
U
+
j o
is
the complex domain variable,
F,,,(s)
is the minimum part which
is
free of
j w
poles,
and
F/(s)
is the Foster part which includes only
j o
poles. On the real frequency axis
j w
,
one has
F ( j o )
=
R ( o )
+
j X ( o )
F A ~ O J )
~ , ( w i + j ~ , ( o )
=
Fj(jo)
=
jx,(o)
(2)
INTRODUCTION
One of the fundamental problems in
the
design and
development of communication systems is to match a
given device to the system via coupling circuits
so
as to
achieve optimum performance over the broadest possibie
frequency band. This problem inherently involves the
design
of
an equalizer network to match the given
complex impedances, and usually referred as
impedance
matching
or
equalization.
Recently introduced immittance data modeling tool can
be employed successfully to design microwave amplifiers
[I].
As
indicated
in
[I],
design of microwave amplifier,
falls
in
problems of
Type
11 category. When a broadband
microwave amplifier
is
designed, optimum termination
immitances for the active device can be generated point
by point employing the Carlin's Real Frequency Line
Segment Technique
[2-51.
Then, the data for the
terminations are modelled by means of the immitance
modeling tool. Eventaully, Positive Real
(PR)
immitances
are
synthesized to yield the front-end and the back-end
matching networks which completes the design.
Therefore, in this presentation, first the immitance based
modeling tool is summarized. In section
111,
Generalized
Real Frequency Technique (GRFT)
is
outlined. The
complete design algorithm is given in Section
IV.
Finally,
utilization of the design algorithm is exhibited with an
example.
The process described in this paper can easily be extended
to
design microwave amplifiers with mixed lumped and
distributed elements
[ 6 ] .
It
is expected that the design
technique introduced in this paper will find application to
It is clear that
R(o)
=
R,
(4
X ( o )
=
x,"
+
x,
(0)
(0)
(3
)
Since
F,,,(s)
is a positive real minimum, which contains
no poles on the
j o
axis, its imaginary part
X , ( w )
is
by the Hilbert
related to the real part
R,(o)
transformation relation;
X,"(W)
=
H{R(w)}
(4)
where
H { .
}
designates the Hilbert Transformation
operation.
In the immittance based modelling technique, the crux of
the matter is to decompose the given data into its
minimum part and Foster part. Hence, the modelling
process is carried out within two major steps: model for
the minimum part and the Foster part.
To
model the minimum part,
it
is sufficient to match an
analytic form
R ( o z )
for the real part data. Then the
complete minimum function
F(s)
can easily be generated
from
R(-s2)
by means of Gewertz procedure
[4].
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The real part forms are classified based on the selection of
the transmission zeros of the matching networks. Let
R ( 0 2 )
=
*,
in this case regarding the zeros of
D(w
)
N(o')
,the real part forms are described as follows:
For modelling Form-A
For modelling Form-B
N ( o )
=
0 '
2
N ( o ) =
oZkfi(cu2
-oZp)'
p=l
Ok-I
ok
For
modelling Form-C
!
Figure
2:
0
,
Line segment approximation of the real part
These choices will be picked in accordance with the given
data for
R(w)
.In order to extract the Foster part from the
original measured data, one has to generate
X,(w)
using
the Hilbert Transformation relation
[3].
Eventually,
realisable analytical forms for the minimum immittance
function and the Foster function are obtained by means of
an appropriate curve fitting or interpolation algorithms
and they
are
synthesized
to
yield the desired model under
consideration.
3.
The coefficients
a I ( w )
in
(6)
can be expressed directly in
terms of sampling frequencies
(
o,,i=1.2.3
n )
as
,......
follows:
GENERALIZED
LINE
SEGMENT
TECHNIQUE
FOR
MATCHING
A
COMPLEX LOAD TO A RESISTIVE
GENERATOR
b , ( w )
in
( 6 )
can be expressed using Hilbert transform
techniques as
b,
(0)
=
In
the Generalized Real Frequency Technique (GRFT),
2,
(jo)
be determined
as
can
Consider the single matching circuit arrangement shown in
Figure
1.
I
I
z,,,
Figure
1:
Single matching problem
Z,
=
R,
1
where,
X,,
designates the Foster part of the equalizer
I
+
j X ,
impedance. It is also noted that
X,,
is among the
unknowns of the problem.
The Transducer Power Gain
(TPG)
of the system can be
written in terms of the reflection coefficient at port
2
as
Let the load impedance
ZL
and the equalizer back
,
impedance
2
be written in terms
of
their real and
imaginary parts on the real frequency axis
as
(8)
can directly be expressed in terms of the real and
imaginary parts of the load impedance
ZL
and the back-
end impedance
Z,
of the equalizer
[2].
Basic
idea is the use of
a
piecewise linear approximation
to represent the unknown real part
R,
(CO)
as a number
of
straight-line segments as shown in Figure
2.
If
the
real
frequency load data
is
given
as
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2002
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Z,(jw)=
R L ( j o ) +
jXL(jca), then the matching
problem becomes essentially
to
that of finding
Z,(jo)point by point such that
T ( o )
is maximized
over the band of operation.
Once Z,(jw)=
R,(o)+
j X , ( o ) i s determined point by
point employing the Generalized Real Frequency
Technique, it is modelled as a positive real function by
means of the
"immittance
based
data modelling
tool[I]".
In the following section, we will introduce the new
microwave amplifier design technique via the immitance
modelling
tool.
3.1
The load impedance
Z L , ( o )
=
RLI(o)+ jX,,(o)
to
Z,,,
which is specified by (IO).
The term
is
set
4
(0)
=
[ I
-
in front of the gain function
:j:r]
can be regarded
as
a weight factor. Thus,
Extension
of
Immittance Based Data Modelling
Tool
to the Design
of
Amplifiers
Let
us
consider the single stage amplifier configuration
shown in Figure
3
where the active two-port device is
denoted by
[A].
The lossless two-ports
NI
and
N,
designate
the front-end and back-end matching networks respectively.
A
single stage microwave amplifier can conceptually be
constructed within
two
steps by using the Real Frequency
s,
,
Figure
4:
Single stage amplifier equalized at the input
In this step, the negative slope of the gain
is
compensated
by optimizing
T,
to a flat gain level
To,
.
In the second step of the conceptual design, the back-end
matching network will be generated
as
set of data. In this
case, the gain
T,(w),
which is subject to optimization, is
expressed in terms
of
the driving point impedance
Z,,
of
the
output-
matching network
N,
Technique. In the first step, the optimum immitance data
Z,, for the front-end matching network is generated point
by point over the band of operation. In this step, we
presume that the output port of the active is closed with
unit termination (i.e.
50
ohms)
(Figure
4).
Hence, the
input impedance of the transistor is given by
and it is considered as the termination
of
the input
matching network.
m
Figure
3:
and output
I
z,,
SI,
=
-
/-si,
+
(10)
In
(14),
the term
S22
is the reflection coefficient of the
active device seen at the output when the front-end
matching network is present. Hence,
Single stage amplifier equalized at both input
In
this case, we face a single matching problem. Thus,
employing the GRFT, optimum impedance data Z! for
,
the front-end matching network is generated. The gain of
the system shown in Figure
4,
is given by
,
In
(15),
S,
is the input reflection coefficient of the front-
end equalizer and it is given by
Furthermore,
In
( 1
I),
the driving point input impedance of the front-end
equalizer is
Z,,
=
-
R,,
+
jX,,
=
I-s2z
I
+
Sn
(17)
Defining a new weight factor
P,(o)
as
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the gain of the overall system is given by
Here, the terms
R,and
X,
refer to the real and
imaginary parts
of
the input impedance of the transistor
when its output is loaded by I-ohm resistor, which is
given by the equation
Z,
=
5
R,
+
jX,
.
The terms
R,,
and
X , ,
=
1-sll
refer
Finally, optimization of
T2(w)
to
a
flat gain level
To,
yields the Thevenin's impedance
Z,,
as set of points.
In the first step, it would be wise to select
To,
as
the
minimum value of
to the real and imaginary parts
of
the
output
impedance
of
the front-end matching circuit respectively.
Step
111:
Optimize the gain function
T,(ru)
to obtain
a
flat
gain level of
min
-
over the operation band.
'sz"
I-IS,,I2
Similarly in the second step, one can choose
To,
as
the
{
-
I!&f]
And determine the break points for
Z,,
as
described
in
the GRTF.
Step
Tv:
Having obtained the
data
for
Z,,
,
generate the
analytic form for it using immittance based modelling tool
and synthesize it.
Step
V
By using this analytic form of the impedance
Z,,
,
compute the front-end and the back-end matching
networks reflection coefficients as follows.
the specified frequencies
of
the
optimizations
Z,,
( i w )
=
R,,
(0)
Jx,,
(a)
+
and
Z,,(jw)
=
R,,(w)+
jX,,(o)
are
computed point by
point
as
described in the Generalized Real Frequency
Technique (GRFT). To improve the optimization, the
imaginary parts
X ,
be computed as
can
where
X,
designates the
Foster parts of driving point impedance
Z ,
.
The above-mentioned process
is
summarized in the
following algorithm.
4.
In
the
course
X ,
=
H { R ,
)+
X,,
i
=
I,?.
,
Using (b) calculate the load impedance
(C)
THE
ALGORITHM. DESIGN OF A SINGLE
STAGE MICROWAVE AMPLIFIER
z ,
=
-
=
R,,
+
jX,,
,
I-s,
I+S,
Part
I:
Design
of
front-end equalizer
Inputs:
S,,,S,,,S,,,S2,
Scattering parameters of the active
:
The
element over the prescribed frequency band.
Computation steps:
Step
I:
Construct the weight function
Save the terms
Tl(w).ZL,.S,
that have just been
computed
.
The first part of
the
algorithm is completed.
Part
11:
Design
of
back-end equalizer
Inputs:
S,,.S,,.S,,,S,,
The Scattering parameters of the active
:
element over the prescribed frequency band.
S,
and
Z,,
(calculated at the end of the first step)
Computation steps:
Step
I:
Construct the weight function
Step 11: Construct the gain function
PJw)
=
T,(w)
I-IS,S
-
Step
11:
Construct the gain function
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T,(~)=pz(~)l
4Rv,RL2
(R,,
+R,,)’
+(x,,
+X,,J~I
Transducer power gain TI is compensated to a flat gain
level To, =17dB.
In
this design, there was no need to
.
,
employ foster part for
Z
Hence,
as
the result of
optimization
R,,
is computed
The terms
R,
and
X,
refer to the real and imaginary
parts of the output impedance of the transistor when its
input is loaded by the front-end matching circuit, which is
given by the equation
R.,
=
-
/1.036168e-i 7.956833e-2
l,943650e-1
3,186138e-
I
7.
1.189832e-1
Z,
=
3
=
R,
+
j X ,
.
The terms
R,,
I-s,
and
X,,
refer
to the real and imaginary parts of the output impedance
Of
the back-end matching circuit respectively.
Step
Ill:
Optimize the gain function
TI(@)
to obtain a flat
gain level of
win[
And
determine
Part
11:
In
this part the back-end matching network is
constructed when the front-end is present. Similarly,
supplying the initial
guess
values for the resistive
excursions
&,
T,
is
optimised to a flat gain level
,
ToZ=15dB.
As
the result of optimisation
Rq2
is
found
as
R,,
=
[7.633953e
-
I
7.549760e
-
I
1.131313 9.398499e-
I
7.707590e
-
I ]
-A}
I-PIII
l-1~221
7.55651 le
-
I
Evaluation of
X,
(0)
at the break frequencies yields
point to
optimize
Z,,point
by
T, employing GRFT.
Step
IV:
Having obtained the data for
Z,,
generate the
analytic form for it using immittance based modelling
tool
and synthesize it.
Now, let
us
introduce an example
to
design a single stage
amplifier.
5.
X,,
=
[8.627670e
-
3 3.909525e
-
2 9. I18513e
-
2
1.265858e-
I
1.727060e-
I
-2.587056e-I]
A‘,,
=
[-7.650150e
-
2
-
2.538549e
-
I
-
5.712840e
-
1
-1.03125OJ
-6.412332e-1
-7.Ol2788e-1
EXAMPLE
In
this example, we wish
to
design a microwave amplifier
employing the immittance-based data-modelling tool.
For
this purpose commerciab’ available transistor HP-
AT4151
1
was selected and its biasing conditions are
V,,
=
8V.1,
=
IOmA.Z,
=
5 0 0
By
using the immittance based data modelling tool, the
minimum reactance functions can be calculated
analytically and this leads to the synthesis of the equalizer
circuits.
For
both front-end and back-end matching
networks, modelling form
A
is
selected
for
R ( 0 2 )
The program code was
run
and at the end the minimum
reactance functions for the input and the
output
equalizers
were found to be
~,,,,-pw
-
,,
2.087~’~5.j89S’+459Ss+1.363
Bandwidth
=
500
MHz. (500MHz-IGHz)
Table 1
:
Typical Scattering Parameters for HP-
AT41511
10955s‘
t
29342’
s 3 4 0 3 I P ~ 3 3 6 9 S S +
19.400
,,.,,,
Z
=
4.4/ls’+2.599s2+4.502s+0.668
t
~
+4.261
10.069s‘ +5.934s3
+
1 5 . 8 5 8 ~
4 . 8 1 4 ~
The final amplifier configuration and overall performance
[align=center]第九章[/align][align=left]1、当线程需要延时，进入阻塞状态，那 CPU 又去干什么事情了？如果没有其它线程可以运行，RTOS 都会为 CPU 创建一个空闲线程，这个时候 CPU 就运行空闲线程。在RT-Thread 中，空闲线程是系统在初始化的时候创建的优先级最低的线程，空闲线程主体主要是做一些系统内存的清理工作。[/align][align=lef
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