Wave transmission lines and networks – Negative resistance or reactance networks of the active type – Simulating specific type of reactance
Reexamination Certificate
2001-03-15
2004-05-18
Pascal, Robert (Department: 2817)
Wave transmission lines and networks
Negative resistance or reactance networks of the active type
Simulating specific type of reactance
C333S215000
Reexamination Certificate
active
06737944
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to an active inductor, and more particularly to an active inductor in which a field effect transistor is employed.
2. Description of the Background Art
In monolithic microwave integrated circuits (hereinafter referred to as “MMICs”), it is required to obtain an impedance matching between circuits and to improve the bandwidth of circuits. To meet these requirements, a capacitor and an inductor are used in MMICs. As an inductor for use in MMICs, a spiral inductor has been employed in many cases which is made of a metal conductor wound in a spiral manner on a dielectric substrate.
A spiral inductor has a simple construction, whereas its configuration has to be enlarged in order to obtain a large inductance. Thus, a spiral inductor practically tends to occupy a large area. Moreover, there have been problems in that a resistance component is high, resulting in an increase in power consumption and that cross-talk occurs between a spiral inductor and a peripheral circuit thereof.
In order to solve the above noted problems encountered in a spiral inductor, there have been proposals for an active inductor using a transistor which is an active element. Advantageously, an active inductor can be miniaturized compared to a spiral inductor and, besides, a resistive component is low, which allows reduction in power consumption. Further, cross-talk rarely occurs between an active inductor and a peripheral circuit thereof. For these characteristics, an active inductor is suitable for MMICs.
Conventionally, combination of a gyrator in a four-port network circuit and a capacitor has been proposed as an active inductor, for a gyrator has a function of converting an impedance. In particular, a field effect transistor has a high input impedance, which is therefore suitable for constituting a gyrator. The technique for forming an active inductor by a capacitor and a gyrator comprising a field effect transistor is disclosed, for example, in Japanese Patent Application Laid-Open No. 4-233312.
On the other hand, another type of active inductor has also been proposed which is not so constructed as to convert an impedance of a capacitor using a gyrator.
FIG. 23
is a circuit diagram showing a construction of an active inductor
200
which is introduced, for example, in “Broad-Band Monolithic Active Inductor and Its Application to Miniaturized Wide-Band Amplifiers”, Hara et al., IEEE Transactions on Microwave Theory and Techniques, MTT-36, No. 12, pp.1920-1924 (December 1988). Transistors M
1
and M
2
are both field effect transistors, each having a drain, a gate and a source represented as D, G and S, respectively. The source of the transistor M
1
is connected to the gate of the transistor M
2
, while the drain of the transistor M
1
is connected to the source of the transistor M
2
. A resistor R is connected between the gate of the transistor M
1
and the drain of the transistor M
2
, and an impedance between the drain and gate of the transistor M
2
acts as an inductor. A bias circuit for operating the transistors M
1
and M
2
is not illustrated in the figure.
Both of the field effect transistors M
1
and M
2
can be represented as an equivalent circuit as shown in FIG.
24
. Specifically, when a parasitic capacitor C
gs
is provided between the source and the gate and the gate-source voltage is V
gs
, operating characteristics of the transistors M
1
and M
2
can be approximated by operations of the equivalent circuit having a current source for flowing current g
m
V
gs
from the drain to the source (g
m
>0: transconductance). For simplification, symbols in the circuit also indicate values of an element, potential or current which they represent. The expression “approximate a circuit by its equivalent circuit”, which will be used hereinafter, represents approximation of operations of a circuit by operations of its equivalent circuit.
Employing the equivalent circuit shown in
FIG. 24
, numerical subscripts
1
and
2
are added to the parasitic capacitor C
gs
, the transconductance g
m
, the gate-source voltage V
gs
, respectively, so as to make clear that they are elements in the equivalent circuit of the transistors M
1
and M
2
. This allows the active inductor
200
to be approximated by the equivalent circuit shown in FIG.
25
.
The drain-gate voltage of the transistor M
2
is indicated by V, and current flowing in the active inductor shown in
FIG. 23
is indicated by I (let positive a direction the current flowing into a junction between the drain of the transistor M
2
and the resistor R). An angular frequency of the voltage V is indicated by &ohgr;, and an imaginary unit (−1)
1/2
is indicated by j. Then, admittances of the parasitic capacitors C
gs1
and C
gs2
are indicated by j&ohgr;C
gs1
and j&ohgr;C
gs2
, respectively.
Therefore, an impedance of the active inductor shown in
FIG. 23
is expressed as follows:
Z
=
V
1
=
1
1
+
(
ω
C
gs2
g
m2
)
2
·
1
+
j
ω
C
gs1
R
g
m1
+
j
ω
[
C
gs1
-
(
g
m1
g
m2
)
C
gs2
+
(
ω
C
gs2
g
m2
)
C
gs1
]
(
1
)
In the case that the transistors M
1
and M
2
have the same characteristics, equations C
gs1
=C
gs2
=C and g
m1
=g
m2
=g are satisfied. Thus, the equation (1) is expressed as follows:
Z
=
1
1
+
(
ω
ω
T
)
2
·
1
g
+
j
ω
CR
g
1
+
j
(
ω
ω
T
)
3
(
2
)
where &ohgr;
T
=g/C.
The common denominator of the right term on the right side of the equation (2) is 1+j(&ohgr;/&ohgr;
T
)
3
. Under the condition where:
(
ω
ω
T
)
3
⪡
1
(
3
)
approximation can be obtained as follows:
Z
≈
1
g
+
j
ω
CR
g
1
+
(
ω
ω
T
)
2
(
4
)
Moreover, under the condition where:
(
ω
ω
T
)
2
⪡
1
(
5
)
the condition of the expression (3) is also satisfied, and the expression (4) can be approximated as follows:
Z
≈
1
g
+
j
ω
(
CR
g
)
(
6
)
Therefore, under the condition of the expression (5), the active inductor shown in
FIG. 23
can be approximated by a circuit having a resistance component (1/g) connected in series to an ideal inductor CR/g as shown in FIG.
26
.
Even when employing the equivalent circuit shown in
FIG. 24
in which a resistive component in the transistors M
1
and M
2
is ignored, a series resistive component exists as shown in the expression (6). This shows that loss is in principle unavoidable in the active inductor
200
.
SUMMARY OF THE INVENTION
A first aspect of the present invention is directed to an active inductor comprising first and second field effect transistors, each having a source, a gate and a drain, wherein the drain of the first field effect transistor is connected to the source of the second field effect transistor, the gate of the first field effect transistor is connected to the drain of the second field effect transistor with no active element interposed therebetween. The active inductor further comprises a feedback path provided between the source of the first field effect transistor and the gate of the second field effect transistor, wherein the gate and the source of the second field effect transistor serve as two ports of the a
Glenn Kimberly
Oblon & Spivak, McClelland, Maier & Neustadt P.C.
Pascal Robert
Renesas Technology Corp.
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