Digitally programmable continuous-time modules for signal...

Details Digitally programmable continuous-time modules for signal... Digitally programmable continuous-time modules for signal...

2000-11-06

2002-10-15

Pascal, Robert (Department: 2817)

Amplifiers

Signal feedback

Variable impedance in feedback path varied by separate...

C330S069000, C327S552000

Reexamination Certificate

active

06466090

ABSTRACT:

BACKGROUND OF THE INVENTION
The present invention relates to transconductor-based programmable gain amplifiers and programmable continuous-time filters. More particularly, the present invention relates to methods of building transconductor-based programmable gain amplifiers and programmable continuous-time filters.
The main parameters of transconductor-based programmable gain amplifiers and programmable continuous-time filters (i.e., in-band gain, cut-off frequency, and quality factor) usually depend on transconductances or ratios of transconductances. The usual methods of changing these parameters are either changing the value of the transconductances (in amplifiers or filters), or changing the value of the capacitors involved (in filters).
A conventional transconductor-transconductor (g
m
-g
m
) voltage amplifier is presented in FIG.
1
. The g
m
-g
m
voltage amplifier
100
includes an input transconductor
110
, a feedback transconductor
120
, and a current-follower, such as a folded cascode
130
.
The output currents of the input transconductor
110
and of the feedback transconductor
120
are summed at the inputs the folded-cascode
130
. The feedback transconductor
120
establishes a negative feedback across the folded-cascode
130
.
The operation of the amplifier is described by the following equations:
i
inp
=
g
mi
⁢
v
ip
-
v
im
2
(
1
)
i
inm
=
-
g
mi
⁢
v
ip
-
v
im
2
(
2
)
i
fbp
=
g
mf
⁢
v
om
-
v
op
2
(
3
)
i
fbm
=
-
g
mf
⁢
v
om
-
v
op
2
(
4
)
where g
mi
is the transconductance of the input transconductor
110
and g
mf
is the transconductance of the feedback transconductor
120
,
At equilibrium
i
inp
=−i
fpb
i
inm
=−i
fbm
  (5, 6)
As a result, the voltage gain A
v
is determined as follows:
A
v
=
v
difo
v
difi
=
-
g
mi
g
mf
,
(
7
)
where
v
difo
=v
op
−v
om
;
v
difi
=v
ip
−v
im
.  (8, 9)
In order to make the voltage gain A
v
programmable, at least one of the transconductances g
mi
, g
mf
must be programmable.
Active G
m
-C filters make use of integrators composed of transconductors, such as OTAs (Operational Transconductance Amplifiers), and capacitors. One particular structure of a cascode/folded-cascode G
m
-C based biquad filter is presented in FIG.
2
.
The G
m
-C based biquad filter
200
shown in
FIG. 2
includes first and second input transconductors
210
and
220
, first and second feedback transconductors
230
and
240
, first and second current-followers (folded-cascodes)
250
and
260
, and first and second capacitors C
1
and C
2
. The first through fourth transconductors
210
,
220
,
230
, and
240
, have transconductances of g
m1
, g
m2
, g
m3
, g
m4
, respectively. The transfer function from (i
p
, i
m
) to (o
p2
, o
m2
) is:
T
2
⁡
(
s
)
=
V
⁡
(
op2
)
-
V
⁡
(
om2
)
V
⁡
(
ip
)
-
V
⁡
(
im
)
=
g
m1
×
g
m2
C
1
×
C
2
×
s
2
+
g
m3
×
C
2
×
s
+
g
m2
×
g
m4
(
10
)
This is a transfer function corresponding to a second-order low-pass filter with the cut-off frequency of:
ω
0
=
g
m2
×
g
m4
C
1
×
C
2
(
11
)
with a quality factor:
Q
=
g
m2
×
g
m4
g
m3
2
×
C
1
C
2
(
12
)
and a DC gain:
T
2
⁡
(
0
)
=
g
m1
g
m4
(
13
)
When the individual transconductances g
mk
are each considered as a multiple of an elementary transconductance g
m
:
g
mk
=a
k
×g
m
, (
k=
1, . . . , 4)  (14)
the parameters of the filter become:
ω
0
=
a
2
×
a
4
×
g
m
C
1
×
C
2
(
15
)
Q
=
a
2
×
a
4
a
3
2
×
C
1
C
2
(
16
)
T
2
⁡
(
0
)
=
a
1
a
4
(
17
)
Thus, in order to change the parameters of the filter one has to adjust the values of the capacitances and/or the transconductances.
A generic transconductor is presented in FIG.
3
. The output current of the transconductor
300
is proportional to the differential input voltage:
i
0
=g
m
=v
in
  (18)
A conventional implementation of the transconductor
300
is shown in FIG.
4
. The transconductor
300
includes first and second differential transistors T
D1
and T
D2
, first and second mirror transistors T
M1
and T
M2
, and a current source
410
. The current source
410
provides a current I
q
. The first and second mirror transistors T
M1
and T
M2
form a current mirror
420
. The first and second differential transistors T
D1
and T
D2
form a differential pair
430
, biased by the current source
410
and the current mirror
420
. The transconductance of this stage depends on the bias current I
q
:
i
out
=
g
m
⁡
(
I
q
)
×
v
in
=
2
×
K
n
′
×
I
q
×
(
W
L
)
1
×
v
in
(
19
)
where (W/L)
1
is the aspect ratio of the first and second differential transistors T
D1
and T
D2
of the differential pair
430
, and K
n
′ is the transconductance parameter for the same transistors.
One conventional way of adjusting the transconductance is by changing the bias current I
q
. This can be done continuously or in steps. The circuit of
FIG. 4
performs the adjustment continually.
However,
FIG. 5
shows a transconductor similar to the circuit of
FIG. 4
, except that the bias current is adjusted in steps. As shown in
FIG. 5
, the transconductor
500
includes first and second differential transistors T
D1
and T
D2
, first and second mirror transistors T
M1
and T
M2
, and a current source
510
. As in
FIG. 4
, the first and second mirror transistors T
M1
and T
M2
form a current mirror
420
, and the first and second differential transistors T
D1
and T
D2
form a differential pair
430
, biased by the current source I
q
and the current mirror
510
. However, the current source
510
further includes first through n
th
bias sources
550
1
,
550
2
, . . . ,
550
n
, for supplying first through n
th
bias currents I
q1
, . . . , I
qn
, which can be coupled to the differential pair
430
through first through n
th
switches
560
1
,
560
2
, . . . ,
560
n
, respectively. In this case the transconductance can be programmed through the digital word D=(D
1
, . . . , D
n
), respectively used to control the first through n
th
switches
560
1
,
560
2
, . . . ,
560
n
, respectively.
The main disadvantage of the circuits of
FIGS. 4 and 5
is that changing the bias current affects not only the transconductance, but the operating point and the input voltage range (for a given amount of distortions).
As a result, another way of setting the transconductance of a differential stage has been proposed, which is shown in FIG.
6
. The transconductor
600
of
FIG. 6
includes first and second differential transistors T
D1
and T
D2
, first and second mirror transistors T
M1
and T
M2
, first and second current sources
610
a
and
610
b,
and a resistor R
s
.
The first and second current sources
610
a
and
610
b
each provide a current I
q
. The first and second mirror transistors T
M1
and T
M2
form a current mirror
420
. The first and second differential transistors T
D1
and T
D2
form a differential pair
430
, and are biased respectively by the first and second current sources
610
a
and
610
b
and the current mirror
420
. The resistor R
s
is placed between the first and second current sources
610
a
and
610
b.
If the transconductance of the differential pair transistor is much larger than the conductance of the degeneration resistor R
s
:
g
m
>>
1
R
s
,
(
20
)
then the output current is given by:
i
out
=
2
×
v
in
R
s
(
21
)
The gain of the circuit can be adjusted through the size of the resistor R
s
. The operating point of the circuit does not change with R
s
, but usually the transconductance of the first and second mirror transistors T
M1
and T
M2
has to be enhanced in order to fulfil condition (20).
The resistance R
s
can be adjusted continuously or in steps. When it is adjusted in discrete steps, the resistor R
s
is replaced by a network including resistors and switches placed in parallel or in series with these resistors. The switches contribute with important parasitic resistance and capacitance to the equiv

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