IEEE Solid-State Circuits Magazine - Winter 2015 - 12
VDD
L1
L2
X
Y
M1
M2
M4
M3
CC
Figure 7: The use of NIC as a fine tuning element.
XCP as Negative Impedance
Converter
As mentioned in the first article in
this series, the XCP can operate as an
impedance negator [a.k.a. a negative
impedance converter (NIC)]. The simplicity of this topology makes it superior to conventional NICs that employ
op amps. A common application is to
create a negative capacitance that
can cancel the positive capacitance
seen at a port, thereby improving the
speed. Figure 5 depicts an example in
broadband transmitter design [9].
With the high current necessary
in the output stage, M 1 and M 2 tend
to be wide, exhibiting a large input
capacitance. The NIC cancels some
of this capacitance, thus increasing
the bandwidth at X and Y.
The NIC design entails two issues.
First, at high speeds, the capacitances of M 3 and M 4 affect the NIC
performance. If only C GS is considered, the admittance presented by
the NIC emerges as [9]
C GS s
gm
.
+ 2) 1 + 1
gm CC s
1-
YNIC = -
(
C GS
CC
(2)
For frequencies well below the transistors' fT (. 2rg m /C GS ), the second
term in the numerator is negligible,
yielding a capacitance equal to - C C
in series with a resistance equal to
- (C GS /C C + 2) /g m . The key point
here is that C GS raises the magnitude of the series resistance and
hence lowers the Q of the negative
capacitance.
Second, in Figure 5, the NIC can
form a relaxation oscillator with R 1
and R 2 or at least cause significant
ringing in broadband data. The value
of C C must therefore be chosen low
enough to avoid these effects.
Another interface exhibiting a high
capacitance occurs at I/O pads that
incorporate electrostatic discharge
protection and hence limit the bandwidth. As shown in Figure 6, an NIC
can be tied to these pads, cancelling
part of the capacitance. This circuit
can be combined with a T-coil for further bandwidth enhancement [10].
The NIC finds other interesting
applications, for example, in digitally controlled oscillators requiring a fine frequency step size [11].
Consider the arrangement shown in
Figure 7, where M 1 and M 2 act as an
oscillator, and M 3 and M 4 as an NIC
[11]. It is possible to "attenuate" the
effect of C C at X and Y by a large
factor, thus providing fine frequency
The XCP finds wide
application as a
negative resistance
in the design of
oscillators.
tuning. This can be seen by expressing the NIC admittance from (2), with
C GS = 0, as
- 2g m C 2C ~ 2
4C 2C ~ 2 + g 2m
g 2m jC C ~
,
4C 2C ~ 2 + g 2m
YNIC (j~) =
(3)
and choosing 4C 2C ~ 2 & g 2m so that
VDD
YNIC (j~) . RL
CL
RL
M4
M3
Vin1
M1
CK
w i n t e r 2 0 15
Vin2
M2
M5
M6
Figure 8: Regenerative amplification provided by the XCP.
12
CL
Y
X
IEEE SOLID-STATE CIRCUITS MAGAZINE
CK
gm
g 2m
+
.
2
4jC C ~
(4)
In these equations, g m denotes the
transconductance of M 3 and M 4 . We
observe that the NIC presents two
parallel impedances equal to - 2/g m
2
, with the latter servand 4jC C ~/g m
ing as a large inductor. If this inductance is much greater than L 1 and L 2
in Figure 7, then moderate steps in
C C translate to small steps in the
oscillation frequency. Another interpretation is to write the second term
as jC C ~ [g m / (2C C ~)] 2 and conclude
that the value of C C is reduced by a
factor of [g m / (2C C ~)] 2 [11].
Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Winter 2015
IEEE Solid-State Circuits Magazine - Winter 2015 - Cover1
IEEE Solid-State Circuits Magazine - Winter 2015 - Cover2
IEEE Solid-State Circuits Magazine - Winter 2015 - 1
IEEE Solid-State Circuits Magazine - Winter 2015 - 2
IEEE Solid-State Circuits Magazine - Winter 2015 - 3
IEEE Solid-State Circuits Magazine - Winter 2015 - 4
IEEE Solid-State Circuits Magazine - Winter 2015 - 5
IEEE Solid-State Circuits Magazine - Winter 2015 - 6
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IEEE Solid-State Circuits Magazine - Winter 2015 - 11
IEEE Solid-State Circuits Magazine - Winter 2015 - 12
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