IEEE Solid-State Circuits Magazine - Summer 2014 - 9
Zin1
again. Due to the hysteresis in the
circuit, only a large input swing can
change the state.
A remarkable inflection point
occurred in the late 1960s, when it
was realized that the XCP could be
clocked. The profound observation
was that regeneration can begin
only when needed, and, therefore,
the circuit can amplify even small
differences. Shown in Figure 5 is an
example where M 1 and M 2 amplify
an initial imbalance between VX and
VY , VXY0 , according to
Z2
M1
M2
M1
M2
Zin2
(b)
Z1
(a)
Figure 3: An XCP as an impedance negator.
VDD
VDD
RD
RD
X
Vin1
M3
M4
X
Y
Y
M1
Vin2
M2
Vin1
M1
(a)
VXY (t) = VXY0 exp t ,
x reg
Vin2
M2
(b)
Figure 4: A differential buffer using (a) resistive loads and (b) the XCP.
RD
X
CL
VX
Y
M2
M1
CK
VXYO
CL
VY
M3
t
Figure 5: The regeneration behavior of XCP.
VDD
I1
Iin
Iin
I2
X
Y
M1
M2
X
with x reg = R L C L / (g m R L - 1) denoting the small-signal regeneration time
constant. This "synchronous amplification" property soon emerged in
sense amplifiers for memory design.
If the XCP begins in
or near equilibrium
(with its drain voltages equal or close
to each other), it
behaves in the smallsignal regime.
VDD
RD
(1)
Y
2
-
gm
Equation (1) suggests that the XCP
can provide infinite gain, another
remarkable advantage over unclocked
(asynchronous) amplifiers. The circuit's ability to regenerate small differences to logical levels proved
useful in analog comparators but it
also brought forth the problem of
metastability. After all, the infinite
gain accrues only if the circuit is given
infinite time.
In the next column, we study digital applications of the XCP.
Questions for the Reader
Figure 6: The XCP operation from two perspectives.
Hysteresis Versus Amplification
The bistable pair in Figure 4(b) creates
hysteresis in the circuit's input-output characteristic. If, for example, M 1
turns on while VX is high, Vin1 must
rise enough for M 1 to overcome M 3,
initiate regeneration around the loop,
and change the state. The regeneration continues until M 3 turns off and
M 1 enters the deep triode region, after
which Vin1 - Vin2 must become quite
negative before the state is changed
The foregoing overview raises a
number of interesting questions:
1) Is negative capacitance the same
as positive inductance?
2) Can the cancellation of positive
capacitance by negative capacitance be a resonance effect?
3) Why is the circuit in Figure 4(b) a
dynamic latch?
IEEE SOLID-STATE CIRCUITS MAGAZINE
su m m e r 2 0 14
9
Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Summer 2014
IEEE Solid-State Circuits Magazine - Summer 2014 - Cover1
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