IEEE Solid-State Circuits Magazine - Summer 2014 - 7

s

A C ircu it for All Season

Behzad Razavi

The Cross-Coupled Pair-Part I

A

An elegant circuit is one that realizes
a function efficiently. A beautiful circuit is one that stands the test of time.
The cross-coupled pair (XCP) is such a
topology: it has evolved for 95 years
and adapted itself to various device
technologies, supply voltages, and
operation speeds. In this and future
columns, we analyze this circuit's
properties and study its applications
in both analog and digital design.

r2

r1

-
+

P1

4V

I

F2 G2

G1 F1

R1

B

B

P2

-
80 V
+

R2

Brief History
The XCP was introduced in June
1919 in two independent papers
published within four days of each
other. Authored by Abraham and
Bloch [1] and Eccles and Jordan [2],
both papers exploited the XCP to
create a multivibrator. (Abraham
and Jordan coined this term to
emphasize the harmonically rich
output of the circuit.) These papers
are difficult to find but Abraham
and Bloch show a multivibrator circuit (Figure 1) in another paper that
they published in December 1919
[3]. [For readers not familiar with
vacuum tubes, terminals F, G, and P
(filament, grille, and plaque, respectively, in French) are somewhat similar to the source, gate, and drain of a
field-effect transistor, respectively.]
Of course, concepts such as positive
feedback and regeneration were well
understood at the time. In the 1920s,
van der Pol analyzed the multivibrator as a "relaxation" oscillator [4].
The XCP's utility as a bistable (memory) element was also recognized by
Eccles and Jordan in another paper in
December 1919 [5]. The "Eccles-Jordan
Digital Object Identifier 10.1109/MSSC.2014.2329234
Date of publication: 26 August 2014

G1

G2

Figure 1: A multivibrator using cross-coupled triodes reported in 1919.

flipflop" (what we call a regenerative
latch today) was thus born. The ENIAC,
the first general-purpose computing
machine, incorporated this structure
for storage [6]. After the invention of
the bipolar transistor in the 1940s, the
XCP naturally began to play similar
roles in semiconductor circuits.

The XCP was introduced in June 1919
in two independent
papers published
within four days of
each other.

In addition to serving as a memory
cell, the XCP also emerged in two distinct types of digital systems, namely,
as a regenerative component in emitter-coupled logic (ECL) circuits, shown
in Figure 2(a) [7], [8], and as a sense
amplifier in memories, shown in Figure 2(b) [9], [10].

The latter eventually morphed
into comparators for use in analog
design [11]. The use of the XCP as a
negative- G m cell in semiconductor
LC oscillators can be traced back to
[12] [Figure 2(c)].

Small-Signal Properties
If the XCP begins in or near equilibrium
(with its drain voltages equal or close
to each other), it behaves in the smallsignal regime. Owing to the internal
positive feedback, the pair can operate
as an impedance "negator." Shown in
Figure 3, the XCP produces an impedance of Z in1 = - Z 1 - 2/g m between the
drains or Z in2 = - Z 2 + 2/g m between
the sources.
Two special cases of Figure 3(a) are
of particular interest. First, if Z 1 = 0,
the pair exhibits a negative resistance
equal to - 2/g m, serving numerous
applications, from amplifiers to oscillators. Interestingly, the real value of
- 2/g m remains unchanged even if all
of the circuit's capacitances are taken

IEEE SOLID-STATE CIRCUITS MAGAZINE

su m m e r 2 0 14

7



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