IEEE Solid-State Circuits Magazine - Fall 2015 - 9

A C ircu it for All Season s

Behzad Razavi

The Bridged T-Coil

T

The bridged T-coil, often simply called
the T-coil, is a circuit topology that extends the bandwidth by a greater factor than does inductive peaking. Many
high-speed amplifiers, line drivers,
and input/output (I/O) interfaces in
today's wireline systems incorporate
on-chip T-coils to deal with parasitic
capacitances. In this article, we introduce and analyze the basic structure
and study its applications.

Brief History
The T-coil circuit can be traced back
to the 1948 classic paper on distributed amplifiers by Ginzton et al. [1].
The authors call the structure the
"bridged-tee connection" and present it along with its equivalent circuits, as shown in Figure 1.
The use of T-coils for bandwidth
enhancement was pioneered by Tektronix engineers in the late 1960s [2].
The need for fast "vertical" amplifiers
for the front end of oscilloscopes had
led to many new wide-band circuit
techniques, and Tektronix designers saw the significant advantage of
T-coils. The instrumentation manufacturer guarded the design details
of T-coil circuits as a trade secret for
many years [2]. It was only in 1990
that Dennis Feucht, a former Tektronix engineer, provided the T-coil
design equations in his book [3].
The early T-coil implementations
were based on discrete, off-chip inductors or transformers, suffering from
board parasitics, bond wire inductances, and unwanted couplings to and
from other signals. A few integrated

-M
L+M
L

1
mLK
2

1
mLK
2

L

Cg

-M

1 - m2
L
4m K

Cg

mCk

Figure 1: A bridged T-coil circuit described by Ginzton et al. in 1948 [1].

GaAs realizations appeared in the late
1980s and early 1990s [4], [5]. With
the RF circuits revolution in the 1990s
and the tremendous work on integrated inductors, the T-coil was bound
to find its way to CMOS chips as well.
Of course, the finite Q and parasitic
capacitances of on-chip structures
would introduce new issues. Moreover, a well-defined coupling factor
would need to be created between two
spiral inductors. In 2003, two papers
described the design of integrated
T-coils and their use in broadband
drivers [6] and electrostatic discharge
(ESD) protection circuits [7].

Basic Idea
The bridged T-coil is a special case
of two-port bridged-T networks. It

CB
L1

L2

1

2
3

Digital Object Identifier 10.1109/MSSC.2015.2474258
Date of publication: 2 December 2015

L+M

Figure 2: A basic bridged T-coil structure.

consists of two mutually coupled
inductors and a bridge capacitor
(Figure 2). The coupling polarity matters and the two inductances are commonly chosen to be equal. With certain loads attached to this circuit, the
impedance seen at node 1 or 2 and
the transfer function from either of
these nodes to node 3 present interesting properties.
As an example, consider the simple common-source stage shown in
Figure 3(a) with a load capacitance C L .
At high frequencies, the small-signal
drain current of M 1 is shunted by C L,
causing | Vout | to fall. We can place an
inductor in series with R D [Figure 3(b)]
so that the series impedance of R D and
L D increases with frequency, thereby
forcing a greater current through C L
and lessening the gain roll-off. Alternatively, we can insert a T-coil circuit in the
signal path as illustrated in Figure 3(c).
We are interested in the transfer function Vout /Vin and its behavior as a
function of component values.
The transfer function can be
derived using the extra element
theorem [8] or the D-Y transformation
[9] and is as follows:

IEEE SOLID-STATE CIRCUITS MAGAZINE

fa l l 2 0 15

9



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