IEEE Solid-States Circuits Magazine - Winter 2020 - 6

C IRCU IT INTU ITIONS

Ali Sheikholeslami

Equalizer Circuit

W

Digital Object Identifier 10.1109/MSSC.2019.2952233
Date of current version: 23 January 2020

6

WINTER 2020

Channel

Transmitter
+
VTx(f )
-

Tx

Equalizer
+
Vid(f )
-

Hw (f )

+
Vod(f )
-

Heq(f )

FIGURE 1: A simplified block diagram of a high-speed wireline transceiver. An equalizer at the
receiver end of the channel compensates for the channel attenuation of the transmit signal.

H w (f )/(dB)

RL
Vid /2
(a)

H eq(f )/(dB)

fN

f

IB

fz fp1

fp2

(b)

f

H (f )/(dB)

Welcome to the 23rd article in the "Circuit Intuitions" column series. As the
title suggests, each article provides
insights and intuitions into circuit
design and analysis. These articles are
aimed at undergraduate students but
may serve the interests of other readers as well. If you read this article, I
would appreciate your comments and
feedback as well as your requests and
suggestions for future articles in this
series. Please email me your comments:
ali@ece.utoronto.ca.
In a previous article [1] in this series,
we discussed how a piece of wire connecting a data transmitter to a receiver
attenuates the transmit signal at high
frequencies, making the task of reliable data recovery by the receiver difficult. To compensate for the channel
attenuation, we design an equalizer
circuit and place it after the channel
(Figure 1). The equalizer circuit has a
transfer function that is the inverse
of the wire's transfer function in the
frequency range of interest, as shown
in Figure 2. The equalizer is designed
such that the combined transfer function of the wire and the equalizer
circuit will be flat up to the Nyquist
frequency fN , defined as half of the
baud rate. In this article, we review a
common equalizer known as the continuous-time linear equalizer. We rely
on the techniques described in the
first article in this series [2] to find the
transfer function of this equalizer.
Figure 3 presents a circuit diagram
of an equalizer consisting of a differential pair with capacitive and resis-

(c)

f

FIGURE 2: (a) The channel's (wire's) transfer
function exhibits a low-pass characteristic.
The attenuation at the Nyquist frequency fN
is highlighted. (b) The equalizer's transfer
function exhibits a high-pass characteristic
at the frequencies of interest. It has one zero
and two poles. (c) The combined transfer
function of the channel and the equalizer
has a flat frequency response up to fN .

tive degeneration (C s and R s) and a
parallel combination of resistive and
capacitive load (R L and C L). The input
to the differential pair is the differential received signal, Vid . This signal is
essentially a low-pass-filtered version
of the transmit signal, and we wish

IEEE SOLID-STATE CIRCUITS MAGAZINE

RL

M1

RS
CS

M2

+
- Vod

-Vid /2
CL

CL

IB

FIGURE 3: A differential circuit implementation of a continuous-time linear equalizer.

to use the equalizer to undo what
the channel (the wire) has done to it.
Intuitively, since the transmit signal is
attenuated at high frequencies, we wish
to amplify the received signal at high
frequencies. Therefore, we need a highpass filter; such a filter will amplify the
high-frequency content of the signal
or, equivalently, attenuate the low-frequency content. With this circuit, all
frequency components of the transmit
signal receive the same treatment and
are, hence, equalized.
Let us first understand intuitively
how this circuit performs equalization. If we assume the input is differential, that is, the left side sees Vid /2
and the right side -Vid /2, then, by
symmetry, the circuit can be reduced
to a half circuit, as demonstrated in
Figure 4(a). Note that the transfer function
IEEE Solid-States Circuits Magazine - Winter 2020

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