IEEE Solid-States Circuits Magazine - Winter 2021 - 37

frequency-the fundamental goal of
the transceiver. Characteristics of the
clock used for this purpose have a significant impact on the overall system
performance. The spectrum of an ideal (or noiseless) clock appears as an impulse at the oscillation frequency; i.e.,
all of the energy is concentrated in one
bin. Noise introduces uncertainty in
the clock zero crossings (also known
as jitter), which is equivalent to random errors in the clock periods. In the
frequency domain, this phenomenon
appears as the spreading in the oscillator frequency into adjacent frequency
bins. The single-sideband phase noise,
illustrated in Figure 3, has units of
dBc/Hz and is defined as the ratio of
the carrier power (PLO) and the noise
integrated over a bandwidth of 1 Hz
and the specified offset frequency.
The slope with which the noise power reduces with frequency can be
influenced by both circuit-level and
architecture-level design choices; for
almost all applications, wireless and
wireline, the oscillator is placed with a
feedback loop to suppress the in-band
or close-in phase noise. The " Tx VCO
Phase Noise " section describes how the
GSM out-of-band spurious emission requirement toughens requirements on
the phase noise of the Tx clock.
A mplifier nonlinea r it y is a n other primary source of performance degradation. The power series
{y (t) = a 1 x (t) + a 2 x 2 (t) + a 3 x 3 (t) + ..}
offers a simple memoryless model
to study the impact of amplifier nonlinearity on the system. Consider the
case where two tones model the modulated input signal at frequencies ~ 1
and ~ 2. Considering only third-order
nonlinearity, intermodulation between two tones will result in

	

y (t) = a 3 " cos ~ 1 t + cos ~ 2 t ,3
= 3a 3 " cos ^2~ 1 - ~ 2h t 
+ cos ^2~ 2 - ~ 1h t , /4.
(1)

In (1), we assume that tuned circuits along the signal path filter all
of the tones at large frequency offsets from the carrier frequency. The
tones at (2~ 1 - ~ 2) and (2~ 2 - ~ 1)
will be unaffected by any filtering be-

	

cause they appear at a frequency offset equal to the difference of ~ 1 and
~ 2. As displayed in Figure 4, the difference in the desired and undesired
signal is called the third-order intermodulation [IM3 (units of dBc)]. If the
two tones model the band edges of
the desired signal, the IM3 products
will fall directly into an adjacent band
(potentially assigned to another user).
Wireless standards define an adjacentchannel-leakage ratio to limit the
spurious emission permitted in the
adjacent channel. For Rxs, third-order
nonlinearity comes into play when
the intermodulation product of two
strong, undesired (blocker) signals
falls within the desired signal band
degrading the SNR.
A large fraction of the issues in
wireless transceivers stems from the

fact that the channel used for data
transmission is a shared resource,
air. The challenge lies in envisioning
all possible coexistence scenarios
and incorporating these system insights into designing Rx circuits robust enough to handle all aggressors
and then designing Tx circuits with
low spurious emissions.

2G
The main application for 2G cellular
standards-GSM, digital cellular system, and personal communications
service-was voice communication.
The plot in Figure 5 illustrates the operating scenario for GSM850. GSM is a
time-division-duplexed (TDD) system
in which the Tx and Rx do not overlap
in either time or frequency. The Tx is
assigned 200-kHz channels between

SNRO

SNRI
LPF

DSP

A /D

LNA

PIn,Rx

Demodulator
Noise Contributors
FIGURE 2: The SNR requirement in a radio Rx. LPF: low-pass filter.

PLO(dBm)

PN(dBc/Hz)
1Hz
Pnoise,SSB(dBm)
Frequency
FLO FLO + Foffset
FIGURE 3: The oscillator phase noise (PN).

P1

P1 + G
P2

IM3

FIGURE 4: The origin of intermodulation (IM) tones.

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IEEE Solid-States Circuits Magazine - Winter 2021

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