IEEE Solid-State Circuits Magazine - Spring 2015 - 42

has a power spectral density equal
to kT (i.e., -174 dBm/Hz), where k
is the Boltzmann's constant and T
the operative temperature expressed
in Kelvin. The noise figure of the
receiver sets the minimum power
that the wanted signal must have to
be detectable. This power is called
sensitivity and is given by

Off-Chip

Antenna

Mixer
Local
Oscillator
Channel
Selection
Filters

0°
90°

Quadrature
Generation

Analog to
Digital
Converter
ADC

Surface
Acoustic Wave
(SAW) Filter

ADC

Low Noise
Amplifier
(LNA)

Psens

Mixer

Figure 5: Typical structure of a wireless receiver.

solutions when the channel is shifted
around DC, phase shift and recombination are done in digital domain
after the ADC, where to realize these
operations is simpler.
The structure in Figure 5 can be
used for two different kinds of receivers, the direct conversion architecture, where the signal is downconverted exactly around DC (i.e.,
fLO = fc), and the low-IF architecture,
where fc - fLO is only slightly above
DC and in-band blockers can still be
rejected using a low-pass filter instead of a band-pass one.

2. Characterization of a Wireless RX
Now that the radio architecture has
been defined, it is important to introduce some metrics in order to
characterize the performance of the
wireless receiver. In this section, four
metrics will be introduced to quantify the quality of the input matching,
the amount of noise and distortion
introduced by the receiver, and the
spectral purity of the local oscillator.

Input Matching (S11)
The quality of the impedance matching realized by the LNA can be evaluated using the magnitude of the reflection coefficient S 11 . The S 11 is
defined as
S 11 =

Z in, LNA - R s
,
Z in, LNA + R s

(1)

where Z in, LNA is the input impedance of the LNA and RS the driving

s p r I n g 2 0 15

impedance. The magnitude S 11 represents the ratio between the amplitude of the reflected wave compared
to the amplitude of the incident wave.
When no reflected way is present the
matching is perfect and S 11 = -3 dB.
A reasonable good matching is obtained when |S11| 1 - 10 dB, which
means that more than 90% of the
power is transferred from the driving
stage to the LNA.

Noise
The noise of the receiver is characterized in terms of noise factor (nf)
and noise figure (NF) defined as
nf = SNR in ,
SNR out

NF = 10Log 10 (nf )
(2)

where SNR in is the signal-to-noise
ratio at the input of the receiver and
SNR out is the signal-to-noise ratio at
the output of the receiver. NF and
nf represent the excess of noise
introduced by the receiver and can
be also expressed as function of
the noise coming from the antenna
(N Rs) and the noise added by the
receiver itself reported at its input
(N RX, in):
nf = 1 +

N RX, in
.
N Rs

(3)

The minimum nf achievable is
equal to 1 when no noise is added (i.e.,
N RX,in = 0), having SNR out = SNR in .
While N RX,in depends on the receiver
implementation, N Rs is fixed and

IEEE SOLID-STATE CIRCUITS MAGAZINE

dBm

= - 174 + 10Log 10 B + NF
+ SNR min dB .

The first two terms represent the
noise N Rs integrated in the bandwidth B of the wanted signal , while
SNR min is the minimum signal-tonoise ratio required at the output
of the receiver to demodulate the
wanted signal.

Distortion
In addition to the noise, the analog
section of the receiver can distort
the input signal due to the presence
of nonlinearities in the signal transfer function. The distortions can be
divided in two categories: hard distortions and weak distortions. The
former involves signals that explore
widely the input-output characteristic, and the latter are generated
when signal swing around the operative point is limited. This article will
focus on the weak distortions that,
in presence of blockers, can produce
undesired components overlapped
to the wanted signals.
The weak distortions can be studied starting from a Taylor expansion
of the input-output characteristic
around the operative point:
y^ t h = ao + a1 x + a2 x2 + a3 x3 + g
(4)
where y ^ t h and x ^ t h are, respectively,
the output and the input signals.
When the characteristic described
by (4) is explored by two tones, with
same amplitude ^A h but different frequencies (~1 and ~2 ), several components are generated at the output.
Among them, the following four contributions will be considered:
a 1 A (cos ^~ 1 t h + cos ^~ 2 t h)

(5)

Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Spring 2015