IEEE Solid-State Circuits Magazine - Spring 2015 - 40

RX Band (e.g., Cellular)
Out of Band
Blocker
(e.g., Wi-Fi)

In-Band Blocker
(e.g., Other Channel)
Wanted Signal
(e.g., Your Channel)

fcarrier

Frequency

Figure 1: Input signal of a wireless receiver.

down-conversion, and filtering. The
down-conversion is the operation of
moving the wanted signal, which is
modulated around a high-frequency
carrier fc, to a lower frequency.
Among these three tasks, to filter
in-band and out-of-band blockers
is generally the most challenging
operation and is crucial to relax the
performance required to the analogto-digital converter for the digitalization of the wanted signal. In the
following, these three tasks will be
discussed identifying the key building blocks for each operation.

Signal Amplification
Since the received signal is very
small, the first blocks of the receiver
chain is typically an amplifier called
low-noise amplifier (LNA). The aim
of the LNA is to amplify the input
signal adding a minimum quantity
of noise.
Since the LNA is the first block of
the RX chain, it is also the interface
with the external components of the

radio. For this reason, the LNA input
impedance must match with the one
provided by the external element
preceding it (e.g., the antenna). This
impedance is indicated with RS and
its value is typically 50 Ω.

Signal Down-Conversion
Once the wanted signal has been
amplified by the LNA, it is shifted
from RF to a lower frequency. This
operation is performed by multiplying the RF signal with a sinusoid
called local oscillator (LO). As shown
in Figure 2, the multiplication of the
wanted signal by the LO corresponds
to a convolution in the frequency
domain that generates four contributions: two centered at the sum of
the carrier frequency (fc) and the LO
frequency (fLO) and two at their difference. The frequency fLO is chosen
very close to fc to have the contributions generated at the difference
close to zero (i.e., at fc - fLO) . Notice
that, regardless the position of the
wanted signal at RF, to tune the LO

xLO(t) = cos(2π fLO t)
xSIG(t) × xLO(t)

xSIG(t)
xSIG(f)

-fc

xSIG(f) ∗ xLO(f)

xLO(f)

-fLO 0

fLO

-fc-fLO fLO-fc 0 fc-fLO fLO+fc f

Figure 2: RF signal down-conversion.

s p r I n g 2 0 15

IEEE SOLID-STATE CIRCUITS MAGAZINE

allows to down-convert the signal always at the same difference
fc - fLO. This significantly simplifies
the design of the blocks following
the mixer.
Although the multiplication with
a sinusoid is very effective to move
the RF wanted signal around dc, there
is another signal that, if convoluted
with the LO, generates two contributions exactly at the same frequency
of the down-converted wanted signal [Figure 3(a)]. This signal is called
image and before the down-conversion is located symmetrically to the
wanted signal with respect of the
LO frequency. To avoid this overlap,
which could degrade our reception,
the modern receivers adopt the Hartley architecture drawn in Figure 3(b).
The Hartley architecture exploits the
asymmetry of the spectrum between
the sine and the cosine functions
performing a dual paths down-conversion scheme. The path with the
cosine multiplication is called inphase path (I) while the other one is
called quadrature path (Q). As shown
in Figure 3(b), after the sine multiplication, a 90° shift is required to put
in phase the two paths before the
recombination. When the outputs of
the two paths are summed together,
the wanted signal is preserved and
the image rejected.

Filtering In-Band and
Out-of-Band Blockers
Since the wanted signal is modulated
around a high-frequency carrier, to filter in-band and out-of-band blockers
before the down-conversion is very
challenging because it would require
a very narrow-band filter centered on
fc . The quality factor of such filter
should be generally greater than 500.
Unfortunately, in the GHz range, resonant filters achievable with a modern
CMOS processes do not exceed a quality factor of 20. For this reason, out-ofband and in-band blockers are filtered
through a two-step strategy, the formers at RF and the latter after the signal
down-conversion (Figure 4).
To filter an out-of-band blocker at
RF, an external surface acoustic wave

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