Global Positioning System Reference
In-Depth Information
First, it is important to discuss the individual components. The local oscillator
for GNSS front-end designs is typically a combination of components. Most crys-
tal oscillators, either standalone or temperature compensated/ovenized for greater
stability, are not capable of generating the desired local oscillator frequency for
the L1 GNSS signal. Thus, a phase lock loop (PLL) is combined with the crys-
tal to achieve the desired higher frequency of the local oscillator. In addition, it is
common practice that the local oscillator be divided down to serve as the sampling
clock, as shown in Figure 4.2. This is an important aspect as a single frequency
source, and any associated frequency error/drift, will serve as the basis for the
receiver.
The mixer operates through the trigonometric identity expressed as
2
cos
(ω
1
−
ω
2
)
t
+
2
cos
(ω
1
+
ω
2
)
t
.
1
1
cos
(ω
1
t
)
cos
(ω
2
t
)
=
(4.3)
It is possible to use the front-end design in Figure 4.2 as an example of the mix-
ing process. In this case
ω
1
equals the GNSS L1 center frequency 1575.42 MHz
and the desired IF is 47.74 MHz, then the desired local oscillator frequency
ω
2
would be
68 MHz. Any modulation, such as the
GNSS spreading codes and navigation data, can be simply expressed as a time-
varying multiplier:
(
1575
.
42
−
47
.
74
)
MHz
=
1527
.
cos
(ω
1
−
ω
2
)
t
+
cos
(ω
1
+
ω
2
)
t
.
d
(
t
)
2
d
(
t
)
2
d
(
t
)
cos
(ω
1
t
)
cos
(ω
2
t
)
=
(4.4)
In this case it is obvious that the output of the mixer will be the sum and difference
frequencies. Of interest here is the difference frequency, which is at the desired
IF. The sum frequency is simply a consequence in this case, and the second filter
depicted in the cascade of Figure 4.2, which follows the mixer, is used to select
only the desired difference frequency.
Note that in Figure 4.2 a bandpass filter is used for this process. However, given
the fact that the goal is to simply remove the sum component, a lowpass filter
should be more than sufficient. In many cases this is true; however, Equations
(4.3) and (4.4) present a simplified model of a mixer, which in reality is more
complicated. Mixer parameters include conversion loss, isolation, dynamic range,
and intermodulation. In this case the bandpass filter is selected to minimize any
complications from intermodulation products that result from the mixing. For this
simplified discussion, only the straightforward model of the mixer is presented.
With the combination local oscillator/mixer it is now possible to translate the
RF carrier to a lower IF. It has been eluded to above that this is required for
the analog-to-digital conversion process, but is that the only reason? Are there
other reasons as to why frequency translation is important in GNSS receivers?
The answer is “yes” with two immediate additional justifications for the frequency
translation.
The first is the quality and cost of the component. The goal of this text is to de-
velop software GNSS receivers for the narrowband L1 signals, with the definition
of narrowband being 2-8 MHz (see Problem 7). It is important to recognize that
it can be quite difficult to fabricate narrowband filters at high frequency.
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