Digital Signal Processing Reference
In-Depth Information
to Q
tot
≈
T
pulse
. While it is true that increasing the capacitance would
reduce the thermal noise voltage,
7
i
injected
·
the voltage related to the signal-of-interest
will decrease by the same factor.
The reader may correctly argue that the above reasoning is only valid as a first
order approximation. For example, it was supposed that all of the rf signal
current is integrated on the capacitor. It is clear that this may not entirely re-
flect reality for frequencies below the passband of the low-pass filter, when
the output impedance is not longer dominated by the capacitor, but by the out-
put resistance of the mixer. For frequencies below the cut-off frequency of the
filter,
8
some of the signal energy leaks away into the resistive part of the fil-
ter. However, only a small portion of the signal is affected by this problem,
since most of the spectral density of the pulses is spread over a much larger
bandwidth than the passband frequency of the low-pass filter.
For example, if the bandwidth of the pulses is 1 GHz, while the cut-off fre-
quency of the filter is 50 MHz (for a symbol rate of 100 Msymb/s), the signal
loss is limited to about 0
.
2 dB. This is the price that must be paid for not using
an ideal matched filter based pulse-to-baseband converter. It might be tempt-
ing to improve the efficiency of the input stage by moving the pole of the filter
towards a lower frequency and later on, in the signal processor, compensate for
the distortion (caused by the non-flat frequency response) of the baseband sig-
nal. Doing so does not necessarily improve the performance: a filter with a low
frequency pole can be considered as an integrator. In an open-loop configura-
tion, low-frequency components will cause large deviations from the average
signal level. The large dynamic range between low- and high-frequency com-
ponents of the baseband signal has an obvious impact on the loading factor
of the ad-converter. The increased dynamic range is not a problem for the
signal-of-interest, but in-band interferers could clip if the signal headroom of
the ad-converter is not scaled accordingly.
Measuring the noise figure of the front-end
The output of the mixer is connected to a variable gain amplifier. The vga itself
is based on a chain of eight 7
.
8 dB-gain segments. The gain of the vga can be
controlled by rerouting the output of one of these segments directly to the out-
put buffer of the chip. Power consumption is further minimized by switching
off unused sections of the amplification chain. The individual amplifier sec-
tions are based on an open-loop amplifier topology, with some special precau-
tions to suppress third-order harmonic distortion (hd
3
). This topic is covered
in greater detail in Appendix 7, so the specific implementation aspects of the
7
Only circuit-induced thermal noise is considered here, not the background noise of the channel.
8
After downconversion of the rf pulses by the mixer, low frequencies emerge in the (wideband) spectrum
of the output current.
