Wireless 101: Sampling band-pass signals

Part 1 looked at the math of sampling and signal reconstruction. Part 3 looks at automatic gain control. It will be published February 25.

7.2 Sampling of Bandpass Signals
The sampling process is critical for radio receivers that digitize signals at RF or IF. Sampling an analog signal at IF or RF results in replicas of the signal's spectrum repeated at uniform intervals. The choice of the sampling rate of such signals is dependent on the signal's bandwidth and the IF or RF center frequency.

Bandpass sampling does not require the use of analog quadrature mixing, thus eliminating certain DC offsets due to the carrier feedthrough in the mixers, VGA gain stages, and filters. Furthermore, it does not require analog phase and amplitude compensation due to IQ imbalance. Bandpass sampling requires only one ADC, as shown in Figure 7.3, allowing for the final IF (or low IF) to baseband conversion to occur in the digital domain. Note that the second DAC feeding off the phase-to-accumulator block is not a transmit DAC, but rather generates a sinusoid as part of the direct digital synthesis (DDS) block. A DDS system is a mechanism for generating a sinusoid digitally and passing the signal through a DAC to be used for mixing.

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Figure 7-3. IF sampling architecture showing the use of only one ADC and one DAC.

On the other hand, bandpass sampling is sensitive to carrier or IF frequency variations, as well as sampling frequency and jitter. In this case, the ADC tends to consume more power due to a faster sample and hold (S/H) and digital circuitry and the performance of the system becomes more prone to degradations due to mixed-signal circuit imperfections.

Furthermore, the requirements imposed on the bandpass filter at IF before the ADC become much more stringent and much more difficult to build compared to the more benign lowpass filters used in analog quadrature downconversion. Note that this IF filter also performs the function of an antialiasing filter used in the lowpass case.

7.2.1 Representation of Bandpass Signals
Consider the conceptual modulator depicted in Figure 7.4. The in-phase I(t) and quadrature Q(t) signals are obtained from discrete-time signals converted to analog by two DACs. The signal at IF, or RF in the case of a direct conversion transmitter, can be expressed as:

again, where I(t) and Q(t) are the real and complex components of the complex analog baseband signal s_a(t) = I(t) - jQ(t). The bandpass signal can then be related to the complex baseband signal as:

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Furthermore, the relation in (7.26) can be expressed as:

Figure 7-4 Conceptual upconversion of baseband signal to IF or RF frequency.