Digital and Mixed Signal RF ADC and DAC for RF Informational

What is the Nyquist sampling theorem and how does it apply to bandpass sampling of RF signals?

Q: Does bandpass sampling degrade the SNR?

Not inherently: the signal power and noise bandwidth are preserved through the sampling process. However: (1) The jitter sensitivity increases with the input frequency (not the sampling rate). At f_c = 3.5 GHz and t_j = 100 fs: SNR_jitter = -20×log10(2pi × 3.5e9 × 100e-15) = 55 dB. This is the same regardless of whether f_s = 7 GHz (direct sampling) or f_s = 300 MHz (bandpass sampling). The signal is at 3.5 GHz, so the jitter effect is the same. (2) The ADC thermal noise is determined by the ADC architecture, not the sampling rate. At lower f_s: the ADC typically has better ENOB (fewer bits lost to comparator speed limitations). This actually improves the SNR. (3) The anti-aliasing filter adds some insertion loss (0.5-2 dB). This reduces the signal power by that amount. Net: bandpass sampling typically provides equivalent or slightly better SNR than direct sampling at the same input frequency.

Q: What are the Nyquist zones?

The Nyquist zones are frequency bands defined by the sampling rate: First Nyquist zone: 0 to f_s/2. Second Nyquist zone: f_s/2 to f_s. Third Nyquist zone: f_s to 3f_s/2. And so on. Any signal in the n-th Nyquist zone is aliased to the first Nyquist zone (0 to f_s/2) after sampling. Signals in odd-numbered zones (1st, 3rd, 5th) are aliased without spectral inversion (the frequency axis is preserved). Signals in even-numbered zones (2nd, 4th, 6th) are aliased with spectral inversion (the frequency axis is reversed). The spectral inversion must be corrected in the digital processing (by conjugating the complex samples or by swapping I and Q).

Q: Can I bandpass sample multiple signals simultaneously?

Yes, if the signals do not overlap after aliasing: (1) Place the anti-aliasing filter to pass all desired signals. (2) Choose f_s so that each signal aliases to a different position in the first Nyquist zone. (3) After sampling: separate the signals using digital filtering (each signal is at a known digital IF). Example: two radar bands at 76-77 GHz and 79-81 GHz (after mixing to IF at 1-2 GHz and 4-6 GHz). Choose f_s = 10 GHz: both bands alias into the first Nyquist zone (0-5 GHz) at their original IF frequencies (1-2 GHz and 4-5 GHz). No overlap. Digital filters separate the two bands. Challenge: the ADC must have sufficient bandwidth and SFDR to handle all signals simultaneously. The dynamic range must accommodate the total power of all signals plus any interference.

The Nyquist sampling theorem states that a signal with maximum frequency f_max must be sampled at a rate f_s ≥ 2×f_max to avoid aliasing. However: for RF signals, which are bandpass (occupying a narrow bandwidth around a center frequency), the sampling rate can be much lower than 2×f_carrier through bandpass sampling (also called subsampling or undersampling): (1) Baseband sampling (standard Nyquist): a signal from DC to f_max requires f_s ≥ 2×f_max. For a 1 GHz signal: f_s ≥ 2 GHz. This is an extremely high sampling rate for the ADC. (2) Bandpass sampling: for a signal centered at f_c with bandwidth BW: the signal occupies f_c - BW/2 to f_c + BW/2. The minimum sampling rate: f_s ≥ 2×BW (not 2×f_c). This is because the bandpass signal has only BW Hz of information content, regardless of the carrier frequency. Example: a 5G NR signal at f_c = 3.5 GHz with BW = 100 MHz. Baseband Nyquist: f_s ≥ 7 GHz (very fast ADC). Bandpass Nyquist: f_s ≥ 200 MHz (much more practical). (3) Valid sampling rates: not every f_s ≥ 2×BW works. The sampling rate must be chosen so that the aliased signal falls within a Nyquist zone without overlapping with other aliases. The valid sampling rates satisfy: f_s_valid = 2×f_upper / n, where f_upper = f_c + BW/2, and n is a positive integer, subject to: f_s ≥ 2×BW. For f_c = 3.5 GHz, BW = 100 MHz: f_upper = 3.55 GHz. n = 1: f_s = 7.1 GHz (direct sampling). n = 2: f_s = 3.55 GHz. n = 3: f_s = 2.367 GHz. n = 10: f_s = 710 MHz. n = 17: f_s = 417.6 MHz. n = 35: f_s = 202.9 MHz (near the minimum 200 MHz). Each valid n places the aliased signal at a different IF frequency; the designer chooses the n that results in a convenient f_s and IF. (4) Anti-aliasing: a bandpass filter before the ADC must pass only the desired signal band (f_c - BW/2 to f_c + BW/2) and reject all other frequencies. Without this filter: noise and interferers outside the signal band alias into the same Nyquist zone, degrading the SNR. The filter must have sharp roll-off to prevent near-band noise from aliasing.

Category: Digital and Mixed Signal RF

Updated: April 2026

Product Tie-In: ADCs, DACs, Clock Sources

Bandpass Sampling for RF

Bandpass sampling is one of the most powerful techniques in digital RF receiver design. It allows the ADC to directly digitize an RF signal without first mixing it down to baseband, simplifying the receiver architecture.

Direct RF Sampling vs Bandpass Sampling

(1) Direct RF sampling: f_s ≥ 2×f_max (sampling at Nyquist rate of the highest frequency). The signal appears at its original frequency in the digital domain. Requirements: extremely fast ADC (multi-GHz sampling rate). The ADC performance (ENOB, SFDR) degrades at high sampling rates. Used for: software-defined radio (SDR) receivers where the entire RF band (DC to 6 GHz) must be digitized. ADCs: TI ADC12DJ5200 (10.4 Gsps, 12-bit), Analog Devices AD9213 (10.25 Gsps, 12-bit). (2) Bandpass sampling: f_s can be much lower (200-500 MHz for a 100 MHz bandwidth signal at any carrier frequency). The signal is aliased to a lower frequency (IF) in the digital domain. The ADC can operate at a lower speed, where it has better performance (more ENOB, better SFDR). The anti-aliasing filter must be high-quality (sharp roll-off to reject out-of-band signals). Used in: digital IF receivers, radar receivers, and instrumentation. (3) The trade-off: direct sampling: simpler architecture (no downconversion), but expensive ADC. Bandpass sampling: lower ADC requirements, but needs a high-quality bandpass filter and careful frequency planning to avoid aliased interference.

IF Frequency Selection

(1) After bandpass sampling at f_s: the signal at f_c is aliased to: f_IF = f_c mod f_s (if the alias falls in the first Nyquist zone) or f_IF = f_s - (f_c mod f_s) (if the alias is in the second Nyquist zone, it folds back). The exact formula: f_IF = |f_c - n×f_s| (where n is chosen so that 0 ≤ f_IF ≤ f_s/2). (2) Design rule: choose f_s so that: f_IF is not too close to DC (avoid 1/f noise and DC offset issues; f_IF > 10% of f_s is preferred). f_IF is not too close to f_s/2 (avoid the ADC anti-aliasing filter roll-off; f_IF < 40% of f_s is preferred). The signal band (f_IF ± BW/2) does not overlap with any other aliased signal or interference. (3) Practical example: a radar receiver with f_c = 77 GHz, BW = 4 GHz. After the analog mixer (downconversion to IF = 1 GHz): bandpass sample at f_s = 10 GHz (f_IF = 1 GHz, Nyquist zone 1). Or: bandpass sample at f_s = 3 GHz (f_IF = 1 GHz, still in zone 1 because 1 GHz mod 3 GHz = 1 GHz). The lower f_s = 3 GHz is preferred (lower ADC speed requirement).

Bandpass Sampling Equations

Baseband Nyquist: f_s ≥ 2f_max
Bandpass: f_s ≥ 2BW (minimum)
Valid: f_s = 2f_upper/n, n = integer
f_IF = |f_c - n·f_s|
Anti-alias filter: passband = f_c ± BW/2

Common Questions

Frequently Asked Questions

Does bandpass sampling degrade the SNR?

Not inherently: the signal power and noise bandwidth are preserved through the sampling process. However: (1) The jitter sensitivity increases with the input frequency (not the sampling rate). At f_c = 3.5 GHz and t_j = 100 fs: SNR_jitter = -20×log10(2pi × 3.5e9 × 100e-15) = 55 dB. This is the same regardless of whether f_s = 7 GHz (direct sampling) or f_s = 300 MHz (bandpass sampling). The signal is at 3.5 GHz, so the jitter effect is the same. (2) The ADC thermal noise is determined by the ADC architecture, not the sampling rate. At lower f_s: the ADC typically has better ENOB (fewer bits lost to comparator speed limitations). This actually improves the SNR. (3) The anti-aliasing filter adds some insertion loss (0.5-2 dB). This reduces the signal power by that amount. Net: bandpass sampling typically provides equivalent or slightly better SNR than direct sampling at the same input frequency.

What are the Nyquist zones?

The Nyquist zones are frequency bands defined by the sampling rate: First Nyquist zone: 0 to f_s/2. Second Nyquist zone: f_s/2 to f_s. Third Nyquist zone: f_s to 3f_s/2. And so on. Any signal in the n-th Nyquist zone is aliased to the first Nyquist zone (0 to f_s/2) after sampling. Signals in odd-numbered zones (1st, 3rd, 5th) are aliased without spectral inversion (the frequency axis is preserved). Signals in even-numbered zones (2nd, 4th, 6th) are aliased with spectral inversion (the frequency axis is reversed). The spectral inversion must be corrected in the digital processing (by conjugating the complex samples or by swapping I and Q).

Can I bandpass sample multiple signals simultaneously?

Yes, if the signals do not overlap after aliasing: (1) Place the anti-aliasing filter to pass all desired signals. (2) Choose f_s so that each signal aliases to a different position in the first Nyquist zone. (3) After sampling: separate the signals using digital filtering (each signal is at a known digital IF). Example: two radar bands at 76-77 GHz and 79-81 GHz (after mixing to IF at 1-2 GHz and 4-6 GHz). Choose f_s = 10 GHz: both bands alias into the first Nyquist zone (0-5 GHz) at their original IF frequencies (1-2 GHz and 4-5 GHz). No overlap. Digital filters separate the two bands. Challenge: the ADC must have sufficient bandwidth and SFDR to handle all signals simultaneously. The dynamic range must accommodate the total power of all signals plus any interference.

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