Understanding ADC Noise for Sm
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 1062085
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Understanding ADC Noise for Sm
Abstract: The following article describes the relationship between smallsignal and largesignal inputs and the noise + distortion performance of a data converter and its impact on the sensitivity and AC performance of a digital receiver system.
IntroductionWhen using a highperformance Nyquist analogtodigital converter (ADC) in a sampling or subsampling receiver design, an RF designer needs to know the ADC's noise performance for both small and largesignal inputs. The receiver must meet sensitivity and blocking (highlevel interference) requirements under these two signal level extremes, and the ADC generates different amounts of noise for each of these levels, which can be expressed in terms of its effective noise figure. It is important for the user to understand the amount of ADC noise contribution in the receiver lineup when determining the ADC's AC requirements. For the following discussion, it is assumed that the noise is flat across the converter's Nyquist band.
Determining the Effective Noise FigureFor small analog input signals (on the order of 35dBFS), the thermal + quantization noise power dominate the ADC noise floor, which is used to approximate the ADC's effective noise figure (NF). Once the ADC's NF is known, the cascaded noise figure equation¹ can be used to determine the overall receiver noise figure at the receiver input terminal. The level of ADC noise contribution for smallsignal inputs is used for signals near and just above the receiver sensitivity. Refer to Figure 1 and use the following steps to approximate the ADC effective noise figure for smallsignal analog input levels:
 Calculate the ADC's fullscale level (in dBm). This step is necessary because the thermal + quantization noise power is commonly given in units of dBFS and noise figure is calculated with respect to dBm.
 Determine the thermal + quantization noise floor level (in dBm) either from the component vendor's data sheet or by measurement (for a small signal input level on the order of 35dBFS).
 Calculate the normalized noise floor level in 1Hzbandwidth by subtracting 10 × log (fSAMPLE/2) where fSAMPLE is given in units of Hz.
 Determine thermal noise power in 1Hz bandwidth;
KTB = 4.002 × 1021 Watts (or in log form = 174dBm), where
K = Boltzmann's constant = 1.381 × 1023 W/Hz/K,
T = 290 K at room temperature
B = Normalized bandwidth of 1Hz  Calculate the effective noise figure by subtracting the result from step 4 from the result calculated in step 3.
In practice, once the ADC's effective noise figure is known, and the cascaded noise figure of the analog circuitry (RF & IF) is determined; the minimum power gain ahead of the ADC is selected to meet the required receiver noise figure. The amount of power gain places an upper limit on the maximum blocker, or highest interference level the receiver can tolerate. For cellular basestation applications, the ADC often does not have sufficient dynamic range to meet both the noise figure requirements (receiver sensitivity) and maximum blocker requirements without implementing some amount of automatic gain control (AGC). The AGC can be included either in the RF or IF stages (or both). When higher resolution converters are used, the thermal + quantization noise is lower thereby decreasing the ADC's effective noise figure. As a result, less gain is needed in the receiver lineup to achieve the receiver noise figure thereby reducing the need for an AGC circuit when higherlevel blockers are present.
Figure 1. Determining an ADC's effective noise figure for smallsignal inputs for receiver sensitivity requirements.
Figure 2. Determining ADC effective noise figure for largesignal inputs for receiver blocker requirements.
Numeric Example using the MAX1428The MAX1428, has the following preliminary specifications (See Table 1):
Table 1. The MAX1428 Preliminary Electrical Characteristics
Parameter  Condition  Symbol  Typ. Value  Units  Resolution   N  15  bits  Analog input Range   VID  2.56  Vpp  Differential Input Resistance   RIN  1000  Ohms  Analog Bandwidth, Full Power   BW1  260  MHz  AC SPECIFICATIONS  fSAMPLE = 80Msps     Thermal + Quantization Noise Floor  Analog Input < 35dBFS  NF  78.3  dBFS  SignaltoNoise Ratio  Analog Input at 2dBFS,
fIN = 70MHz  SNR  73.7  dB  SignaltoNoise and Distortion Ratio  Analog Input at 2dBFS,
fIN = 70MHz  SINAD  72.5  dB 
The MAX1428 ADC Noise ContributionsAssume that a terminating resistance placed across the differential input pins of the MAX1428 produces a total differential resistance of 200Ω. The fullscale input level is calculated to approximately equal +6 dBm (2.5VPP across 200Ω). For a clock rate of 80Msps, the thermal + quantization noisefloor power equals 78.3dBFS or 72.3dBm in the first Nyquist region. As the 70MHz analog input level is increased above 35dBFS, but not close to fullscale, the converter DNL noise adds 1.3dB to the total converter noise floor to 71dBm. As the input level is increased further and approaches fullscale, the noise floor increases an additional 1.3dB due to ADC clock jitter to a value of 69.7dBm resulting in an effective noise figure of 28.3dB (per procedure outlined in Figure 2).
Figure 3. The MAX1428 ADC noise contributions illustrated in the first Nyquist region.
Blocker Absent Scenario for Receiver Sensitivity
Figure 4. Blocker absent scenario.
Blocker Present ScenarioWith 35dB gain ahead of the ADC, a maximum single tone blocker level above 29dBm at the antenna terminal will exceed the ADC fullscale input. The cdma2000® cellular base station standard specifies a maximum allowable blocker level of 30dBm at the antenna terminal. In any practical application, margin to this maximum blocker level needs to be included in the design when receiver gain tolerances are taken into consideration. For this example, 6dB gain reduction is used to increase the largest allowable blocker signal applied to the ADC. This amount of gain reduction results in a maximum blocker level of 25dBm at the antenna and +4dBm (at 2dBFS) at the ADC input. The cdma2000 airinterface standard allows 3dB degradation in overall (noise + distortion) relative to reference sensitivity when a singletone blocker is present. The allocation of (noise + distortion) components is left up to the designer for any particular receiver configuration. As an example, suppose the designer allows the RF frontend cascaded noise figure to degrade by 0.5dB (from the nominal 3.5dB) when 6dB of AGC is applied. With only 29dB of gain in front of the ADC and an effective noise figure of 28.3dB, the cascaded receiver noise figure is 5.3dB in the 'blocked condition', which is a 1.6dB degradation from 3.7dB noise figure calculated for receiver sensitivity. This is 1.4dB less than the 3dB degradation (noise + distortion) allowed in the cdma2000 standards.
Figure 5. Blocker present scenario.
ADC Noise and Distortion (SINAD)If the ADC's SINAD value of 72.5dB were used instead of SNR (taking into account the ADC's noise and distortion components), the overall degradation in noise figure due to the RF frontend noise figure and ADC (noise + distortion) would be 2.1dB, which is still below the allocated 3dB for this measurement. Therefore, 0.9dB degradation is still allocated for the (noise + distortion) performance of the analog frontend of the receiver if needed.
ConclusionThis application note illustrates that the ADC generates different levels of noise power depending on the signalinput level, and that the ADC noise affects the overall receiver response for small and largesignal level extremes. If cascaded contributions of the ADC noise (and distortion) power is not properly accounted for in the receiver design, the converter might be either over or under specified for any particular application.
Notes
1. 10 × log Feq = 10 ×log (F1 + (F2  1)/G1 + (F3  1)/G1G2 +...+ (Fn  1)/G1G2...G(n  1))
References  Digital Techniques for Wideband Receivers, James Tsui, Artech House Publishers, 1995.
 RF Design Guide, Systems, Circuits, and Equations, Peter Vizmuller, Artech House Publishers, 1995.
 Recommended Minimum Performance Standards for cdma2000 Spread Spectrum Base Stations, 3GPP2 TSGC4.1, Release A, March 30, 2001.
cdma2000 is a registered trademark of Telecommunications Industry Association. 




