In an effort to build smaller digital receivers, the aerospace and defense industry is embracing modern direct radio-frequency (RF) sampling analog-to-digital converters (ADCs). These ADCs eliminate RF mixing stages and are closer to the antenna, simplifying digital receiver designs while also saving cost and printed circuit board (PCB) area.

One critical (and often misunderstood) parameter is the ADC noise figure, which sets the amount of RF gain to detect very small signals. This article explains how to calculate the noise figure of an RF-sampling ADC, and illustrate how the ADC noise figure affects RF signal-chain designs.

The digital receiver operates in one of two distinct scenarios as illustrated in Figure 1. In the blocking condition, an interferer or jammer is present and the receiver has to operate with reduced RF gain in order not to saturate the ADC. In this setup, the ADC is driven close to full scale by the interferer; thus, the large-signal signal-to-noise ratio (SNR) of the ADC determines how weak a signal can be detected. There are additional degrading mechanisms such as phase noise and spurious free dynamic range.

In the second scenario, there is no interferer present. Detecting the weakest signal possible is solely dependent on the inherent noise floor of the receiver, a condition typically measured as receiver sensitivity. The noise figure measures the SNR degradation caused by components in the receiver signal chain.

The noise figure of the ADC is typically the weakest link of the receiver (approximately 25 to 30 dB), while low-noise amplifiers (LNAs) have noise figures as low as <1 dB. It is possible, however, to improve the ADC noise figure by adding gain to the analog RF front end (close to the antenna) using LNAs. The difference between a 1-dB receiver system noise figure and a 2-dB receiver system noise figure translates to approximately 20%. This difference means that a receiver with a 1-dB noise figure can detect signals with approximately 20% weaker amplitude. In a software-defined radio (SDR), that translates to radios with reduced output power – saving battery life – while in radar, that makes it possible to cover a longer distance.

Modern receiver designs in SDRs or digital radars use direct RF-sampling ADCs in order to reduce size, weight and power. This architecture simplifies receiver designs by eliminating the RF downconversion mixing stage. The better the ADC noise figure, the less gain required, which results in additional savings. Furthermore, using less additional RF gain means that when a jammer is present, there is less gain to reduce, with a higher dynamic range maintained in the receiver.

You can use the Friis equation to calculate a receiver system’s noise figure. Assuming a simplified, ideal receiver with two amplifiers and one ADC, as shown in Figure 2, Equation 1 calculates the cascaded system noise factor as:

where F_x are the noise factors and G_x are the power gains.

The system noise figure in decibels is:

There are two important things to highlight: the system noise figure is primarily dominated by the noise figure F₁ of the first element, as long as gain G₁ and G₂ are large enough to where the ADC noise figure F₃ is negligible.

Comparing two different ADCs with 20-dB vs. 25-dB noise figures in a system with two cascaded LNAs shows a drastic difference in system noise figures (see Table 1).

Getting the system listed in the ADC2 column (with a 5-dB worse noise figure) to a system noise figure below 2 dB would require an additional 10 dB of gain using a third LNA (noise figure = 3 dB), as shown in Table 2.

Table 2 highlights the impact of the ADC noise figure on the overall system noise figure. Adding a third LNA increases cost, board area (matching components, routing and power supply) and system power consumption, and further reduces the full-scale headroom.

Assuming a target receiver sensitivity of –172 dBm, or very weak signals just 2 dB above the absolute noise floor (–174 dBm + 2 dB = –172 dBm), this receiver requires an noise figure better than 2 dB. Let’s use the above example with ADC1 (with a 20-dB noise figure, as listed in Table 1) and a cascaded system noise figure of 1.8 dB.

As shown in Figure 3 and Table 3, LNA1 with a gain of 12 dB raises both the input signal and noise by 12 dB while degrading the noise figure by 1 dB (noise figure_LNA1 = 1 dB). LNA2 raises both signal and noise by 15 dB. Even though LNA2 has a higher inherent noise Figure 3 dB, its impact is reduced to just 0.2 dB because of the 12-dB gain of LNA1.

Finally, the noise contribution of ADC1 (noise figure = 20 dB) reduces to just 0.6 dB, as it gets reduced by the 27-dB gain of both LNAs. Therefore, you end up with a system noise figure of 1.8 dB, which leaves approximately 0.2 dB of headroom to detect weak input signals.

High-speed data converters rarely list noise figure in the device-specific data sheet. The noise figure for an ADC can be calculated using Equation 3 using the common data-sheet parameters (see Table 4) for the ADC32RF54 RF-sampling ADC.

ADC Noise figure (dB) = PSIG,dBm + 174 dBm – SNR (dBFS) – bandwidth (Hz) 

For the ADC32RF54, the noise figure calculates to:

Noise figure (1x AVG) = 20.3 dB

10log[(1.1/2/sqrt(2))²/100 x 1000] +174 – 64.4 – 10log[2.6e9/2]

Noise figure (2x AVG) = 19.3 dB

10log[(1.35/2/sqrt(2))²/100 x 1000] +174 – 67.1 – 10log[2.6e9/2]