Synopsis

Noise figure measurements have the reputation of being intricate and needing special equipment. Here, we will demonstrate that a simple setup involving an RTL-SDR dongle achieves convenient results. It requires, besides the inexpensive dongle, only common equipment, which should be available in all MRI coil labs.

Purpose

Methods

More than 70 years ago, the term “Noise Figure” was introduced by Friis$$$^2$$$ as the ratio of the signal-to-noise ratio (SNR) at the input and output of a network: $$F=\frac{SNR_i}{SNR_o}$$ Today, this quantity is typically referred to as “Noise Factor”, and the Noise Figure is expressed in dB according to$$$^3$$$ $$NF=10log_{10}F.$$ From Figure 1A, it is obvious that the signal power, $$$P_{sig,i}$$$ (in W), at the input of the device under test (DUT) only depends on the generator output level, $$$L_{gen}$$$ (in dBm), as well as the total attenuation in the cabling and attenuator, $$$ATT$$$ (in dB). The input noise power, $$$P_{noise,i}$$$, is given by Boltzmann’s constant, $$$k_B$$$, the temperature, $$$T$$$, and the bandwidth, $$$B_{noise}$$$ (in Hz). Hence, the $$$SNR_i $$$ becomes: $$SNR_i=\frac{P_{sig,i}}{P_{noise,i}}= \frac{10^ {\frac{L_{gen}-ATT}{10}}10^{-3}[W]}{k_BTB_{noise}}$$ The RTL-SDR dongle converts the output of the DUT into a complex 2×8-bit data stream,$$$^1$$$ from which $$$SNR_o$$$ is obtained: $$SNR_o=\frac{P_{sig,o}}{P_{noise,o}}$$ Figure 1B shows a corresponding block diagram. After data acquisition, a flattop window is applied to the complex time series followed by an FFT to yield a complex spectrum, from which the power spectrum is determined. Only after this step, spectra are averaged. This is important for obtaining $$$P_{noise,o}$$$ within the noise detector, where spectral lines from the chosen noise bandwidth are summed. Due to windowing, every line also represents noise contributions from adjacent lines. Hence, the sum must be divided by the normalized effective noise bandwidth, $$$NENBW$$$, a property of every window function.$$$^4$$$ Among potential window functions, the maximal amplitude error, $$$e_{max}$$$, is minimal for the flattop windows.$$$^4$$$ Thus, $$$P_{sig,o}$$$ is easily obtained as the strongest peak in the power-spectrum (CW detector).

According to Figure 1A, the generator can be switched on and off to determine signal and noise power consecutively. However, application of an FFT allows both measurements in one pass. Certainly, a sufficient range of spectral lines close to the generator frequency has to be omitted in the noise detector to avoid distortions from noise sidebands of the generator signal.

The one-pass version, supplemented inter alia by the dongle control and graphic visualization, was implemented in gnu-octave (FSF, Boston, MA). The instrument-control toolbox enables remote control of the signal generator (N5182A, Agilent, Santa Clara, CA) within the script. Temperatures have to be entered manually. The attenuators were FAT-AM5AF5G10G2W20 (JYEBAO, Taipei Shien, Taiwan) and Bird 8304-100N (Bird, Solon, OH). An empty PC-tower case, sealed with copper tape, was used as Faraday cage to prevent RF interference. Because the RTL-SDR dongle (NESDR Mini with R820T tuner, NooElec, Niagara Falls, NY) is not an ideal device, its properties were measured by connecting the attenuator directly to its input. We note that meanwhile a successor product (R820T2 tuner) is available that was not investigated here.

Results and Discussion

Only the highest gain settings of the dongle are suitable for noise measurements (Figure 2) because, otherwise, quantization-noise of the analog-to-digital converter dominates. The usable input-level range was found to be less critical. At the expense of longer acquisitions, it can be extended to lower values by improved FFT resolutions (Figure 3). There are considerable gain changes over the frequency range (Figure 4), requiring a careful input-level selection at frequency sweeps.

Among the error sources, deviations of the generator output power had the strongest influence. We recommend to test attenuators by a network analyzer. Caution is required if the attenuator heats up e.g. by signal power or heat produced by the DUT. It is equally important to avoid unwanted mixing products (“birdies”) within the adjusted noise bandwidth. According to the Friis formula for cascaded networks,$$$^2$$$ an assumed dongle-NF of 10dB produces about 0.1dB additional error as long as the DUT gain exceeds 26dB. Known noise properties of the dongle can be easily used to further improve the accuracy.

As a first application, the noise figures of different 7T preamplifiers were measured (Figure 5) yielding realistic results. For comparative measurements (relative to a reference-DUT), knowledge of the exact values of temperature and signal-power is not required, however, negligible drift is important.

The described approach is related to the “signal generator twice-power method”,$$$^3$$$ but avoids its disadvantages due to the two separate FFT-based detectors.

Conclusion

Acknowledgements

References

1. R. Müller, T. Schlumm, A. Pampel, H.E. Möller. The RTL-SDR USB dongle: A versatile tool in the RF lab. Proc. Intl. Soc. Mag. Reson. Med. 2015; 23: 1822.

2. H.T. Friis. Noise Figures of Radio Receivers, Proc. of the IRE, July, 1944, pp. 419-422.

3. Fundamentals of RF and Microwave Noise Figure Measurements. Application Note 57-1. Agilent Technologies. October 2010.

4. G. Heinzel, A. Rüdiger, R. Schilling, Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), including a comprehensive list of window functions and some new flat-top windows, Internal Report, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Hannover, 2002.