International Journal of Microwave Science and Technology

Volume 2015, Article ID 757591, 7 pages

http://dx.doi.org/10.1155/2015/757591

## Implementation of a Cross-Spectrum FFT Analyzer for a Phase-Noise Test System in a Low-Cost FPGA

^{1}Institute for Communication Systems ICOM, University of Applied Sciences of Eastern Switzerland, 8640 Rapperswil, Switzerland^{2}Anapico Ltd., 8152 Glattbrugg, Switzerland

Received 1 June 2015; Revised 1 September 2015; Accepted 2 September 2015

Academic Editor: Giovanni Ghione

Copyright © 2015 Patrick Fleischmann et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The cross-correlation method allows phase-noise measurements of high-quality devices with very low noise levels, using reference sources with higher noise levels than the device under test. To implement this method, a phase-noise analyzer needs to compute the cross-spectral density, that is, the Fourier transform of the cross-correlation, of two time series over a wide frequency range, from fractions of Hz to tens of MHz. Furthermore, the analyzer requires a high dynamic range to accommodate the phase noise of high-quality oscillators that may fall off by more than 100 dB from close-in noise to the noise floor at large frequency offsets. This paper describes the efficient implementation of a cross-spectrum analyzer in a low-cost FPGA, as part of a modern phase-noise analyzer with very fast measurement time.

#### 1. Introduction

Phase noise, the random phase fluctuations of a periodic signal, is an important parameter to characterize high-frequency devices, in particular reference oscillators and microwave synthesizers. Phase noise is important because it has a large impact on the performance of many applications [1], such as high-speed communications [2], radar, and precision navigation [3].

There exist various methods for phase-noise measurement, of which the cross-correlation method achieves the best sensitivity and the widest frequency range, at the expense of a relatively complex setup [4–6]. Various fully automated integrated phase-noise analyzers that implement this method are available on the market, for example, the Anapico APPH6040/20G (7 or 26 GHz), the Agilent E5052B, or the Rohde & Schwarz FSUP.

In this paper, we will first review the basics of modelling phase noise and give an outline of the associated terminology. After that, the basics of phase-noise measurement methods will be discussed. Finally, the design and implementation of a novel cross-spectrum FFT analyzer in a low-cost FPGA are described in detail.

#### 2. Phase-Noise Modelling and Terminology

A perfect fixed-frequency oscillator without noise would produce a perfect sine wave. In reality, any oscillator is affected by internal random noise processes, such as thermal and flicker noise, as well as aging and external influences, such as temperature and vibrations. To be able to characterize the phase noise of a real oscillator, its output signal can be modelled bywhere denotes the random phase fluctuations, the nominal amplitude, and the nominal frequency. The random amplitude fluctuations can generally be neglected for high-quality oscillators [7].

Phase fluctuations are characterized in the frequency-domain by their one-sided power spectral density , defined aswhere is the root mean squared (rms) phase fluctuation and is the measurement bandwidth. The Fourier frequency ranges from 0 to in this one-sided spectrum which contains the power of both sidebands around the nominal frequency [8].

The standard measure of phase noise in the frequency-domain is the single-sideband phase-noise defined by the IEEE standard 1139 [8] as is usually specified in dBc/Hz, that is, dB below the carrier in a 1 Hz bandwidth.

#### 3. Measuring Phase Noise

The simplest phase-noise measurement method is the direct spectrum measurement using a spectrum analyzer. However, this method is only suitable for sources with relatively high noise because the phase noise of the spectrum analyzer must be significantly lower than the noise of the device under test. Furthermore, the dynamic range of this method is very limited because the carrier signal is not suppressed.

Another class of measurement methods are the frequency-discriminator methods. The advantage of these methods is that they do not require a reference oscillator. However, these methods cannot achieve the sensitivity of the phase detector methods described below [6].

The method whose implementation is described in Section 4 is the cross-correlation method. Therefore, the remainder of this section will first describe the single-channel quadrature method, which is the basis of the cross-correlation method, before the cross-correlation method is explained.

##### 3.1. Quadrature Method Phase-Noise Measurement

The basic principle of the quadrature method is depicted in Figure 1. The device under test (DUT) signal is mixed with a reference (REF) signal at the same frequency using a phase detector mixer. A phase locked loop (PLL) ensures that the DUT and REF signals stay in phase quadrature during the measurement, so that the output of the mixer (after low-pass filtering) will be approximately proportional to the phase fluctuations of the input signals. Thus, the mixer operates as a phase detector. The output voltage can then be measured using a baseband FFT spectrum analyzer [6].