An Oscilloscope Correction Method for Vector-Corrected RF Measurements

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 1 An Oscilloscope Correction Method for Vector-Corrected RF Measurements Sebastian Gustafsson, Student Member, IEEE, Mattias Thorsell, Member, IEEE, Jörgen Stenarson, Member, IEEE, and Christian Fager, Member, IEEE Abstract— The transfer characteristics of the RF front-end circuit components. As these errors must be compensated for circuitry of a real-time oscilloscope (RTO) are not only frequency to achieve accurate signal sampling [4], several correction dependent and nonlinear with signal amplitude but also depen- techniques have been introduced [5], [6]. Other correction dent on the voltage range setting of the oscilloscope. A correction table in the frequency domain is proposed to account for the techniques have also been introduced [7]–[12], but they are additional gain and delay introduced when switching between only valid for sampling oscilloscopes. Previous research different voltage ranges. The table was extracted from the has focused on correction techniques for a certain set of measured data in which a continuous-wave signal source was instrument settings, e.g., a particular voltage range. Hence, connected to the oscilloscope ports, whereas the input power, the changing the settings would make the correction invalid. frequency, and voltage ranges were varied. The importance of the corrections is demonstrated by its use in an RTO-based two-port However, changing the range is desirable in some applications, vector-corrected measurement system. Measurements from the to fully utilize the voltage range of the ADC. oscilloscope-based system are compared with a vector network Measurement receivers in any digitizing instrument have a analyzer (VNA), leading to less discrepancy in the measured S- limited dynamic range determined by the number of bits of parameters of two amplifiers when using the proposed correction the ADC. It is therefore of interest to maximize the voltage technique. swing into the ADC to accurately capture the signal, hence Index Terms— Calibration, dynamic range, frequency-domain reducing the impact of quantization noise. Thus, to measure analysis, microwave measurements, oscilloscopes. a large voltage span with high accuracy, a gain-controlling I. INTRODUCTION circuit is placed before the ADC. In the case of the LSNA, EASUREMENT systems like the large-signal network this is achieved using precalibrated step attenuators in front Manalyzer (LSNA) are nowadays standard instruments of the down-converter [13]. In an RTO, this can be done by for nonlinear device characterization. The LSNA was first adjusting the variable gain amplifier (VGA), or equivalently introduced in 1989 [1] and included full magnitude and voltage range setting, in the oscilloscope [14]. Hereby, an phase calibration, with a phase accuracy of ±10° at the additional gain and delay is introduced to the input signal, first four harmonics for a fundamental tone of 5 GHz. It is which instrument suppliers compensate for with self-alignment based on a wideband down-converter, utilizing subsampling, procedures in the oscilloscope [15]. followed by an analog-to-digital converter (ADC). The However, as we demonstrate in this paper, the instrument baseband bandwidth is thus limited by the ADC. In contrast, alignment procedures are not sufficient. We propose a method, real-time oscilloscopes (RTOs) with a bandwidth of 65 GHz which corrects for the gain and delay due to the VGA, that is are available today. Hence, there is interest in using RTOs not handled by the built-in alignment procedures. Our method in two-port measurement systems [2], [3]. A real-time is a table-based approach described in the frequency domain, oscilloscope has, like any other receiver, nonideal circuits which means that the gain and delay is translated into a change that need to be characterized and corrected. in amplitude and phase of the measured signal. We extract the The RF front end of an RTO introduces gain and delay correction table from measurements, using a CW signal source errors to the measured input signal because of nonideal connected to the oscilloscope ports. Although the method is applied to an RTO used as a vectorial measurement receiver Manuscript received September 9, 2014; revised November 4, 2014; in a two-port sampling network, it can be applicable to other accepted December 15, 2014. This work was supported in part by the Swedish Governmental Agency of Innovation Systems, in part by the Chalmers measurement setups using RTOs as well. University of Technology, in part by Comheat Microwave AB, in part by This paper is organized as follows. An oscilloscope-based Ericsson AB, in part by Infineon Technologies Austria AG, in part by measurement setup is presented in Section II. RTO RF per- Mitsubishi Electric Corporation, in part by NXP Semiconductors BV, in part by Saab AB, in part by the SP Technical Research Institute of Sweden, and in formance versus voltage range is investigated in Section III. part by United Monolithic Semiconductors. The Associate Editor coordinating In Section IV, the theory behind the proposed correction the review process was Dr. Wendy Van Moer. method is presented, as well as the procedure for correcting S. Gustafsson, M. Thorsell, and C. Fager are with the Microwave Electronics Laboratory, GigaHertz Centre, Department of Microtech- the oscilloscope. The validity of the method is discussed nology and Nanoscience, Chalmers University of Technology, in Section V. Finally, the conclusion is given in Section VI. Gothenburg SE-412 96, Sweden (e-mail: [email protected]). J. Stenarson is with the SP Technical Research Institute of Sweden, Borås SE-501 15, Sweden, and also with the Microwave Electronics II. TWO-PORT MEASUREMENT SETUP Laboratory, GigaHertz Centre, Chalmers University of Technology, Gothenburg SE-412 96, Sweden. Since the proposed correction method is tested using an Digital Object Identifier 10.1109/TIM.2015.2407451 RTO-based two-port measurement system, a short description 0018-9456 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 2 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT Fig. 1. RTO-based two-port measurement setup [16]. of the setup and its calibration procedure are presented in this section. As shown in Fig. 1, the setup consists of a 4 GHz two-channel Agilent M8190A arbitrary waveform generator and a 4 GHz four-channel RTO. The broadband waveform generator lets the user define an arbitrary signal containing frequencies between dc and 4 GHz and can be utilized for new kinds of measurements, e.g., multiband and wideband load pull [16]. A two-port calibration of the setup is carried out as follows. First, a suitable calibration, e.g., short-open- load-reciprocal, is made at the measurement ports versus frequency. Then, a power calibration with a power meter Fig. 2. Port match versus frequency for oscilloscope A for different voltage as well as a phase calibration is done at the auxiliary range settings. (a) Magnitude of S11.(b)PhaseofS11. reference plane, to obtain correct magnitude readings and cross-frequency phase relationships of the device under The signal amplitudes during calibration are usually small test (DUT) port voltages and port currents. The calibrated in comparison with signals measured with, for instance, complex voltage waves, a1, b1, a2,andb2, are calculated a high-power amplifier as a measurement device. This is from the measured waves, m1, m2, m3,andm4,as a problem in wideband RTOs due to the low number of bits ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ in the ADCs, which constrains the dynamic range. Additional 1 − a1 x e11 m1 amplifiers could be used during the calibration stage, but ⎢ ⎥ ⎢ − 0 ⎥ ⎢ ⎥ ⎢b1⎥ = α ⎢c1 e00 1 ⎥ ⎢m2⎥ would instead limit the calibration bandwidth. Another option ⎣ ⎦ ⎣ 1 − ⎦ ⎣ ⎦ a2 y e22 m4 would be to adjust the gain of the signal before being digitized 0 − b2 c2 e33 1 m3 by the ADC, which is handled with VGAs in the RF front (1) end of the RTO. This will, however, affect the transfer characteristics of the input circuitry of the oscilloscope. where c1 = e10e01, c2 = e10e32, x = e00e11 − e10e01, y = e22e33 − e32e23,andα gives the absolute magnitude and phase information according to [17]. The terms denoted III. RTO RF PERFORMANCE by exx are the linear error terms, which describe systematic In this section, two RF attributes of RTOs are discussed: errors in the setup due to cables, couplers, mismatch, and 1) input port impedance and 2) RF front-end transfer so on. The setup is calibrated using a Schroeder-phased characteristics. Both are studied versus voltage range setting multisine signal to reduce the crest factor [18], exciting the and characterized in the frequency domain. Errors related to frequencies of interest, fk , according to ADC interleaving are also important for the performance of N an RTO, but they are not treated in this paper and will be considered as an additional measurement noise. xcal(t) = A cos(2π fkt + φk) (2) k=1 k(k − 1) A. Input Port Impedance φk =− π. (3) N The port match of two RTOs (A and B) was measured Although linear CW stimuli measurements are made with with a commercial vector network analyzer (VNA) for a set the measurement setup in this paper, removing the need of five different voltage range settings, from 20 to 1000 mV for α in (1) and the multisine signal, they are included here with near-logarithmic spacing. Port match versus frequency for to give a complete description of the calibration algorithm. oscilloscopes A and B is shown in Figs. 2 and 3, respectively.

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