Fine frequency grid phase calibration setup for the Large Signal Network Analyzer Liesbeth Gommé, Alain Barel, Yves Rolain and Frans Verbeyst Vrije Universiteit Brussel (Dept. ELEC/TW); Pleinlaan 2; B-1050 Brussels (Belgium) Phone: +32.2.629.28.68; Fax: +32.2.629.28.50; Email:
[email protected]
The next paragraph of the paper describes the frequency converting and phase calibrating properties of the crystal detector. After describing the experimental setup by means of which we record input and output signals of the squared detector in section III, measurements are discussed in section IV.
Abstract - Large signal analyzers measure calibrated waves. Besides the classical linear SOLT-calibration, this requires two additional calibration steps : a power and a phase calibration over frequency. Nowadays phase relations can be calibrated with a frequency resolution of 2MHz. The aim of this paper is to obtain a fine frequency grid phase calibration for the Large Signal Network Analyser [1] based on a coarse grid phase calibration. The approach uses a frequency conversion performed with a crystal detector.
II. THE SQUARED DETECTOR Observe an amplitude modulated (AM) signal, x AM (t) consisting of one carrier frequency fc and two modulation tones, f1=fc -fmod and f3=fc+fmod, as shown in figure 2.1. The modulated AM-signal is,
Index Terms - Fine frequency grid LSNA, phase calibration, squared crystal detector.
I. INTRODUCTION
xAM(t)=U1cos[2π(fc-fmod)t+φ1]+U2cos[2πfct+φ2]+ U3cos[2π(fc+fmod)t+φ3] (II.1)
In the analysis of nonlinear systems, it is required to excite the device-under-test with a signal which comes very close to the signal that will be used during the normal operation of the device. Hence, it is often required to use modulated signals containing many spectral lines in a narrow band. To obtain distortion-free measurements, the phase difference between the lines of the measured spectra needs to be calibrated. For continuous wave (CW) carriers, the calibration relies on the well-established step recovery diode (SRD) method [1]. The current state of the art is that the modulation lines are then calibrated using some interpolation of the wideband calibration. In this paper a measurement based method is proposed instead. The knowledge of the phase relations between the harmonics of the SRD comb, with repetition frequencies between 600MHz and 1200MHz, yields a calibration on a coarse frequency grid. A narrow band modulated RF signal is used next to construct a calibration signal with a known phase relation between its spectral lines. This signal is then shifted by use of a crystal detector which abides the squared detection law. With the knowledge of the phase differences between spectral lines on the coarse frequency grid and the measurement of the phases of the spectral lines of the detected output signal, the phase difference between lines on a fine frequency grid can be obtained. By characterizing the squared detector using a nose-2-nose calibrated digital sampling oscilloscope (DSO) [2], its influence can be removed and a calibration on a fine frequency grid is obtained.
XAM f
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Figure 2.1 : AM-signal with U1, U2, U3 and φ1, φ2, φ3, the amplitudes and phases at respectively fc-fmod, fc and fc+fmod. If the signal, xAM(t), is now exciting an uncalibrated instrument, the modulated signal will be distorted by the linear dynamics of the channel. This will result in an asymmetry in the upper and lower side band of the modulated signal. When this experiment is repeated at different carrier frequencies that are all located on the fine frequency grid, it becomes possible to calculate the phase difference on the fine grid. Of course, this requires the excitation signal to be known. Feeding xAM(t) to a squaring device [3] results in a signal containing spectral lines in the vicinity of DC and 2fc. The lines located around DC are, 1/2(U12+U22+U32)+U1U2cos[2πfmodt-(φ1-φ2)]+ U2U3cos[2πfmodt+(φ3-φ2)]+U1U3cos[2π(2fmod)t+(φ3-φ1)] (II.2) This term contains the signal contributions of interest, as these spectral lines allow to characterise the modulation of the AM signal using low frequent measurements only. As it 1
is impossible to assume a perfect detector in practice, the detector itself will need to be calibrated. Signal generator HP8648
To this end, the crystal detector is characterised by a nose-2nose calibrated DSO. This will be used to characterise the modulated signal.
Modulation signal OUT
Repeating this procedure on a dense frequency grid results in a calibrated phase grid with a spacing of for example 100kHz instead of the standard 600MHz, which is achievable with LSNAs nowadays.
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Figure 2.2 : Fine frequency grid Trigger
In order to apply this approach we need to quantify the influence of frequency folding by the squared detector on the phase, which is discussed in the next section.
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Figure 3.2 : Measurement set-up (600MHz-2GHz)
III. EXPERIMENTAL SET-UP Signal generator HP83640
Signal generator HP8648
In order to take a first step in characterizing the squared detector, an amplitude modulated signal, xAM (t), with a modulation bandwidth of 2f mod situated around the RF carrier frequency, fc, is applied at its input. (Fig.2.1)
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Figure 3.1 : Output spectrum of the squared detector Figure 3.1 shows the spectrum XOUT(f) of the output signal x out (t), which can be easily obtained by following the analytic development. The detection method incorporating a squared law detector allows to detect the low frequency envelope of an AM-signal.
Trigger
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Figure 3.3 : Measurement set-up (1GHz-40GHz) Next, in both setups the amplitude modulated signal is fed into the square law detector. The output of the detector enters the isolation amplifier, which provides a high impedance termination and a low load capacitance at the output of the square law detector. Finally, the signal enters the HP54120 calibrated sampling oscilloscope for visualisation and further processing. In both schemes the modulation signal is used as a trigger signal for the sampling oscilloscope after it was converted into a pulse train by means of the Agilent 81101 pulse generator.
In order to study different carrier frequency regions, two different setups, each incorporating different signal generation schemes were examined. The first setup described in figure 3.2 makes use of the HP8648 signal generator which generates carrier frequencies up to 2 GHz. The second setup shown in figure 3.3 uses the signal generator from scheme 3.2 to provide the low-frequency modulation signal while the carrier frequency is now extracted from the HP83640 signal generator which can generate frequencies up to 40 GHz. 2
In order to study the dependency of the characteristic of the detector on the modulation bandwidth, the SMIQ06 RohdeSchwarz signal generator (300kHz- 6,4GHz) is used, instead of the HP83640 signal generator in figure 3.3, for enabling modulation frequencies up to 10 MHz.
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IV. MEASUREMENTS
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In order to provide calibrated measurements, we need to quantify the phase shift between the modulation signal at the input of the detector and the downconverted modulation at the output of the squared detector. This in fact corresponds to studying the phase of the ratio of the modulation input signal and the detected modulation output signal. By performing 32 repeated measurements, the envelope of the AM-signal can be determined as the standard deviation of the 32 AM-signals at the input of the detector (input 1 of the sampling oscilloscope). This low frequency modulation signal (f mod =1KHz) can then be compared to the output of the squared detector with regard to the phase behaviour.
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Figure 4.1: Input AM signal (a), calculated input modulation signal (b) and downconverted output modulation signal (c). -9.7 -9.8
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Figure 4.1 a, b and c show the AM-input signal, the input modulation and the detected output modulation. For each of the two setups in figures 3.2 and 3.3, input and output signals of the squared detector were recorded for different carrier frequencies.
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For each frequency the spectral mean of the output modulation signal was calculated together with the spectrum of the input modulation signal. These two q u an t i ti e s w er e d iv i d e d i n o r d e r t o r e s u l t i n t h e transferfunction at fmod of the squared detector. The am plitude and phase characteristics of these transferfunctions, each for a different carrier frequency, lead to figure 4.2 for carrier frequencies of 600MHz up to 2GHz and figure 4.3 for 1GHz up to 40 GHz. These graphs clarify that the phase shift between input modulation and output modulation signal is independent of
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Figure 4.2 : Amplitude (a) and Phase (b) in function of carrier frequency (600MHz - 2GHz)
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the carrier frequency, meaning that a phase calibrated coarse frequency grid can be used to obtain a phase calibrated fine frequency grid by means of a crystal detector with a negligible dependency on coarse grid frequencies. The variation in magnitude can be flattened by means of a power sensor configuration. Figure 4.3 reveals that the input frequency range is about 11GHz, as predicted by datasheets of this device[4]. The phase difference remains small up to 30GHZ.
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Figure 4.4 : Amplitude and Phase in function of modulation frequency (1kHz -10MHz)
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V. CONCLUSION
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By means of a crystal detector one is able to achieve a fine frequency grid phase calibration. Initial experiments suggest that the phase characteristics of this type of detector can be well quantified. The next step is to build a reliable setup capable of providing the fine frequency grid calibration.
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ACKNOWLEDGEMENT
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Research reported here was performed in the context of the network TARGET– “Top Amplifier Research Groups in a European Team” and supported by the Information Society Technologies Programme of the EU under contract IST-1507893-NOE, www.target-net.org and supported by the Belgian government (IUAP-V/22).
Figure 4.3 : Amplitude (a) and Phase (b) in function of carrier frequency (1GHz -40GHz). In the region of 1-2GHz, where measurements with both setups overlap, differences in amplitude (figure 4.2a and 4.3a) and phase (figure 4.2b and 4.3b) are due to differences in connectorizing, resulting in a different attenuation and delay. The next set of measurements varies the modulation frequency and keeps the carrier frequency constant at 1GHz. F mod ranges from 1kHz to 10MHz in figure 4.4, where amplitude and phase of the conversion transferfunction at fmod are shown. This figure shows that there is a need for phase correction. The magnitude rapidly decreases as the frequency reaches 10MHz due to capacitive losses. By limiting these losses the modulation frequency can reach 3MHz. All the experiments described above were performed using a perfect symmetric amplitude modulated signal. The theory of fine frequency grid phase calibration by square law detection also stands for asymmetric modulated signals, as was confirmed by simulations and experiments with Single Side Band (SSB) signals.
REFERENCES [1] F. Verbeyst. Contributions to Large-Signal Network Analysis, Phd. Dissertation, Vrije Universiteit Brussel, February 2006. [2] J.Verspecht. Broadband Sampling Oscilloscope Characterization with the Nose-To-Nose Calibration procedure: a Theoretical and Practical Analysis. IEEE Trans. Instrum. Meas., Vol. 44, No. 6, pp. 991-997, December 1995. [3] A.Barel, Y.Rolain. A microwave multisine with known phase for the calibration of narrowbanded nonlinear vectorial network analyzer measurements. 1998 IEEE MTT-S Int. Microwave Symp.Digest, Vol.3, pp. 1499-1502, Baltimore, June 1998. [4] Agilent RF and Microwave Test Equipment, Crystal Detectors. www.agilent.com
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