Operation and Calibration of VNA-based Large Signal RF I-V Waveform Measurements System without using a harmonic phase reference standard A.Aldoumani*, P. J. Tasker*, R. S. Saini**, J. W. Bell*, Tudor Williams** and J. Lees* * School of Engineering, Cardiff University, Cardiff, UK, CF24 3TF Tel +44 2920 75938 ** Mesuro Limited, Pen coed Technology Park, Pencoed, CF35 5HZ
[email protected] Abstract. A new approach is presented that allows a Vector Network Analyzer to be operated as a Large Signal Network Analyzer without the need for a harmonic phase reference generator. The mode of operation exploits the architecture of a Rohde and Schwarz ZVA-67, which incorporates internal signal and local oscillator sources based on direct digital synthesis [1]. This unique capability leads to a Vector Network Analyzer based Large Signal Network Analyzer configuration that provides for time coherent receivers. This feature combined with a modified calibration procedure, allows the instrument, to provide error corrected RF current and voltage waveform measurements, requiring only the internal signal sources and an external phase (time) meter [2-5]. This approach simplifies the Large Signal Network Analyzer architecture and removes the complexities and bandwidth limitations introduced when employing a harmonic phase reference generator. Keywords—Nonlinear, LSNA, NVNA, Waveform measurements, Harmonic phase reference.
I.
of DDS components should provide a VNA with time coherent receivers and a constant relative phase response, hence eliminating the need for a HPR generator for triggering. In addition, relative phase (time) calibration can be performed by simply using a relative phase (time) meter, such as a broadband sampling oscilloscope, thus avoiding, if desired, the need for a HPR generator altogether [6]. It is this approach to operation and relative phase (time) calibration, using a ZVA-67 based LSNA that is investigated in this paper. Initially the ability of the ZVA-67 to provide the necessary time coherent receiver functionality will be verified. Following this, a calibration procedure using only the internal signal sources and an external relative phase (time) meter will be presented and demonstrated. Finally measurements verifying the operation of the ZVA-67 as a fully functional LSNA, without a HPR generator will be shown. II.
INTRODUCTION
RF current and voltage (RF I-V) waveform measurements are essential for investigating the operation of devices and circuits, in terms of performance and reliability, under large signal operating conditions. Large Signal Network Analyzer (LSNA) is the general term for a measurement instrument that can perform such waveform measurements, and can be assembled using either a time-domain based receiver such as sampling a oscilloscope or a frequency-domain based receiver such as a vector network analyser (VNA) [2]. The typical limitation of VNA based systems is that they need harmonic phase reference (HPR) generators for both triggering and relative phase (time) calibration. This leads to increased system complexity and cost, including the requirement for an additional receiver. In addition, further hardware development of the phase reference generators is required each time the bandwidth needs to be increased. Also when employing a HPR, both the calibration bandwidth and required frequency grid is restricted by the functionality of the HPR generator, this can make certain measurements e.g. modulated measurements very challenging [5]. This paper presents a solution that allows a VNA to operate as a LSNA without requiring a HPR generator, either for triggering or calibration. The concept exploits the fact that emerging VNA architectures, for example the Rohde and Schwarz ZVA-67 incorporate internal signal excitation and local oscillator (LO) sources based on direct digital synthesis (DDS) [1]. The use
LSNA OPERATION
An LSNA is required to measure the time varying travelling wave signals !! ! and !! ! present at each port of the device under test. A generic LSNA block diagram is shown in Fig. 1, in which dual directional couplers are used to separate the time varying signals !! ! and !! ! and direct them to pairs of receivers [7]. 4-Channel Receiver
a1_raw
b1_raw
b2_raw a1_corr b1_corr
DUT
a2_raw
a2_corr b2_corr
Fig. 1. A generic LSNA RF architecture 2 ports.
If the receivers operate in the time domain then !! ! and !! ! signals are directly time sampled, with reference to a common time trigger. However, if the receivers operate in the frequency domain, which is the case in VNA based systems, it is the frequency components of the time varying signals, their Fourier coefficients !! (!) and !! (!), that are sequentially measured. Transformation of these Fourier coefficients back into the time domain is only possible if, during the swept frequency VNA measurements, there is a common time reference. Typically this is not the case as each time a VNA
performs a frequency sweep, the relative phase of the LO is randomized. Reconstruction of the signal in the time domain thus requires some means of measuring, directly or indirectly, the phase of the LO, again relative to a common time reference. Typically the HPR generator, attached to an additional receiver, provides this common time trigger. This additional component increases both the complexity and cost of VNA based LSNA systems compared to the time sampling alternative. In addition, operational functionality is totally dependent of the quality and availability of an appropriate HPR generator. Even with these restrictions, VNA based LSNA systems are becoming, the solution of choice, due to their significantly improved dynamic range [8-9]. III.
PHASE (TIME) COHERANCE
Relative Phase a0 (deg)
Relative Phase b0 (deg)
Consider now a VNA based LSNA system using the Rohde and Schwarz ZVA-67. This VNA incorporates multiple internal DDS signal sources, for both the device excitation and the local oscillator - hence, all the sources should be “time coherent”. If this is the case, the relative phase of the LO is no longer random, and should be repeatable between measurements. This VNA system should, following a relative phase (time) calibration, be able to directly measure the Fourier coefficients !! (!) and !! (!) with respect to a common time trigger, and hence accurately measure !! ! and !! ! without the requirement of attaching a HPR generator to an additional receiver. 40 0 -40 0
10
20 30 Frequency (GHz)
40
50
and LO sources, the scatter should not be observed in the ratio ! !!,!"# !
! !!,!"# !
(raw S11), as confirmed in Fig. 3.
Fig. 3. Measured phase jitter observed over a 24hr period for raw S11, as a function of frequency. Average values is also identified with dot.
The observed increase of this relative phase scatter with frequency is consistent with the source being related to frequency independent timing jitter (see Fig. 4), in the DDS internal signal generators; port signal generator, phase jitter !Δ!! and/or the LO signal generator, phase jitter !Δ!!" .
40
Fig. 4. Measured Time Jitter observed over a 24hr period for !!,!"# (!) as a function of frequency. An identical result is achieved for !!,!"# (!).
0 -40 0
10
20 30 Frequency (GHz)
40
50
Fig. 2. Measured Phase Jitter observed over a 24hr period for !!,!"# (!) and !!,!"# (!), as a function of frequency.
To investigate the possibility of exploiting the “time coherence” of the ZVA’s mode of operation, the instrument was configured to perform swept frequency measurements on a 1 GHz grid from 1GHz to 50 GHz. A subroutine was written to collect a dataset sequence; the raw ZVA data from port 1, the measured frequency response !!,!"# (!) and !!,!"# (!), for each one minute interval during the first hour followed by 30 minutes intervals for the next 24 hrs. Of critical interest was the variation in the measured relative phase response Δ! over time, normalized to first measurement dataset. The measured dataset at the ith time interval is thus given by; ! ! ! !!,!"# ! = !!,!"# ! ! !!! = !!,!"# ! ! !" !!! !!!!" ! ! ! !!! !!,!"# ! = !!,!"# ! ! = !!,!"# ! ! !" !!! !!!!"
(1)
The results obtained are shown in Fig. 2 and clearly confirm that although the measured relative phase is not randomized, there is a considerable scatter observed. Since these travelling wave signals have common internal excitation
However, a closer inspection shows that not all this time jitter, +/- 1.6 psec, is random and that a major component is in fact a time drift term that is identical (coherent) across the measured 50 GHz bandwidth, as clearly shown in Fig. 5.
Fig. 5. Measured time drift observed over (a) 1hr period and (b) 24hr period for !!,!"# (!), as a function of observation time at selected frequencies. An identical result is achieved for !!,!"# (!).
Critically, this coherent time drift has no influence on the determined time varying signals !! ! and !! ! computed from the measured Fourier coefficients !! (!) and !! (!), when time aligning the individually computed spectral components since it is common for all. The residual measured LO time (phase) jitter after removal of the coherent drift component is observed to be below +/- 0.3 psec, as shown in Fig. 6. The above investigations prove that the ZVA-67 is a “time coherent” system, which, after relative phase (time) calibration should be able to perform accurate measurement of time varying signals !! ! and !! ! ,
without requiring a HPR generator connected to and occupying an additional channel
HPR generator. As the requirement for a triggering HPR generator standard during the measurement step has been removed, its complete elimination from the phase calibration step would further simplify the system architecture [3, 8-10]. ZVA a‘0
S4 b‘0
“Time” Meter
Trigger
f0
LO
DSA8200 Digital Sampling Oscilloscope
a0
S1
b0
a1 bTM
nf0
Fig. 6. Measured residual Time Jitter observed over a 24hr period for !!,!"# (!), as a function of frequency after removal of the coherent drift component (determined in this case at 5 GHz). An identical result is achieved for !!,!"# (!).
IV.
CALIBRATION
Initially the LSNA performs un-calibrated or ‘raw’ measurements that must be transformed to error corrected measurements at the desired DUT reference plane. For a twoport device measurements this operation is achieved via the following mathematical transformation; !!,!"# (!)
!!,!"# (!)
!!,!"# (!) !!,!"# (!) = !(!) !(!) !!,!"# (!) !!,!"# (!) !!,!"# (!)
where
1 !!" (!) !(!) = 0 0
(2)
!!,!"# (!)
!!" (!) !!! (!) 0 0
0 0 !!! (!) !!" (!)
0 0 !!" (!) !!! (!)
(3)
!!"#$% (!) !!" ! !!,!"# ! !!!! ! !!,!"# !
Fig. 7. Hardware configuration for ZVA relative phase calibration using a Phase Meter.
Consider instead an alternative approach to relative phase calibration: To determine the relative phase, a phase (time) meter is connected to the relevant port (in this case port 1). In this demonstration, a Tektronix DSA 8200 sampling scope with high frequency (67GHz) sampling head is used as the relative phase meter [6]. To ensure a common time reference for the relative phase measurements, the Tektronix sampling scope is triggered using one of the spare internal ZVA-67 DDS signal sources, as shown in Fig. 7, which in this case is set to an appropriate reference frequency of 1 GHz. A stepped frequency CW stimulus signal is then applied to the port of interest, and since the angle ∠!!,!"# (!) is now directly measured, it is equal to ∠!!!!"# (!) (the phase component of the Fourier transformed sampling scope measured waveform), the relative phase ∠!(!) is computed as follows; ∠! ! = ∠!!!!"# ! − ∠ !!" ! !!,!"# ! + !!! ! !!,!"# !
The error terms inside the error matrix !(!) are the same as those required for s-parameters [7], hence are determined on a selected frequency grid, using one of the standard VNA calibration procedures, i.e. SLOT, TRL, TRM, etc. Critical for LSNA operation is the determination of the additional vector error term !(!). This typically involves a two-step process where the magnitude and relative phase of !(!) are determined separately. To determine magnitude, a power meter is connected to the relevant port (in this case port 1). If a CW frequency stimulus signal is now applied and steppedthru the calibrated frequency grid, since in this case the magnitude of !!,!"# (!) is directly measured, it is equal to !!"#$% (!) , (the power meter reading), the magnitude of !(!) is computed as follows;
!(!) =
b1
(4)
Typically, to determine relative phase, the next step involves connecting a HPR generator - a known harmonically rich stimulus, to the relevant port (in this case port 1). Calibration can only be achieved if the HPR generator is able to generate a stimulus that has frequency components covering the desired frequency grid. Hence, both the calibration bandwidth and required frequency grid is restricted by the functionality of the
(5) In this case, a simple, easily generated, single frequency signal of appropriate power level is all that is required for phase calibration. Using the internal ZVA-67 sources ensures that LSNA operation can be achieved over its full bandwidth of 67GHz. At this point, the ZVA-67 LSNA system is fully calibrated and ready to perform coherent measurements of time varying signals !! ! and !! ! at all four ports. This is now possible as the fourth port is no longer required as a reference receiver to measure the HPR. V.
SYSTEM VERIFICATION
To verify the functionality of the calibrated ZVA based LSNA system, measurements were performed using the experimental setup shown in Fig. 8. Here two of the ZVA’s internal DDS sources set to different frequencies, power levels and phases, are combined in order to synthesize complex time varying signals at one of the calibrated port (in this case port1). Both the ZVA and the Tektronix sampling scope measure these signals simultaneously. Typical results achieved are shown in Figures 9 and 10, indicating that the displayed ZVA DDS waveforms!!,!"## ! , computed from vector error correct measurements performed in the frequency domain, !!,!"# (!) and !!,!"# (!), are
identical to those measured directly in the time domain with the Tektronix Sampling Scope !!"#$% ! . The results confirm that the calibrated ZVA LSNA system is fully functional and can perform waveform measurements over its full bandwidth. The relative phase uncertainly observed in these measurements is again consistent with the previously observed value of +/- 0.3 psec.
f0
S4
S2
a‘0
b‘0
a0
b0
Trigger
“Time” Meter
LO mf0
b1
nf0 R&S ZVA 67GHz
DSA8200 Digital Sampling Oscilloscope
Fig. 8. Experimental setup used for ZVA waveform measurement verification.
Fig. 9. Synthesized power amplifier type time varying signal containing frequency components at (a) 10 GHz and 30 GHz and (b) 20 GHz and 40 GHz.
VI.
Fig. 10. Synthesized mixer type signals containing frequency components at (a) 9 GHz and 10 GHz and (b) 1 GHz and 11 GHz.
a1 bTM
S1
ports are available for DUT characterization, eliminating the need for multiplexing measurement signals, and allowing a simple and rapid measurement approach.
CONCLUSION
A new approach for operating and calibrating emerging VNA based LSNA measurement systems has been developed, implemented and verified. A key feature of this approach is that both the operation and calibration of the VNA based LSNA system is achieved without the requirement of a harmonic phase reference HPR generator. The implementation exploits the fact that emerging VNA architectures, e.g. the Rohde and Schwarz ZVA-67 incorporate internal signal and local oscillator (LO) sources based on Direct Digital Synthesis. The use of such DDS components provides a VNA receiver that is both repeatable and coherent in terms of relative phase over its full frequency bandwidth, in this case to within +/- 0.3 psec. The calibration approach developed uses a relative phase (time) meter, i.e. a sampling oscilloscope to perform the relative phase (time) calibration. Since calibration in this case is carried out using the VNA internal sources and a broadband sampling scope, there are reduced restrictions on the frequency grid and bandwidth. Importantly, as no dedicated channel is required for triggering during waveform measurements, all four VNA
ACKNOWLEDGEMENTS The authors would like to thank the support and collaboration of Rohde and Schwarz and in particular Philip McCluskey and Jamie Lunn. This work is part funded EPSRC iCase project number EP/J501888/1. REFERENCES [1]
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