Network Analyzers From Small Signal To Large Signal Measurements

Network Analyzers From Small Signal To Large Signal Measurements
Doug Rytting

Agenda Small Signal Measurements & Error Correction
Compression and AM to PM Hot S22 Measurements Load Pull Measurements Pulse Measurements Large Signal Network Analyzer Measurements

Network Analyzer Block Diagram
This is a generic block diagram of a 4 channel network analyzer. The source can be switched to excite port-1 or port-2 of the device under test (DUT). The switch also provides a Z0 termination for the output port in each direction. Directional couplers are used to separate the incident, reflected and transmitted waves in both the forward and reverse direction. Mixers are used to down convert the RF signals to a fixed low frequency IF. The IF is digitized by A/D converters. The LO source is tuned to the frequency of the RF + IF. The S-parameters of the DUT can be defined as follows: S11 = b1/a1, switch in forward direction S21 = b2/a1, switch in forward direction S12 = b1/a2, switch in reverse direction S22 = b2/a2, switch in reverse direction

Improvements with Correction
A linear calibration procedure is applied to remove as many of the errors as possible. The loss, directivity, match, and main leakage errors can be greatly reduced depending on the accuracy of the calibration standards used. However, the noise and linearity errors can not be reduced using a simple linear calibration procedure. If fact the noise and linearity errors increase a small amount. Residuals also remain that are caused by A/D quantization errors, clock leakage, etc. Once the network analyzer is calibrated the drift, stability, and repeatability errors will degrade the system performance. This usually means that the system will need to be recalibrated at some interval depending on the system usage, environment and required accuracy. There are some lower level leakage paths in the RF hardware that are not modeled in many of the error correction schemes.

Improvements with Correction
To see the improvements offered by error correction lets compare the measurement results before and after error correction when measuring a beaded airline. The two test cases will be with a response only calibration, which will not remove the port match and directivity errors, and a full two port calibration which will remove all the errors. There is a twenty dB improvement in the reflection measurements when the directivity errors are reduced. The transmission tracking errors are greatly improved with error correction. The error was mainly caused by port match. It should be pointed out that the uncorrected response errors are only a tenth dB which means the uncorrected return loss at both test ports must be at least 20 dB. After correction they have been reduced 20 db more.

Calibration Examples – 8 Term Model
There is a number of calibration techniques that have been developed based on the 8-term error model. Seven or more independent conditions must be measured. There must be a known impedance termination or a known transmission line. And port-1 and port-2 must be connected for one of the measurements. The list of calibration approaches can be much longer than the ones shown above. And there continues to be new and novel ways to solve for the seven error terms and calibrate the system. The 8-term error model approach has yielded more accurate calibration methods as well as simplified the calibration process. TRL and LRL provide the best accuracy. The other methods simplify the calibration steps compared to the older TOSL 12 term model. In one case (UXYZ above) the thru standard does not need to be known as long as it is reciprocal.

Power Sweep - Compression
Saturated output power Output Power (dBm) Compression region Linear region (slope = small-signal gain) Many network analyzers have the ability to do power sweeps as well as frequency sweeps. Power sweeps help characterize the nonlinear performance of an amplifier. Shown above is a plot of an amplifier's output power versus input power at a single frequency. Amplifier gain at any particular power level is the slope of this curve. Notice that the amplifier has a linear region of operation where gain is constant and is independent of power level. The gain in this region is commonly referred to as "small-signal gain". At some point as the input power is increased, the amplifier gain appears to decrease, and the amplifier is said to be in compression. Under this nonlinear condition, the amplifier output is no longer sinusoidal -- some of the output power is present in harmonics, rather than occurring only at the fundamental frequency. As input power is increased even more, the amplifier becomes saturated, and output power remains constant. At this point the amplifier gain is essentially zero, since further increases in input power result in no change in output power. Saturated output power can be read directly from the above plot. In order to measure the saturated output power of an amplifier, the network analyzer must be able to provide a power sweep with sufficient output power to drive the amplifier from its linear region into saturation. A preamp at the input of the amplifier under test may be necessary to achieve this. Input Power (dBm)

Power Sweep -Gain Compression
CH1 S og MAG dB/ REF 32 dB dB 12.3 dBm C2 IF BW 3 kHz SWP 420 msec START -10 dBm CW MHz STOP 15 dBm 1 dB compression: input power resulting in 1 dB drop in gain Ratioed measurement Output power available (non-ratioed measurement) The most common measurement of amplifier compression is the 1-dB-compression point, defined here as the input power* which results in a 1-dB decrease in amplifier gain (referenced to the amplifier's small-signal gain). The easiest way to measure the 1-dB-compression point is to directly display normalized gain (B/R) from a power sweep. The flat part of the trace is the linear, small-signal region, and the curved part on the right side corresponds to compression caused by higher input power. As shown above, the 1-dB-compression point of the amplifier-under-test is 12.3 dBm, at a CW frequency of MHz. It is often helpful to also know the output power corresponding to the 1-dB-compression point. Using the dual-channel feature found on most modern network analyzers, absolute power and normalized gain can be displayed simultaneously. Display markers can read out both the output power and the input power where 1-dB-compression occurs. Alternatively, the gain of the amplifier at the 1-dB-compression point can simply be added to the 1-dB-compression power to compute the corresponding output power. As seen above, the output power at the 1-dB-compression point is 12.3 dBm dB = 43.3 dBm. It should be noted that the power-sweep range needs to be large enough to ensure that the amplifier under test is driven from its linear region into compression. Modern network analyzers typically provide power sweeps with 15 to 20 dB of range, which is more than adequate for most amplifiers. It is also very important to sufficiently attenuate the output of high-power amplifiers to prevent damage to the network analyzer's receiver. * The 1-dB-compression point is sometimes defined as the output power resulting in a 1-dB decrease in amplifier gain (as opposed to the input power).

Power Sweep - AM to PM Conversion
1:Transmission Log Mag 1.0 dB/ Ref dB 2:Transmission /M Phase 5.0 deg/ Ref deg Ch1:Mkr dBm dB Ch2:Mkr dB deg Use transmission setup with a power sweep Display phase of S21 AM - PM = 0.86 deg/dB 2 1 2 1 Start dBm CW MHz Stop dBm 1 Start dBm AM-PM static conversion can be measured by performing a power sweep with a vector network analyzer, using the same transmission setup that we used for gain compression. The displayed data is formatted as the phase of S21 (transmission) versus power. AM-PM conversion can be computed by choosing a small amplitude increment (typically 1 dB) centered at a particular RF power level, and noting the resultant change in phase. The easiest way to read out the amplitude and phase deltas is to use trace markers. Dividing the phase change by the amplitude change yields AM-PM conversion. The plot above shows AM-PM conversion of 0.86 o/dB, centered at an input power of -4.5 dBm and an output power of 16.0 dBm. Had we chosen to measure AM-PM conversion at a higher power level, we would have seen a much larger value (around 7 o/dB). CW MHz Stop dBm

Hot S22 Measurement System
Small signal S-parameters of a nonlinear device in the presence of a high power drive signal Df away from test frequency. Osc a b b 3 a 3 High Power Load High Power Combine a 1 b 2 DUT [A] b 1 a 2 High Power Osc The high power oscillator along with the bias sets the operating point of the DUT under large signal operation. The high power oscillator provides the RF operating point around which the small signal measurements can be made. Normally there is a small frequency offset so that the s-parameters can be measured without interference from the large drive signal. The power level of the high power oscillator, bias, and high power load can be adjusted to help extract the operating behavior and large signal model for the DUT.

Hot S22 Measurement System
S-parameters of a nonlinear device at a defined input or output power. OSC b 1 a 2 3 DUT [A] A G B Under large signal conditions the Device Under Test (DUT) parameters change as a function of the drive level. It is possible to measure the so called “large signal S‑parameters” which is no more that the small signal parameters vs drive level. This describing function type of parameter requires that the input power is connected even when the output parameters are measured. Typically for small signal measurements of S22 and S12, the device is driven at the output and the input is terminated. However, for high power measurements it is possible to measure all 4 S‑parameters while only driving the input by providing two conditions at the output. These unknown load conditions (A and B) generate 4 equations that can be solved for the 4 S‑parameters..

Load Pull Measurement Need to measure nonlinear device behavior under actual operating conditions Low power High power S 22 Constant output power contours versus output load impedance Pmax -1 dB -2 dB -3 Another approach (called load‑pull) is also used for large signal devices and amplifiers. It is known that the output impedance and other parameters vary as a function of the output power, thus correspondingly the amplifier's input RF level. These changing parameters cause the delivered power to the load to change with different load and drive conditions. The most common result of a load pull measurement is a series of constant output power contours (not always circular) plotted on a Smith chart which represent all possible output impedances. A load pull measurement is required at each power level and frequency of interest since the output contours are sensitive to these variables for most high power amplifiers. The output power contours shown are with a constant input power level. Parameter changes vesus output power level

Load Pull System X X X X DUT
INPUT IMPEDANCE AND POWER MEASUREMENT SYSTEM OUTPUT IMPEDANCE AND POWER MEASUREMENT SYSTEM X X X X DUT INPUT TUNER OUTPUT TUNER A basic load pull measurement system typically consists of input and output load tuners, signal separation devices and impedance and power measurement capabilities. A vector network analyzer is commonly used with tunable loads as the core instruments of a load pull measurement system. Input and output measurements allow direct measurement of the input and output load values. As an example, the output tuner can be adjusted for maximum power transfer and measured with a network analyzer. The conjugate match or the load is the output match of the amplifier under large signal operating conditions. The same type of measurement can be applied to the input of the amplifier to determine the input match.

Types of Output Tuners Harmonic load-pull Passive load-pull
Active load-pull Simultaneous Drive OSC The passive load‑pull tuner adjusts the magnitude and phase of the terminating impedance. There are both mechanical and electrical techniques used to realize the passive tuner. Due to the losses in the passive tuner, the active load-pull tuner adds an amplifier in a stabilized feedback loop to provide very high reflection coefficients. The termination impedance of the harmonics can effect the device parameters. The harmonic load-pull tuner provides independent load conditions to study the interaction of the harmonics on the device performance. It is common to couple the active load‑pull technique with the harmonic tuner to overcome the additional losses. Load pull data can also be obtained by simultaneously driving both the input and output at the same time. The input is driven at the desired level and the output is driven to simulate the reflection from a general load termination. This technique is known as "simultaneous drive” active load‑pull. DUT

Harmonic Load Pull System
LO Synthesizer HP 8360 GHz Four Channel Frequency Converter HP 8510C/85110A a 1 b 1 b 2 a 2 LO Synthesizer Can be Tuned to Harmonics T fo 2fo 3fo Source Synthesizer HP 8360 GHz Port 3 Coaxial and power cals. DUT Reflectometer Mounted on Prober Input Amplifier GHz TWA Port 1 Input Probe Port 2 Output Probe T Port Drive PIN Switch The network analyzer measures the error-corrected two port S‑parameters of the DUT with using four mixers. The receiver is not phased locked, the required coherency being provided by the RF and LO synthesizers. The system measures power with a 90 dB dynamic range. In a conventional test set the power range is limited to 20 dB by the -phase locking receiver. In this system power can be changed by adding attenuation before the input amplifier without loosing phase lock or influencing the calibration. For high power measurements, the port-drive PIN switch is set to drive the input of the DUT. The network analyzer measures the input reflection coefficient and the load reflection coefficient. The raw a1 and b2 powers are measured and vector corrected. The net input power, the net output power and the associated gain are then calculated. For harmonic measurements, the test set LO is set to measure the harmonic frequency with the first (50 GHz) synthesizer, while driving the DUT at the fundamental frequency with the second (50 GHz) synthesizer. The harmonic power levels are vector corrected to the DUT reference plane by a broadband calibration. The load reflection coefficients at the different harmonic frequencies are also measured. Therefore, in addition to tuning the load at the fundamental frequency, the loads at the harmonic frequencies can also be adjusted. Calibration is first done on wafer at ports 1 and 2. Then the coax Port 3 is calibrated as a one port which allows calibrated coax power measurements. The calibrated coax power measurements can then be mathematically moved to the on wafer ports 1 and 2. Calibration is required at the fundamental and harmonic frequencies.

High Power Device Pulse Measurements
Control DUT Temperature Eliminate temperature as a variable Test high power devices on-wafer at full power Measure devices in "unsafe" DC operating area Test "pulsed" devices in a pulsed environment Test environment = final application (GSM) Pulsed radars/phased array antennas/high power MMIC's Improve device characterization data Model power FET's at full power level Measure IV curves without temperature effects Investigate trapping effects in GaAs Pulsed measurements can help us to investigate and model the effects of thermal heating in high power Si and GaAs devices such as BJTs, HBTs and MESFETs. They can also help us to investigate trapping effects in GaAs material. Finally, they will allow us to characterize devices and amplifiers that are designed for pulsed applications.

Pulse System Capabilities
Gate/Base Drain/Collector RF RF PW T1 T2 Synchronization of pulses IV plane characterization Point in pulse vs Frequency or Pulse profile vs Time I D V Q1 Q2 DC Safe Operating Limit The isothermal system handles all of the pulse synchronization. For most measurements this means setting the gate pulse width, the delay from the leading edge of the gate pulse to the beginning of the drain (T1), the drain pulse width, the delay of the RF pulse , and the RF pulse width. All of these variables can be independently controlled to generate a specific set of stimulus pulses. Once the desired stimulus pulses have been set-up, it is now time to make measurements. The isothermal system can be used to make either DC measurements alone, or a combination of pulse DC and pulse RF measurements. Pulse IV curves can be created. We all remember the curve tracers back in the electronics labs, this system is the Cadillac of curve tracers. The isothermal system can generate a set of IV curves that is free from the thermal artifacts that corrupt most CW curve tracers. The system can establish several quiescent points (Q-point) and draw the curves associated with the power dissipation at that Q-point. In addition the system can pulse into the "Unsafe operating" region of the device that is set by the thermal power dissipation curve. In addition to the DC only measurements, the isothermal system can measure swept S-parameter data (point-in-pulse) such that the measurement data is completely synchronized with the pulses. Pulse profile mode allows the operator to view the RF pulse envelope in time domain. This mode is extremely useful in looking at the pulse envelope to see if the amplitude is flat or if the phase varies across the pulse shape.

Pulsed Bias/RF Meas System
RF Synthesizer Pulsed-RF Test Set LO Synthesizer Measurement Controller Network Analyzer T T Bias Network Gate / Base Bias Pulser Drain / Collector Bias Pulser T DC Power Supply Digital Multimeter T Trigger Pulse Generator Here is one proposed solution for making pulsed bias/RF measurements. The synthesizers and test set can be chosen based on frequency and RF power requirements. The bias pulsers can be designed to meet specific pulse width and current handling requirements. High Frequency IC-CAP software can be added to perform the mathematical extraction of device model parameters.

Large Signal Network Analyzer
Acquisition (LSNA) Stimulus Response ESG 50 Ohm or Tuner Complete Spectrum Waveforms Harmonics and Modulation A Large Signal Network Analyzer looks similar to a vector network analyzer. There is a test-set to separate incident and reflected waves. A microwave source can inject a one tone or modulated signal into a component. If this component is nonlinear, it will generate harmonics. These harmonics are reflected back by the mismatch created by the measurement system. A broadband acquisition system is able to take proper samples of the broadband incident and reflected waves. With the proper calibration techniques, the systematic errors of the measurement system are eliminated. The complete spectrum (amplitude and phase) of incident and reflected waves can be acquired and the time waveforms reconstructed.

Large Signal Network Analyzer
Measures magnitude and phase of incident and reflected waves at fundamental, harmonic, and modulation frequencies. Calibrated for relative and absolute measurements for both linear and nonlinear components at the device under test. Calculate calibrated voltage and current in both the time and frequency domains. Combination of a vector network analyzer, sampling scope, spectrum analyzer and power meter. The large signal network analyzer is a combination of the capabilities of a standard vector network analyzer, power meter, sampling scope and spectrum analyzer. This provides error corrected measurements of incident, reflected and transmitted wavefroms. These can be converted to voltage and current waveforms that can be displayed in both the time and frequency domains. This capability is new and provides the microwave engineer the same capabilities as a low frequency designer.

LSNA System Block Diagram
Sampler Front End Requires high BW IF Requires Harmonic LO The hardware architecture of the Large-Signal Network Analyzer is relatively simple. 4 couplers are used for sensing the spectral components of the incident and scattered voltage waves at both DUT ports. The sensed signals are attenuated to an acceptable level before being sent to the input channels of a 4 channel broadband frequency converter. This frequency converter is based upon the harmonic sampling principle and converts all of the spectral components coherently to a lower frequency copy. The resulting IF signals are digitized by a set of 4 analog-to-digital converters (ADCs). The DSP and processor can do all the signal processing which is needed to finally end up with the calibrated data in the preferred format (a/b or v/i, time, frequency or envelope domain). Note that additional synthesizers and tuners can be added externally. This allows different excitation schemes to investigate DUT nonlinear behavior.

Sampling Converter Fundamentals
LP Freq. (GHz) 1 2 3 50 fLO 100 fLO 150 fLO Freq. (MHz) RF IF fLO=19.98 MHz = (1GHz-1MHz)/50 IF Bandwidth: 4 MHz Harmonic sampling is best illustrated for the case of a single frequency grid. Assume that we need to measure a 1 GHz fundamental together with its 2nd and 3rd harmonic. We choose a local oscillator (LO) frequency of MHz. The 50th harmonic of the LO will equal 999 MHz. This component mixes with the fundamental and results in a 1 MHz mixing product at the output of the converter. The 100th harmonic of the LO equals 1998 MHz, it mixes with the 2nd harmonic at 2 GHz and results in a 2 MHz mixing product. The 150th harmonic of the LO equals 2997 MHz, it mixes with the third harmonic at 3 GHz and results in a 3 MHz mixing product. The final result at the output of the converter is a 1 Mhz fundamental together with its 2nd and 3rd harmonic. This is actually a low frequency copy of the high frequency RF signal. This signal is then digitized, and the values of the spectral components are extracted by applying a discrete Fourier transformation. The process for a modulated signal is very similar but more complex. After the RF-IF conversion all harmonics and modulation tones can be found back in the IF channel, ready for digitizing and processing.

LSNA System Block Diagram
Mixer Front End Requires harmonic sync Can use high BW IF for modulation Or low BW IF if no modulation An alternative block diagram uses mixers as the frequency converter. This approach reconstructs the waveform by tuning to each of the harmonics one at a time and then reconstructing the waveform from the measured series of data. This method requires an additional mixer preceded with a harmonic generator to provide the phase coherency at each of the measured harmonics. If there is no modulation on the signal, a narrowband IF detection will work just fine. To reconstruct the modulation with a narrowband IF each of the tones will need to measured and the modulation reconstructed. Or a wide band IF could be used to capture the modulation waveform directly.

Nonlinear Calibration - Model
50 Ohm or Tuner Acquisition Stimulus Response Modulation Source Measured waves Actual waves at DUT 7 relative error terms same as a VNA Absolute magnitude and phase error term This model is based on the 8-term model we used for the vector network analyzer. However we can not normalize one of the branches of the flow graph because we will be making absolute measurements as well as relative (s-parameter) measurements. The K term above contains the information needed for power measurements and the phase relationship between the harmonics. With this calibration the complete spectrum (amplitude and phase) of incident and reflected waves are acquired and the time waveforms reconstructed. The K term requires additional calibration steps using a power meter for the magnitude of K and a reference generator for the phase of K.

Nonlinear Calibration
Relative calibration at the fundamental and harmonic frequencies determines the 7 normal error terms. Power calibration at the fundamental and harmonic frequencies determines the magnitude of K. Phase reference generator calibration determines the phase of K relative to the fundamental frequency. Reference generator is an impulse that must be accurately modeled or measured. The relative calibration is exactly the same as a vector network analyzer error correction. Both TOSL and TRL type calibrations can be done. This calibration must be done for the fundamental and harmonic frequencies. For the power calibration a power meter is connected to port-1 of the LSNA and the power measured at the fundamental and harmonic frequencies. The power measurements can be further improved using the relative error correction. For the phase calibration of the harmonics a phase reference generator is connected to port-1 of the LSNA. The phase reference generator is driven by a source at the fundamental frequency and generates a harmonic frequency comb at the output which is connecter to port-1. This phase reference generator can be calibrated very accurately so that the harmonic phase relative to the fundamental is very well known. For on wafer calibrations an additional calibration is performed at the wafer probe reference planes. The power measurements can then be “mathematically moved” from the coax connectors to the wafer probe reference planes.

Example # 1 Complete device measurement capability using a Large Signal Network Analyzer (LSNA).

Device Measurement -1.2 V -0.2 V 50 Ohm load Open port
The LSNA with a force/sensing bias supply can measure and compare both DC i/v curves and dynamic loadlines. One can look at the incident and reflected waves or voltages and currents in the frequency or time domain.

Example # 2 Device measurement verification and measurement-based model improvement.

Model Verification & Improvement
MODEL TO BE OPTIMIZED generators apply LSNA measured waveforms “Chalmers Model” “Power swept measurements under mismatched conditions” GaAs pseudomorphic HEMT gate l=0.2 um w=100 um Parameter Boundaries The approach of optimizing existing empirical models is pretty straightforward. For our example the so-called “Chalmer’s model” is used. First a set of experiments with measured data is gathered which covers the desired application for the model. This data is imported into the simulator. The measured incident voltage waves are applied to the model in the simulator.

During OPTIMIZATION Time domain waveforms Frequency domain gate drain voltage current Voltage - Current State Space The model parameters are then found by tuning them such that the difference between the measured and modeled scattered voltage waves is minimized. Note that one can often use built-in optimizers for this purpose. As with all nonlinear optimizations it is necessary to have reasonable starting values (these can be given by a simplified version of the classical approaches). The figures above represent one of the initially modeled and measured gate and drain voltages and currents, and this in the time domain, the frequency domain and in a “current-versus-voltage” representation. Note especially the large discrepancy between the measured gate current and the one which is calculated by the initial model.

Time domain waveforms Frequency domain gate drain voltage current Voltage - Current State Space After OPTIMIZATION The above figures represent the same data after optimization has taken place. Note the very good correspondence that is achieved. This indicates that the model is accurately representing the large-signal behavior for the applied excitation signals.

Vector Network Analyzer References
Basic Error Correction Theory S. Rehnmark, “On the Calibration Process of Automatic Network Analyzer Systems,” IEEE Trans. on Microwave Theory and Techniques, April 1974, pp J. Fitzpatrick, “Error Models for Systems Measurement,” Microwave Journal, May 1978, pp TRL and Self Calibration Techniques G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual 6-Port Automatic Network Analyzer,” IEEE Trans. on Microwave Theory and Techniques, MTT , Dec. 1979, pp 983 – 987. H. J. Eul and B. Schiek, “A Generalized Theory and New Calibration Procedures for Network Analyzer Self-Calibration,” IEEE Trans. on Microwave Theory & Techniques, vol. 39, April 1991, pp R. A. Speciale, “A Generation of the TSD Network-Analyzer Calibration Procedure, Covering N-Port Scattering-Parameter Measurements, Affected by Leakage Errors,” IEEE Trans. on Microwave Theory and Techniques, vol. MTT-25, December 1977, pp 8-Term Error Models Kimmo J. Silvonen, “A General Approach to Network Analyzer Calibration,” IEEE Trans. on Microwave Theory & Techniques, Vol 40, April 1992. Andrea Ferrero, Ferdinando Sanpietro and Umberto Pisani, “Accurate Coaxial Standard Verification by Multiport Vector Network Analyzer,” 1994 IEEE MTT-S Digest, pp Andrea Ferrero and Umberto Pisani, “Two-Port Network Analyzer Calibration Using an Unknown ‘Thru’,” IEEE Microwave and Guided Wave Letters, Vol. 2, No. 12, December 1992, pp Andrea Ferrero and Umberto Pisani, “QSOLT: A new Fast Calibration Algorithm for Two Port S Parameter Measurements,” 38th ARFTG Conference Digest, Winter 1991, pp H. J. Eul and B. Scheik, “Reducing the Number of Calibration Standards for Network Analyzer Calibration,” IEEE Trans. Instrumentation Measurement, vol 40, August 1991, pp 16-Term Error Models Holger Heuermann and Burkhard Schiek, “Results of Network Analyzer Measurements with Leakage Errors Corrected with the TMS-15-Term Procedure,” Proceedings of the IEEE MTT-S International Microwave Symposium, San Diego, 1994, pp Hugo Van hamme and Marc Vanden Bossche, “Flexible Vector Network Analyzer Calibration With Accuracy Bounds Using an 8-Term or a 16-Term Error Correction Model,” IEEE Transactions on Microwave Theory and Techniques, Vol. 42, No. 6, June 1994, pp A. Ferrero and F. Sanpietro, “A simplified Algorithm for Leaky Network Analyzer Calibration,” IEEE Microwave and Guided Wave Letters, Vol. 5, No. 4, April 1995, pp Switch Terms Roger B. Marks, “Formulations of the Basic Vector Network Analyzer Error Model Including Switch Terms,” 50th ARFTG Conference Digest, Fall 1997, pp Overview Papers – Available upon Request Douglas K. Rytting, “An Analysis of Vector Measurement Accuracy Enhancement Techniques,” Hewlett Packard RF & Microwave Measurement Symposium and Exhibition. Includes detailed appendix. March 1982. Douglas K. Rytting, “Advances in Microwave Error Correction Techniques,” Hewlett Packard RF & Microwave Symposium, June, 1987. Douglas K. Rytting, “Improved RF Hardware and Calibration Methods,” Hewlett Packard detailed internal training document later released to the public. Douglas K. Rytting, “Network Analyzer Error Models and Calibration Methods,” 62nd ARFTG Conference Short Course Notes, December 2-5, 2003, Boulder, CO. Vector Network Analyzer References

Large Signal Network Analyzer References
Signal Representations R. Marks and D. Williams, “A general waveguide circuit theory,” Journal of Research of the National Institute of Standards and Technologies, vol. 97, pp , Sept./Oct Large-Signal Network Analyzer Hardware Jan Verspecht, ”Calibration of a Measurement System for High-Frequency Nonlinear Devices,” Doctoral Dissertation – Vrije Universiteit Brussel, Belgium, November 1995. Large-Signal Network Analyzer Calibration Jan Verspecht, Peter Debie, Alain Barel, Luc Martens,”Accurate On Wafer Measurement of Phase and Amplitude of the Spectral Components of Incident and Scattered Voltage Waves at the Signal Ports of a Nonlinear Microwave Device,” Conference Record of the IEEE Microwave Theory and Techniques Symposium 1995, pp , USA, May 1995. Kate A. Remley, ”The Impact of Internal Sampling Circuitry on the Phase Error of the Nose-to-Nose Oscilloscope Calibration,” NIST Technical Note 1528, August 2003. Jan Verspecht, ”Broadband Sampling Oscilloscope Characterization with the ‘Nose-to-Nose’ Calibration Procedure: a Theoretical and Practical Analysis,” IEEE Transactions on Instrumentation and Measurement, Vol. 44, No. 6, pp , December 1995. D.F. Williams, P.D. Hale, T.S. Clement, and J.M. Morgan, “Calibrating electro-optic sampling systems,” IEEE International Microwave Symposium Digest, Phoenix, AZ, pp , May 20-25, 2001. Waveform Measurements Jan Verspecht, Dominique Schreurs, ”Measuring Transistor Dynamic Loadlines and Breakdown Currents under Large-Signal High-Frequency Operating Conditions,” 1998 IEEE MTT-S International Microwave Symposium Digest, Vol. 3, pp , USA, June 1998. Jonathan B. Scott, Jan Verspecht, B. Behnia, Marc Vanden Bossche, Alex Cognata, Frans Verbeyst, M. L. Thorn, D. R. Scherrer, “Enhanced on-wafer time-domain waveform measurement through removal of interconnect dispersion and measurement instrument jitter,” IEEE Transactions on Microwave Theory and Techniques, Vol. 50, No. 12, pp , USA, December 2002. D. Barataud, F. Blache, A. Mallet, P. P. Bouysse, J.-M. Nébus, J. P. Villotte, J. Obregon, J. Verspecht, P. Auxemery, “Measurement and Control of Current/Voltage Waveforms of Microwave Transistors Using a Harmonic Load-Pull System for the Optimum Design of High Efficiency Power Amplifiers,” IEEE Transactions on Instrumentation and Measurement, Vol. 48, No. 4, pp , August 1999. Schreurs, J. Verspecht, B. Nauwelaers, A. Barel, M. Van Rossum, “Waveform Measurements on a HEMT Resistive Mixer,” 47th ARFTG Conference Digest, pp. , June 1996. State-Space Models Dominique Schreurs, Jan Verspecht, Servaas Vandenberghe, Ewout Vandamme, ”Straightforward and Accurate Nonlinear Device Model Parameter-Estimation Method Based on Vectorial Large-Signal Measurements,” IEEE Transactions on Microwave Theory and Techniques, Vol. 50, No. 10, pp , 2002. John Wood, David Root, “The behavioral modeling of microwave/RF Ics using non-linear time series analysis”, International Microwave Symposium Digest 2003 IEEE MTT-S, Vol. 2, pp , USA, June 2003. Scattering Functions Jan Verspecht, ”Everything you’ve always wanted to know about Hot-S22 (but we’re afraid to ask),” Introducing New Concepts in Nonlinear Network Design - Workshop at the International Microwave Symposium 2002, USA, June 2002. Jan Verspecht, Patrick Van Esch, “Accurately Characterizing Hard Nonlinear Behavior of Microwave Components with the Nonlinear Network Measurement System: Introducing ‘Nonlinear Scattering Functions’,” Proceedings of the 5th International Workshop on Integrated Nonlinear Microwave and Millimeterwave Circuits, pp , Germany, October 1998. Publications database by “Jan Verspecht bvba” Many papers authored or co-authored by Jan Verspecht are available at the following URL: Large Signal Network Analyzer References

Network Analyzers From Small Signal To Large Signal Measurements

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