1. Linear and Nonlinear Device Measurements
Doug Rytting

2. Agenda Microwave Measurement Methods
Linear Measurements with a Vector Network Analyzer
Block Diagram
Error Correction
Nonlinear Measurements with a Large Signal Network Analyzer
Examples
The presentation will cover vector network analyzer block diagrams and state of the art error correction techniques.
Network analyzer techniques will then be extended to measuring nonlinear devices with large signals.

3. Microwave Measurement Methods
Power Meter
Oscilloscope
Spectrum Analyzer
Vector Network Analyzer
Power meters, oscilloscopes, spectrum analyzers, and vector network analyzers are the principle measurement tools used by the microwave industry.
The power meter and spectrum analyzer can only be corrected for scalar (magnitude only) measurements since phase is not available.
The oscilloscope and vector network analyzer can both be error corrected to the measurement plane. In fact they are duals of each other. The scope measuring in the time domain and the network analyzer in the frequency domain. However, we seldom see an error corrected oscilloscope in practice.
In this presentation we will focus on vector network analyzer techniques starting with basic block diagrams and the foundations of error correction. Then extend the network analyzer technique to new measurement methods that combine the features of all four instruments.

4. Linear Measurements with a Vector Network Analyzer

5. 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

6. 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.

7. 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.

8. One Port: 3-Term Error Model
The most simple case is the one port 3-term error model. From this model the same approach will be used for the two port cases.
In the one-port calibration procedure the model simplifies to just the terms describing the directivity, port match , and tracking errors at port-1.
The errors can be lumped into a fictitious error adapter that modifies the actual DUT reflection coefficient which is then measured by a ‘perfect’ reflectometer.

9. One Port: 3-Term Error Model
Solving the one-port flow graph yields a bilinear relationship between the actual and measured reflection coefficient. The actual reflection coefficient is ‘mapped’ or modified by the three error terms to the measured result. This equation can be inverted to solve for the actual reflection coefficient knowing the measured result and the three error terms.
The three error terms can be determined by measuring three known standards (such as an open, short and load) that yield three simultaneous equations. These three equations can then be solved for the three error terms.
Another popular calibration standard is called e-cal. With this technique the reflection coefficient is selected electronically from a set of pre measured states. These were measured using a network analyzer calibrated with primary standards. This is strictly a transfer standard but as long as the e-cal standard is stable it is very accurate. This type of standard allows fast calibrations, ease of use and less operator error.

10. 12-Term Error Model
Many of the older and lower cost network analyzers use three couplers instead of four for two port measurements. This puts the switch between the incident and reflected couplers. If the switch characteristics change as the switch is flipped from forward to reverse, the error adapter’s error terms will change. Even some four coupler network analyzers use this method as well, choosing not to use the fourth coupler for all measurements.
This is the original technique uses in the 1960’s for the first automatic network analyzers. This TOSL (through, open, short, load) 12-term model has been used for many years and is still widely used today.

11. 12-Term Error Model
The two-port case can be modeled in the same manner as the one-port. A fictitious error adapter is placed between the two-port DUT and the ‘perfect reflectometer’ measurement ports. This error adapter contains the 6 error terms for the forward direction. A similar 6 term model is used in the reverse direction.

12. 12-Term Error Model
Solving the forward flow graph yields measurements S11M and S21M. These two equations contain all four actual S-parameters of the DUT and the six forward error terms.

13. 12-Term Error Model
Solving the reverse flow graph yields measurements S22M and S12M. These two equations contain all four actual S-parameters of the DUT and the six reverse error terms.
The forward and reverse equations combine to give four equations containing the four actual S-parameters of the DUT and 12 error terms. If the 12 error terms are known these four equations can be solved for the actual S-parameters of the DUT.

14. 12-Term Error Model
This is the result of solving the four simultaneous measured s-parameter equations. Note that each actual s-parameter calculated requires measuring all four S-parameters as well as knowing the 12 error terms.

15. 12-Term Error Model
The 12 error terms will now be determined. First solve for the 6 terms in the forward direction. Then the same procedure can be used to solve for the 6 reverse terms.
Step one calibrates port-1 of the network analyzer using the same procedure used in the one-port case. This determines the directivity, match, and reflection tracking at port-1 (e00, e11, and De). From De the reflection tracking (e10e01) can be calculated.
Step two measures the leakage or crosstalk error (e30) from port-1 to port-2 directly by placing loads on each of the ports.
Step three consists of connecting port-1 and port-2 together. Then measure the port-2 match (e22) directly with the calibrated port-1 reflectometer. Then with the ports connected, measure the transmitted signal and calculate the transmission tracking (e10e32).

16. 16-Term Error Model
The complete system can be modeled using an error adapter between the DUT and the actual measurements. This error adapter describes all the possible stationary and linear errors that are caused by the system. Since the adapter is a 4-port it contains 16 error terms. If these error terms can be determined then the DUT S-parameters can be calculated from the measured S-parameters.
When making ratio measurements one of the terms can be normalized to 1 leaving 15 error terms.
When using 4 couplers placed after the switch the errors of the switch can be removed and will be discussed later.

17. 16-Term Error Model
There are 16 terms of which 8 are critical. These 8 include the directivity, port match and tracking errors.
The leakage terms add 8 additional error terms to the model. Not only is the traditional crosstalk term included, but switch leakage, signals reflecting from the DUT and leaking to the transmission port, common mode inductance, and other leakage paths are included. In a coaxial or waveguide system, assuming the switch has high isolation, these errors are small. But in a fixtured or wafer probe environment these errors can be much larger.
In a wafer probe environment it is important that the error terms do not change as the probes are moved around the circuit. If the error terms change, the 16-term model then changes and the accuracy will reduce.
Again the error terms can be normalized so that for ratio measurements there are only 15 error terms.

18. 16-Term Error Model
One method of solving this system is to use T-parameters (cascade parameters) that relate the measured waves to the DUT waves. This system is solved by partitioning the T matrix into 4 2x2 matrices and then solving the matrix equations which yields the bi-linear form above. This allows us to form a linear set of equations that can be solved for the error terms.
By using enough known standards, a set of linear equations is created that can be solved for the individual error terms. At least 5 two port standards are required to solve the system of equations. However, most of these can be degenerate two port standards that involve combinations of opens, shorts, loads and transmission lines.

19. 8-Term Error Model
The 8-term model can be derived from the 16-term model. First assume that the leakage terms are all zero. Or that the two primary leakage terms can be determined in a separate calibration step. Then assume that the switch is perfect and does not change the port match of the network analyzer as it is switched from forward to reverse. This assumption is valid if there are 4 measurement channels that are all on the DUT side of the switch. Then it is possible to mathematically ratio out the switch. This mathematical approach will be discussed later.

20. 8-Term Error Model
The flow graph consists of an error adapter at the input and output of the DUT. For ratio measurements of S-parameters, the number of error terms is reduced to 7 since the error terms can be normalized.

21. 8-Term Error Model
This is one of many possible mathematical formulation for the 8-term error model. Consider the error adapter as just one adapter between the perfect measurement system and the DUT. Then model this error adapter using the cascade T-parameters. This T-parameter matrix (T) can be partitioned, as described in the 16-term method, into the four diagonal sub matrixes T1, T2, T3, and T4. The 7 error terms are now defined as DX, kDY, e00, ke33, e11, ke22, and k. Which are the tracking, directivity, and match errors.

22. 8-Term Error Model
Using this approach the measured S-parameters formulation is a ‘bilinear matrix equation.’ The equation can be ‘inverted’ to solve for the actual S-parameters. And most important the relationship can be put in linear form. Expanding this matrix equation for the two-port case yields 4 equations with 4 measured S-parameters, 4 actual S-parameters, and 7 error terms. Note that these 4 equations are linear with regards to the 7 error terms.
This approach is particularly attractive for multi-port measurement systems. The matrix formulation does not change as additional ports are added.

23. 8-Term Error Model
Another approach is to cascade of the input error box (X), the DUT, and the output error box (Y). The measured result of this cascade is most easily calculated by using the cascade matrix definition (T-parameters).
This formulation was used by Engen and Hoer in their classic TRL development for the six-port network analyzer. And is the same approach used in the HP 8510 network analyzer.
From the last equation in the slide above, the 7 error terms are easily identified. There are 3 at port-1 (DX, e00, and e11) and 3 at port-2 (DY, e22, and e33) and one transmission term (e10e32).
The calibration approach require enough calibration standards to allow at least 7 independent observations of the measurement system.

24. 8-Term Calibration Examples
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.

25. Measuring S-parameters
Normally we measure S-parameters by terminating one port with a Z0 impedance and then measure the input reflection and transmission coefficients then flip the switch and make the same set of measurements in the reverse direction. However, with 4 couplers we can measure both the forward and reverse terminating impedances of the switch. This allows us to “ratio out” or remove the effects of the imperfect switch.
Note that the measurement channels are all on the DUT side of the switch. This allows the measurements of the incident and reflected signals at both outputs of the switch and the switch match errors can be calculated.
Mathematically the S-parameters of the system generate 4 equations. 2 in the forward direction and 2 in the reverse direction. These 4 equations can then be solved for the 4 measured S-parameters. This general way of measuring S-parameters does not require the DUT to be terminated in a Z0 environment.

26. Measuring S-parameters
Solving the 4 previous equations yield the above results. Note that the equations are written to allow ratio measurements by the network analyzer. Typically the network analyzer is more accurate making measurements this way. Noise and other common mode errors are reduced.
Using this method for measuring the 4 S-parameters requires 6 ratio measurements. The additional two measurements are required to remove the effects of the switch. However, these two additional measurements (G1 and G2) need only be made during the calibration step since they do not change during measurement assuming the switch is stable.

27. Multiport Error Model
The error correction process can be extended to multiport measurements. The same mathematical methodology is used with just the number of ports increased.

28. Accuracy of Error Correction
The flow graph after error correction is the same as before correction but with the error terms reduced. The flow graph can be solved and simplified to show the total system uncertainty. These equations calculate the magnitude uncertainty (DS11 and DS21) with each error term defined by its absolute magnitude. The first part of the equation describes the systematic errors and these errors typically add up in a worst case manner. The random, drift and stability errors are typically characterized in an RSS fashion in the second part.
The various error terms are defined in Slide 18. The subscript 1 refers to port 1 and the subscript 2 refers to port 2.
d: Residual Directivity Error
t: Residual Tracking Error
m: Residual Match Error
A: Dynamic Accuracy (linearity) of the network analyzer.

29. Accuracy of Error Correction
APC-7 (7 mm Coax) at 18 GHz
Residual Errors
OSL
Fixed Load
Sliding Load
TRL
TRM
Directivity d
-40 dB
-52 dB
-60 dB
Match m
-35 dB
-41 dB
Reflection Tracking t
± .1 dB
± .05 dB
± .01 dB
This table gives the tradeoff in accuracy for various coax calibration methods. The example is for APC-7 mm but can be scaled to other connector types. The relative differences stay about the same. The OSL (Fixed Load) cal is the least expensive and easy to use. The tradeoff is that it has the lowest accuracy, but this may be fine for many measurements. The directivity error is determined by the load. The match and tracking errors are mainly determined by the the phase error of the open.
The OSL (Sliding Load) is the traditional calibration that has been used for many years for accurate measurements. It is fairly expensive and sometimes the sliding load is not as easy to use. OSL calibrations are popular for one-port measurements.
With the OSL calibrations the short and open determine most of the match and tracking error and this error does not change dramatically with improved directivity values.
The TRL method provides the best accuracy and particularly for the match and tracking terms. It is not always easy to use and the precision lines are reasonably expensive. The TRM calibration does not change the directivity error over the OSL (load-fixed) method but reduces the match and tracking errors. The TRL and TRM calibration methods need a two port measurement system in order to calibrate. The TRM calibration is the easiest to use.

30. Accuracy of Error Correction
The first graph shows the transmission accuracy after error correction using APC-7 connectors. The main error at high levels is due to compression. At low levels it is primarily due to noise and uncorrected leakage.
The APC-7 reflection magnitude accuracy using the sliding load calibration is shown in the second graph. The main error at small reflection coefficients is due to the sliding load residual match. At high levels the sliding load match and the open circuit phase error are the primary contributors.

31. Other Network Analyzer Topics
Amplifier Measurements
Mixer Measurements
Pulse Measurements
Non-Insertable Measurements
Fixture and Probe Calibration
Two-Tier Calibration
Multiport Measurements
Balanced & Differential Measurements
There are many interesting measurement topics that could be covered but not in the scope of this paper.
Many topics in the industry today are driven by active devices. These include amplifiers and mixers. Some of these operate under pulsed RF and bias conditions.
Some connectors can not be mated during calibration. For example, two SMA male connectors are needed to connect to a device with female connectors. Non-insertable measurement techniques are required.
Modern devices no longer have the traditional connectors and fixtured or on wafer measurements are key. Two-tier calibrations are very useful for these on wafer and fixture calibrations.
Multiport networks are becoming more commonplace such as diplexers, etc. And, single ended devices are being replaced by balanced and differential devices.

32. Nonlinear Measurements with a Large Signal Network Analyzer

33. Vector Network Analyzer
50 Ohm
Acquisition (VNA)
Stimulus
Response
S-parameters
A vector network analyzer is a complete measurement system, containing internally an experiment generation and model extraction capability. The experiment generation consists of a forward and reverse excitation and measurement of the component under test. The model extraction refers to the equation solving using the measurements, resulting in S-parameters.
The vector network analyzer contains a test-set to separate incident from reflected waves, an acquisition system for uncalibrated measurements and a microwave source. Restricting its usability to linear components and based on the S-parameter theory, a vector network analyzer can internally apply a signal once to the input and once to the output of the device. From these measurements it can calculate the S-parameters using some calibration technique to eliminate the systematic errors introduced by the system.
Linear Theory

34. 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.

35. 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.

36. 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.

37. Sampling Converter FundamentalsLP
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.

38. Periodic Modulation RF IF 1 2 3 1 2 3 Freq. (MHz)
fLO=19.98 MHz = (1GHz-1MHz)/50 RF
50 fLO
100 fLO
150 fLO 1 2 3 IF
IF Bandwidth: 4 MHz
Under a periodic modulation of limited bandwidth, the same sampling scheme is used as for the continuos wave case. One can see that the periodic modulation tones show up around the downconverted fundamental and harmonic spectral components.
For wideband modulation the test frequencies can be chosen so that they will not interfere with each other even though they are contained in the same IF frequency bandwidth. 1 2 3
Freq. (MHz)

39. 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.

40. 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.

41. Relative Calibration Acquisition Load Open Short 50 Ohm
Thru
{1 GHz, 2 GHz, …, 20 GHz}
The relative calibration is exactly the same as for a vector network analyzer. Both TOSL and TRL type calibrations can be done.
Referring to the example where one wants to characterize a transistor on a frequency grid of 1 GHz with 20 harmonics, the microwave source is stepped in steps of 1 GHz and measuring the S-parameters of the known calibration devices.

42. Power Calibration Acquisition Power Meter 50 Ohm
Amplitude
50 Ohm
Acquisition
Power Meter
{1 GHz, 2 GHz, …, 20 GHz}
For the power calibration a power meter is connected to “Port 1” of the LSNA. The source is stepped on the frequency grid. For each step the power is measured and calculated through the acquisition system. This results in a power error table as function of the frequency.
The system has had a traditional “relative” calibration performed so the power measurements can be error corrected for higher accuracy.
For on wafer calibrations an additional calibration is performed at the wafer probe reference planes. The power measurements can then be “mathematically moved” to the wafer probe reference planes.

43. Phase Calibration Acquisition ... Harmonic Phase 50 Ohm
Reference Generator
1 GHz
...
For the phase calibration a reference generator is connected to “Port 1” of the LSNA. The source generates one tone at 1 GHz. The harmonic phase reference generator is a pulse generator with a repetition rate of 1 GHz or different frequency as required. In the frequency domain this corresponds to spectral components on a frequency grid of 1 GHz. At manufacturing time this generator can be calibrated very accurately and traceably with the nose- 2-nose calibration process explained later.

44. Characterization of the Harmonic Phase Reference Generator
Sampling oscilloscope
Harmonic Phase
Reference generator
The harmonic phase reference generator is characterized by a broadband sampling oscilloscope. A discrete Fourier transformation returns the phase relationship between all of the relevant harmonics (up to 50 GHz).
Note that the harmonic phase reference generator needs to be characterized across a whole range of fundamental frequencies with enough resolution to allow interpolation. The present generator covers one octave of fundamental frequencies, from 600 MHz up to 1200 MHz.
The main components of the harmonic phase reference generator are a power amplifier, a step recovery diode and a pulse sharpening “nonlinear transmission line” (together with cables and padding attenuators).

45. Nose-to-Nose Calibration Procedure
The accuracy of the harmonic phase reference generator characterization is determined by the accuracy of the sampling oscilloscope.
The sampling oscilloscope is characterized by the so-called “nose-to-nose” calibration procedure, which was invented by Ken Rush (Agilent Technologies, Colorado Springs, USA) in 1989.
The basic principle is that each sampler can also be used as a pulse generator. This pulse occurs when an offset voltage is applied to the hold capacitors of the sampler. One can show that this “kick-out” pulse is a very good scaled approximation of the oscilloscope’s “impulse response.”

46. Nose-to-Nose Measurement
During a nose-to-nose measurement two oscilloscope inputs are connected together and one oscilloscope is measuring the kick-out pulse generated by the other oscilloscope.
Supposing that both oscilloscopes are identical, the resulting waveform is the convolution of the scope’s impulse response with the scope’s kick-out pulse. Knowing that both are proportional allows to calculate the impulse response. The needed de-convolution is done by taking the square root in the frequency domain.

47. 3 Oscilloscopes are Needed1 2 1 3 2 3
The assumption that the scopes are identical is no longer needed if the nose-to-nose measurements are made with three oscilloscopes.
Research on the accuracy of the nose-to-nose calibration procedure was performed at the NIST (DeGroot, Hale & al., Boulder, Colorado, USA).

48. Electro-Optic Sampling*
* The schematic that is shown is “U.S. Government work not subject to copyright.” D.F. Williams, P.D. Hale, T.S. Clement, and J.M. Morgan, "Calibrating electro-optic sampling systems,“ Int. Microwave Symposium Digest, Phoenix, AZ, pp , May 20-25, 2001.
The technique of electro-optic sampling is a more accurate standard for harmonic phase recently introduced by D. F. Williams of NIST. Such an electro-optic sampling set-up can characterize the small phase error of a nose-to-nose calibration.
The basic principle of an electro-optic sampler is illustrated on the above slide. At the core of the technique is a pulsed laser which generates very short optical pulses. The duration of a pulse of a state-of-the-art pulsed laser is between 100 and 200 femtoseconds. These laser pulses are polarized and travel through a special nonlinear optical crystal which is exposed to the electric field to be measured (sampled). The polarization change of the laser pulses as they travel through the crystal are proportional to the strength of the electrical field in the crystal during the time the laser pulse was present in the crystal. A precise optical polarization analyzer can then be used to get a read out of the sampled value of the electrical field. It is important that the signal generator is synchronized with the optical pulse.
For more details please check the following reference:
D.F. Williams, P.D. Hale, T.S. Clement, and J.M. Morgan, "Calibrating electro-optic sampling systems,“ Int. Microwave Symposium Digest, Phoenix, AZ, pp , May 20-25, 2001.

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

50. 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.

51. Breakdown Current Time (ns)
As explained previously, the LSNA measures both the amplitude and the phase of all significant harmonics of both the incident and the scattered traveling voltage waves) Applying an inverse Fourier transform results in corresponding time domain waveforms. The time domain traveling voltage waves can be transformed into a current and a voltage waveform. In the time domain current/voltage visualization mode the LSNA behaves like a broadband oscilloscope having calibrated voltage and current probes. Such information can be very valuable to get a unique insight in e.g. transistor reliability issues, which are often related to hard nonlinear phenomena.
In the above figures we see the voltage and current time domain waveforms as they appear at the gate and drain of a FET transistor. These measurements were performed while applying an excitation signal of 1 GHz at the gate. The signal amplitude is increased until we see a so-called breakdown current. It shows up as a negative peak (20 mA) for the gate current, and as an equal amplitude positive peak at the drain. We actually witness a breakdown current which flows from the drain towards the gate. This kind of operating condition deteriorates the transistor and is a typical cause of transistor failure.
The above figures show the first measurements ever (we think) of breakdown current under large-signal RF excitation.
(Transistor provided by David Root, Agilent Technologies - MWTC)

52. Forward Gate Current Time (ns)
Another similar measurement is shown above.
This time the device is biased at a less negative gate voltage then the one used for the breakdown measurements.
The gate junction is turned on (forward conductance) by the large 1 GHz input signal. We see a clipping of the gate voltage (which is behaving like a rectifier), with a positive peak of 50 mA in the gate current. The drain current is clipped to 0 mA on the low end, and at a value of 150 mA at the high end (this occurs during the time the gate is conducting).

53. Example # 2
Resistive mixer with all waveforms available.

54. Resistive Mixer Schematic
HEMT transistor (no drain bias applied)
(Transistor provided by Dominique Schreurs, IMEC & KUL-TELEMIC)
Another example is the use of a HEMT transistor in a resistive mixer configuration.
A large local oscillator signal is driving the gate. This causes the drain of the transistor to behave as a time dependent switch. The switch is toggled at the rate of the local oscillator (in our example 3 GHz).
Any incident voltage wave at the drain (in our example 4 GHz) experiences a fast time varying reflection coefficient (toggling at a 3 GHz rate). The voltage wave reflected from the drain will thus be equal to the incident wave multiplied by the time varying reflection coefficient. The scattered wave will contain the mixing products (1 GHz and 7 Ghz) of the local oscillator and the incident RF signal.

55. Time Domain Waveforms
This working principle is nicely demonstrated by looking at the measured time domain representation of the voltage waves.
The figure illustrates how the incident wave (RF) and reflected wave (IF) are in phase or in opposite phase depending on the instantaneous amplitude of the LO. For a high LO the RF experiences a low drain impedance and behaves like a short, corresponding to a reflection coefficient close to -1 (reflection in opposite phase), for a low LO the RF experiences a high drain impedance and behaves like an open, corresponding to a reflection coefficient close to +1 (reflection in phase).
Note that one can clearly distinguish a 1 GHz and a 7 GHz component in the resulting reflected wave (IF).

56. Example # 3
Modulation envelope measurements shows harmonic distortion effects.

57. Modulation Trans Characteristics
Carrier Modulation B2
3rd harmonic
Modulation
Harmonic Distortion
Compression
The figures above represent the incident and transmitted time domain signals as they were measured at the signal ports of a 1.9 GHz RFIC amplifier.
The incident signal has characteristics similar to a CDMA signal.
The transmitted signal clearly suffers from compression and harmonic distortions whenever the input amplitude is high.
Another way of visualizing this behavior is a so-called “dynamic harmonic distortion” plot.
This is interpreted in exact the same way as a classical harmonic distortion plot, but now the input amplitude does not change step-by-step but changes very fast throughout the modulation period.
Note the compression characteristic for the fundamental.

58. Modulation Trans Characteristics
Carrier Modulation B1
3rd harmonic
Modulation
Harmonic Distortion
2nd harmonic
Expansion
The LSNA allows also to measure the same dynamic harmonic distortion plot for the reflected fundamental at the input.
Note that there is an expansive characteristic for the fundamental. This implies that the input match is worse for higher amplitudes.

59. Example # 4
Mismatch effects can be measured and shows contamination of the modulated signal from the source.

60. Effect of Source Mismatch
Acquisition
ESG
50 ohms A1
Spectral
Regrowth
A set of periodic modulation tones are used to characterize a RFIC amplifier on an evaluation board. The set of periodic modulation tones emulate the CDMA signal statistics.
A major advantage of a Nonlinear Network Measurement System is that it can measure the actual incident wave to the component under test instead of using what one assumes the modulation source is sending out. In the graph it is seen that some spectral regrowth is present in the incident wave which was not present when measuring the source alone (5 dB difference).

61. Example # 5
Error corrected waveform measurements improves digital signal integrity results.

62. High-Speed Digital Signal Integrity
Calibrated Eye Measurement On Wafer
Oscilloscope Data
Another interesting application is the calibrated on wafer measurement of high-speed digital signals. The classic technique for performing such measurements uses a microwave sampling oscilloscope. The cables, connectors and probes that are used to connect the oscilloscope to the wafer introduce significant distortions in the measurement of so-called eyediagrams of digital signals. Performing similar measurements with an LSNA results in fully error corrected waveforms all the way up to the tip of the probe. On the slide above one can clearly see that the oscilloscope data lacks certain details like offset and overshoot when compared to the calibrated LSNA data. This is due to dispersion of the oscilloscope cables as well as to the presence of jitter on the timebase of the oscilloscope. These distortions are totally compensated by the LSNA calibration procedure. Although not shown in the picture, the data as measured by the LSNA was much closer to the data generated by the circuit simulator.
(Courtesy of Jonathan Scott, Agilent Technologies)

63. Improved device and system design using waveform measurements

64. Present Nonlinear Design Approach
Measure (VNA)
S-parameters
Simulate
Nonlinear
Model
Build
Can’t Easily Adjust Model to
Match Measurements
Measure (SA)
Spectrum
Measure (PM)
Power
Measured S-parameters, spectrum and power insufficient to provide complete verification of design.
Nonlinear models are inaccurate and difficult to use.
Cut and try design approach.
The present nonlinear design process is still not optimized. The models are not perfect and the way we measure the data for the models is not in the same format as the models in the simulator. The magnitude spectrum and small signal S-parameters are measured while the simulator many times uses voltages and currents. Also the devices can not be easily characterized in their highly nonlinear regions.
The fabricated circuit is verified using a VNA, SA, and PM which measure only a part of the circuits total characteristics. This whole process makes it difficult to close the loop and have a efficient design process.
So there are many design turns as the whole process goes forward.

65. New Nonlinear Design Approach
Measure (LSNA)
Complete
Nonlinear Waves
Simulate
(Modified)
Improved
Nonlinear
Model
Build
Adjust Model to
Match Measurements
Measure
NEW
Measured nonlinear waveforms provides complete verification of design.
New types of nonlinear models extracted to match application (CDMA, GSM, etc).
Easy to couple measured data through a model and simulate much faster.
Measuring the voltage and current waveforms yield an improved nonlinear model and the final constructed results can be verified using the same type of waveform measurements.
This allows the loop between verification and design to converge much faster and yields better results.
In the next few slides the design process using waveforms will be illustrated.

66. Example # 6
Device measurement verification and measurement-based model improvement.

67. 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.

68. Model Verification & Improvement
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.

69. Model Verification & Improvement
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.

70. Example # 7
Power amplifier PAE optimization using waveform measurements and improved model developed from these measurements.

71. IRCOM & Thompson Example
34% better PAE performance through waveform engineering1
Verified Model
with traditional tools
Load Pull System
Spectrum Meas.
Designed
Virtual PA
Expected 80% PAE2
Measured
MesFET #1
w/prototype
LSNA plus
Impedance
Tuner
Modified Model
Designed Model
for MesFET #1
Built PA
PA #1
50% PAE
Measured ≠ Simulated
Re-designed PA
w/Waveform Analysis
PA #2
Achieved
84% PAE!!
Customer predicted best case results (the
old way) would have been mid-70% PAE
after numerous design iterations
1 MesFET Class F PA
f0=1.8 GHz
2 Power Added Efficiency
The normal design cycle starts with a MesFET model that has been verified as best it can with traditional measurement tools. A PA design is then completed, built and measured against design goals with the same traditional measurement tools. This process is repeated a number of times until a satisfactory PAE result is achieved.
With the LSNA the MesFET device can be completely characterized. Then using load pull the terminating impedances are adjusted until the viewed voltage and current waveforms meet the desired result. Then with this information the PA is designed and built and then verified using the LSNA. The design was completed in one pass with better PAE than the earlier iterated design.

72. Waveform Engineering Block Diagram
DUT
Test
Set
Data-Acquisition
Source PC
Sampling Converter
Filter f0
2f0
3f0
IRCOM Setup LO
Using waveform engineering the tuners can be adjusted to synthesis different source and load conditions to create a certain waveform shape in (usually) output voltage and current. For example, for an optimal power added efficiency (PAE), one will try to have a low current at a high output voltage and vice versa. This is realized by presenting proper load conditions to a transistor for the different harmonics.
To perform waveform engineering the Nonlinear Network Measurement System must be extended with tuners to control impedances at the different harmonics. In this case active tuners for each harmonic were selected because this allows independent control of the impedances at 3 harmonics. Each loop samples the transmitted wave, changes it in amplitude (usually decreases it) and in phase and reinjects it towards the component. In this way a reflection factor is synthesized which is independent of the transmitted wave.

73. IRCOM & Thompson Example
MesFET Class F
f0=1.8 GHz
Ids0=7 mA
Vds0= 6 V
Z(f0)=130+j73 
Z(2f0)=1-j2.8 
Z(3f0)=20-j97 
PAE=84%
PAE50%
Waveform
Engineering
Here the different voltages and currents at the gate and the drain can be seen for different power levels while the transistor is working in class F mode. By proper impedance tuning, 84% PAE was achieved.

74. Example # 8
Nonlinear model for two individual amplifiers used to predict performance of the combined cascade configuration.

75. Modeling - Two Separate Amps
The characteristics of a TWA and BTA are measured using the LSNA. From this data models were extracted for each and then compared to measurements.
The results compare very well. Also not shown but available are the phase plots.

76. Modeling - Cascaded Amplifiers
Then the two amplifiers are cascaded and the measured and modeled results are compared. They compare very well except in the area where the model was extrapolated for the second stage. We could have gone back and changed our design experiment to include the appropriate power range of the second stage and fixed the extrapolation errors.
The models were based on a VIOMAP (Volterra Input Output Map) which allows nonlinear networks to be cascaded in much the same way as T-parameters or S-parameters provide in small signal design.

77. Example # 9
Nonlinear model of a communications channel enables the inverse model to accurately pre-distort the signal to improve performance.

78. Inverse Model Compensation
An IQ modulator was designed and then measured using a VIOMAP modeling technique developed as part of the LSNA project. Included in the model were the time varying characteristics caused by memory effects.

79. Pre-Distortion of 16 QAM Channel
The inverse model was then calculated and then fed in as pre distorted modulation compensation.
The results show two cases. One without the memory effects being included and the second and better results using modeled memory effects.

80. Acknowledgments Agilent Technologies NIST NMDG Marc Vanden Bossche
Jan Verspecht
And Team
Agilent Technologies and Hewlett Packard funded the work presented in this paper. The slides are used with permission of Agilent Technologies.
NIST has been heavily involved with linear and nonlinear calibration methods for many years. We appreciate their great support of this work.
Marc Vanden Bossche and Jan Verspecht developed the Large Signal Network Analysis measurement and modeling technologies while working at Hewlett Packard and Agilent Technologies in Belgium. Most of the nonlinear slides presented were prepared by them.
Thanks to the other key members of the Belgium team:
Frans Verbeyst, Ewout Vandamme, and Steve Vandenplas.
Marc ( and Jan ( now have their own companies focused on nonlinear measurements and modeling.

81. Appendix

82. Example: TRL
The best know calibration method using the 8-term model is TRL. We will now review this calibration method. The math nomenclature is slightly different in this review.
The first step involves separating the system into a perfect reflectometer followed by a 4-port error adapter. This error adapter represents all the errors in the system that can be corrected. It can be split into two 2-port error adapters, X (at port-1) and Y (at port-2), after removing the leakage (crosstalk) terms as a first step in the calibration. Since X and Y are 2-ports it would appear there are 8 unknowns to find, however since all measurements are made as ratios of the b's and a's, there are actually only 7 error terms to calculate. This means that only 7 characteristics of the calibration standards are required to be known. If a thru (4 known characteristics) is used as one of the standards, only 3 additional characteristics of the standards are needed.

83. Example: TRL
It is convenient to use T-parameters because it allows one to represent the overall measurement, M, of the DUT, A, as corrupted by the error adapters as a simple product of the matrixes,
M = XAY.
In a similar manner, each measurement of three 2-port standards, C1, C2, and C3 can be represented as M1, M2, and M3.
M1 = XC1Y
M2 = XC2Y
M3 = XC3Y

84. Example: TRL
While there are 7 unknowns, measuring three 2-port standards yields a set of 12 equations. Due to this redundancy, it is not necessary to know all the parameters of all the standards. X and Y can be solved for directly plus 5 characteristics of the calibration standards.

85. Example: TRL
All 4 parameters of C1 must be known but only 2 parameters for C2 and one for C3 if S11 = S22. The simplest of all known standards is a through line, so let C1 be a thru, C2 a Z0 matched load or line with S12 = S21 and C3 a high reflect with S11=S22. If needed, impedance renormalization can be used to shift to a different impedance base. The other parameters of C2 and C3 can be solved from the calibration process.
For this calibration method there are several combinations of standards that fit the requirements. However, there are also choices that generate ill-conditioned solutions or singularities. In choosing appropriate standards, one standard needs to be Z0 based, one needs to present a high mismatch reflection, and one needs to connect port-1 to port-2. In addition, all three standards need to be sufficiently different to create three independent measurements.

86. Example: TRL
There are several possible strategies in choosing standards. For the first standard (C1), the use of a zero length thru is an obvious selection. But a non-zero length thru is also acceptable if its characteristics are known or the desired reference plane is in the center of the non-zero length thru. This standard will determine 4 of the error terms.
The second standard (C2) needs to provide a Z0 reference. In this solution, only the match of this standard needs to be of concern. Its S21 and S12 can be any value and do not need to be known. In fact, they will be found during the calibration process. This opens up the choices to a wide range of 2-port components, such as a transmission line, pair of matched loads, or an attenuator. This standard will determine 2 of the error terms.
For the final standard (C3) only one piece of information is needed. This could be an unknown reflection value for the same reflection connected to each port (S11 = S22). Since the other standards have been well matched, this standard should have a higher reflection. This standard determines the last error term.
The table shows a partial list of possible calibration configurations with appropriate three letter acronyms.

87. Example: TRL
The unknown device characteristics can be easily calculated by knowing the parameters of the X error adapter, the known standard C1, and the measured data of the test device and measured data for C1.

88. Example: Unknown T, Known A & B
This example is for the unknown thru calibration method (UXYZ). This is most easily developed using the cascaded t-parameter formulation. With 3 known standards at port-1 and port-2, 6 conditions are provided. The thru standard with S21 = S12 provides the 7th required condition. The key to solving this approach is that the determinant of T is unity for the passive thru calibration connection (S21 = S12).

89. Example: Unknown B, Known A & T
This example calibration approach (TXYZ) requires 3 known standards on port-1 but none on port-2 as long as the thru connection is known. The known thru connection provides 4 observations. The 3 known reflection standards connected to port-1 complete the required 7 known conditions.

90. 8-Term to 10-Term -Forward
The 12-term and 8-term models describe the same system. So there must be a relationship between them. First lets reduce the 12 term model to 10 terms by removing the crosstalk terms which can easily be measured in a separate step. Then the 8-term model can be modified as shown above. First the 4th measurement channel (a3) is removed by defining the ‘switch match’ as G3. Then the forward model error terms for port match and transmission tracking (e´22 and e´32) can be calculated. This gives the standard forward model if we form the two products e10e01 and e10e´32 and normalize e10 to 1.

91. 8-Term to 10-Term -Reverse
The same procedure can be used for the reverse model.
There is a constraining relationship for the 8-term and 10-term models. This is the same as saying that the 8-term model can reduce to 7 terms when making ratio measurements. And the 10-term model can reduce to 9 terms.
8-term: (e10e01)(e23e32) = (e10e32)(e23e01)
10-term: [e10e01 + e00(e´11 - e11)][e23e32 + e33(e´22 - e22)] = (e10e´32)(e23e´01) .

92. Calibration and Error Correction Techniques for Network Analysis
Abstract
Calibration and Error Correction Techniques for Network Analysis
The accuracy of Vector-Network-Analyzer (VNA) measurements depends critically on calibration and error correction techniques. This talk will cover the evolution of conventional VNA calibration methods from the start of network analysis through the development of new calibration methods for waveform and large-signal analysis. Included will be the original SOLT (Short-Open-Load-Through) methods, the newer self-calibration techniques like TRL, LRL and Unknown-Thru, and the strengths and weaknesses of these various VNA calibration approaches. The talk will conclude with a discussion of new state-of-the-art extensions of the traditional VNA calibration strategy for calibrated waveform measurements at microwave frequencies capable of capturing the both the temporal and large-signal behavior of microwave and digital devices.

93. 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

94. 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
Copyright 2003
Jan Verspecht bvba

95. Doug Rytting Biography
Rytting Consulting Doug Rytting Microwave Measurement Consultant
4804 Westminster Place, Santa Rosa, CA 95405, (707) , cell (707)
Doug Rytting Graduated with a BSEE from Utah State University and MSEE from Stanford University.
Joined HP in June 1966 and worked on virtually all microwave network analyzers introduced since Hardware designer on the 8405 vector voltmeter and network analyzers. Hardware project manager of the 8540, 8541, and 8542 automatic network analyzers, Section manager of the 8505, 8754 RF network analyzers, and the 8510C microwave network analyzer family. Managed the development of the 8340 microwave synthesized sources and the startup of the microwave CAE design software. Provided technology support for the RFMT (RF Manufacturing Test) system products.
Most recently supported the architecture design and analysis of the new Microwave Performance Network Analyzer family. And served as director of the Microwave Measurement Center of Technology at Agilent Technologies developing new measurement methods, instrument and system block diagrams, error correction techniques, and key microwave components for future products.
Doug Rytting is now retired and consulting on microwave measurements and calibration techniques.
Heavily involved in error correction methods, accuracy analysis, nonlinear measurements, and general measurement techniques in the microwave industry. Served on various advisory boards and committees for universities, government agencies, and industry.
Thanks for attending the presentation,
Doug Rytting
May 2006
Doug Rytting
Biography