VNA Receiver Dynamic Accuracy Specifications and Uncertainties – A Top Level Overview
Ken Wong – Master Engineer, CTD Santa Rosa
1.0 Introduction
Dynamic accuracy of a vector network analyzer (VNA) receiver may be defined as the linearity of the receiver over its specified dynamic range. It is one of the sources of uncertainty in VNA measurement systems. Other key sources of uncertainty include calibration uncertainty, connector repeatability, cable stability and repeatability, system drift and noise, as illustrated by figure 1 [1]. Cross talk errors are correctable.
Figure 1: Signal flow graph representation of VNA error corrected measurement error model
The total S-parameter measurement error can be expressed as functions of the systematic, random and drift & stability errors.
(1)
Dynamic accuracy is one of the systematic error terms:
(2)
Typical modern network analyzer receivers consist of functional blocks shown in figure 2. The sources of signal processing errors are represented by the signal flow graph of figure 3.
Figure 2: Modern VNA Receiver Block Diagram
Figure 3: Error Model
EN = Noise; ECO = Compression Error; EFL = Filter Linearity Error; EG = Gain Setting Error; EX = Residual Cross Talk Error; EADC = Residual ADC Linearity Error; EQ = ADC Residual Quantization Error
These errors may be quantified individually, in assembly blocks or in totality. An analysis of these error sources follows.
2.0 Sources of Linearity Errors
2.1 Noise
Noise level is specified and tested. It is also included in the uncertainty model.
2.2Compression in the conversion chain.
All amplifiers have nonlinear behavior. One way to describe that nonlinear behavior is in terms of compression, the deviation from a straight line relationship between input and output levels. This usually occurs at high level signal input. The other compression mechanism is the mixer. Regardless of the source of the nonlinearity, total compression is characterized during product qualification test. It is also tested per specification in factory test and field calibration. The compression error is accounted for separately as part of the dynamic accuracy model. For certain VNA product lines, the compression is characterized and corrected. Then, the characterization error is used instead of the actual compression error.
2.3Filter linearity
Discrete component filters are linear at low power levels. As power level increases, inductors can become nonlinear when its magnetic core becomes saturated. Another possible cause of filter nonlinearity is cross talk or coupling between inductors. Either case happens at higher power levels where the complete receiver‘s linearity is measured.
2.4Gain Setting Error
Amplifier gain switching is designed to compensate for signal path loss variations over frequency. At any given frequency, the gain setting is not change and therefore there is no error associated with gain setting.
2.5 ADC linearity and Residual Quantization Error.
The ADC is guaranteed by its manufacturer to have integral linearity errors within a small amount like a few LSB of an ADC’s resolution. For example, LSB of a 14 bit ADC is a part in 214. With a 14 bit resolution ADC and pseudo-random noisedither signal of5.4% at 5 sigma of full scale, nonlinearity is negligible [2]. See Appendix A for details.
3.0 Specification Regions
Linearity of a receiver may be divided into three regions, the compression region, the linear region and the noise+cross talk region, figure 4. Specifications for each region may be treated separately. In the compression region, receiver compression is usually specified as 1dB compression, 0.1 dB compression at some power level, such as -10 dBm. Table I shows the compression specifications of a particular Network Analyzers. Other network analyzers have different specifications.
Table I: Compression @8 dBm Test Port Power500 MHz to 16 GHz / <0.17 dB
16 GHz to 24 GHz / <0.23 dB
24 GHz to 26.5 GHz / <0.29 dB
A model of the receiver’s compression characteristic is a curved fitted model based on actual measurements of sample instruments during instrument qualification phase.
Noise floor is also a specified parameter. Table II shows the test port noise floor specification of the same instrument as Table I. Figures 1 and 3 and equation 1 show how it is accounted for in measurement uncertainty computations.
Table II: Test Port Noise Floor (dBm)Description / Specification / Typical
500 MHz to 20 GHz / -114 / -117
20 GHz to 24 GHz / -110 / -115
24GHz to 26.5 GHz / -107 / -113
The linear region is where the receiver should provide the best dynamic accuracy. Typically, this region covers the -20 dBm to -70 dBm input power range. Figure 5 shows plots of dynamic accuracy specifications that includes the noise and compression regions.
Figure 5: Typical Plot of Magnitude Dynamic Accuracy Specification
4.0 Measurement System, Method and Limitations
4.1 General Method
Typically receiver linearity is measured by comparing the receiver’s measure power change to a known level of power change. This define power level change may be established by a precision power sensor, a precision AC voltmeter a precision attenuator or a precision power level signal generator. Linearity, then, may be defined as:
4.2 Noise and Cross Talk Errors
It is evident from Figure 1 that the receiver’s measured power includes noise power.
Measurements made at signal power levels that are impacted by noise power and cross talk power will be highly compromised. Table III shows the impact of noise power and cross talk power to measured power.
Table III: Worst Case Measurement Error Caused by Noise and Cross Talknoise power ( dBm) / -110
cross talk power (dBm) / -130
IFBW / 10 Hz / 1K Hz
signal (dBm) / rms / peak / rms / peak
-50 / 0.000004 / 0.000006 / 0.000043 / 0.000061
-60 / 0.000044 / 0.000061 / 0.000435 / 0.000609
-70 / 0.000439 / 0.000614 / 0.004345 / 0.006082
-80 / 0.004384 / 0.006137 / 0.043257 / 0.060440
-90 / 0.043644 / 0.060979 / 0.414322 / 0.569582
-100 / 0.417873 / 0.574379 / 3.012471 / 3.804645
-110 / 3.031961 / 3.827373 / 10.417873 / 11.764964
-120 / 10.453230 / 11.801259 / 20.047512 / 21.496501
-130 / 20.086002 / 21.535100 / 30.008677 / 31.468719
Since cross talk level is below noise, its contribution to measurement uncertainty is less significant. From Table III, it is evident that at -60 dBm signal level, noise + cross talk error contributions is about 0.0006 dB peak at 1KHz IFBW setting. This level of error is still acceptable relative to other sources of measurement errors. At -70 dBm signal level and smaller, measurement variations are too large to be meaningful when a linearity error specification of < 0.01 dB is desired .
Linearity of the receiver at low power levels, < -70 dBm, depends solely on the linearity of the ADC. Given that a Gaussian dithering signal is employed to remove ADC linearity errors, no additional linearity testing is required at these low signal levels.
4.3 Reference Linearity
Linearity of the measurement system must be significantly better than the linearity of the receiver. Theoretically, linearity of thermal couple power sensors should be <0.003 dB over a 10 dB power level change. If performed as expected, it may be used as a linearity reference. Some of the systematic linearity errors may be quantified and removed. However, other factors that can cause linearity measurement errors must be quantified and addressed as well.
4.4 System Drift
Because of the number data points that must be measured, the test time can be lengthy. Instrument drift, both short term and long term, is a major consideration. Measurement system repeatability and reproducibility must be performed to obtain Type-A uncertainties. These studies are test station and test method specific.
Appendix A: ADC Linearity Improvement with Dither
The figure below shows the transfer function of an analog-to-digital converter (ADC) that is worst case in terms of meeting its vendor specifications while still causing linearity problems: It has a step change of error at the midpoint of the input voltage. This is known as quantizing error.
It has been demonstrated in [2], [3], and [4] that by adding a dithering signal to the input, the ADC’s quantizing error can be cancelled. For dithering signal of the Gaussian form, the most natural and least sensitive to dithering level changes and errors, the deviation of the averaged transfer characteristic from a straight line may be express as below for dithering signal with an amplitude standard deviation greater than 0.3 of LSB:
Without dithering, the quantizing error where = quantization step, s = signal
With dithering, where ; = standard deviation of the Gaussian dithering signal.
With a dithering signal at 1.1% of full scale, , therefore deviation from a straight line, exp(-22104), is essentially zero.
At relatively large signal region to the level of dither noise, ADC's integral non-linearity (INL) can not be cancelled. If the ADC has a manufacturer specification of +/-3-LSB INL, so in the worst case the error at a full-scale input of ADC would be less than
1 / 2^14 * 3 * 2 (bipolar scaling) ~= 370 [ppm] ~= 3 [mdB]
This is negligibly small compared to a typical receiver compression error at large signal region. Also this error element would be tested with receiver compression test.
References:
[1] D. Rytting, “Network Analyzer Accuracy Overview”, 58th ARFTG Conference Digest, Nov. 29, 2001,
[2] P. Carbone, D. Petri, “Effect of Additive Dither on the Resolution of Ideal Quantizers”, IEEE Transactions on Instrumentation and Measurement, Vol. 43, No. 3, June 1994 pp.389-396
[3] B. Brannon, “Overcoming Converter Nonlinearities with Dither”, Analog Devices AN-410
[4] M.F. Wagdy, “Effect of Various Dither Forms on Quantization Errors of Ideal A/D Converters”, IEEE Transactions on Instrumentation and Measurement, Vol. 38, No. 4, August 1989, pp 850-855
Ken Wong Page 1 of 7June25, 2010