Understanding the Limits of VNA Calibration

The previous article in this series introduced the basic concepts of vector network analyzer (VNA) user calibration. In some ways, the user calibration process is analogous to taring or zeroing a weighing system to remove the error from the container. When you want to weigh an object, you first place its empty container on the scale and press the tare or zero button. This sets the scale to zero and instructs it to ignore the weight of the container.

Similarly, during user calibration, we first measure some known standards. We might use the Short, Open, and (matched) Load calibration standards from the preceding article, for example. These measurements allow us to determine the effect of the interconnects—as well as the VNA’s imperfections—and correct for their error terms. This unique user calibration feature makes VNAs among the most accurate RF test instruments.

These techniques aren’t without limitations, however—though VNA calibration can minimize systematic errors in magnitude and phase measurements, it can’t correct drift or random errors. We’ll discuss these error types in this article. We’ll also take time to clarify the difference between factory and user calibration. Together with the discussion of random and drift errors, this should help you better understand the scope of VNA user calibration.

 

Factory Calibration vs. User Calibration

For most instruments, “calibration” refers to factory calibration, which is performed by the manufacturer or a service center to make certain that the instrument meets the manufacturer’s specifications. Factory calibration may need to be repeated periodically—typically annually—to ensure that the instrument continues operating within these specs.

Just like any other test equipment, VNAs come factory-calibrated. This ensures, among other things, that the VNA’s receivers measure signals to the specified level of accuracy, and that the output power and frequency of the VNA’s internal signal source are in line with the manufacturer’s requirements. As illustrated by the simplified block diagram in Figure 1, factory calibration encompasses all of the VNA up to the test port connectors.

 

Figure 1. VNA factory calibration encompasses all parts of the test setup enclosed in the blue outline. Image used courtesy of Steve Arar

 

Some non-idealities will persist past factory calibration. The directional coupler within the VNA will still have limited directivity, for example. Likewise, the ports of a factory-calibrated VNA provide a decent match, but not a perfect one.

In addition to these residual error terms from the VNA, error is introduced to measurements by the imperfections of the cables, adapters, and so forth used in the test setup. The mismatch error referenced above is affected by the cable’s loss and phase response, which in turn depend on the signal frequency and cable length. In short, the error terms depend on all of the following:

• The VNA.
• The cables and connectors used in the test setup.
• The properties of the DUT itself.

That’s why user calibration is required—it accounts for the imperfections, not only of the VNA, but also of the accessories used in the test setup. This moves the overall calibration reference plane from the VNA’s test ports to the DUT’s ports, as we see in Figure 2. With the effect of the interconnects factored out, we can now measure the performance of the DUT alone.

 

Figure 2. Simplified block diagram of a VNA test setup. The reference plane for VNA user calibration is marked in green. Image used courtesy of Steve Arar

 

User calibration is effective when dealing with systematic errors, which are imperfections of the test setup that tend to be consistent over time. This consistency makes the error terms predictable, enabling calibration techniques to determine and correct them. Test port mismatch and limited coupler directivity—illustrated by the red and magenta paths, respectively, in Figure 3—are two common sources of systematic error in VNAs.

 

Figure 3. Paths of undesired signals resulting from limited coupler directivity (magenta dashes) and test port mismatch (red dashes) when using a VNA for an input reflection measurement. Image used courtesy of Steve Arar

 

Before applying user calibration, the directivity and port match of the VNA might be about 30 dB and 22 dB. User calibration can improve those values to about 45 dB and 40 dB, respectively. However, measurement uncertainty produced by random errors—which, by definition, are not consistent over time—will remain even after calibration.

 

Random Error Due to Noise

Noise limits the measurement accuracy both during calibration and the actual measurements. While user calibration can’t reduce noise, we can use other techniques—such as reducing the intermediate frequency (IF) bandwidth or increasing the averaging factor—to minimize the effect of noise on our measurements. These reductions in noise come at the cost of increased measurement time, however.

Furthermore, though IF bandwidth reduction can significantly reduce the noise for measurements involving a low-power stimulus, it’s unlikely to have much effect on high-power measurements. To understand why, it’s important to know that there are two major contributors to the measurement noise:

• The white noise produced by the VNA’s receiver.
• The phase noise of the VNA’s signal source.

When the VNA’s receiver measures a signal with a low power level, the dominant noise source is the receiver itself—the VNA’s signal source creates a relatively small amount of noise when producing a low-level stimulus. However, if our measurement requires a high-level stimulus, we’re increasing both the power level and the noise level of the stimulus signal.

At higher power levels, the phase noise of the signal source can rise above the receiver’s noise floor. This phase noise then becomes the dominant contributor of noise to our measurement. As we get closer to the IF carrier frequency, the phase noise continues to increase. For that reason, reducing the IF bandwidth of the VNA may not improve the noise performance as much as expected when using high-level signals.

Figure 4 shows a VNA source’s spectral content for signals with two different power levels.

 

Figure 4. Spectral content of a VNA’s signal source for a higher-power (dark trace) and lower-power (light trace) signal. Image used courtesy of Joel P. Dunsmore

 

The light gray curve in Figure 4 corresponds to a stimulus signal with a power level of –10 dBm. As we can see, the noise in this case has a flat frequency characteristic. This is because the phase noise of the signal source is below the noise floor of the receiver.

When we increase the power level to +10 dBm, we get the figure’s darker trace. In this case, the noise level increases as we get closer to the carrier frequency. This is consistent with the typical behavior of phase noise, confirming that the signal source’s phase noise at +10 dBm.

Going from an IF frequency of 100 Hz to 10 Hz normally leads to a 10 dB increase in the signal-to-noise ratio (SNR) when measuring low-level signals. However, the same change in IF bandwidth might produce a smaller improvement in SNR when dealing with high-level signals, due to the phase noise being the dominant noise source.

Noise isn’t the only type of random error we need to contend with. Next, we’ll discuss errors that result from lack of repeatability.

 

Random Error Due to Poor Connector and Cable Repeatability

Repeatability refers to how consistent the measurement results are when we repeat the same measurement over a short time span under the same conditions. It’s important to note that low-cost, low-quality cables and connectors can produce errors that aren’t repeatable. If they aren’t repeatable, they can’t be corrected by calibration.

To examine the cable repeatability, we first measure the response of the cable and store it in memory. Next, we put some flex or bend in the cable, measure the response of the bent cable, and normalize it to the result of the first experiment. Using that information, we can make an initial assessment of the cable repeatability.

Figure 5 shows the result of this procedure for two different types of cable—a consumer-quality RG400 cable on the left and a higher-quality cable on the right. The same bending radius and bending angle have been applied to both cables.

 

Figure 5. Results of a repeatability test for a consumer-quality cable (left) and a higher-quality cable (right). Image used courtesy of Rohde and Schwarz

 

The normalized magnitude of the consumer-quality cable’s forward transmission (S₂₁) changed by about 0.4 dB over the tested frequency range. The deviation of the high-quality cable was only 0.004 dB over the same range.

We can see that higher-quality cables provide a higher degree of repeatability, including a more repeatable phase response. The above discussion also suggests that we should minimize cable movement in our test setup after VNA calibration has been performed.

It should be noted that the repeatability of the connectors can have a significant influence on measurement accuracy. For more tips on properly handling connection assemblies, please refer to the following documents:

• Rohde and Schwarz’s Fundamentals of Vector Network Analysis.
• Copper Mountain Technologies’ Introduction to the Metrology of VNA Measurement.

 

Drift Error

The final type of error we’ll discuss, known as drift error, is caused by any change that occurs in the conditions of the test system after calibration. We can remove existing drift errors by recalibrating the measurement system to reflect the new conditions. However, calibration won’t prevent performance from drifting further.

Drift often occurs due to variations in ambient temperature and humidity, and so temperature- and humidity-controlled rooms are sometimes used to reduce drift error over time. On the topic of thermal effects, it’s worthwhile to mention that we must allow sufficient time for the internal temperature of the VNA to stabilize. To achieve the best measurement accuracy, the abovementioned Copper Mountain Technologies app note recommends a VNA warm-up time of one hour.

Figure 6 shows how the internal temperature of a pair of TR1300/1 VNAs changes after we place the instruments in a 45 °C temperature chamber and power them up.

 

Figure 6. Change in VNA internal temperature over time after the VNA is powered up. Image used courtesy of Copper Mountain Technologies

 

In both cases, we see that it takes about an hour for the VNA’s internal temperature to stabilize.

 

Wrapping Up

As we’ve seen, VNA user calibration techniques can’t correct for all types of imperfection in the test setup. However, they do minimize systematic errors well enough to make VNAs one of the most accurate measurement instruments in RF and microwave engineering. By introducing the 12-term error model and an accompanying calibration technique, the next article in this series will dive more deeply into how.
 

This article is Part 7 of a series on vector network analyzers. In order of publication, the articles in this series are:

1. Introduction to the Directional Coupler for RF Applications
2. Understanding RF Power Measurement Errors in Directional Couplers
3. Understanding the Inner Workings of Vector Network Analyzers
4. Understanding the Significance of Dynamic Range and Spurious-Free Dynamic Range
5. How to Estimate and Enhance the Dynamic Range of a Vector Network Analyzer
6. Introduction to VNA Calibration Techniques
7. Understanding the Limits of VNA Calibration
8. Understanding the 12-Term Error Model and SOLT Calibration Method for VNA Measurements
9. Understanding RF Calibration Using Short, Open, Load, and Through Terminations