Everyone in the EMC business is familiar with the traditional Normalized Site Attenuation test (NSA). However, in February of 2007 CISPR 16-1-4 was published complete with the new Site Voltage Standing Wave Ratio (SVSWR) test. At the time, the American National Standards Institute (ANSI) Accredited Standards Committee (ASC) C63^{®} had developed a draft proposal for C63.4 (Draft 1 – May 20, 2005) called the Time Domain Reflectivity (TDR) measurement. The critical question addressed by this article is which method – SVSWR or TDR – more accurately provides an assessment of the test site. Given the investments companies make in test sites for EMC compatibility, this is key assessment question.

## Background

Conceptually, the SVSWR method is quite straightforward and easily understood. As with any VSWR measurement, the objective is to measure the maximum and minimum values of a standing wave, as illustrated in Figure 1. The ratio of these values is the VSWR. The most common application of the VSWR measurement is in evaluating transmission lines. If there is an impedance mismatch at the end of a transmission line between the impedances of the transmission line and the load (for example), there will be a boundary condition that results in a reflected wave. The reflected wave will, at various locations on the transmission line, be constructively or destructively interacting with the continuous wave from the source. The resulting construct (direct and reflected wave combination) is a standing wave. A simple example of this is found in the conducted power test required for appliances in CISPR 14-1. In this test, a transducer (power clamp) is moved along an extended power cord of the product in an effort to measure the maximum voltage on the power cord over the frequency range of interest. The same event is realized on an imperfect test site. The transmission line is the path from the equipment under test to the receiving antenna. Reflected waves are created from other objects in the test environment. Those objects could range from chamber walls to buildings and cars (at open area test sites). Just as in the case of a transmission line, a standing wave is created. The test set up for the site VSWR or SVSWR test is shown in Figure 2.

**Figure 1: VSWR Measurement Values**

**Figure 2: SVSWR Test Set Up**

**Under Sampling**

The physical dimensions of the standing wave are a critical factor in accurately measuring a standing wave. The objective, again, is to find the maximum and minimum value. The SVSWR test in CISPR 16-1-4 proposes to measure the standing wave on a test site by moving a transmitting antenna along a straight line in the chamber and measuring the received voltage with the emissions antenna in the normal location used for product testing. Just as in a conducted power test or similar VSWR measurement, a continuous movement of the transducer, or in the case of SVSWR the transmitting antenna, is needed to ensure the capture of the maxima and minima of the standing wave. This could be done at each frequency but only at considerable expense and time. Consequently, the CISPR working group decided to compromise and measure only six physical positions for each of the volumetric locations (see Figure 3). The only other option for reducing the test time was to reduce the frequency resolution of the measurement (e.g. measure fewer frequencies but at each frequency measure more positions). The problem with that option is that many objects that reflect can have narrow spectral characteristics. In other words, some materials can be significantly reflective for a narrow frequency range. Consequently, the working group decided to apply a maximum 50 MHz step size to the test resulting in a minimum of 340 frequencies from 1-18 GHz but with only six positions as shown in Figure 3.

**Figure 3: SVSWR Measurement Locations and Positions**

The sampling of a standing wave at only a discrete number of positions may plausibly provide sufficient accuracy to compute an approximate SVSWR depending on the size of the steps. However, another compromise was to have the same prescribed positions for every frequency so that the test would save time by moving the antenna and sweeping frequency. The chosen positions are 0, +2, +10, +18, +30, +40 cm. Try to imagine a sign wave superimposed on a ruler with six marks on it. Now imagine compressing the sign wave into shorter and shorter wavelengths. Figure 4 illustrates this thought experiment. There will be frequencies where the chosen locations will never come close to the true maxima or minima of the sign wave. This is a compromise that will result in a compliance bias, e.g. a result that is always lower than the true SVSWR. This bias is an **error term** and should not be confused with a measurement uncertainty contribution.

**Figure 4: SVSWR Measurement Locations vs. Wavelength**

How large is the error term? If we think of the example illustrated in Figure 4 it is clear the wavelength is 2 centimeters. That would be a 15 GHz sign wave. At that frequency, there would be no measured standing wave because the wavelength is 2 cm and the other locations are even multiples of 2 (10, 18, 30 and 40 cm)! Of course, the same issue occurs at 7.5 GHz. At virtually every frequency the sampling results in measuring neither the maximum nor the minimum.

**Test Time**

A laboratory must measure four locations as shown in Figure 3 in two polarities and at least two heights in accordance with CISPR 16-1-4. The measurement range is 1-18 GHz. Until recently, the only antennas available that met the pattern requirements were available in 1-6 GHz and 6-18 GHz models. The consequence is that the test time is shown in Equation 1:

(1)

Where: t_{x} = time to perform function x, n_{y} = number of times activity Y must be performed.

**Equation 1: Estimate test time for SVSWR**

The result of this combination of positions, locations, polarities, heights and antennas results in a rather lengthy test. This time represents an opportunity cost to the laboratory.

The opportunity cost is the revenue that could otherwise have been realized in lieu of conducting this lengthy test. As an example, a typical test time for this test is at least three test shifts. If a lab were to charge $2,000 USD for a shift, this test represents an annual opportunity cost, assuming the site is checked annually as recommended, of at least $6,000-$12,000 USD. This does not include the initial costs of the special antennas ($14,000 USD).

## Positioning Uncertainty

Each measurement of the SVSWR method requires the positioning of the transmitting antenna to the positions specified (0, 2, 10, 18, 30, 40 cm). Since the computations are corrected for distance, the repeatability and reproducibility of the positioning directly impacts the measurement uncertainty. The question then becomes, how repeatable and reproducible is the positioning of the antennas in increments as small as 2 cm? A recent gage study conducted at UL has demonstrated this contribution to be approximately 2.5 mm or about 15% of the 18 GHz wavelength. The magnitude of this contributor will depend on frequency and the amplitude of the standing wave (an unknown).

A second factor related to positioning is angle versus the antenna pattern. The antenna pattern requirements in CISPR 16-4-1 has variability of roughly +/-2 or 3 dB in H-plane and even wider in E-plane. If you pick two antennas with different patterns but both meet the pattern requirements, you can have very different results. In addition to this antenna to antenna variability (a reproducibility problem), the antennas used to transmit do not have perfectly symmetric patterns (e.g. patterns vary with small increments in angle) as shown in the standard. As a consequence, any change in alignment of the transmitting antenna to the receiving antenna results in a changed received voltage (a repeatability problem). Figure 5 illustrates the actual pattern changes of a SVSWR antenna with small increments in the angle. These true pattern characteristics result in significant angular positioning variability.

**Figure 5: SVSWR Antenna Pattern**

The changes in antenna gain as a function of relatively small angular rotations causes as much as 1 dB of variability in the example shown.

## Time Domain Method to Obtain SVSWR

The SVSWR method in CISPR 16-1-4 is based on moving antennas spatially to vary the phase relationship between the direct wave and reflected waves from chamber imperfections. As discussed previously, when the waves add constructively, there is a peak response (E_{max}) between the two antennas and when the waves add destructively, there is a minimum response (E_{min}). The transmission can be expressed as

(2)

where E is the received field strength.

*E _{D}* is the direct path signal,

*N*is total number of reflections from the site (this could include single or multiple reflections from the chamber walls or open area site imperfections).

*E*is the

_{R}(i)*I*

*reflected signal. For ease of the derivation, let us assume there is only one reflected signal (this will not lose the generality). The site VSWR (or the relative ripple size) of the site can be expressed as*

^{th}(3)

By solving Equation 3, we obtain the ratio of the reflected signal to the direct signal

(4)

As can be seen from Equation 4, the two terms, i.e. the reflected to direct signal ratio (*E _{relative}*) and the site VSWR (

*S*) describe the same physical quantity – a measure of the level of reflections in the site. By measuring the site VSWR (as is the case in CISPR 16-1-4), we can determine how large the reflected waves are relative to the direct wave. In an ideal situation there is no reflections, resulting in

*E*= 0, and

_{relative}*S*= 1.

As previously discussed, to detect the ratio between the reflected and the direct signal, in the site VSWR method in CISPR 16-1-4, we change the separation distance so the phase relationship between the direct path and reflected signals can be varied. Subsequently, we derive the SVSWR from these scalar responses. It turns out that we can acquire the same SVSWR using vector (voltage and phase) measurements without the need to physically move the antennas. This can be done with the aid of a modern vector network analyzer (VNA) and time domain transformations. Notice that Equations 2 to 4 hold true in either frequency domain or time domain. In time domain, however, we can distinguish the reflected signals from the direct signal because the point in time at which they arrive at the receive antenna is different. This can be viewed as a pulse sent out from the transmit antenna. In time domain, the direct wave will arrive at the receive antenna first, and the reflected wave will arrive later. By applying time gating (a time filter), the effect of the direct signal can be separated from the reflected ones.

The actual measurements are performed in frequency domain with a VNA. The results are then transformed to time domain using inverse Fourier transform. In time domain, time gating is applied to parse the direct and reflected signals. Figure 6 shows an example of the time domain response between two antennas (by using inverse Fourier transform from frequency domain measurements). Figure 7 shows the same time domain response with the direct signal gated out. The time domain data (after the parsing) are finally converted back to frequency domain using Fourier transform. For example, when the data in Figure 7 is transformed back to frequency domain, it represents *E _{R}* versus frequency. In the end, we obtain the same

*E*as the CISPR spatial varying method, but by going through a different route. Although the inverse Fourier transform (or the subsequent Fourier transform) sounds like a daunting task, it is actually a

_{relative}**built-in function**in a modern VNA. It takes no more than the pushing of a few buttons.

**Figure 6: Time domain response (from inverse Fourier Transform of the VNA data) between two bore sighted antennas. Marker 1 shows the direct signal which occurs at 10 ns x (3 x 108 m/s) = 3 m from the transmit antenna.**

**Figure 7: Time domain response with the direct signal gated out – leaving only late arrival (reflected) signals.**

## Next Steps: Improving the Time Domain SVSWR Method Further

We have established that the SVSWR by spatial movement and SVSWR by time domain produce equivalent data. Empirical measurements can validate this point. Questions that still linger are: whether this is the most representative data for Equipment Under Test (EUT), and what uncertainties we can achieve due to antenna selections? Referring to Equation 2, all reflections are modified by the antenna pattern before being summed. For simplicity, let us consider a test chamber where multi-reflections are negligible. We then have seven terms in the transmission path, namely the direct signal, and reflections from four walls, the ceiling and the floor. In CISPR 16-1-4, there are very specific requirements on the transmitting antenna pattern. For practical reasons, these requirements are by no means restrictive. For example, assume the back wall reflection is the dominant imperfection, and the front to back ratio of the antenna is 6 dB (within CISPR 16 specification). For a site with a measured SVSWR=2 (6 dB) using a perfect isotropic antenna, *E _{R }/E_{D}* is 1/3. If we use an antenna with a front-to-back ratio of 6 dB, the measured SVSWR becomes

(5)

The antenna with a front-to-back ratio of 6 dB underestimates the SVSWR by 20*log (2.0/1.4) = 2.9 dB. The above example is obviously overly-simplified. When considering all other reflections of the chamber, and all variations of the antenna patterns, the potential uncertainty is even larger. In the other polarization (in E-plane), it is not possible to have a physical isotropic antenna. It is an even greater challenge to define a strict antenna pattern, which all real physical antennas must meet.

The quandary related to pattern variations can be solved by rotating the transmitting antenna. In this scheme, we do not need an antenna with a broad beam – a familiar double ridged waveguide antenna commonly used in this frequency range will work fine. It is still preferred to have a large front to back ratio (which can be easily improved by placing a small piece of absorber behind the antenna). The implementation is the same as discussed earlier for the time domain method, except that we also rotate the transmitting antenna by 360° and perform a maximum hold. Instead of trying to illuminate all walls at the same time, this scheme does it one at a time. This method may yield results that are slightly different from ATTEMPTING to broadcast to all walls at the same time. It can be argued that it is a better metric of a site performance, as a real EUT is likely to have a narrow beam rather than looking like a specifically crafted antenna. In addition to avoiding the messy situation due to the antenna patterns, we can pinpoint where an imperfection occurs in a chamber or an OATS. The location can be identified from the rotation angle, and time needed for the signal to travel (thus the distance to where the reflection occurs).

## Conclusion

The benefits of the time domain method are numerous. It avoids the pitfall of the under-sampling issue discussed earlier. The method does not depend on physically moving the antennas to a few discrete locations, and the SVSWR from time domain represents the true value of the site. Also, in the CISPR method, to normalize the influence due to the path length, the exact distance between the antennas must be known. Any uncertainties due to the distance translate into uncertainties of the SVSWR (considering the small increments needed, it is even more challenging). In time domain, there are no distance normalization uncertainties. In addition, perhaps the most attractive feature for an end user is that time domain SVSWR is much less time consuming. The test time is reduced almost six fold (see Equation 1).

**A fully anechoic chamber features absorber treatment on all four walls, floor and ceiling of the chamber. Time Domain Reflectivity (TDR) measurements not only can provide an accurate assessment of a test site such as this, but can also provide additional information such as where the largest contributors to deviations from an ideal site come from.**

One might be tempted to argue that in the CISPR method, because the antennas are moved, the reflection points move on the chamber walls, and more areas of the imperfections are covered. This is a red herring. The purpose of moving the receive antenna is to vary the phase relations only. The total distance varied is 40 cm. It translates to 20 cm (7.9”) coverage on the wall due to geometry translations (if the transmission path is parallel to the chamber wall). For the theory to work out, we in fact need to assume the reflection properties of the absorbers are uniform along the whole 20 cm. To cover more areas, one needs to move the antennas much more drastically, as is done in CISPR 16-1-4 (the front, center, left and right locations).

## More Information

- The Application of Time Doman Measurements
- Moving Forward in ANSI C63
^{®}and IEC/CISPR with Time Domain Measurements - Free Space Antenna Factors Through the Use of Time-Domain Signal Processing