Program predicts VSWR-mismatch RF uncertainties

Steve Hageman, Agilent Technologies, Santa Rosa, CA -- EDN, 2/1/2001

Hewlett-Packard (now Agilent Technologies) once offered a useful little cardboard slide rule for calculating the uncertainty in RF measurements stemming from VSWR (voltage-standing-wave-ratio) mismatch. Unfortunately, this handy device is no longer available. A Visual Basic program accomplishes the same function on a PC, however. You can download the executable program and its associated setup utilities on a blind page at http://www.sonic.net/~shageman/vswr.html. Mismatch uncertainty is one of the most common calculations an RF engineer makes when determining the uncertainty of RF power measurements. The source and load VSWR interact along an unknown length of line to produce some uncertainty in the power measurement. This uncertainty stems from the fact that, at high frequencies, the length of a transmission line connecting a source and load may be sufficient to transform the impedance at one end of the line to another value at the other end.

System specifications usually include the VSWR values, which lack phase information. So, one certainty about a measurement is that it lies between some range of values. In reality, even the connectors and the transmission line in the measurement path add uncertainty because their true electrical length and, hence, phase is unknown. So, the true power at the load may be higher or lower than the measured value. The conservative way to account for this error is to assume that the phase is unknown and assume the worst case: The incident and reflected signals interact in the worst possible way—in other words, at the peaks and valleys. You express this scenario as VSWR=E_MAX/E_MIN, where E_MAX and E_MIN are the maximum and minimum voltages along the line. VSWR is a common specification in data sheets for RF devices, such as amplifiers, sources, and power meters. VSWR relates to the absolute value of the reflection coefficient

in the expression

and, in turn

relates to the return loss in decibels in the expression R_L=–20log₁₀. Because the source and load each have a VSWR, the product of the two gives the maximum VSWR: VSWR_MAX=VSWR₁·VSWR₂. The two VSWRs produce a combined return loss, as follows:

The uncertainty in the total measurement stemming from the source and load VSWRs is Uncertainty(+)=20log₁₀ (1+ ₁ · ₂ ) dB, and Uncertainty(–)=20log₁₀ (1– ₁ · ₂ ) dB.

As a result, you have a range of either plus or minus uncertainty. At small VSWRs, the plus and minus converge to the same value. At higher VSWRs, the plus and minus uncertainties diverge, so you need to calculate both. As an example, consider a Hewlett-Packard ESG-3000 microwave source operating at 900 MHz. Its VSWR is specified at 1.4 to 1. Then, assume that you measure the source's output power with a Hewlett-Packard E4412A power sensor that has a specified VSWR of 1.15 to 1. If you input these figures into the VSWR Calc program, you obtain the screen shown in Figure 1. The "Copy to Clipboard" function transfers the VSWRs and the calculated data to the Windows clipboard so that documenting the calculations is easy in any Windows application. (The cardboard slide rule cannot perform this function.) Figure 1 shows the clipboard data of this example. The uncertainty in the example is +0.100 to –0.102 dB. You should know the measurement uncertainty, because it is relatively easy to obtain totally uncertain measurements at high frequencies if the VSWRs are uncontrolled or unknown. The VSWR Calc program is a Microsoft Visual Basic 32-bit application that runs on Windows 95, 98, and NT 4.