By: Steve Hageman

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. 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=EMAX /EMIN , where EMAX and EMIN 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 RL =–20log10 (Gamma) . 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 + Gamma1 * Gamma2 ) dB, and Uncertainty(–)=20log10 (1– Gamma1 * Gamma2 ) 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 Agilent 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 Agilent 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 the screen shot above. 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.). 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 9x, 2k and NT 4.

New Version: 1.2, May 2002 - I have recently had to make some calculations on power loss at antennas, etc. So I added a calculation for the mismatch loss at the load. The mismatch loss (in dB) is = -10Log(1-Rho^2), where Rho is calculated from: 10^ (-Return Loss/20). So with this new feature you can immediately see how much of your power is bouncing off your Antenna! Naturally the terms 'source' and 'load' may be interchanged if you really want to see how much power is bouncing off your source. The math works the same in either direction as long as you are consistent.

Here is what the clipboard text output looks like:

VSWR 1 (Source) = 1.40 Return Loss = 15.56 dB

VSWR 2 (Load) = 1.15 Return Loss = 23.13 dB

Gamma 1 = 0.167

Gamma 2 = 0.070

Maximum VSWR = 1.61

Combined Return Loss = 12.63 dB

Plus Uncertainty = 0.100 dB

Minus Uncertainty = -0.102 dB

Mismatch Loss @ Load = 0.02 dB

Use the link below to download the VSWR Calculator program.

Unzip the program in a directory and then run a virus scan on it, just to be sure. Run the Setup.exe program. The install files may then be removed. The program may be removed later by using the Control Panel -> Add / Remove programs applet. The program has been tested on Win 95, 98, 2k and NT 4x.

• vswr.zip Version 1.2.0 May 18, 2002

I PROVIDE THIS FREE SOFTWARE "AS IS". ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO ANY WARRANTY OF NON-INFRINGEMENT, THE IMPLIED WARRANTIES OF MERCHANTABILITY, SATISFACTORY QUALITY, REASONABLE CARE AND SKILL, AND FITNESS FOR A PARTICULAR PURPOSE ARE EXPRESSLY DISCLAIMED.

Agilent Technologies (formerly Hewlett-Packaard) has many application notes available on RF technology,

• Fundamentals of RF and Microwave Power Measurement (AN64) <- This is an excellent article that will give you a complete understanding of measurement uncertainty. A must have!
• Agilent EPM and EPM-P power meters data sheets (models E4416A, E4417A, E4418B, E4419B)

You might be able to find the application notes by following this link... www.agilent.com/find/apps Or just search the site for the app note title.