Reflected Power Measurements: Definitions and History

Once you know the background, it makes sense why there are three ways to measure and define reflected power measurements, VSWR, return loss and rho measurements can be converted from one to the other.

Three methods

Three common terms describe reflected waves in transmission systems: voltage standing wave ratio (VSWR), return loss and rho.

Each term expresses the amount of energy reflected and returned from a load or antenna to the source in a transmission system.

Every transmission system has the following three elements:
1. a generator
2. a transmission line (and not necessarily a perfect one).
3. a load (usually an antenna, however punc an open and a short are loads, too).

In the ideal transmission system, all energy emits from the generator and passes unattenuated through the transmission line to be radiated or absorbed by the load.

Actual systems have losses, though. For example, transmission lines may not exhibit their rated impedance; they radiate some of the energy they pass; and their dielectric absorbs some energy.

Loads--especially antennas--may present an incorrect impedance. Often, they are tuned to the wrong frequency.

Why three methods were developed for the same measurement is revealed from history.

VSWR--Early transmission lines were 600 ohm open wire balanced feeders. Radio communication took place at frequencies below 1.5 MHz.

At these wavelengths (200 meters and up), standing wave measurements could be made with a light bulb. With the transmitter on, a radio operator could move a lamp along the transmission line and observe a changing brilliance if the line had reflected waves.

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Three Methods-cont

With the line open or shorted, the lamp would extinguish completely at some points and become brightest at others. Similar experiments conducted with an ac voltmeter instead of a bulb quantified the measurements. Based on these measurements, this formula was derived.

Voltage difference = Emax/Emin

Because these measurements correlated to the standing waves on the line as theorized by James Clerk Maxwell, this ratio was defined as the voltage standing wave ratio.

The term VSWR is used commonly because it makes sense, and it precisely defines the phenomenon. Therefore, VSWR is defined as Emax/Emin.
Modern VSWR equipment does not measure VSWR by tapping into parts of the transmission line. The VSWR meter, calibrated in SWR, uses a directional coupler.
The meter usually contains circuitry that extracts the reflected wave's voltage and current. If there is no reflected wave, the current and voltage are exactly out of phase; thus the resultant voltage is 0. When this voltage is compared with the incident (forward) votage, a ratio, the VSWR, is established.
The term SWR is not exactly synonymous with VSWR, but for practical purposes they are interchangeable. An SWR indication measures the percentage of power loss. Most bridges that are calibrated in SWR have a voltage ratio on top of the scale and a power percentage on the bottom.
With a full scale forward power reading, a half-scale reflected power reading indicates a 3:1 VSWR. The power lost is 25%, as shown by the equation P=E²R. With a half-scale reading, E=0.5. The calculation is E²=0.5x0.5=0.25 = 25%.

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Return Loss

The telephone company developed the return loss concept of reflected measurements. The purpose was to measure subscriber lines at audio frequencies.
A bridge circuit with an audio voltmeter connected across two arms of a bridge measures the reflected power in the transmission system.
Because the voltmeter reads directly in decibels, return loss specifications were developed in decibels as a power ratio instead of VSWR.
To this day, return loss measurements usually are specified in decibels. Return loss in decibels yields the difference in power level, which generally is a more useful quantity.
For example, if the return loss is 10 dB and the forward power is 1000W, then 100W is reflected; 10 dB is a power ratio of 10:1.

Rho

Also known as reflection coefficient; rho is a coefficient related to the magnitude of the ratio of forward and reflected voltages.
Reflected voltage is a percentage of open circuit voltage. The reference for a 100% (infinite) reflection is 1.0 rho.
With early return loss bridges, the reflected voltage port usually was connected to an ac vacuum tube voltmeter (VTVM> such as the HP410B. To improve accuracy, a precision terminating resistor also was connected to load the bridge properly.
The reflection coefficient measurement was made as follows: With the bridge open or shorted to give a full reflection, the generator's power level was adjusted to a convenient level. If power output was limited maybe 1.0 Volt. If possible adjusting to 10 volts was better as this is still easily divisable and at lower coefficients usually gave a more accurate reading.
The bridge then was connected to the device under test (DUT), and the voltage noted. If, for example, the initial voltage with the bridge open or shorted is 1V and the voltage with the bridge connected to the DUT is 0.5V, the measurement represents a reflection coefficient of 0.5.

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Table of Conversions

The following table contains common values in all three systems. Included is return loss, VSWR, rho and mismatch loss. Rho is included for reference but was never very popular with field service.

Reflection Conversions

RL dB

VSWR

RHO

Mismatch Loss dB

0.0

Infinity

1.00

Infinity

1.0

17.40:1

0.89

6.87

2.0

8.72:1

0.79

4.33

3.0

5.85:1

0.71

3.02

5.0

3.57:1

0.56

1.65

6.0

3.01:1

0.50

1.25

9.54

2.00:1

0.33

0.51

10.0

1.93:1

0.32

0.46

14.0

1.50:1

0.20

0.18

15.0

1.43:1

0.18

0.14

20.0

1.22:1

0.10

0.04

25.0

1.12:1

0.06

0.014

30.0

1.06:1

0.03

0.004

40.0

1.02:1

0.01

<0.001

Modern Measurements

All EAGLE Return Loss Bridges have an RF reflected port. The availability of low cost spectrum analyzers with tracking generators allows for sweep frequency testing using the bridge. The RF reflected port is simply connected to the spectrum analyzer input. Then the return loss measurement is read directly in decibels, which easily is converted into VSWR when necessary.

The spectrum analyzer not only reads power but signal frequency. If another signal is close to the measurement frequency, it may be observed on the analyzer, but it will not affect the desired signal's level. Unwanted signals often appear when measuring antenna's at crowded sites.

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14 Dec 2004 ccs-a