Synopsis:
Return loss is the difference, in dB, between forward and reflected power measured at any
given point in an RF system and, like SWR, does not vary with the power level at which it
is measured.
Discussion:
As stated above, RETURN LOSS IS THE DIFFERENCE, IN DB, BETWEEN THE FORWARD AND REFLECTED POWER
MEASURED AT A GIVEN POINT IN AN RF SYSTEM. Typically, but not always, this point of
measurement is the input of a "component exhibiting a frequency response" used in an RF system.
Note that this subtraction uses logarithm-based quantities (dB). This is radically
different from a subtraction of Watts or milliWatts. Remember "0 dBm" means "1 mW", while 0
milliWatts means "no power" (none, zero, zip, nada). Running some example calculations through
the power level addition worksheet might help
with understanding this principle.
A "component exhibiting a frequency response" is anything with characteristics that vary with
frequency. An example with which most hams are familiar is a single-band, high-gain yagi
antenna. It is generally understood that such an antenna is GENERALLY designed to work over a
limited range of frequencies, or a bandwidth, within a specific ham band. Within this useful
frequency range (bandwidth), the SWR (Standing Wave Ratio) is relatively low, typically 1.5:1
or less, 1.0:1 being the best possible SWR. As one varies the frequency outside the useful
bandwidth, the SWR increases. Depending on several variables, discussion of which is beyond
the scope of this article, it is generally accepted that an antenna is useful only within the
bandwidth at which the SWR is 2.0:1 or lower, with 1.5:1 often cited as the maximum acceptable
SWR.
Note that the SWR of a yagi antenna is a mathmatical relationship between the forward power
and the reflected power measured at the driven element of the antenna. Here, again, the
relationship is linear, not logarithmic, and the less reflected power (the better situation),
the lower the value of SWR. With return loss, less reflected power means smaller number of
dBm (or dBW; see below) to be subtracted off, resulting in larger return loss for the better
situations.
Using our antenna example and the definition of return loss given above, return loss is the
difference between forward and reflected power, in dB, generally measured at the input to the
coaxial cable connected to the antenna. Ideally, one would want to measure the antenna input
directly, but since said antenna is generally at the top of a tower, this is not practical. The
accepted practice is to make the measurement as mentioned, at the input to the coaxial cable
going to the antenna. See the CAVEAT below
regarding the pitfalls of this practice.
Calculations:
Since return loss is in dB, one must convert power levels to dB units, generally either dBm
(decibels referenced to one milliWatt; 1 mW = 0dBm) or dBW (decibels referenced to one
Watt; 1W = 0dBW = 30dBm). To calculate return loss:
1. Convert forward and reflected power to dB (as above).
dBm=10logP where P is in milliWatts
dBW=10logP where P is in Watts.
2. Subtract reflected power in dB from forward power in dB.
NOTE: Subtract dBm from dBm and dBW from dBW, do NOT mix dBm and dBW!!
Example 1: The BEST case; a perfect match (SWR=1:1).
Fwd pwr = 1500 Watts (61.76 dBm); Ref'd pwr = 0 Watts
This example appears to break down mathematically because it is not possible to calculate
10log(0). It does have a solution, however (see MATH
refresher, below), and we can say 10log(0) is, to all practical purposes, equivalent to
negative infinity.
Return Loss = 61.76 dBm - (-INFINITY) dBm = INFINITY dB
Remember your arithmetic: Subtracting a negative is like adding a positive ("two negatives make a positive!).
Also, remember that any finite number added to infinity doesn't increase infinity enough to make a difference,
so 61.76 + infinity = infinity, as shown.
Example 2: OUTSTANDING (SWR=1.05:1).
Fwd pwr = 1500W (31.76 dBW); Ref'd pwr = 1W (0 dBW)
Return Loss = 31.76 dBW - 0 dBW = 31.76 dB
Example 3: Not so great (SWR=1.92:1).
Fwd pwr = 100W (20 dBW); Ref'd pwr = 10W (10 dBW)
Return Loss = 20 dBW - 10 dBW = 10 dB
Example 4: The WORST case; (SWR=INFINITY:1).
Fwd pwr = Ref'd pwr = 100W (50 dBm)
This situation illustrates a dead short or complete open, with 100% of the forward power reflected back to the source.
Return Loss = 50 dBm - 50 dBm = 0 dB
The relationship between practical values of SWR and the associated return loss is shown below.
Examples of forward and reflected powers are given and return loss calculated by subtracting
reflected power in dB from forward power in dB, per the examples above. NOTE that the
difference between all Fwd and Ref'd powers in dB at each SWR is identical. Note also,
as in the four examples above, return loss increases as SWR decreases, i.e. high return loss
is good and low SWR is good.
|
SWR |
Forward Power
W / dBm / dBW |
Reflected Power
W / dBm / dBW |
Return Loss
dB |
|
2:1 |
10 / 40 / 10 |
1.1 / 30.5 / 0.5 |
9.5 |
| 100 / 50 / 20 |
11 / 40.5 / 10.5 |
| 1000 / 60 / 30 |
111 / 50.5 / 20.5 |
| 1500 / 61.8 / 31.8 |
166.7 / 52.3 / 22.3 |
|
1.92:1 |
10 / 40 / 10 |
1 / 30 / 0 |
10 |
| 100 / 50 / 20 |
10 / 40 / 10 |
| 1000 / 60 / 30 |
100 / 50 / 20 |
| 1500 / 61.8 / 31.8 |
150 / 51.8 / 21.8 |
|
1.67:1 |
10 / 40 / 10 |
0.6 / 28 / -2 |
12 |
| 100 / 50 / 20 |
6.3 / 38 / 8 |
| 1000 / 60 / 30 |
63.1 / 48 / 18 |
| 1500 / 61.8 / 31.8 |
94.7 / 49.8 / 29.8 |
|
1.5:1 |
10 / 40 / 10 |
0.4 / 26 / -4 |
14 |
| 100 / 50 / 20 |
4 / 36 / 6 |
| 1000 / 60 / 30 |
39.8 / 46 / 16 |
| 1500 / 61.8 / 31.8 |
59.7 / 46.8 / 26.8 |
|
1.38:1 |
10 / 40 / 10 |
0.25/ 24 / -6 |
16 |
| 100 / 50 / 20 |
2.5/ 34 / 4 |
| 1000 / 60 / 30 |
25.1 / 44 / 14 |
| 1500 / 61.8 / 31.8 |
37.7 / 45.8 / 25.8 |
|
1.29:1 |
10 / 40 / 10 |
0.16 / 22 / -8 |
18 |
| 100 / 50 / 20 |
1.6 / 32 / 2 |
| 1000 / 60 / 30 |
15.9 / 42 / 12 |
| 1500 / 61.8 / 31.8 |
23.8 / 45.8 / 25.8 |
|
1.22:1 |
10 / 40 / 10 |
0.1 / 20 / -10 |
20 |
100 / 50 / 20 |
1 / 30 / 0 |
1000 / 60 / 30 |
10 / 40 / 10 |
| 1500 / 61.8 / 31.8 |
15 / 41.8 / 11.8 |
|
1.1:1 |
10 / 40 / 10 |
0.025 / 14 / -16 |
26 |
100 / 50 / 20 |
0.25 / 24 / -6 |
1000 / 60 / 30 |
2.51/ 34 / 4 |
| 1500 / 61.8 / 31.8 |
3.77 / 35.8 / 5.8 |
Values are rounded off, e.g., 1.76 to 1.8, 40.46 to 40.5, etc.
CAVEAT: Making antenna measurements at the input to the transmission line (coax)
can result in an artifically good reading of antenna SWR. The higher the loss (attenuation),
the worse the disparity. Run some sample calculations, varying transmission line attenuation,
at Antenna System Paramters to see how coax
loss affects the actual value of SWR at an antenna versus that measured at the input of the
associated transmission line!
MATH: One can do myriad example calculations of 10 log(P) with powers of ever
decreasing magnitude, and it is clear that as power gets smaller and smaller, approaching 0,
10log(P) becomes more and more negative (the negative number becomes larger and larger),
approaching negative infinity. Mathematically, anything "close" to infinity is so "huge"
that it cannot be differentiated FROM infinity, so we can say 10log(0) is, to all practical
purposes, equivalent to negative infinity.
The valuation of return loss in the "zero reflected power" situation can be verified as well
by a quick refresher on the exponential basis for logarithms:
The discussion above should remind the reader that subtraction of logaritms is the same as
division, i.e.
We know division by zero is undefined. We recall also, however, as in the discussion
above about "approaching zero" and "approaching infinity" that in division, as the divisor
gets smaller and smaller (approaching zero), the quotient gets larger and larger (approaching
infinity).
