Return Loss Bridge

Return loss (RL) may be a new concept to many radio amateurs. It may surprise you, but in this case, more loss is better. Return loss is the decibel portion of the input power that is taken by the load; greater return loss means less reflected power and lesser SWR (Standing Wave Ratio). In fact, when the SWR is 1:1 the return loss is infinite!

On the picture (click to enlarge) on the right you will see a simple build of my Return Loss Bridge, with 3 BNC connectors. The transformer is a commercial piece DLF4000, the black square in the background.

For some applications, return loss is easier and more useful than SWR measurements. Let’s look at a couple of examples.

attachment:wobbulator_RLB_DSC05177.jpg

Suppose you know your coax loss and SWR at your transmitter, but want to know the SWR at your antenna feed point. Factoring transmission-line loss into the SWR equations is difficult, but the problem becomes a piece of cake when you use return-loss measurements. Here’s the recipe:

Where RLAnt and RLTX are the return losses at the antenna and transmitter, respectively, and LCoax is the coax loss. All three quantities must be in decibels. You may wonder why we double the coax loss in this calculation. The reason is that the power returned by the mismatch travels through the feed line twice—once as forward power, and then again as reflected power.

Let’s now consider some real numbers. Suppose the SWR measured at the transmitter is 2:1 and the coax loss is 1.75 dB. The first step of course requires us to convert SWR to return loss. We can translate between several measures of load match by reading a table (see Table 1) or applying math equations. [1] Table 1 shows that a 2:1 SWR equals a return loss of 9.5 dB. Plugging in the numbers, we get:

The wobbulator graph on the right side shows with the 0 dB curve the short from DDS-Generator to the logarithmic amplifier.

The -12 dB curve the zero point (RL = open) of the RLB in the frequency range from 1 to 31 MHZ (3 MHz per division). The vertical scaling is 10 dB per division.

The center curve shows the directivity (- zero curve = 30 - 35 dB, RL = 50 Ohm) of the bridge.

The lower curve (-70 dBm) shows the logarithmic amplifier with open input.

attachment:wobbulator_RLB_directivity_1coil.png

Table 1—ρ, ρ2, Return Loss and SWR

ρ (V) Pr/Pf (ρ2) RL (dB) SWR
0.00  0.00        ∞      1.00
0.05  0.00       26.4    1.10
0.09  0.01       20.8    1.20
0.10  0.01       20.0    1.22
0.13  0.02       17.7    1.30
0.15  0.02       16.5    1.35
0.17  0.03       15.6    1.40
0.20  0.04       14.0    1.50
0.23  0.05       12.7    1.60
0.25  0.06       12.0    1.67
0.26  0.07       11.7    1.70
0.29  0.08       10.9    1.80
0.30  0.09       10.5    1.86
0.31  0.10       10.2    1.90
0.33  0.11        9.5    2.00
0.35  0.12        9.1    2.08
0.40  0.16        8.0    2.33
0.45  0.20        6.9    2.64
0.50  0.25        6.0    3.00
0.55  0.30        5.2    3.44
0.60  0.36        4.4    4.00
0.65  0.42        3.7    4.71
0.70  0.49        3.1    5.67
0.75  0.56        2.5    7.00
0.80  0.64        1.9    9.00
0.85  0.72        1.4   12.33
0.90  0.81        0.9   19.00
0.95  0.90        0.4   39.00
1.00  1.00        0.0    ∞

The 6 dB return loss converts to a 3:1 SWR at the antenna feed point.

As you might guess, we can reverse this procedure. Suppose you want to know the SWR at your transmitter if your antenna SWR is 1.5 and coax loss is 1 dB. From Table 1, we see that a 1.5:1 SWR corresponds to a return loss of 14 dB. This time, the calculation looks like this:

The SWR at the transmitter is about 1.35:1.

attachment:ReturnLossBridge.png

Schematic of the RLB

This basic schematic is from Wes Hayward’s (W7ZOI). The connection is made with BNC plugs.

The resistors are made from two 100 Ohm resistors in parallel with a tolerance of 1%.

The transformer is a commercial unit DLF4000, which gives a mean directivity in the frequency range 3 to 30 MHz of >30 dB, which is excellent.

As you can see in the table above, for practical reason a directivity range of 27 dB is sufficient.

The DLF4000 has 4 coils on the toroid. When using 2 coils for the transformer, the -1 dB lower frequency limit was -3 dB at 2 MHz, the directivity >30 dB.

A toroid transformer Amidon T37-6 with two times 10 turns 0.4 mm diameter wire achieved 29 dB directivity only.

attachment:wobbulator_RLB_LC15MHz.png

Measuring with the RLB

Together with the RaspberryPiWobbulator you will get a powerful measurement equipment, to measure the effective Bandwidth and the Quality (matching) of an impedance in the short wave range 1 - 30 MHz, e.g. your antenna.

One practical example is to measure the center frequency of a LC parallel circuit, 100 pF parallel to 1uH (adjustable core). The LC circuit must be connected on the Output (Load) parallel with a 50 Ohm resistor.

In the picture on the right, the center frequency of the parallel LC circuit is about 11/15/21 MHz (core in, half in, out). It is interesting so see, that the core affects the quality of the coil at the resonance frequency. The upper trace is the zero curve. The lower curve shows the directivity.

Next step was to measure some real amateur radio antennas.

Below are three diagrams from three different antennas (click on diagram to enlarge). For the cable loss 2 x 1 dB is added to the measured value. The SWR values measured with a real SWR meter are behind in parenthesis.

attachment:RLB_Dipol_80m.png

attachment:RLB_Dipol_40m.png

attachment:RLB_Fritzel_FB23_2.png

attachment:RLB_Windom-1m_SWR.png

Dipol, Windom

I got now a Windom Dipol (13.8 + 27.7 = 41.5 m) from a friend and measured with the wobbulator and the Return Loss Bridge the SWR (Standing Wave Ratio) of the antenna, and compared the values with the MFJ-269 SWR Analyzer.

The height of the antenna is at the feed point about 9 m, at the ends 6 m above ground.

The 50 Ohm feed cable (HSR195) has a mechanical length of 17.04 m, electrical 21.3 m (about 80 m Lambda/4).

The diagram on the right was measured with the wobbulator, Frequency Range is 1 to 31 MHz in 100 KHz steps.

The upper 3 straight curves are the SWR values: ∞ (blue), 1:2 (red), and 1:1.2 (green). The lower straight curve is the 50 Ohm matching, means a SWR of 1:1.

The MFJ-269 showed the best SWR for the following Bands:

Band

MHz

SWR 1:

80 m

3.1

2.0

40 m

6.7

1.4

20 m

14.6

1.2

10 m

29.1

1.1

attachment:MFJ-941B_DSC05760.jpg

With a MFJ-941B matchbox I achieved in all bands a SWR of better than 1:1.2. One exception was the 80 m CW band with 1:1.4. The 80 m band is a problem, because I had to route the last 5 m in an angle of 45 about degree. In order to move the resonance point a little bit higher, I shorted the antenna at both ends for 0.5 m each.

attachment:MFJ-269_DSC05761.jpg

The MFJ-269 SWR Analyzer is very useful for measuring antennas, see the picture on the right.

The Windom antenna is connected to the input via adapter. The instrument does have a N-connector, while the antenna has a BNC connector.

A 2-line LCD show the measurement results:

The upper line the work frequency in MHz, and the SWR.

The lower line shows the complex impedance in resistive and reactive part.

Below are two analog instruments showing the SWR and the load impedance.

At the bottom of the front plate are the frequency analog adjustment and the band switch.

To check the antenna, you tune to the desired frequency and read the SWR, or you tune to a minimum SWR and read the frequency.

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-- RudolfReuter 2014-03-19 10:09:29


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