Saturday, December 21, 2019

Decoding Antenna Factor In Ferrite Loops

Mediumwave DXers and signal measuring enthusiasts, let's have a look at Antenna Factor and see if we can use it.

Q: What is Antenna Factor?

A: A correction factor translating arriving field strength to antenna output. Bonus: It can also be used in reverse, translating antenna output to arriving field strength.

Q: Can the mediumwave DXer with a modern portable DSP receiver use Antenna Factor to any advantage?

A: Yes, of course. You may not realize it, but you are holding a rudimentary field strength measuring device in your hand.


Antenna factor is often greatly mis-understood. Antenna factor is the relationship between the electric field strength "E", which is the strength of the radio wave field surrounding the antenna (usually referred to in millivolts per meter) to the voltage output "V" of the antenna itself (usually measured in microvolts).

Simply, it is the ratio of the former to the latter - antenna field to antenna output - and shows the antenna's ability to convert the surrounding received field to a usable voltage. It is literally the relationship between field strength and signal strength. In the mediumwave DXer's case, "V" is the ferrite loop's voltage output - signal strength! And another bonus for us - they are directly proportional - that is, an increase in the antenna's surrounding field results in a proportional increase in the ferrite loop's voltage output.


Wouldn't it be interesting if we knew the antenna factor of our ferrite loop? Or at least its approximate value? What might we do with that? With our modern DSP chip radios displaying an RSSI (Received Signal Strength Indicator) voltage, the output of its ferrite loop, we could easily determine an approximate value of the electric field strength of the station at our location, a value right in line with the published values gotten from V-Soft Zip Signal and radio-locator, or an expensive signal measuring device.

Let's take this apart, piece by piece, and see how we can get there.

Although the field strength and antenna output measurements we talk about in the paragraphs above are voltage, antenna factor is generally expressed in "dB" microvolts per meter, or simply "dB".

The decibel (dB) unit of measurement is used to express the ratio of one value of a power or field quantity, or a voltage, to another. It is a logarithmic measurement, in that the decibel equals 10 times the common logarithm of the power ratio or 20 times the common logarithm of the voltage ratio. Remember, dB, used alone with no reference, is a ratio. 0 dB means no change, or an equal ratio.

In our case we are dealing in voltage ratios here, not power ratios, so our formula will be 20 times the common logarithm of the voltage ratio.

So, if our voltage ratio of E/V is 2 for example, or double, our dB value is 20 times the log of 2, or 6 dB. Note that a doubling of the voltage (i.e., 2) is a 6 dB improvement.

National NC-270 S-Meter

Devopedia has a great summation of the decibel if you would like to delve into it further.

Old timers will remember the analog S-meter on the old receivers. It was calibrated S-0 to S-9, then in dB above S-9. Each S-unit was a doubling of received voltage from the previous S-unit, or a 6 dB gain. Consequently, each S-unit increase is an increase by the power of 2. S-9 is 2^9 stronger than S-1, or 512 times greater signal voltage! S-9 represented 50 microvolts of receiver input measured right at the antenna - signal strength. Thus the S-meter was commonly called a signal strength meter. Be sure not to confuse field strength with signal strength. Field strength is the electromagnetic field surrounding an antenna and signal strength is the converted voltage at the antenna output.

Now, what about ferrite loops and frequency dependence? Many will recognize that their radio might be a little more sensitive at one end of the band than the other. At one given frequency, for all stations received on that frequency, the relationship between their field surrounding the antenna and the output voltage of our field converter (our ferrite loop) is constant. This being so, the antenna factor is also a constant for all at that given frequency. It may be slightly different at a different frequency as we will see.

RSSI - 19 dBµV

So by knowing the antenna factor and the RSSI voltage we can work in reverse to determine the field strength at the antenna. The antenna factor (in dB microvolts per meter) can simply be added to the value of voltage measured (in dBµV) at the ferrite antenna output! It is a simple matter then to convert that antenna factor dB value back to a field voltage in millivolts or microvolts per meter.

What are the two values dB microvolts per meter (dBµV/m) and dBµV telling us? A ratio, that's all. It's the amount of field or voltage compared to one millionth of a volt (the "µ", or "micro", means one millionth).


The three pieces of information are:

  1. E - Field strength of the radio station's signal at the antenna (in dBµV/m).
  2. AF - Antenna factor of our antenna (our ferrite loop), in dB/m.
  3. V - Voltage output of our ferrite loop (the RSSI reading in dBµV).

Our formula for determining antenna factor AF is this:

                              AF(dB/m) = 20 * LOG(E/V)

                              Note: E and V must be in the same units - voltage!
Our formula for determining field strength E is then this:

                              E(dBµV/m) = V(in dBµV) + AF(dB/m)

Our formula for determining signal strength V (RSSI) is then this:

                              V(dBµV) = E(dBµV/m) - AF(dB/m)

Knowing any two of the three values, we can calculate the third value. We can determine a variety of useful information knowing our RSSI reading and one other parameter.

We will first need the E, or field strength values, of some nearby sample stations. We will use those values in our formula to calculate some antenna factors for various frequencies in the mediumwave band. They should prove relatively close in value. We will then average them to get an overall average antenna factor value, or AF.

Item #1, field strength E, for daytime reception out to about 200 miles of our chosen stations can easily be gotten from the V-Soft Zip Signal site. Accuracy is very good, and compares to within approximately 5% of the enhanced Norton signal strength formula I use in pattern calculation. Field strengths are published to your zip code origin, which is generally your post office latitude-longitude. Using some sample field strength values and the RSSI values from our receiver, we can calculate an approximate antenna factor for our radio.

Once we know the antenna factor, using simple addition we can calculate the field strength of any station we receive by adding the antenna factor dB right to the RSSI reading!

Note the value "A" in the pictured formula - Cable attenuation. We can ignore this in our formula as we have no feed line! We are measuring right at the antenna itself.

Before we get to our calculation examples, let me clear up one item of mis-represented terminology, the dBµV/m. In engineering parlance, field strength, or millivolts per meter (mV/m) is usually converted to dBµV/m and casually referred to as dBu (lower case "u"). It is NOT the same as the dBµ sticker (the RSSI value) on your DSP radio. "Engineer's dBu", the decibel representation of microvolts per meter, is RF field at the antenna and is short for dBµV/m. The radio's value "dBµ" is voltage output of the ferrite loop as compared to one microvolt, properly known as dBµV. Shame on Tecsun and others for printing dBµ on their radios. Inaccurate and very confusing.


The mediumwave E field at the receiver site (the antenna) is usually measured in millivolts per meter, mV/m. Though V-Soft will show the conversion of millivolts per meter to dBµV/m for you, you might want to be able to do it for yourself at some point.

If you'd like to figure it yourself, you can by using the following formula:

                              dBµV/m = 20 * Log(mV/m * 1000)

To reverse the computation, converting dBµV/m back to mV/m:

                              mV/m = 10 ^ (dBµV/m / 20) / 1000

                              ...or back to microvolts per meter:

                              µV/m = 10 ^ (dBµV/m / 20)

Note: Log is the common logarithm, or base 10.

Let's try some calculation examples to get a baseline. We'll start at the lower end of the band using our Tecsun PL-880.


Phoenix's daytime KTAR-620 is 129 miles east of me over fairly flat desert terrain. The station runs 5 KW daytime. Center tuned to KTAR on the Tecsun PL-880, the RSSI display shows a 35 dBµV signal off the ferrite loop. The V-Soft chart for my zip code shows the expected field strength of KTAR should be 0.83 mV/m (830 microvolts per meter), equivalent to 58.3 dBµV/m. We subtract our RSSI dB reading from the V-Soft dB value (58.3 - 35) = 23.3 to arrive at our antenna factor in dB. So our AF = 23.3 dB/m.


Yuma, AZ daytime KBLU-560 is 69 miles south of me over rugged, mountainous desert terrain. The station runs 1 KW daytime. Center tuned to KBLU on the PL-880, the RSSI display shows a 35.5 dBµV signal off the ferrite loop. The V-Soft chart for my zip code shows the expected field strength of KBLU should be 1.28 mV/m (1280 microvolts per meter), equivalent to 62.1 dBµV/m. We subtract our RSSI dB reading from the V-Soft dB value (62.1 - 35.5) = 26.6 to arrive at our antenna factor in dB. So our AF = 26.6 dB/m.

Another example, but this time let's use a different frequency at mid-band.


Daytime Lake Havasu, AZ KNTR-980 is 58 miles north of me over varied desert terrain. The station runs 1 KW daytime. Center tuned to KNTR on the PL-880, the RSSI display shows a 28 dBµV signal off the ferrite loop. The V-Soft chart for my zip code shows the expected field strength of KNTR should be 0.77 mV/m (770 microvolts per meter), equivalent to 57.7 dBµV/m. Our difference here between the V-Soft reading and the RSSI reading is 29.7 dB. So our AF = 29.7 dB/m.

Let's do one more example, this one a little farther up in the band.


Phoenix's daytime KPXQ-1360 is 116 miles east of me over fairly flat desert terrain. The station runs 50 KW daytime. Center tuned to KPXQ on the PL-880, the RSSI display shows a 20 dBµV signal off the ferrite loop. The V-Soft chart for my zip code shows the expected field strength of KPXQ should be 0.33 mV/m (330 microvolts per meter), equivalent to 50.3 dBµV/m. Our difference here between the V-Soft reading and the RSSI reading is 30.3 dB. So our AF = 30.3 dB/m.


So we are seeing that the antenna factor for our ferrite loop in the PL-880 is generally in the upper 20s on average. The antenna factor will vary a little from the low end of the band to the high end. This is because our ferrite may be less sensitive at one end versus the other. Not unusual. Mine tends to run in the low 30s near the high end and the middle 20s at the low end, signifying that the sensitivity of my PL-880 is a little better at the low end of the band. It's exactly the reverse of what you might think. The lower the antenna factor's dB value is, the better is the ferrite's (or any antenna's) ability to convert the field to a voltage.

I have averaged these stations above and several others and have chosen an average antenna factor value of 27 dB to work with.


Now that we have an average antenna factor of 27 dB for the PL-880 let's find a strong station at night and see what kind of field strength it's putting into my location here in Arizona. KCBS-740 (50 KW) out of San Francisco, CA is a good choice, and puts in a tremendous signal here at night. Average RSSI readings on the PL-880 are in the 48 dBµV area when the signal is peaking.

Adding our antenna factor, 27 dB, to 48 dBµV, we get 75 dBµV/m. 75 dBµV/m is 5623 µV/m (microvolts per meter) or 5.623 mV/m (millivolts per meter). Now of course being skywave, this value will hardly be published as such in a field strength chart due to the extreme number of variables involved in skywave propagation. However, with our DSP radio we can read it's instantaneous value and calculate what its instantaneous field strength is.

Remembering the radio-locator signal strength scheme for daytime strengths:

  • 2.5 mV/m (68 dBuV/m, local)
  • 0.5 mV/m (54 dBuV/m, distant)
  • 0.15 mV/m (43.5 dBuV/m, fringe)

We can see KCBS-740 at 5.623 mV/m puts a whopping signal into southwestern Arizona, at urban levels at night, stronger than any daytime station due to our remote location.


Let's check the base reception level of our PL-880 - its ability to pick up the weakest signal it can. High daytime KMZQ-670 out of Las Vegas, NV (25 KW), 198 miles distant, is right at the noise level on my PL-880, running about 15-16 dBµV. Adding our antenna factor 27 dB to 16 dBµV, we get 43 dBµV/m. Converting 43 dBµV/m back to microvolts per meter we get 141 µV/m or 0.141 mV/m (millivolts per meter). This can be confirmed by radio-locator, as the radio-locator coverage map shows KMZQ's fringe (blue line, 0.15, or 40 dBµV/m) to be very close to my location.

So we see that our PL-880 has the ability to receive signals during the daytime out to radio-locator's fringe ring, or 0.15 mV/m (40 dBµV/m).


Generally in quiet locations, the mediumwave broadcast band's atmospheric noise level runs about 0.063 mV/m, or 36 dBµV/m. What will our PL-880's ferrite loop output be for a signal right at the noise? We can calculate that easily. 36 dBµV/m - 27 dB = 9 dBµV or 2.81 microvolts. This is also -97.9 dBm into a 50 ohm load. dBm is a figure generally used in defining sensitivity of receivers, meaning the decibel ratio compared to one milliwatt (m). In this case we are -97.9 dB less than one milliwatt! Remember, -107 dBm is equivalent to 1 microvolt signal strength at the antenna output, or 1 millionth of a volt. The lower the number in dBm (the more negative), the weaker the signal is. We see that the PL-880 hears down to about 0.15 mV/m, but not quite to the 36 dBµV/m atmospheric noise level of 0.063 mV/m.


I have an Eton Traveler 3 from which I've removed the ferrite loop and replaced it with an 18 inch box loop. The loop is wired directly to the radio's input. This means the DSP chip's RSSI value will be directly reading the voltage off the loop. We can determine it's antenna factor too.

For our test station let's use Yuma's daytime KBLU-560 signal again, 69 miles distant running 1 KW. Our RSSI display shows a 58 dBµV signal off the hardwired loop. The V-Soft chart (as before) shows the expected field strength of KBLU should be 1.28 mV/m (1280 microvolts per meter), equivalent to 62.1 dBµV/m. We subtract our RSSI dB reading from the V-Soft dB value (62.1 - 58) = 4.1 to arrive at our antenna factor in dB.

So the antenna factor for our 18 inch box loop is very low at 4.1 dB. Notice also that we have a 58 dBµV signal voltage being output as compared to the 35.5 dBµV signal voltage off the PL-880's ferrite, meaning much greater signal gain. Quite an improvement from the ferrite loop of the PL-880! A quick subtraction shows we have a 58 - 35.5 or 22.5 dB voltage gain. Converting the dBuV values to actual voltage, we have jumped our output from 59.5 microvolts to 794 microvolts, a 13.3 ratio increase by using our 18 inch passive loop!


So there you have it. A new field strength measuring device awaits your testing! Be sure to remember to use the same units in your calculations. Don't mix millivolts per meter with microvolts per meter, or dB with actual voltage.

I hope I've provided for you some new and interesting things to try. Be sure to realize that the values we are calculating are ballpark values. They are not exact like might be read off a $15K dollar field strength device like the Potomac 4100. But even ballpark values can tell us many interesting things about our radio environment and the modern marvel DSP receiver.

Potomac 4100 - $15K

No comments: