2. Coil form factor. Most authors of amateur radio articles on the subject recommend a small length to diameter ratio which leads to a coil that is short with large diameter such as the one recommended on the SSTRAN site. I have seen recommendations of 1:1 but I don't see the advantage of this over the SSTRAN recommended coil.
Regarding coil form factor
I see that the 160 meter experimenters wind coils with pretty significant spacing between each winding, for example, Texas bug catcher antennas use a coil like ths:
And that site states it's "...wound with 63 turns of 12 gauge wire on a 6 inch form at 6 turns-per-inch. A 10-foot whip, made up of a 102-inch whip and an 18- or 24-inch extender mast, and a 20-inch capacity hat to this combination will extend operation down into the 1700 kHz"
This is quite different from the sstran sketch coil in diameter and winding spacing. Would increasing diameter and spacing improve performance?
Experimental broadcasting for a better tomorrow!
OK, so here is another question... Does the height above the ground plane of the shortened 3m whip play any role in the efficiency? Just wondering if it would be pratical to mount the antenna at 1/2 or 1/4 wavelength above the ground.
Yes. But a base-loaded, 3-m vertical antenna and the Part 15 AM tx need to be connected to some type of r-f ground in order to radiate as efficiently as possible. If it is installed above a buried r-f ground such as radials, ground rods etc and connected to them by a conductor of any kind, then the r-f current flowing between the ground plane and the elevated tx system will radiate. Then this tx/antenna system (3-meter section plus the long conducting path to r-f ground) is longer than the 3-m length permitted by FCC Rule 15.219.
Here is a link to a paper with more on this subject...
http://www.freefilehosting.org/public/26150/Elevated%20Part%2015%20AM%20Antennas.pdf
SCWIS,
Thanks for the picture since this makes it easier for all to visualize an "open form" coil. This coil appears to have a shorter L/D ratio than the SSTRAN coil.
Here are some differences between an open form coil and a coil such as the SSTRAN loading coil:
Open form coils have:
Bare windings which make tapping easy.
Spacing between the windings which increases the interwinding breakdown voltage allowing high power operation.
Virtually no form material which reduces dielectric losses from the form material.
Lower interwinding capacitance which raises the self resonance frequency caused by interwinding capacitance.
Possibly higher Q (lower resistance) compared to narrower, longer coils for a given L.
Are available as "coil stock", so the builder need only cut off the coil to get the L needed.
The coil in your picture appears to have shorter and wider dimensions than the SSTRAN coil but I don't see any advantage of this over the SSTRAN coil with one exception. A coil close wound with insulated wire will have a lower self resonance frequency that the open form type. I don't know what this is for the SSTRAN coil, but I wound a similar coil using #14 insulated house wire and measured the self resonant frequency at 3.3 MHz. This is about the second harmonic of the upper end of the AM band and may allow second harmonic radiation above desired levels.
Other than this, considering the low power and low frequency of operation for part15 AM, and considering that the resistive losses of the coil are small compared to ground losses and need not be mininmized, I see no advantage of one over the other.
Neil
This subject has interested me for years. Once, I thought that it was possible to increase the efficiency of a 3 m AM antenna to above 10%. This is theoretically possible. Several articles have been written about small antennas, probably the best being: Chu, Journal of Applied Physics, Vol. 19, p. 1163, 1948. The way to maximize the efficiency of an electrically short antenna is to make its volume as large as possible. A fat antenna is more efficient than a thin antenna. Unfortunately, Frank Charlie Charlie doesn't like fat antennas for Part 15 AM. I know that because I wrote and asked. Capacitive hats are prohibited because they increase the electrical length of the antenna. Large antenna diameter to reduce antenna capacitive reactance is prohibited, but not for any reason that makes sense to me. Apparently, the FCC simply doesnn't like antenna designs that significantly increase the radiated power of Part 15 AM transmitters. The primary concern of the FCC is to limit the potential for interference to licensed stations.
They implied that the word "ground" in Section 15.219(b) means earh ground. This makes any conductive paths between the transmitter and the earth part of the "ground lead." I understand that others making similar inquiries got similar answers.
None of these things, however, have been included either in the Part 15 rules or the published opinions of the FCC Office of Engineering and Technology, which administers Part 15. So, these things are not "official." I think, however, that they reflect the inclinations and intentions of the FCC staff.
I stated in my previous contribution that it is not possible to get as much as 1% effficiency on the AM broadcast band from a 3 meter whip above ground if the full audio bandwidth is transmitted. I will use the antenna described by Rich to illustrate my point. A 3 meter long, 1/2 inch diameter, antenna has a capacitance of 29.1 pF, giving a capacitive reactance of 3397 ohms at 1610 kHz. (There are several formulas for this calculation, and the ones I know agree with each other to about 15%.) The loading coil inductance is 336 uH. The radiation resistance is .102 ohms. The radiation resistance formula in The Low Power AM Broadcaster Handbook, which I downloaded from Part15.us, gives a value four times this amount. This is because the formula given in the Handbook is for a toploaded antenna, not a whip. The loss resistance of Rich's antenna is given as 10.65 ohms. This does, indeed, give about 1% efficiency, as Rich claims. The problem is that the audio bandwidth allowed by Rich's antenna is only about 2.5 kHz. This is because the Q of the antenna is 3397/10.752 = 316. The RF bandwidth is 1610/316 = 5.1 kHz. Since there are two sidebands, the audio bandwidth is about 2.5 kHz. Rich supplied a link to two curves intended to show the VSWR bandwidth of his antenna. These curves, however. are for wider bandwith antennas than the one being discussed here. For the +/- 2.5 kHz antenna, the VSWR is 1 at resonance, 2.6 at 2.5 kHz from resonance, 5.7 at 5 kHz from resonance, and 17.2 at 10 kHz from resonance. My data gives much higher VSWR values than Rich's curves.
If loss resistance is added to Rich's antenna so that the audio banwidth is increased to 10 kHz, the antenna efficiency reduces to about .25%. More loss resistance than Rich indicated is easy to get because a poor ground is the rule , and not the exception, in Part 15 AM radio. The FCC does not like the installing of ground radials, metal sheet, or metal mesh to reduce ground resistance. It is difficult to get more than .1% antenna efficiency in practice.
I was surprised that Rich chose to plot the frequency response of his antenna using VSWR instead of dB. It seems to me that VSWR is not appropriate because Part 15 AM transmitters usually do not use transmission lines, since they count toward the 3 m limit in the rules. I say "usually," because I know of one FCC certified transmitter to which an antenna is connected by a long length of coaxial cable.
When I calculated my own VSWR bandwidth curve, I assumed that an ideal, lossless, impedance transformer was used to match the transmission line to the antenna at resonance. In practice, if an antenna does not match a transmission line, an impedance matching network would be needed between the transmission line and the antenna.
In a reply to one of my previous posts, Neil asked me how circuit capacitance can cause power loss in a Part 15 transmitter. After all, it is understood by everybody that resistances dissipate power, but capacitances do not. I will give an example:
A loading coil used for antenna tuning has an inductance, of course, but it also has an equivalent parallel capacitance. The loading coil capacitance increases losses. Here's why:
Because of the equivalent parallel capacitance of the loading coil, the inductance of the loading coil is less than needed to resonate with the antenna capacitance. The capacitance causes the inductive reactance of the coil to increase. The loading coil capacitance causes the bandwidth of the system to decrease below what it would be if the impossible condition of there being no loading coil capacitance existed. This lower bandwidth suppresses the higher audio frequencies to be transmitted. To restore the audio bandwidth, the Q of the system would have to be decreased by adding losses to the system. For similar reasons, it is undesirable to tune a loading coil using a variable capacitor. It is better to use a variable inductor.
Capacitances at the output of the final stage, and in the matching network that couples the final stage to the antenna, all cause losses by reducing bandwidth. The bandwidth is restored by decreasing Q by increasing losses.
Neil made a very interesting observation a few messages ago about looking instead at the efficiency of the part15 AM transmitters. Modulation over 100% like the old Pan Axis AM 100 offered, and a more efficient use of the 100 mW we have to work with really seem like effective goals.
I had an AM 100 and it was really LOUD. When the Hamilton Rangemaster was first available Keith sent out some info to the effect that the benefit of his XMTR was in it's better efficiency, more effective use of the 100 mW available.
Keith's approach is likely proprietary, but I was wondering what some general approaches might be to improved modulation and better transmitter efficiency.
Experimental broadcasting for a better tomorrow!
The problem is that the audio bandwidth allowed by Rich's antenna is only about 2.5 kHz. This is because the Q of the antenna is 3397/10.752 = 316. The RF bandwidth is 1610/316 = 5.1 kHz. Since there are two sidebands, the audio bandwidth is about 2.5 kHz. Rich supplied a link to two curves intended to show the VSWR bandwidth of his antenna. These curves, however. are for wider bandwith antennas than the one being discussed here. For the +/- 2.5 kHz antenna, the VSWR is 1 at resonance, 2.6 at 2.5 kHz from resonance, 5.7 at 5 kHz from resonance, and 17.2 at 10 kHz from resonance. My data gives much higher VSWR values than Rich's curves.
The plots I linked to about this were made earlier for a different system and frequency than I described in my post, sorry about that. This morning I used my NEC file for a 3-m x 0.5" OD copper radiator on 1610 kHz with a 2 ohm coil R and an 8.65 ohm ground R, and generated the applicable plots showing system VSWR and input impedance across a 20 kHz r-f bandwidth (see link below). The VSWR values calculated by NEC are about 2.6:1 at +/- 5 kz, and less than 5.5:1 at +/- 10 kHz -- which are better than stated above, but not as good as I first posted. The system r-f bandwidth shown in the following link certainly is sufficient for the typical AM receiver these days, which has rather poor audio response beyond 5 or 6 kHz.
If usable r-f bandwidth is defined as that bandwidth within which the radiated power is at least 50% of the value at resonance, then for the impedance plot for this system linked below, that r-f bandwidth is better than 20 kHz. This is calculated from the R and j values shown at +/- 10 kHz, which show that the return loss at the input terminal of the antenna system at Fc +/- 10 kHz will be better than 3 dB (3.31, actually), and the VSWR there will be 5.305:1.
I was surprised that Rich chose to plot the frequency response of his antenna using VSWR instead of dB. It seems to me that VSWR is not appropriate because Part 15 AM transmitters usually do not use transmission lines, since they count toward the 3 m limit in the rules.
But VSWR does not require transmission line in order to exist. For example, if a transmitter output connector is left unterminated (or shorted), the VSWR at that plane will be infinite, and that's what an accurate "VSWR meter" will indicate.
//
Ermi,
You wrote:
In a reply to one of my previous posts, Neil asked me how circuit capacitance can cause power loss in a Part 15 transmitter. After all, it is understood by everybody that resistances dissipate power, but capacitances do not.
The key word which enables me to understand and agree with you is "cause" and you made it clear that the capacitor itself does not dissipate power yet can affect the circuit in such a way to cause loss by other components with resistive properties.
Just a few comments about the base loaded antenna coil.
The equivalent parallel capacitance does indeed increase the inductive reactance of the coil at frequencies below resonance and makes the coil reactance capacitive above resonance. But if we are operating below the self resonance frequency of the coil, the coil series resonates with the antenna capacitance if we set it up correctly. So for an antenna model we consider a series LCR circuit. Off series resonance, such as the sidebands will be, the circuit presents a complex impedance. With a perfect coil and capacitor in series to ground the transmitter will see a perfect reactance and no real power will be transferred. At resonance the transmitter will see 0 ohms to ground and no power will be transferred. Connect the L and C in series with the antenna radiation resistance. At resonance, the tx. transfers real power to the R since the series reactance is 0. Off resonance, the tx. still transfers real power to R but it is less due to the series reactance of the LC which is no longer zero ohms. Therefore, the sideband real power transferred will be less than it would be without the added reactance. The full carrier power is transferred and the sidebands will be weakened. We can call this a loss in sideband power and it is caused by the L and C in the circuit but reduction in power occurs somewhere else such as in the output amplifier of the transmitter.
As you said, one fix to sideband attenuation is to add resistance to the circuit which makes the drop in real sideband power less sensitive to frequency. This is the same as reducing the Q of the LCR circuit by increasing R and which increases the bandwidth, but reduces the power delivered to the radiation resistance.
We are both describing the same effects and I must have misread your first post on this, but it is clear now.
Neil
Rich,
With the new link you supplied for your new antenna plots, we may be approaching what, I hope, will be ultimate agreement. Your new data indicates that your antenna has an RF bandwidth of about 10 kHz. I, on the other hand, calculated that it is about 5 kHz. This 2/1 ratio in our results suggests that there is some common ground, and it is only necessary to find the factor that caused one of us to calculate twice the bandwidth the other did. A 10 kHz bandwidth at 1610 kHz means that the antenna Q is 161. The total antenna resistance is about 11 ohms. This means that the capacitive reactance of the antenna is 11 X 161 = 1771 ohms. The antenna capacitance must be about
1/[(1771)(2pi)(1610)(10^3)] = 56 pF.
I calculated that the antenna capacitance is 29.1 pF, which is a little more than half of 56 pF. We can now pose the question a little bit differently than before: What is the antenna capacitance? Is around 30 pF, or is it around 60 pF? I used several different formulas, and got around 30 pF with all of them. The formula I used to get 29.1 pF was taken from Antenna Engineering Handbook (Jasik). The two antenna capacitance formulas in The Low Power AM Broadcasters Handbook (which I mentioned in a previous post) both give around 30 pF. Could it be that your program has a built-in assumption that the antenna has a capacitive hat, and is adding an extra 30 pF to the antenna capacitance calculation?
The bandwidth of the antenna establishes the half-power points of the banwidth curve, which correspond to the 3dB points, and the 2.618 VSWR points. I prefer dB notation to VSWR notation because, for AM, RF bandwith is closely related to audio bandwidth, and dB notation is used for audio bandwidth curves.
Your new data indicates that your antenna has an RF bandwidth of about 10 kHz. I, on the other hand, calculated that it is about 5 kHz. .... A 10 kHz bandwidth at 1610 kHz means that the antenna Q is 161. The total antenna resistance is about 11 ohms. This means that the capacitive reactance of the antenna is 11 X 161 = 1771 ohms. The antenna capacitance must be about 1/[(1771)(2pi)(1610)(10^3)] = 56 pF.
Probably the difference arises from our definitions of r-f bandwidth. I gave mine in my post of yesterday.
NEC calculates the Xc of this system with no loading coil to be about 3136 ohms. Using your equation above shows that a radiator capacitance of 31.5 pF is needed to produce that Xc. When 3136 ohms of inductive reactance is added to the system, NEC shows the VSWR and impedance data in the plots I linked to yesterday.
Could it be that your program has a built-in assumption that the antenna has a capacitive hat, and is adding an extra 30 pF to the antenna capacitance calculation?
No chance of that at all. The calculations done by NEC are based only on the model parameters defined in its input data. My model consists of a 3-m, linear, vertical radiator broken up into 50 conductor segments. The segment at the bottom contains an 8.65 ohm resistance in series with it (the r-f ground connection). The next one up contains the r-f source (the transmitter), and the one above that contains an impedance of 2 +j 3136 ohms (the loading coil). The rest of the segments have no added sources or loads. No other structure is defined in the model.
//
The way to maximize the efficiency of an electrically short antenna is to make its volume as large as possible. A fat antenna is more efficient than a thin antenna. .... Large antenna diameter to reduce antenna capacitive reactance is prohibited, but not for any reason that makes sense to me.
Just to note that the equations for the feedpoint impedance of a short monopole radiator, such as found in standard antenna engineering texts and other publications* show that the radiation resistance of these antennas is independent of their diameter. Radiation resistance is related to the electrical length (height) of the radiating structure at the operating frequency. The diameter of the structure determines the feedpoint reactance.
Of those two impedance components it is only the radiation resistance that affects radiation efficiency, in conjunction with other resistive losses in the antenna system (mainly coil loss and ground system loss).
Going back to the 1610 kHz, ground-mounted Part 15 antenna AM system with 2 ohm coil loss and 8.65 ohm ground loss used earlier in this thread, NEC calculations were run for structure ODs varying from 1/4" to 24". The peak field from the antenna in the horizontal plane was constant within about 0.1dB across this range of structure diameters.
As predictable, the feedpoint reactance is lower with greater structure diameters (-j 3800 ohms with 1/4" OD to -j 292 ohms with 24" OD). The slower rate of change of reactance vs frequency for larger ODs would give those systems more 3 dB bandwidth, but systems across that entire range of ODs would produce essentially the same field strength at 1610 kHz. The lower coil inductances for larger ODs would reduce the coil loss by a small amount, but not enough to make a significant difference in the fields used by an AM receiver.
Also 47 CFR 15.219 does not appear to prohibit or restrict the use of "fat antennas."
Could you please expand on your statements? Thanks in advance.
*eg, "Performance of Short Antennas" by Carl E. Smith (Proceedings of the IRE, October 1947)
//
Rich,
Since we both agree that the antenna capacitance is about 30 pF, the graphs for the input impedance and the VSWR can be calculated by hand. This is important for this discussion, because the differences in the RF bandwidth we calculated are not due to differences in definition, but brcause of some error in calculation. Now we can eliminate the computer program from the discussion, and just determine if the results obtained are correct or not.
Your link gives two graphs: One is the input impedance of the antenna vs. frequency. The other is VSWR vs. frequency. The VSWR plot follows directly from the input impedance, so we only need to determine if the input impedance plot is correct or not.
I will demonstrate that that the reactance shown on your input impedance plot for 5 kHz below resonance (which is about 10 ohms of capacitive reactance) is incorrect. It should actually be about 20 ohms of capacitive reactance, as I claimed in a previous post.
As is well-known, inductive reactance is proportional to frequency. Capacitive reactance is inversely proportional to frequency. 5 kHz is 5/1610 = 3.1056(10^-3) of the resonant frequency of 1610 kHz. The inductive reactance has the same absolute value at resonance as the capacitive reactance (3136 ohms). At 5 kHz below resonance, the inductive reactance is
3136(3.1056)(10^-3) = 9.74 ohms less than the inductive reactance at resonance. Because 5kHz is much smaller than 1610 kHz, it can be estimated that the capacitive reactance is very nearly 9.74 ohms more than the capacitive reactance at resonance. By algebraically adding the inductive and capacitive reactances, we get the input reactance of the antenna. The inductive reactance at 5 kHz below resonance is
j(3136-9.74) ohms. The capacitive reactance at 5 kHz below resonance is -j(3136+9.74) ohms. Algebraically adding these two reactances gives: -j(3136+9.74) + j(3136-9.74) =
j3136-j3136 -j9.74-j9.74 = -j19.48 ohms.
So, the capacitive reactance at the antenna input at 5 kHz below resonance is not about 10 ohms, as your plot shows, but about 20 ohms, as I claimed. There is some error in your calculations that doubles the frequency shift from resonance over what it should be. Because of this error, the VSWR values you reported are also incorrect. The correct VSWR values are more like the ones I gave in a previous post.
There is some error in your calculations that doubles the frequency shift from resonance over what it should be. Because of this error, the VSWR values you reported are also incorrect.
Carl E. Smith in his paper "Performance of Short Antennas" gives an equation for the 3 dB bandwidth of an antenna, and goes on to say that the equation assumes a generator impedance of zero ohms, and that when the generator and antenna are matched, the bandwidth will be doubled.
I have contacted the authors of my NEC software to see if this explains the differences in our two results.
//
Rich,
I agree that matching the generator to the antenna doubles the bandwidth of the transmitter and antenna system. This is because the source resistance of the transmitter adds to the losses of the antenna, increases system losses, decreases system efficiency, and increases bandwidth.
This, however, has nothing to do with the input impedance of the antenna itself, and does not explain the difference in our results. Nevertheless, it is important to realize that the final stage of the transmitter, and the coupling circuit to the antenna, contribute greatly to the overall efficiency of the system. If the transmitter output is from the emitter (or source or cathode), the output impedance should be as low as possible. If the transmitter output is from the collector (or drain or plate) the output impedance should be as high as possible. Impedance matching makes no sense here.
Referring to your previous post, it is not quite correct to say that radiation efficiency depends only upon the radiation resistance and the loss resistance, and not on the antenna capacitance. This viewpoint is a little bit like putting the cart in front of the horse.
In order to transmit intelligence, it is necessary for the antenna to have some bandwidth. A lossless antenna will have zero bandwidth and transmit no intelligence. It will be possible to transmit only the carrier with a lossless antenna, but no sidebands, which contain the intelligence. In order to transmit intelligence, the antenna must have losses. It would be preferable if the losses were due mostly to radiation resistance, but this does not happen in Part 15 AM. From the previous discussion, we know that we must include the generator losses to calculate the antenna bandwidth. The higher the antenna capacitance, the less will be the losses required for a particular bandwidth.
I mentioned in a previous post that the FCC staff considers a lot of things illegal that are not specifically mentioned in Part 15. Some time ago, I wanted to make a highly-efficient (a few percent) antenna for Part 15 AM. The OET laboratory staff rejected all of my proposed improvements. So, any antenna I might construct will look like an ordinary whip. A 1 1/4 inch TV mast, or, at the outside, a 3 inch diameter lampost, would be the biggest diameter I would consider. I was originally thinking of a diameter much bigger than that, with an additional capacitive hat. Now, I would not consider anything like that, even if it is not specifically forbidden by the letter of the law in Part 15. I would not want to have to explain to an administrative law judge why my antenna design should be allowed.