# Determining one exact antenna length for a whole band (e.g. FM/AM broadcast, Bluetooth and others)

How does a single FM antenna length work in the entire FM frequency band range, when there are theories which state that the antenna size should always be close to wavelength/4 for proper reception & transmission?

For example: The FM frequency band ranges from 88 MHz to 108 MHz. How will an FM antenna length will match all the frequencies from 88 MHz to 108 MHz? Does the antenna length scale itself within that range or how does it work?

• Hello and welcome to ham.stackexchange.com! Commented May 10, 2020 at 19:01
• In order to make sure questions get clear and rankable answers, it's important to ask only one question in a single question post. I've removed the second shorter question you included, about transmission range; you can ask it separately, but please give more detail when you do. Commented May 10, 2020 at 21:02
• The question is specific to the 88 - 108 MHz FM band. Hence the title is to be altered. Commented May 11, 2020 at 3:58
• This question was already answered by Andy's answer (scroll down to end of answer) on electronics.SE: An antenna isn't for only a single frequency. There might be a single frequency for which it's optimal, but that doesn't mean other frequencies won't work. Commented May 16, 2020 at 9:53

Design goals for a receiving antenna and a transmitting antenna can be very different. For transmitting antennas, the goals are generally efficient power transfer, directivity (a.k.a. "gain"), and efficiency. Directivity has to do with the radiation pattern of the antenna (omnidirectional or aimed in a certain direction); efficiency generally has to do with the size of the antenna relative to the wavelength of the transmitted signal.

For efficient power transfer, the impedance of the transmission line and the load have to be matched to the output impedance of the transmitter. In ham radio terms, the SWR should be as close to 1:1 as possible. If the load (the transmission line and antenna) is not perfectly matched to the source (the transmitter), then reflected power makes the output current and voltage rise. Transmitters can often tolerate a certain degree of mismatch, but beyond that the output power must be reduced, or the transmitter may be damaged.

The impedance of an antenna varies with frequency. Transmitting antennas are typically tuned so that the mismatch is lowest at the center of the frequency band of interest. The changing impedance of the antenna, combined with the degree of mismatch that the transmitter will tolerate, gives a range of frequencies that the transmitter, feed line, and antenna can be used to transmit at full power.

For receive-only antennas, efficient power transfer is not necessarily a concern. Impedance bridging, where the load impedance (of the receiver) is chosen to be much larger than the source impedance (of the antenna and transmission line), may be enough. Impedance bridging maximizes the signal voltage rather than the signal power. Maximum power transfer is generally unnecessary in a broadcast receiver because amplifier circuits can usually be designed to have as much gain as necessary. (The limiting factor in how much gain can be used generally has to do with noise generated by the receiver itself, which is usually not a concern for a broadcast receiver.) In an impedance bridging situation, as used by a typical FM broadcast antenna and receiver, small changes in the impedance of the antenna don't matter very much, because the input impedance of the receiver is much larger than that of the antenna and feed line anyway. So a receive-only antenna can have a much broader bandwidth than a transmitting antenna, which needs to be concerned with efficient power transfer.

• This is only true at HF, where you're externally noise limited. But by 100 MHz your amplifier noise probably dominates, so maximum power transfer is essential for best signal to noise ratio. Adding gain does not improve the SNR. Commented May 11, 2020 at 15:23
• @tomnexus so are you saying that the broadcast FM whip antenna on my car is tuned for a low SWR, and if I were to substitute a longer whip then it wouldn't work nearly as well? Commented May 11, 2020 at 16:34
• longer - depends on a lot of things. But shorter - yes it wouldn't work as well. FM antennas on a car are a compromise because too long is a pain, wastes fuel etc. Everything you say is true for a 1 metre whip for 0.5-30 MHz. It's connected to a high gain, high impedance amplifier and it is still externally noise limited, most of the time. But at 100 MHz, or 144, you design for best match. It just happens that you can cover ~20% bandwidth without much loss of performance at the edges. Commented May 11, 2020 at 18:55
• @tomnexus that would explain why the radio in my car picks up FM broadcast stations better than the boom box in the garage, or the FM radio built into my MP3 player that uses the headphones as an antenna. I'll edit my answer. Commented May 11, 2020 at 19:17
• @rlocher Let me be the first to point out that this is an academic argument! The difference between 15 cm and 75 cm whip is not as big as the difference between radios. In a city near a 10+ kW FM transmitter either will work.Car radios are often quite good quality, and don't have to optimise for power consumption. I'm constantly amazed at how good they are, even with short stubby antennas. Commented May 11, 2020 at 20:47

FM antennas (the sort that come with your receiver) are trimmed for best performance in the middle of the FM band. Because that band is not very wide, and the signals they receive are generally not weak, they work adequately well at the low and high ends of the band.

For picking up weak signals, you'll use a broadbanded FM antenna on a mast, where there are enough antenna elements in the design to allow adequate operation all the way across the band.

It appears that only reception on the 88 -108 MHz FM is being referred to.

With high power FM transmitters located in the heart of a city, a 75 cm length of wire would suffice to receive stations across the band. In the case of a receiver with a telescopic antenna, it's length could be adjusted, if required, to receive weaker signals.

In fringe areas, a broadband log-periodic antenna, covering 88-108 MHz, would be the right solution.

The answer to your question would be that reception across the 88-108 MHz FM band would be possible using a single log-periodic antenna specifically designed for the FM band and having a bandwidth of 20 MHz.

More details on log-periodic antennas at

Bandwidth of an antenna is primarily dependent on the design of the antenna and the electrical radius of the active element(s).

With FM radio stations, the high power 1 - 100+ kilowatt transmitters, allows a lot of loss with respect to the receive antennas: any approximately eighth wavelength wire or longer will adequately receive any station in range(20 to 150 miles depending on terrain and antenna gain or loss).

Most car antennas are given a length the corresponds close to the center of the FM band. The power output of the stations make up the difference.

In the AM band the output power tends to be lower overall( .01 - 5KW+), since the band will travel longer distances. AM Reception is done in car radios through the use of loading coils applied to the FM antenna. The efficiency of the antenna + loading coils is about 5 to 60 percent of the power available in the airwaves. Reception depends on propagation factors.

Bluetooth is a whole different story, it operates on the 2.4 GHZ spectrum with a power in the milliwatt power range. To minimize interference with WiFi occupying the same bands, it produces a signal that hops through all of the allocated frequencies in such a way to cause the minimal amount of disruption to the WiFi channels it conflicts with.

Now back to antenna bandwidth:

There are very wide designs based on angles like the rhombic design (high gain, highly directional, 1+ decade of 3db bandwidth)

The length specified wideband: (each band must be represented as a length in the elements of the design)

log-periodic(Medium gain and directional)

fan dipole

I would be failing to represent all widebands, I am sure I skipped many, if I did not include the End-Fed-Half-Wave(EFWH). The high impedance of an EFWH makes it a perfect longwire antenna for evenly divisible frequencies.

Back to the electrical radius(where surface area dominates):

The bowtie UHF, similar in concept to VHF rabbit ears: Four, or two, short sticks emanating from a common point and spaced appropriately. The bounding frequencies of this design are dependent on the length and size of the elements.

For a dipole, the bandwidth is most dependent on the size of the conductor, but may be extended by introducing a second(or more wires) of the same length using (relative to wavelength) small spacers.

For microwave frequencies like 2.4GHz when space is a consideration, microstrip fractals tend to replace conventional antennas. The fractals offer a wider bandwidth and more electrical length, therefore more bandwidth for a smaller design.

Maximizing surface area leads to a higher bandwidth antenna.

• So, Microwave frequency band and WiFi frequency band are the same, around 2.4GHz? Won't this cause interference when placed nearby each other? Commented May 15, 2020 at 9:19
• Yes, both WiFi and Bluetooth operate on the same frequencies. The difference is the Bluetooth hops across all 3 distinct/12 available channels assigned in the 2.4 GHz ISM band, using a tiny amount of the bandwidth available. This does cause some occasional dropped packets on the WiFi, but that is normal operation on WiFi. A leaky microwave oven(or neighbors WiFi) will do the same thing. Error detection and correction and retries are built into the 802.11g(n) standards to gracefully handle the dropped or corrupted frames. Commented May 15, 2020 at 9:41
• Thank you. Two questions : 1. After you mentioned 2.4GHz ISM band, I checked the specification of the Band. It seems to have 14 channels. But you are saying 3 / 12 available channels. What does it mean? And What do you mean by when you said "using a tiny amount of the bandwidth available?" What is the value range of the tiny bandwidth. Please help to clarify Commented May 15, 2020 at 9:44
• The total number of channels in the US is 12. The number varies around the world. Due to the frequency overlap, there are only three distinct non-overlapping channels in the US. The amount of data in tiny, depends on the application, mouse movements are usually small, while speakers may use much more bandwidth. It depends on the application. Commented May 15, 2020 at 9:51
• My apologies it is 11 not 12 in the US. Commented May 15, 2020 at 9:58