The Chu-Herrington theorem provides interesting insight into antenna behavior. The theorem states that for an antenna of a given size there is a minimum limit to the Quality Factor (Q). This limit is called the Chu Limit.
The selectivity of an LC tank circuit is typically defined by Q. A tank circuit made with low-loss components will have a high Q. Antennas have Q as well; they can be broadband or selective just like a tank circuit. Generally, antennas are fairly broadband, which leads to a lower Q. This does not mean the antennas are “lossy” in the usual sense, however. They lose power by radiating, which is exactly what they are intended to do. So for an antenna, a low Q is by no means a bad thing.
Broadband antennas have two advantages:
- They are less affected by the tolerances of the parts used.
- They are less susceptible to changes in resonant frequency by outside influences.
However, there is another important factor that comes into play with bandwidth. A narrow-bandwidth antenna will not be able to transfer data as quickly as wideband one. The greater the Q, the sharper the bandwidth. Therefore, it is preferable that the Q not be too great.
The Limit on Bandwidth
As an example of the significance of bandwidth, let us consider an AM radio. Each AM station is allotted 10 KC to work in. The audio spectrum is roughly 20 KC broad, but 10 KC is sufficient to allow most of the usable frequency spectrum through; many of the higher frequencies are nonessential.
If the LC circuitry in our AM radio has a bandwidth of 10 KC, we will hear only the station we are tuned to — no more and no less. But as we increase the Q, we will start losing the edges of the audio spectrum. The sound quality will get worse. If we continue to narrow the bandwidth, eventually we will lose too much of the frequency spectrum and the signal will be unrecognizable.
If an antenna is too small, the typical way to increase radiation performance is to retune it with the aid of external inductors and/or capacitors. The antenna becomes a more efficient LC circuit in its own right, and the Q goes up. It also radiates less efficiently than a larger antenna would.
The Chu limit states that for an electrically small antenna of a given size, there is a minimum Q that will be obtained. The more we shrink the antenna, the more we rely on external inductors and capacitors to make it work. This means the Q of the antenna goes up and the bandwidth narrows.
For small devices, such as a cell phone, if our allotted antenna size is too small, the bandwidth will suffer in our effort to keep the antenna radiating well enough to be usable.
Ways Around the Chu Limit
The Chu limit is theoretical. The Q of any resonant circuit can be dropped with the aid of a resistor.
In home AM receivers in the 1930s, this was a popular solution to an annoying problem. The long external antenna required for the receiver affected the tuning of the front end of the radio. The solution was to loosely couple the antenna to the radio (loss) and add a resistor shunting the antenna to the ground (more loss). This was an effective solution. The antenna was somewhat isolated by the loose coupling to the front end of the receiver, and the Q of the whole circuit was greatly reduced by the resistor. Since the front end was adequately broadband, the effect of the antenna on the tuning was minimized.
The trade-off was that the efficiency of the system suffered. A more efficient solution would be to tune the antenna independently from rest of the receiver using two tuning knobs. This was frequently done in the 1920s when radio was considered more of a novelty than an everyday device. In the end most users preferred simplicity of use over premium performance. With the advent of high-gain amplifiers, the lossy solution was deemed “good enough.”
Like those used in radios in the ‘30s, resistors are still used to broaden the bandwidth of modern antenna designs. However, the resistor will add loss, and the final results will be less efficient. Additional amplification may need to be added to make up for the loss. And also as in the early days of radio, to make up for loss of efficiency, throwing more amplification at the situation is a popular solution. Again similarly, we reach a practical limit on how much we can rely on increased amplification due to cost and noise.
Conclusions
AM radio reception tends to be far more forgiving than cell and Bluetooth applications. Adding losses with resistors to broaden the bandwidth of antennas can lead to poor overall performance and spotty coverage. There is simply less power available for the antenna application.
In the end, we face the following compromises:
- Is it better to sacrifice bandwidth or gain?
- Can we reliably and inexpensively add more amplification to the system without compromising the signal-to-noise ratio? Or should the size of the antenna be increased?
The application often defines the correct solution.
ARSI 
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