In the wireless world, antennas are used to transmit radio frequency energy from location A to location B in the most efficient manner. That is, they radiate the power that is fed to them. When dealing with UHF RFID systems, this hypothesis is true. However, at 13.56 MHz, the picture is quite different.

The wavelength in free space at 13.56 MHz is 22.12 meters. A standard ground plane antenna has a length of one-quarter of the wavelength, which is 5.53 meters. It has a radiation resistance close to 50 Ω. In the world of 13.56 MHz RFID systems, it's unlikely to come close to such dimensions. Even if it does occur, the amount of radiated power will remain quite small.

Consider the following example: a loop antenna with an area that is one square meter. The radiation resistance is given by:

In this case, the equation yields RR = 130 milliOhms, but it would probably require four meters of wire to construct the loop, assuming a square shape. If it doesn't radiate energy, then how can it be transferred to the tag it intends to communicate with?

The answer is magnetic coupling. Some people refer to RFID base stations as “couplers;” a term that is quite appropriate in this case as the RFID system (antenna plus tag) can be considered as a loosely coupled transformer, with the base station antenna acting as the primary of this transformer. This concept is of paramount importance for the system designer. The tag and the base station “antenna” constitute the system, and cannot be studied separately. Another point to remember is that if 5 W are fed to a loop RFID “antenna,” these 5 W, being not radiated, will have to be dissipated somewhere.

### Coupled circuits

In the preceding paragraph, the concept of a loosely coupled transformer was surreptitiously introduced. While the complete theory of coupled circuits is beyond the scope of this document, involving quite lengthy calculations, it is possible to somewhat alleviate this burden by using a circuit simulator like SPICE. Now, it's necessary to define the characters, and assign a role to each of them.

The first character is the base station antenna. In order to maximize the communication range with the tag, it is necessary to create the strongest possible magnetic field so that the tag will be able to pick up enough power in order to energize itself. Since the magnetic field from the loop is proportional to the current flowing through the conductor that actually constitutes the loop, this current has to be maximized.

The second character is the tag. The tag wants to be able to collect in as much energy as possible from the ambient magnetic field generated by the base station loop antenna. This energy-gathering capacity must, therefore, be maximized as well.

These goals can be achieved in various ways. However, the next paragraphs will show that the art of RFID system design requires a careful understanding of the pitfalls and conflicts that will inevitably arise. These characters are not team players. More often than not they are unfair to each other.

### The Q conflict

From the base station antenna point of view, there is only one way to have a strong current flowing through the conductors: the loop has to be tuned and made resonant. The same holds true for the tag. Here comes the first problem. If there is no data to transmit back and forth, the Q factor of both devices could be increased up to the tolerances or the components used. This would be the best way on both sides to fulfill the characters' requirements. However, if a system is designed to be compliant with the ISO 15693 standard, there is a subcarrier at 423 KHz, possibly on/off keyed if the single subcarrier modulation is used at a data rate of 27 kbps. For the ISO 14443 standard, the subcarrier is at 847 kHz, and the data rate is 106 kbps. A tuned circuit acts as a bandpass filter. Enough bandwidth must be left for the subcarrier and its modulation sidebands.

### Minimum bandwidth requirements

Let's take a look at how the tag modulation sees the tag antenna. In most cases, a tag can be modeled as a parallel resonant circuit (first-order approximation). The modulation spectrum can be approximated quite accurately. In Figure 1, the tag frequency response for a Q value of 12 (deep green curve) is represented, along with the ISO15693 single subcarrier/ASK power spectrum for a pseudo random bit sequence. The tag modulation is attenuated by about 1 dB, which is acceptable.

However, if the tag has a Q factor of about 16 (red curve), the modulation peaks are attenuated by 3 dB. This is a limit that should not be trespassed otherwise the communication range between the base station and the tag could be severely affected. In practice, the optimal Q value will be chosen between 9 and 16, depending on other system constraints that are going to be analyzed later.

The calculation of the modulation power spectrum is more complicated in the frequency-shift keying (FSK) double subcarrier case. However, it yields essentially the same results, as can be seen in Figure 2. For the ISO 1443 standard, the modulation power spectrum is similar to an ASK spectrum for Part A and Part B. The only difference is the subcarrier frequency, which is higher. This will, of course, change the Q requirement for the tag as it will have to be lower. The tag optimum Q will range from 4 to 9.

A set of rules can now be defined for the minimum bandwidth requirements, as seen from the tag point of view:

B = FTOL + FSUB + data rate (for single subcarrier/ASK mode)

BW = FTOL + FSUB + data rate (for double subcarrier FSK or BPSK mode)

Where:

BW is the minimum bandwidth, that is fc/2*Q, fc = 13.56 MHz.

FTOL is the frequency tolerance of the tuned circuit.

FSUB is the subcarrier frequency.

Also, there is:

The base station antenna point of view is exactly the same as the tag antenna point of view. In fact, the base station antenna must have enough bandwidth to recover the tag modulation. The base station sends commands to the tag by direct modulation of the 13.56 MHz carrier. The protocol does not use a subcarrier for the base station to tag communications. For both ISO standards, the data rates and modulation techniques used yield spectrums that have much smaller bandwidths than the tag. Therefore, for all practical purposes, the minimum system bandwidth requirements are set by the tag modulation spectrum. However, it should be emphasized that this assertion is only valid when the tag and the base station antenna are loosely coupled. Note that these bandwidth requirements only are a good starting point. Always remember that only experimental results should have the final word.

### The coupling factor (K)

Now it's time to look closer at the loosely coupled transformer hypothesis. The minimum bandwidth requirements are valid only if the coupling factor between the tag and the base station antenna is kept low. As an example, consider some simulation results using the schematic depicted in Figure 3.

On the left, is a model of a base station antenna. On the right, is a model of a tag. For the sake of simplicity, both devices are identical, and the base station antenna is, for the time being, driven by a perfect current source that will not change its intrinsic properties. Because we are dealing with a magnetic coupling problem and know that the magnetic field induced by a coil is proportional to the current flowing through it, we shall visualize this current. Both the antenna and tag are tuned to 13.56 MHz. In the middle, the linear coupling factor k = 0.1 is introduced. The Q factor of both devices is equal to 9.

If the linear coupling factor were kind, then the result would be that depicted in Figure 4a. Unfortunately, “k” is not kind and the actual result is depicted in Figure 4b. Instead of having a single peak in the frequency response, there are two bumps. One corresponds to the tag tuned circuit, and the other to the base station antenna. It looks as if there were two different resonant frequencies, well separated. In fact, this annoying effect is what makes possible the design of a class of RF filters, made with cavities or helical resonators, slightly mistuned and carefully coupled to one another until the desired frequency response is obtained.

In this case, it's possible to imagine that the effect of the coupling factor will have serious consequences on the design of a usable RFID system. To begin with, let's look at a multiple run simulation, where the coupling factor is increased from 1% to 20% in a logarithmic fashion (Figure 5).

It is obvious that, for a coupling factor higher than 10% (corresponding to the second largest frequency spreading illustrated in Figure 5), the tag and the base station will have difficulties communicating with one another. The paradox is that such communication problems will arise in a situation where intuition dictates the opposite, e.g., when the tag and the base station are close to each other. As a result, this situation must be avoided. The good news is that through careful system design it is possible to avoid this scenario. Remember also that if the coupling factor is too low, no energy transfer will be possible, and the system will not work. One can now understand why it is not possible to design an RFID system by considering only one side of the problem, either the tag or the base station. Because of the coupling factor, both sides must be considered at once.

### Calculating coupling factor

Since the coupling factor depends only on geometrical parameters, the inductance values and the number of turns of the coils, for example, are not involved in calculating its value. Consider the diagram in Figure 6.

On the left, the base station antenna coil has a diameter d1 = 2 × r1. On the right, the tag antenna coil has a diameter d2 = 2 × r2, tilted along the axis by an angle α. The coupling factor can be expressed as:

Of course, this equation is valid only for circular coils, but the design guidelines that will be inferred from it are valid whatever the shape. From the equation, it is obvious that the coupling factor will be maximum when r1 = r2.

### Avoiding the coupling factor

A number of different strategies can be employed to avoid a situation were the coupling factor would be too high:

• The system can be designed whereby the base station antenna is much larger than the tag coil. This is generally the case for long-range systems.

• For a short-range system, where the sizes may be comparable, the communication range must be sacrificed to system reliability. This can be done by using a much lower Q for the tags. One can also deliberately mistune the tags.

• The most critical situation is for medium-range systems, where antenna sizes are not sufficiently different to prevent coupling factor frequency spreading at short range. In this case, one is advised to maintain, by means of a physical obstacle, a minimum distance between the tag and the antenna in order to maintain the system in a functional state. Also, the output power stage driving the base station antenna must be resistant to mismatch. Even medium-power stages can die quickly if they do not see the right load.

However, for short- and medium-range systems, the use of diodes will mitigate the coupling factor's actions. All tags have a maximal power supply voltage. To protect the chip from an overvoltage condition, chip manufacturers usually place a pair of zener diodes that start to conduct before the limit is reached in parallel with the coil inputs. When the diodes are placed in strong conduction, they completely destroy the tag Q factor. This is important because, in most cases, the coupling factor's deleterious effects are sufficiently alleviated to maintain the system in a functional state.

Denis Ruffieux is an application engineer at Melexis RFID business unit. He is responsible for hardware development and customer support. Ruffieux holds an engineering degree in electronics from Ecole d'Ingenieur du Canton de Vaud in Yverdon les Baines, Switzerland.