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.

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.

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.

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