Finkenzeller K.RFID handbook.2003
.pdf188 6 CODING AND MODULATION
signals (sinusoidal oscillation). However, there is one significant difference between keying and analogue modulation. In keying, a carrier takes on the amplitude uˆ 0 in the unmodulated state, whereas in analogue modulation the carrier signal takes on the amplitude uˆ m in the unmodulated state.
In the literature the duty factor is sometimes referred to as the percentage carrier
reduction m during keying: |
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For the example in Figure 6.7 the duty factor would be m = 0.66 (= 66%). In the case of duty factors <15% and duty factors >85% the differences between the two calculation methods can be disregarded.
The binary code signal consists of a sequence of 1 and 0 states, with a period duration T and a bit duration τ . From a mathematical point of view, ASK modulation is achieved by multiplying this code signal ucode(t ) by the carrier oscillation uCr(t ). For duty factors m < 1 we introduce an additional constant (1 − m), so for this case we can still multiply uHF(t ) by 1 in the unkeyed state:
UASK(t ) = (m · ucode(t ) + 1 − m) · uHF(t ) |
(6.4) |
The spectrum of ASK signals is therefore found by the convolution of the code signal spectrum with the carrier frequency fCr or by multiplication of the Fourier expansion of the code signal by the carrier oscillation. It contains the spectrum of the code signal in the upper and lower sideband, symmetric to the carrier (Mausl,¨ 1985).
A regular, pulse-shaped signal of period duration T and bit duration τ yields the spectrum of Table 6.1 (see also Figure 6.8).
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ASK modulator |
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Figure 6.7 The generation of 100% ASK modulation by the keying of the sinusoidal carrier signal from a HF generator into an ASK modulator using a binary code signal
6.2 DIGITAL MODULATION PROCEDURES |
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Table 6.1 Spectral |
lines for a pulse-shaped modulated carrier |
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Carrier oscillation |
fCR |
uHF · (1 − m) · (T − τ )/T |
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uHF · m · sin(π · τ /T ) |
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fCR ± 2/T |
uHF · m · sin(2π · τ /T ) |
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3rd spectral line |
fCR ± 3/T |
uHF · m · sin(3π · τ /T ) |
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nth spectral line |
fCR ± n/T |
uHF · m · sin(nπ · τ /T ) |
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Figure 6.8 Representation of the period duration T |
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Amplitude
Digital signal
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Figure 6.9 The generation of 2 FSK modulation by switching between two frequencies f1 and f2 in time with a binary code signal
6.2.22 FSK
In 2 frequency shift keying the frequency of a carrier oscillation is switched between two frequencies f1 and f2 by a binary code signal (Figure 6.9).
The carrier frequency fCR is defined as the arithmetic mean of the two characteristic frequencies f1 and f2. The difference between the carrier frequency and the
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6 CODING AND MODULATION |
characteristic frequencies is termed the frequency deviation fCR:
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From the point of view of the time function, the 2 FSK signal can be considered as the composition of two amplitude shift keyed signals of frequencies f1 and f2. The spectrum of a 2 FSK signal is therefore obtained by superimposing the spectra of the two amplitude shift keyed oscillations (Figure 6.10). The baseband coding used in RFID systems produces an asymmetric frequency shift keying:
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2 |
In these cases there is also an asymmetric distribution of spectra in relation to the mid-frequency fCR (Mausl,¨ 1985).
6.2.32 PSK
In phase shift keying the binary states ‘0’ and ‘1’ of a code signal are converted into corresponding phase states of the carrier oscillation, in relation to a reference phase. In 2 PSK the signal is switched between the phase states 0◦ and 180◦.
Mathematically speaking, the shift keying of the phase position between 0◦ and 180◦ corresponds with the multiplication of the carrier oscillation by 1 and −1.
The power spectrum of a 2 PSK can be calculated as follows for a mark-space ratio τ /T of 50% (Mansukhani, 1996):
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where P is transmitter power, Ts |
is bit duration (= τ ), f0 is centre frequency, and |
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sin c(x) = (sin(x)/x). |
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Figure 6.10 The spectrum of a 2 FSK modulation is obtained by the addition of the individual spectra of two amplitude shift keyed oscillations of frequencies f1 and f2
6.2 DIGITAL MODULATION PROCEDURES |
191 |
The envelope of the two sidebands around the carrier frequency f0 follows the function (sin(x)/x)2. This yields zero positions at the frequencies f0 ± 1/Ts, f0 ± 2/TS, f0 ± n/TS. In the frequency range f0 ± 1/TS, 90% of the transmitter power is transmitted. See Figure 6.11.
6.2.4 Modulation procedures with subcarrier
The use of a modulated subcarrier is widespread in radio technology. In VHF broadcasting, a stereo subcarrier with a frequency of 38 kHz is transmitted along with the baseband tone channel. The baseband contains only the monotone signal. The differential ‘L–R’ signal required to obtain the ‘L’ and ‘R’ tone channels can be transmitted ‘silently’ by the modulation of the stereo subcarrier. The use of a subcarrier therefore represents a multilevel modulation. Thus, in our example, the subcarrier is first modulated with the differential signal, in order to finally modulate the VHF transmitter once again with the modulated subcarrier signal (Figure 6.12).
In RFID systems, modulation procedures using a subcarrier are primarily used
in inductively coupled systems in the frequency ranges 6.78 MHz, 13.56 MHz |
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27.125 MHz and in load modulation for data transfer from the transponder to |
the |
reader. The load modulation of an inductively coupled RFID system has a similar effect to ASK modulation of HF voltage at the antenna of the reader. Instead of switching the load resistance on and off in time with a baseband coded signal, a low frequency subcarrier is first modulated by the baseband coded data signal. ASK, FSK or PSK modulation may be selected as the modulation procedure for the subcarrier. The subcarrier frequency itself is normally obtained by the binary division of the operating frequency. For 13.56 MHz systems, the subcarrier frequencies 847 kHz (13.56 MHz ÷ 16), 424 kHz (13.56 Mhz ÷ 32) or 212 kHz (13.56 MHz ÷ 64) are usually used. The modulated subcarrier signal is now used to switch the load resistor on and off.
The great advantage of using a subcarrier only becomes clear when we consider the frequency spectrum generated. Load modulation with a subcarrier initially generates
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Figure 6.11 Generation of the 2 PSK modulation by the inversion of a sinusoidal carrier signal in time with a binary code signal
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6 CODING AND MODULATION |
Subcarrier 212 kHz
Data stream − baseband coded |
ASK-Modulation 1 |
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Figure 6.12 Step-by-step generation of a multiple modulation, by load modulation with ASK modulated subcarrier
two spectral lines at a distance ± the subcarrier frequency fH around the operating frequency (Figure 6.12). The actual information is now transmitted in the sidebands of the two subcarrier lines, depending upon the modulation of the subcarrier with the baseband coded data stream. If load modulation in the baseband were used, on the other hand, the sidebands of the data stream would lie directly next to the carrier signal at the operating frequency.
Signal
f T = 13.560 MHz
0 dB
Carrier signal of the reader, measured at the antenna coil
Modulation products by load modulation with a subcarrier
13.348 MHz |
13.772 MHz |
−80 dB
f f H = 212
Figure 6.13 Modulation products using load modulation with a subcarrier
6.2 DIGITAL MODULATION PROCEDURES |
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In very loosely coupled transponder systems the difference between the carrier signal of the reader fT and the received modulation sidebands of the load modulation varies within the range 80–90 dB (Figure 6.13). One of the two subcarrier modulation products can be filtered out and demodulated by shifting the frequency of the modulation sidebands of the data stream. It is irrelevant here whether the frequencies fT + fH or fT − fH are used, because the information is contained in all sidebands.
RFID Handbook: Fundamentals and Applications in Contactless Smart Cards and Identification, Second Edition
Klaus Finkenzeller Copyright 2003 John Wiley & Sons, Ltd.
ISBN: 0-470-84402-7
7
Data Integrity
7.1The Checksum Procedure
When transmitting data using contactless technology it is very likely that interference will be encountered, causing undesired changes to the transmitted data and thus leading to transmission errors (Figure 7.1).
A checksum can be used to recognise transmission errors and initiate corrective measures, for example the retransmission of the erroneous data blocks. The most common checksum procedures are parity checks, XOR sum and CRC.
7.1.1Parity checking
The parity check is a very simple and therefore a very popular checksum procedure. In this procedure a parity bit is incorporated into each byte and transmitted with it with the result that 9 bits are sent for every byte. Before data transfer takes place a decision needs to be made as to whether to check for odd or even parity, to ensure that the sender and receiver both check according to the same method.
The value of the parity bit is set such that if odd parity is used an odd number of the nine bits have the value 1 and if even parity is used an even number of bits have the value 1. The even parity bit can also be interpreted as the horizontal checksum (modulo 2) of the data bit. This horizontal checksum also permits the calculation of the exclusive OR logic gating (XOR logic gating) of the data bits.
However, the simplicity of this method is balanced by its poor error recognition (Pein, 1996). An odd number of inverted bits (1, 3, 5, . . .) will always be detected, but if there is an even number of inverted bits (2, 4, 6, . . .) the errors cancel each other out and the parity bit will appear to be correct.
Example
Using odd parity the number E5h has the binary representation 1110 0101 p = 0.
A parity generator for even parity can be realised by the XOR logic gating of all the data bits in a byte (Tietze and Schenk, 1985). The order in which the XOR operations