Coding and Modulation - RFID: Fundamentals and Applications in Contactless Smart Cards and Identification - page 186

characteristic frequencies is termed the frequency deviation f CR :

f 1 + f 2
2

f CR = | f 1 + f 2 |
2

f CR = ( 6 . 5 )

From the point of view of the time function, the 2FSK signal can be considered
as the composition of two amplitude shift keyed signals of frequencies f 1 and f 2 .
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:

T
2

τ = ( 6 . 6 )

In these cases there is also an asymmetric distribution of spectra in relation to the
mid-frequency f CR (Mausl, 1985).

6.2.3 2 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):

−

P · T s
2

[sin c 2 π(f − f 0 )T s + sin c 2 π(f + f 0 )T s ]

P(f) =

·

( 6 . 7 )

where P is transmitter power, T s is bit duration ( = τ ), f 0 is centre frequency, and
sin c(x) = ( sin (x)/x) .

f CR

P

f 1 f 2

Sidebands

f

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 f 1 and f 2