Square Wave Frequency Modulation Systems
5.3 PFM and SWFM Demodulation
5.3 PFM and SWFM Demodulation
[(ncoc +ka)m) t - k t o mT /2
]
(5.4)
Similarly, the expression for SWFM is [84]
00 00
f i t ) = ADj^ Sine (imD) J|t| {np)txp{j(ncoc + kcon)i\ (5.5)
The spectra are plotted in Fig. 5.2 and the general characteristics attributed to PTM spectrums (section 4.3.3) can be identified. The presence of the baseband component in PFM signal indicate that information can be recovered directly from the PFM signal. The strength of the baseband presence is determined by the modulation index, carrier frequency, pulse width and the modulating frequency.
For a multi-tone modulating signal, the baseband frequency response depends on the relationship between the pulse width and the modulating signal. Provided that
the original baseband signal will be present in the PFM signal without any amplitude distortion [82]. The sideband structure of the PFM signal is slightly asymmetric compared to conventional FM spectrum. However, Carson’s rule [85] can still be used to give an upper limit of spectrum spreading.
The baseband component and the even carrier harmonics are not present in a SWFM signal, provided the square wave duty cycle is 50%. However, in practice the duty cycle tends to deviate slightly from the 50% value resulting in a small baseband and even harmonic presence [82]. Amp. fc < ► 2 (Af+fm) 2(3 Af+fm) (a) SWFM Amp. Baseband fm fc 4--- ► 2 (4/¥m) 2(24/%) 2(3 Af+fm) (b) PFM
Figure 5.2 SWFM and PFM spectrum distribution.
The demodulation techniques of PFM and SWFM can be deduced from their spectral characteristics. Ordinary FM demodulation techniques may be adopted, locked on to the carrier or its harmonics using a phase locked loop (PLL). However, this approach usually
results in limited linearity and noise performance as a consequence of selecting only a restricted spectral slice. The presence of a distortionless baseband component indicate that information can be recovered directly from the PFM signal and baseband recovery is indeed the technique widely employed in PFM and SWFM demodulation [70].
The simplest form of demodulation would be to recover the baseband component directly from the incoming PFM signal. However, this technique generates poor SNR performance as both leading and trailing edges of the PFM signal are affected by noise. Therefore, in PTM systems, the incoming signal is regenerated at the receiver before employing baseband recovery [81].
The PFM regenerator consists of a threshold detector and a constant width pulse generator. The incoming PFM or SWFM signal is passed through a threshold detector with a threshold crossing set at half the pulse amplitude for optimum pulse detection, as will be explained in section 5.4.2. The output of the threshold detector is fed to a monostable in order to trigger constant width pulses at the leading or lagging edge. The baseband component of the regenerated PFM signal can be recovered by employing a low pass filter (see Fig. 5.3).
incoming
SWFM/PFM
signal Threshold recoveredbaseband
detector generatorPulse
The transmitted PFM pulse width is determined by the required level of signal performance and the available channel resources, as will be shown later in the chapter. It was stated earlier that one of the parameters which influence the strength of the baseband component present in a PFM signal, is the pulse width. Therefore, when employing baseband recovery technique, the width of the regenerated PFM pulse influences the recovered signal power level.
The baseband signal power at the output of the PFM regenerator can be optimised by choosing an optimum width for the regenerated pulse train. The relationship between baseband signal power and the regenerated pulse width can be determined by further
examining the PFM spectral expression (Eqn. 5.4). Hence, the baseband signal power Sb,
can be expressed as:
where d is the duty cycle of the regenerated signal, R is the sampling ratio and other
symbols are as defined before.
The above equation is plotted against d, for a range of R values, in Fig. 5.4. Here the
baseband signal power is normalised to the amplitude of the carrier frequency and a /? value of 1 is assumed. A parabolic increase can be identified for the baseband signal
power as d increases. The baseband distortion level dictates the R value in PTM systems
(see section 5.5) and therefore, for a chosen R, the baseband signal power is maximised
by optimising the duty cycle of the regenerated PFM pulses.
A= R=2 R=3 R= 4 fl=5 c Q. o •o -15 -20 100 Duty ratio, %
Figure 5.4 Baseband signal power variation in regenerated PFM signals.
In SWFM systems, it is also possible to generate pulses at both the leading and lagging edges of the SWFM signal, resulting in a 3 dB SNR improvement compared to single edge detection technique [81]. The sampling ratio requirements are also lowered by nearly half, as will be explained in section 5.5.2. Practical circuit implementation of the double-edge demodulation is particularly simple using a number of EX-OR gates in a logic rectification and delay circuit. The logic circuit diagram and the associated signal waveforms are illustrated in Fig. 5.5, where pulses are generated at both the rising and falling edges of the SWFM signal. The pulse width is determined by the number of gates, and the propagation delay of each gate, included in the delay path [82].
LOW logic
(a) logic circuit diagram
propagation delay pulse width X : SWFM signal Y : delayed SWFM signal S rising-edge triggered pulse
falling-edge Z : double-edge output signal
triggered pulse
(b) illustrated waveforms