4 FSK Demodulators. 4.1 FSK Demodulation Zero-crossing Detector. FSK Demodulator Architectures Page 23
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1 FSK Demodulator Architectures Page 23 4 FSK Demodulators T he previous chapter dealt with the theoretical aspect of Frequency Shift Keying demodulation. The conclusion from this analysis was that coherent demodulation will theoretically perform best over non-coherent demodulation. But numerous unsolved problems arises when trying to actually implement the coherent demodulation principle. This motivates a search for non-optimal solutions to the demodulation problem that does not involve e.g. the phase reconstruction problem. This chapter therefore describes some of the approaches to 1200 baud FSK Demodulation found in literature, to judge the demodulation process from a more implementational point of view. This traverse through already applied demodulation techniques might seem a bit historical. But most attempts to implement monolithic modem circuits was reported in FSK Demodulation In the following a summary is presented of three selected papers dated from the middle eighties. The two first /Larber 84/ and /Apfel 84/ presents complete monolithic modem circuits whereas the third /Fleige 88/ only discusses the properties of complex digital processing for demodulation of FSK signals. The three papers are selected, because they represent three "levels" of complexity. I.e. the effort spent into constructing the demodulator is raising through the three papers Zero-crossing Detector Larber /Larber 84/ published in 84 a paper describing the design of "A monolithic 1200 Baud FSK CMOS Modem". Larber describes the demodulator part of the FSK modem as being the most critical section, and follows this statement with a selection of the zero-crossing demodulator for his circuit. The principle in a zero crossing detector is rather simple. The instantaneous frequency of the incoming carrier is determined by counting the number of its zero crossings per unit time. It is therefore crucial for this kind of detector to have a precise and high-performance front-end hard limiter that can deliver low-jitter zero crossings even for minimum level input carriers. The block diagram of the demodulator circuit is shown in Fig. 4.1.
2 Page 24 Chapter 4 Bias distortion trim Hard-Limited Signal Digital differentiator and rectifier Pulse Generator Switched Cap. + - Output Clock Fig. 4.1 Zero-crossing demodulator block diagram. The demodulator is made of a digital monostable, a switched capacitor low-pass and a slicer comparator Fig. 4.1 shows the zero-crossing demodulator. The hard-limited signal is digitally differentiated and rectified in order to create a pulse every time the carrier crosses zero. This is implemented as shown in Fig. 4.2 by a D-type flip-flop and an exclusive-or gate. The pulse thus obtained is used to a down counter to create a pulse of fixed duration. This is corresponding to converting the hardlimited FSK input to a Pulse Width Modulated (PWM) signal, from which the switched capacitor then extracts the base band component. The switched-capacitor is a fifth-order LC ladder whose amplitude response is approximately equal to a full-raised cosine function with linear phase, thus minimizing intersymbol interference. In D flip-flop Out Clock Fig. 4.2 Differentiator and rectifier. A positive pulse is generated for every input signal transition. To handle different baud rates, the demodulator is clock and logic programmable. For using 1200 baud fsk, a Hz clock is applied, which puts the SC- cutoff frequency at 438Hz. After the SC, the output is sliced by the comparator, to produce the demodulated output. This demodulator is as seen reconfigurable to several baud rates, whereby it may be an alternative for the DSC-ASIC demodulator. The switched capacitor is, however, by nature technology dependent, and further more it may become sensitive to digital line noise, if proper cautions are not taken to minimize digital interference in the DSC ASIC Product demodulator Instead of using a zero crossing detector for demodulation, Apfel proposes a more complex scheme in which he performs the demodulation process all digitally by use of small digital signal processor (DSP) cores /Apfel 84/. Apfel implements the system shown in Fig. 4.3
3 FSK Demodulator Architectures Page 25 Receive Carrier Analog ADC Decimation Bandpass Filters AGC A A x Interpolator Decision 90 deg phase shift at f c Fig. 4.3 The modem receiver with its hardware pieces dedicated to perform demodulation. Fig. 4.3 shows a block diagram of the DSP modem receiver. The analog lowpass eliminates energy which may alias into the passband after sampling by the analog-to-digital converter. The analog to digital converter operates at a 496 khz sampling rate, which thereby reduces the burden on the pre, which is only a single-pole RC lowpass. Mux and Tri-state drivers Bidirectional bus Write BUF buf RAM sel Mux zero Shift code Shift REG Mux sel Add/Sub Temp REG Output latch Fig. 4.4 Block diagram of the DSP modem ALU /Apfel 84/. The decimator then reduces the sampling rate down to the basic ALU signal processing rate, and following the decimator, a group-delay equalized bandpass removes out-of-band energy which may corrupt the demodulation process. The bandpass s as well as the decimation is all performed in the Signal processor core shown in Fig From the band-pass, the signal is fed trough an automatic gain control (AGC) which ensures that the received signal is of the proper signal strength to perform the demodulation. After gain control the actual demodulation is performed. The signal is passed trough a 90 deg. phase shift at f c (1700Hz) and is then multiplied by it self. This principle is known as a product demodulator, but some theory books may also refer to this principle as a quadrature demodulator, as the signal is modulated by its own quadrature. However the term product demodulator will be used here. The result from multiplication is a baseband term containing the desired digital information, and a useless double frequency component, which is removed by the following lowpass. The succeeding interpolator is included for accurately detecting the zero crossings, thus reducing phase jitter. This demodulator principle is closer to what can be used in the DSC Asic. The principle uses digital signal processing extensively, and the analogue front end is based on analogue-to-digital converters. Furthermore the signal processor core which executes the demodulator algorithm could be multiplexed by constructing faster versions which are capable of executing both the demodulation as well as a modulation algorithm. But unfortunately Apfel does not report any performance
4 Page 26 Chapter 4 characteristics for this demodulation principle, which could have made it an obvious choice for the DSC Asic project. In particular since standard programmable Digital Signal Processors have become available Complex Signal Processing. In 88 Fleige published an article concerning the properties of digital band pass s for FSK modems /Fleige 88/. In this paper Fleige takes a "step up in complexity" by using complex signal processing to perform the FSK demodulation. The schematic for this principle is shown in Fig. 4.5 exp( j ω o t ) FSK input Signal Bandpass lowpass Demod out Fig. 4.5 The demodulator principle suggested by Fleige /Fleige 88/. The FSK input signal in Fig. 4.5 is given by: /Fleige 88/ (4.1) where u(t)=1 for mark and u(t)=-1 for space. This signal is first multiplied by exp(-jω c t) where ω c is the center frequency between the to signal frequencies, i.e. 1700Hz for V.23. Both the real and imaginary part of this frequency shifted signal are ed by means of low-pass s resulting in the complex envelope signal. (4.2) From this signal it is possible to extract the original baseband signal u(t) by using the configuration shown in Fig cos( ω ο t) d dt FSK input s(t) x(t) + - u(t) d dt sin( ω ο t) Fig. 4.6 Detailed block diagram over the complex digital signal processing involved in the demodulation process. The derivation of the demodulation principle shown in Fig. 4.6 is as follows. Considering differentiation of the signal x(t): which can be manipulated to equal: (4.3)
5 FSK Demodulator Architectures Page 27 I.e the imaginary part of this product is equal to the baseband signal u(t), which is the tasks performed on the signal x(t) in Fig Fleige reports this scheme to have only one problem, namely the distortion introduced in the lowpass s, which is why he pais a lot of attention to constructing phase linear FIR s and sample reductions. 4.2 Summary Three "historical" methods of FSK demodulation has been presented. Ideally the principles should be simulated and compared in order to form a basis for comparison to the modem solution which is to be constructed later. However due to the fact that all these demodulator circuits have been optimized in the intervening years, for use in other industry products, it would be a doubtful task to merely simulate these demodulator configurations and conclude upon this simulation. This is because minor unreported improvements might have changed the picture partly or completely. In stead the demonstrated demodulation principles are used as inspiration for defining a new On- Line arithmetic CORDIC based architecture for the demodulation process. This is treated in more details in chapter 7, but before the idea can be presented it is necessary to gain some insight into the subjects CORDIC and On-Line arithmetic. Therefore the following two chapters take a sort of "jump to something completely different" 1. (4.4) 1 Which, as will be shown in chapter 7, is not that completely different.
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