Synthesis and Study of Digital Frequency Modulator-Demodulator

Journal of Communications Technology, Electronics and Computer Science, Issue, 7 ISSN 47-9X Synthesis and Study of Digital Frequency Modulator-Demodulator Boyan Karapenev Department of the Communication Equipment and Technologies Technical niversity of Gabrovo Gabrovo, Bulgaria bkarapenev@tugab.bg Abstract This paper presents the synthesis of a digital frequency modulator-demodulator, the design of its main block non-coherent digital frequency demodulator containing a lowpass active filter and an amplitude detector, the performance of simulation studies, implementation of a laboratory model on developed complete technical documentation and presentation of the results obtained by his experimental study. Keywords synthesis; study; digital; frequency; modulator; demodulator I. INTRODCTION The transmission of information at long distances is related to the use of modulation and demodulation processes and corresponding devices - modulators and demodulators. Initially, the amplitude, frequency and phase analog modulators/demodulators have found a wide application in practice [7]. The improvement of communications systems in recent years has led to their digitization - of the input information s, their method of processing and their transmission over the communication channel. The block diagram of a communication system as shown in Fig.. The Transmitter, Receiver and Transmission environment form the so-called Radio channel or Connection channel. Modulators and demodulators are nonlinear devices that in modern duplex communication systems often merge and form a common module MoDem [8]. The modulation in digital modulation u Ω(t) is a numerical series of logical and logical, and the carrier oscillation is sinusoidal and has the form u H ( Hm H H t) sin( t ). () The carrier oscillation parameters in the modulation process change by jumping between two states defined by the digital - logical or logical. Thus the amplitude, frequency and phase of the carrier oscillation receive discrete values in tact with the modulating digital series. The main types of digital manipulations are: Amplitude Shift Keying ASK, Frequency Shift Keying, Phase Shift Keying PSK and Qadrature-Amplitude Modulation QAM which is of higher degree. The modulated in frequency manipulation () is formed as the sum of two ASK s, each with the corresponding carrier frequency f C and f C. The mathematical model of the modulated has the form u ( C Ct t) A.sin( f t) Asin( f ). () Its functions are binary and accept only two values - logical or logical. II. SYNTHESIS OF DIGITAL FREQENCY MODLATOR- DEMODLATOR - A PRELIMINARY DESIGN The transmitted information from the source to the receiver to be transferred over a communication channel requires it to be modulated and accordingly demodulated. The digital frequency modulator-demodulator is designed for formation, their transmission - transfer over the communication channel and reception. The connection channel may be a cable or ethereal (terrestrial, satellite). Radio channel / Connection channel Input Coder Modulator Power amplifier Transmission environment High Freq block Demodulator Decoder Output Fig.. The block diagram of a communication system. Transmitter Channel Receiver

Journal of Communications Technology, Electronics and Computer Science, Issue, 7 ISSN 47-9X Input digital information f S S V Hz Input modulator m=m fc, fc Communication channel Analog, SNR (Digital) demodulator demodulated Output V f Hz Fig.. Block diagram of digital frequency modulator-demodulator. The block diagram of a digital frequency modulatordemodulator is shown in Fig.. The input digital into the modulator, the information carrier, is converted to a continuous one, which is transmitted over an analogue connection channel. It is characterized by the following more important parameters and characteristics: Signal-to- Noise Ratio (SNR) and linearity of amplitude and phase responses. The continuous input in the demodulator is converted into an output digital carrier of the information. The modulator can be implemented on the basis of various circuit solutions, such as using the widely distributed module-timer or Schmitt-trigger comparator using different capacities to provide a different frequency of the output. In order to ignore the influence of the communication channel it is assumed that the channel is ideal i.e. there is a direct connection between the modulator and the demodulator. The demodulator can be [8]: - built on the basis of a non-coherent scheme, in which direct frequency demodulation of the oscillations is performed; - differential-coherent, in which the digital series is differentially encoded before performing the frequency manipulation; - coherent, where synchronous demodulation is performed using an automatic frequency adjustment system. In this case, a specialized PLL integrated circuits (IC) is used; - implemented with a Digital Signal Processor (DSP). The implementation of an demodulator with discrete elements, i.e. without the use of specialized IC, DSP and processors, can only be done through a noncoherent scheme []. The circuit of a non-coherent demodulator can be synthesized based on the block diagrams in Fig. and Fig. 4 []. Non-coherent demodulation of binary modulated s can be performed by frequency discrimination as shown in Fig.. Two parallel-connected circuits transmit one of the two frequencies f C and f C and form the amplitudes of the s from the demodulation performed. The output digital frequency demodulated is formed by comparing the two m(t) and m(t) s, which can be performed by a comparator. Band-pass filter fc fc fc fc fc fc Band-pass filter Amplitude detector Amplitude detector m(t) demodulated Comparator Fig.. Block diagram of non-coherent digital frequency demodulator. Frequency converter in amplitude fc fc fc m (t) Amplitude detector Fig. 4. An non-coherent digital frequency demodulator. demodulated The block diagram of the non-coherent demodulator of Fig. 4 consists of a converter of frequency into amplitude and an amplitude detector. The two frequencies f C and f C are in the fall of the amplitudefrequency response (AFR) of low-pass filter or the rising or falling slope of the AFR of band-pass filter for which the voltage transmission coefficient is different. This process is illustrated by the timing diagrams shown in Fig. [].

Journal of Communications Technology, Electronics and Computer Science, Issue, 7 ISSN 47-9X Fig.. Time-diagrams of the amplitude-demodulated. In the non-coherent demodulator (Fig. 4), as frequency/amplitude converter, will be used two identical series connected units of low-pass active filters (LPAF) to be able to provide the corresponding voltage transmission coefficients in the course of the AFR for the frequencies f C and f C. The output amplitude-demodulated s should be submitted to a voltage comparator with positive feedback and a hysteresis zone of its switching x and the input digital modulation carrier of the information appears at the output. The choice of drop of the amplitude-frequency response of the LPAF used is of great importance. The analytical expression of the transfer function (AFR) is the type Т Н OT IN s n b s n n Н... b s b where OT and IN are respectively the input and output voltages. The steepness of the drop of the AFR outside the overspeed frequency band is determined by the order of the filter. The transmission coefficient H does not depend on the type of LPAF but on its schematic implementation and is involved in determining the transmission coefficient T H of the low-pass filter at the frequency f = (T H= H /b ). The most appropriate choice of the unit of LPAF - from I order and polynomials and ratios of II order with different quality factor Q is between a Sallen-Key topology filter and a II order unit(s) with a quality factor from to. Since the Sallen-Key Low-pass units have a simpler configuration and implementation as well as the design they are chosen when building the demodulator. III. DESIGN OF DIGITAL FREQENCY MODLATOR- DEMODLATOR. SIMLATION RESLTS Design and studies of digital frequency modulators - using Module-timer and Schmitt-trigger are presented in [4] and [] respectively., () A. Design of the Sallen Key Filter from the Structure of the Digital Frequency Demodulator The active filters by Sallen-Key topology are some of the most commonly used in practice because of the simple construction and the good quality parameters and characteristics which they provide. They are built using an active element (operational amplifier), two series connected resistors R and R (R, R4) to the non-inverting input and two capacitors C and C (C, C4) Fig. []. Input R LFAF nit I R C C cc -cc R LFAF nit II Fig.. Low-pass active filter by Sallen-Key topology. R4 C4 C cc -cc The transfer function T H(s) of such a filter is of the type Т Н OT IN s R. C. R. C s R. C R. C R. C. R. C where OT and IN are the input and output voltages respectively, and s - complex variables. The design of the low-pass unit by Sallen-Key topology can be done with the electronic web-calculator []. For input data R = R = kω, C = nf and C = nf the following more important results are obtained: Transfer function Cut-off frequency Quality factor Attenuation ratio 9 T H(s) Т Н ; 4 9 s..s f C,9 Hz; Q PH,88; ξ,77. The design of the low-pass unit by Sallen-Key topology can be performed in the following simplified sequence []: - set the cut-off frequency f C = khz; - the value of the capacitor C is chosen within the range of pf nf. In this case С = nf; - determine the value of С = ( ).С, as С =.С = nf; - calculate the values of R и R by dependence (4) Output

Journal of Communications Technology, Electronics and Computer Science, Issue, 7 ISSN 47-9X,77 R R. ().. f.(. C) For resistors R and R standard values of kω each are selected. B. Design of the Amplitude Detector from the Structure of the Digital Frequency Demodulator RL =,7 V is accepted for logical and RL =,8 V is accepted for logical for the reference levels (RL) defining the hysteresis of Schmitt-trigger. Its width is obtained X = RL RL =,9 V. With a selected value of R = kω in equations () is compiled a system of two equations with two unknowns from which the resistance of resistors R 948 Ω и R4 49 Ω is determined. Their default values are chosen accordingly kω and 4, kω (Fig. 7). R4. R4 R R RL CC C and R4 R RL. () CC R R4 R Since the designed demodulator can be simulated only in the structure of the synthesized modulatordemodulator (Fig. ) and in Fig. 7 presents the circuit for its simulation study. It also contains the modulator and two units by Sallen-Key topology. The oscillogram of s in nodes 4 ( modulated ) and - after both low-pass units are shown in Fig. 8. The latter appears to be the input for the demodulator (4). The obtained oscillogram of the s in nodes 4 ( modulated ) and - after the demodulator is presented in Fig. 9. Since the output of the comparator of the demodulator continuously switches with the frequency of the amplitude demodulated with the greater amplitude (Fig. 9) available at logic of the input modulation which requires its smoothing. For this purpose, the structure of the demodulator envisages the use of a full-wave rectifier D (Graetz circuit) and a pulsating smoothing capacitor C8, in which case both intermediate s of different amplitude are rectified Fig.. 7 R kω R 4.kΩ R4 kω C nf Q N R kω R kω nf C 74 8 R 47Ω V V C R7 4 µf kω D N8B D4 N4 nf R8 8 kω C C4 nf 74 XSC Ext Trig R kω 7 R kω C nf C7 nf 4 74 V Hz V R kω 9 R4 4.kΩ R 4 74 D N8B A B R7 kω kω D N4 Fig. 7. Circuit for simulation study of the synthesized modulator-demodulator. 4

Journal of Communications Technology, Electronics and Computer Science, Issue, 7 ISSN 47-9X output is dephased at approximately 8 o is shown in Fig.. The obtained oscillogram of the modulated (node 4) and the rectified node after Graetz rectifier (Fig. ) is shown in Fig.. Fig. 8. An oscillogram of the modulated (node 4) and filtered after the two series connected LPAF (node ). Fig.. An oscillogram of the modulated (node 4) and the rectified node after Graetz circuit. Fig. 9. An oscillogram at the input and output of the synthesized modulator-demodulator. The complete schematic circuit of the synthesized modulator-demodulator containing the Graetz rectifier and an inverter at the output of the demodulator since the The presence of a Graetz rectifier circuit in the demodulator structure changes the DC levels for frequencies f C and f C. In this case, the reference levels defining the hysteresis of Schmitt-trigger for the demodulator assume values RL =, V for logic and RL =, V for logic. This requires a recalculation of the values of the elements R, R4 and R (Fig. ), as a result of which the value of hysteresis x is changed. At the selected value of R = Ω in equations (), after solving the system of two equations with two unknowns, the resistances of resistors R4 49 Ω and R 9 Ω are determined. For their standard values are selected respectively Ω and kω. The simulated oscillogram at the input and output of the synthesized modulator-demodulator (Fig. ) is shown in Fig..

Journal of Communications Technology, Electronics and Computer Science, Issue, 7 ISSN 47-9X 7 R kω R 4.kΩ R4 kω V Hz V C nf C8 Q N D R kω R kω C nf nf 74 8 R 47Ω V V C 4 R Ω 9 R4 Ω µf D N8B D4 N4 R7 kω R kω nf R8 8 4 74 kω C C4 nf D N8B R kω D N4 4 74 R9 kω R.8kΩ R kω R7 kω 7 4 7 7 74 R kω C nf R8 kω C7 nf 4 A XSC B 74 Ext Trig Fig.. The complete circuit of the synthesized modulator-demodulator. IV. EXPERIMANTAL STDIES OF DESIGNED DIGITAL FREQENCY MODLATOR-DEMODLATOR Table presents the measured DC voltages in the respective nodes since some of the modulatordemodulator circuits have a DC operating mode, for example, the reference levels (voltages) of the non-inverting inputs of the Schmitt-triggers, 4 and inverter (nodes, 9 and 4 in Fig. ). They are compared to the simulated ones and the relative error between them is determined. Fig.. An oscillogram of the input and output s of the synthesized modulator-demodulator. TABLE I. DC OPERATING POINT OF THE MODLATOR- DEMODLATOR Node 9 4 simulation, V,,9,89 experimental, V 4,9,7,89 ε, % 8 4,9 The experimentally obtained oscillograms in the specified nodes of the modulator-demodulator synthesized circuit (Fig. ) are shown in Figures. A generator is connected to the input of the circuit and the is bi-polar with square pulses with amplitude 4 V and frequency Hz - Fig..

Journal of Communications Technology, Electronics and Computer Science, Issue, 7 ISSN 47-9X Fig.. An oscillogram of the input digital modulation - node 7. Fig. 4. An oscillogram of output of modulator at logic with f C = 8, khz - node 4. Fig.. An oscillogram of output of modulator - amplitude value - node 4. After passing the input to the comparator ( in Fig. ) at the output a with two different frequencies is obtained as frequency f C is khz - Fig. 4, and f C is 8, khz - Fig.. The measured peak to peak voltage is shown in Fig. and has a value of 8,4 V and it has positive polarity of,9 V and negative of -4, V. After converting the input digital into a modulated, it enters the low-pass active filters to provide different amplitudes for frequencies f C and f C. The obtained oscillograms of the LPAF with one unit are shown in Figures 7. pp of is 8,4 V for frequency f C (Fig. 7) and for f C -,4 V Fig. 8. The periods of frequencies f C and f C were determined by the experimental studies shown in Figures 9 and, as for frequency f C ΔT = μs - Fig. 9 and for frequency f C ΔT = μs - Fig.. Fig.. An oscillogram of output of modulator at logic with f C = khz - node 4. Fig. 7. An oscillogram of the output of LPAF with ΔYC = 8,4 V - node. 7

Journal of Communications Technology, Electronics and Computer Science, Issue, 7 ISSN 47-9X After the filtration of the first LPAF, the enters the second unit for second filtration and provides the necessary amplitudes for frequencies f C and f C. The oscillograms of the LPAF can be compared and determine the differences in the s between the first unit shown in Figures 7 and 8, and the second - Figures and. Voltage drop after the second filter is approximately V. Fig. 8. An oscillogram of the output of LPAF with ΔYC =,4 V - node. Fig.. An oscillogram of the output of LPAF with ΔYC = V - node. Fig. 9. An oscillogram of the output of LPAF with ΔXC khz, Т = µs node. Fig.. An oscillogram of the output of LPAF with ΔYC =,84 V - node. The oscillograms from which were measured the frequencies and the time-intervals of following the s after the LPAF with two units are shown in Figures and 4. The measured values fully match those of the LPAF with one unit shown in Figures 9 and. Fig.. An oscillogram of the output of LPAF with ΔXC = 8, khz, Т = µs node. 8

Journal of Communications Technology, Electronics and Computer Science, Issue, 7 ISSN 47-9X Fig.. An oscillogram of the output of LPAF with ΔXC = khz, Т = μs node. choice and implementation. The design, simulation, and experimental study of a digital frequency modulator with a timer-module and a Schmitt-trigger has been carried out. Among the choices of demodulator - coherent, differential-coherent and non-coherent, the latter is chosen because its implementation is not related to the use of specialized integrated circuits such as PLL and DSP. It was synthesized by LPAF - a two Sallen-Key topology units and an amplitude detector (Schmitt-trigger comparator). The simulation and experimental studies were performed for all composite modules as well as for the entire synthesized non-coherent digital frequency modulator-demodulator by presenting the results obtained which visualize the processes in progress. The presented synthesis, design and the obtained simulation and experimental results illustrate the work and explain the principle of operation of the synthesized circuit of a digital frequency modulator-demodulator. They could also be used in the design, simulation and experimental study of other circuits widely used in communications and practice. Analogously, other types of modulators, demodulators, as well as other similar circuits can be synthesized, designed, implemented, simulated and experimentally studied. REFERENCES Fig. 4. An oscillogram of the output of LPAF with ΔXC = 8, khz, Т = μs node. Summary The behavior of the synthesized circuit of a non-coherent digital frequency modulator-demodulator during the simulation and experimental studies is analogous while preserving the form and character of the intermediate s in the individual nodes. However, there are minimal differences in both the operating frequencies and the amplitudes of the intermediate s. V. CONCLSION The synthesis of a digital frequency modulatordemodulator is related to the development of a preliminary design in which are presented the requirements for the individual component blocks and the possibilities for their [] Sallen-Key Low-pass Filter Design Tool, Okawa Electric Design, http://sim.okawa-denshi.jp/en/ OPseikiLowkeisan.htm, 7. [] Sallen-Key Low-pass Filter, ecircuit Center, http://www.ecircuitcenter.com/circuits/opsalkey/ opsalkey.htm, 7. [] Thierry Taris, Hassène Kraimia, Didier Belot and Yann Deval, An and OOK Compatible RF Demodulator for Wake p Receivers, Journal of Low Power Electronics and Applications, ISSN 79-98, pp. 7-77, November, www.mdpi.com/journal/jlpea [4] B. Karapenev, A digital frequency modulator using module-timer, Scientific papers at the niversity of Rousse, Volume 4, Series., ISSN -, pp. 4-4,, http://conf.uniruse.bg/bg/docs/cp/./.-.pdf [] B. Karapenev, A digital frequency modulator using Schmithtrigger, Scientific papers at the niversity of Rousse, Volume 4, Series., ISSN -, pp. 9-98,, http://conf.uniruse.bg/bg/docs/cp/./.-4.pdf [] B. Karapenev, Macromodel synthesis of digital non-coherent frequency demodulator and simulation studies of modulatordemodulator, Journal of the Technical niversity of Gabrovo, volume 4, ISSN -8, pp. 4-48, 7. [7] D. Dobrev, L. Yordanova, Radiocommunications, parts one and two, Publishing house SIELA, Sofia, respectivelly and. [8] I. Nemigenchev and B. Karapenev, Communication Transform Devices, niversity Publishing House "Vasil Aprilov", ISBN 978-94-8--7, Gabrovo, 7. 9