SIMPLE STEREO FM BASEBAND GENERATOR USING TIME- DIVISION MULTIPLEXING MIXING TECHNIQUE

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1 SIMPLE STEREO FM BASEBAND GENERATOR USING TIME- DIVISION MULTIPLEXING MIXING TECHNIQUE 1 EDWARD JEN, 2 CHUNG-HSING CHAO 1 Undergraduate, Department of Electrical Engineering, University of Wisconsin - Milwaukee, USA 2 Prof., Department of Electrical Engineering, Ta Hwa University of Science and Technology, Taiwan 1 ljen@uwm.edu, 2 davidee@tust.edu.tw ABSTRACT Most, if not all, modern frequency modulation transmitters today implement the baseband processing using application-specific integrated circuits (ASICs) or digital signal processors (DSPs). Although ASICs and DSPs present the most cost-effective and turnkey solutions, it is an intellectually stimulating and rewarding endeavor to generate the baseband signal using widely available, inexpensive, discrete components. Many available published discrete designs have been optimized for cost and low part count, condensing multiple steps into one processing stage. Other designs utilize discrete parts that have been deprecated and are no longer widely available or inexpensive to acquire. Using only two PIC microcontrollers with an internal RC oscillator, 4051 analog multiplexer, and LF351N op amps, this paper - demonstrates the feasibility of the time-division multiplexer frequency mixing technique in a stereo FM baseband circuit. Keywords: signal synthesis, signal sampling, frequency modulation, time division multiplexing, mixers 1. INTRODUCTION In the late 1950s, the Federal Communications Commission (FCC) in the United States received more than a dozen standardization proposals for stereo frequency modulation (FM), including from companies such as General Electric (GE), Zenith, and Halstead [1]. According to [1], field tests of the various systems were conducted using experimental FM transmitters in Uniontown, Pennsylvania. Once the tests concluded, the FCC adopted the GE and Zenith proposals, which were both identical, in April 1961 as the standard stereo FM broadcasting method. pilot tone. Next, the difference (L-R) channel is mixed with a 38 khz subcarrier, which means that the range of possible frequencies spans from 23 khz (38-15 khz) to 53 khz (38+15 khz). In modern systems, there may be some Radio Data System (RDS) information appended to the upper end of the allocated spectrum typically modulated with a 57 khz subcarrier [2]. As the allocated single-side bandwidth per FM channel is 57 khz, only the lower side band of the RDS modulation is used. Mono FM transmitters simply sum both the left and right (L+R) channels together [1]. In order to maintain compatibility with mono FM receivers, the stereo FM transmitters also sum the left and right (L+R) channels together, but also add an upconverted difference (L-R) channel along with a stereo pilot tone. For a typical FM baseband spectrum, the mono channel, which is the sum of the left and right (L+R) channels, reserves the first 15 khz of bandwidth, as shown in Fig. 1? If stereo is available, the transmitter will broadcast a 19 khz 29 Figure 1: Diagram Showing FM Baseband Spectrum Spanning From 0 to 57 KHz. At first glance, it appears that baseband signal generation can be performed using the method shown in Figure 2. First, the sum and difference of the left and right channel are determined. Next, generate a 38 khz subcarrier using a tuned LC tank oscillator and mix the signal with the difference (L- R) channel. The 19 khz pilot tone is then

2 generated by dividing the 38 khz subcarrier in half or by using another tuned LC tank oscillator. Finally, the 19 khz pilot tone, mixed difference (L- R) channel, and the standard mono (L+R) channel are summed together to produce the final baseband signal to be upconverted to the FM carrier frequency. internal 8 MHz oscillator and a 4051 analog multiplexer directly upconverts the left and right audio channel to the 38 khz subcarrier without the need for a separate mixer. A simple cascaded active low-pass filter is used to further suppress the odd harmonics to prevent intermodulation in the allocated bandwidth. A completely functional FM subcarrier circuit will also be constructed and demonstrated. Figure 2: Block Diagram Of Conventional Method Of Producing The FM Baseband Spectrum. As stereo FM radio was developed before the preeminence of integrated circuits and digital computing, the original circuits were designed with discrete analog components. According to the standard procedure of constructing the stereo FM baseband as described previously, transistors would have to be biased using innumerable numbers of different resistors and capacitors [3]. Also, the 19 khz pilot tone and 38 khz subcarrier would have to be generated using a tuned tank circuit, whose resonant frequencies can change based on many factors, including temperature or changes in loading [4]. Although variations in temperature, loading, and component values can be compensated in the circuit, it leads to greater parts count, complexity, and most importantly, cost. It has been reported that stereo FM multiplexing has been proposed and built previously, but the results obtained from mixing the signals appear to be poor owing to the harmonics generated by the square wave. Most solutions rely on a simple firstorder passive RC low-pass filter after adding the 38 khz mixed subcarrier with a 19 khz pilot tone [5]. Although this scheme is indeed very simple and requires few parts, the odd harmonics from the square wave are insufficiently and ineffectively suppressed, which causes several undesired intermodulated frequencies will cause interference not only within the allocated channel, but also with devices using adjacent channels. An example of such a system is shown in Figure 3. In this paper, a very simple multiplexing technique utilizing only a PIC microcontroller using the Figure 3: Cappel s Stereo Multiplexer Output Showing Intermodulation Interference Is Shown On The Left, And The Adapted Block Diagram Is Shown On The Right. 2. METHODS: In order to construct and demonstrate the stereo FM baseband circuit, the theoretical principles on which the operation of the most critical part of the baseband circuit rests, the mixer, must be established first. 2.1 THEORETICAL ANALYSIS: According to the standard mixing technique as described in the introduction, the left and right audio baseband intermediate waveforms are shown below. In Figure 4a, the left and right audio channels are operating at 2 khz at 2 V pk-pk and 8 khz at 1 V pk-pk, respectively. Figure 4b shows the difference (L-R) channel. Figure 4c shows the resulting waveform after mixing the difference channel with a 38 khz sine wave subcarrier signal. Figure 4: Difference Channel (L-R) From Conventional FM Baseband Generation Method. a) Shows 30

3 Left And Right Wave Forms. b) Shows Difference (L-R) Channel. c) Shows Difference Channel Mixed With 38 KHz Subcarrier. As pure sine waves are difficult to generate on the PIC microcontroller without the need for external components, it is easiest to generate a 38 khz, 50% duty cycle PWM signal as the subcarrier, as shown in Figure 5b. From Figures 5b and c, it can be seen that when the subcarrier is high (1 V) or low (-1 V), the output follows the right and left channels, respectively. This is essentially a very simple timedivision multiplexing scheme that alternates sampling two channels at 38 khz. same as multiplication in the frequency domain [6]. It can also been shown that the converse of that theorem is also true, such that the multiplication of two signals in the time domain is the same as the circular convolution in the frequency domain [6]. where n = 1, 3, 5, etc. The previous mathematical representation is not very intuitive, so the frequency spectrum of the representation is shown in Figure 4. When the convolution of the two frequency spectra is performed, there is copy of the sine wave spectrum (Figure 6a) at every 38000πn where n = 1, 3, 5, etc., as shown in Figure 7. Figure 5: Shows Time-division Multiplexing Method Of Mixing The Left And Right Channels In One Step. A) Shows The Left And Right Audio Channels. B) Shows The 38 KHz Chopper Signal. C) Shows The Mixed Signals. To understand what effect the time-division multiplexing (TDM) mixing scheme has on the frequency spectrum of the output signal, it is necessary to derive the underlying mathematical relationships. From Figure 4a, the left and right channels can be represented as follows. Figure 6: Convolution Of The Sine Wave (Left) And Square Wave (Right) Frequency Spectra. Since the difference channel is simply the sum of the left channel and the inverse of the right channel, the convolution of the ideal 2 khz and 8 khz is distributive over the sum [6]. This results in a spectrum that has copies of the mixed 8 khz signal at each odd harmonic of the square wave. Figure 7 shows the actual frequency spectra of both (a) the TDM mixer and (b) the original mixer. Now consider the left channel only. Contrary to what is shown in Figure 4b, let the square wave alternate between the values of 0 and 1 instead of -1 and 1, respectively. The periodic, time-domain representation of the left channel wave is shown below. Figure 7: Result Of Convolution Between The Square Wave And Sine Wave Frequency Spectra. Comparing Figures 8a and b, there are odd harmonics caused by the square wave mixer that will need to be filtered out before being passed into the final upconversion to the carrier frequency. where square represents the periodic square wave function at 50% duty cycle. According to the convolution theorem, the convolution of two signals in the time domain is the 31

4 Figure 8: Comparing The Time-division Multiplexing Mixer (Left), And The Output Of The Difference Mixer (Right). 2.2 FILTER DESIGN: In order to suppress the odd harmonics owing to the frequency characteristics of the 19 and 38 khz square waves, a low-pass filter must be designed and implemented in order to attenuate high frequency signals. From previous experiments, it was shown that a first-order low-pass passive RC filter was insufficient in suppressing the two closest harmonics. It can also be shown that the cutoff frequency of the passive RC filter can be dramatically shifted based on circuit loading. In order to maintain simplicity in circuit topology and frequency-load independence, a simple cascaded second-order active low-pass Butterworth filter could be used to double the attenuation from -20 db/decade to -40 db/decade in the stopband. From the cascaded active low-pass filter designing procedure found in [4], C3 and C4 should both be 2 nf for the 38 khz subcarrier signal for a cutoff frequency of 53 khz. C3 and C4 should both be 5.6 nf for the 19 khz pilot tone. Figure 9: Two First-order Cascaded Low-pass Filter With 1 KΩ Resistors. 2.3 FM BASEBAND CIRCUIT: was shown that a first-order low-pass passive RC filter was insufficient in suppressing the two closest harmonics. It can also be shown that the cutoff frequency of the passive RC filter can be dramatically shifted based on circuit loading. In order to maintain simplicity in circuit topology and frequency-load independence, a simple cascaded second-order active low-pass Butterworth filter could be used to double the attenuation from -20 db/decade to -40 db/decade in the stopband. Two PIC18F14K50s were programmed using a Microchip PICkit 2 using the CCS C compiler to output a 38 khz and 19 khz, 50% duty cycle PWM, respectively, clocked from the internal 8 MHz RC oscillators as shown in Figure 10. The audio was then generated using an Asus Nexus 7 with the Keuwl Dual Channel Function Generator in order to generate pure tones or with the Amazon Music App to playback commercially produced music. The Nexus 7 was interfaced with the circuit using a 3.5 mm audio and S-Video to RCA stereo and composite cable with alligator clips and wires leading to the op amps. Two STMicroelectronics LF351N JFET op amps were used as a voltage buffer and amplifier for each channel. A Texas Instruments CD74HC4051E 8-channel analog multiplexer was configured so that the analog pins 0 and 1 could be toggled based on the state of the 38 khz PWM, which mixes the subcarrier and mono audio in one stage. The odd harmonics introduced by the square wave can be filtered out using two cascaded first-order active low pass filters with a cutoff frequency set at 53 khz to give a -40 db/decade stopband attenuation [4]. In order to designate the audio as stereo-capable, there must be a 19 khz pilot tone present. The second microcontroller outputs a 19 khz, 50% duty cycle PWM square wave, which is filtered through another cascaded first-order active low pass filter with a frequency cutoff set at 19 khz. The filtered 19 khz pilot tone and the 53 khz filtered, 38 khz subcarrier modulated signal is then summed together and fed to the transmitter. The raw voltage data and FFT was collected using a Hantek 6022BE 20 MHz bandwidth PC-based Oscilloscope using the Open6022BE v1.0 Beta PR18 application written by Richard Krupski. In order to suppress the odd harmonics owing to the frequency characteristics of the 19 and 38 khz square waves, a low-pass filter must be designed and implemented in order to attenuate high frequency signals. From previous experiments, it 32

5 db in a simple first-order RC design. Unlike the stereo FM multiplexer designed by Cappel [5], this stereo FM multiplexer with a cascaded active lowpass filter nearly eliminates all odd harmonics derived from the square wave without any intermodulation interference, as can be seen in the FFT output (red) in Figure 12. Figure 10: Block Diagram Of The Circuit Is Shown On The Left. The Actual Constructed Circuit Is Shown On The Right. 3. RESULTS AND DISCUSSION: Figure 11 shows the signal output (yellow) and the Fast-Fourier Transform (FFT) (red) after the multiplexer samples between the left and right channels at 38 khz. As described previously, the left and right audio channels are operating at 2 khz at 2 V pk-pk and 8 khz at 1 V pk-pk, respectively. The previous mathematical derivation proved that there would be copies of the mixed frequencies on each odd harmonic of the square wave, and the FFT concurs with the results of the mathematical derivation. In the raw signal output, there are small peaks that are simply caused by the underdamped step response in the 4051 multiplexer when there are large swings in current. Otherwise, the raw output signal appears to match the theoretical signal exactly as modeled in MATLAB. Figure 12: Signal From The 4051 Multiplexer That Is Filtered Through The Cascaded Active Low-pass Filter. Raw Voltage Is Shown In Yellow, And FFT Is Shown In Red. The final step in producing the baseband spectrum of the stereo FM is to add the 19 khz pilot tone into baseband spectrum, as shown in Figure 13. The signal in Figure 13 is now ready to be mixed with the FM carrier signal, amplified and broadcast over the air. Figure 11: Signal Output Directly From The 4051 Multiplexer. Raw Voltage Is Shown In Yellow, And FFT Is Shown In Red. Figure 12 shows the signal output (yellow) when the output from Figure 12 is filtered through the unity-gain cascaded active low-pass filter with a cutoff frequency set at 53 khz and a stopband attenuation of -40 db/decade. As the next odd harmonic of the 38 khz square wave is at 114 khz, the expected attenuation at the nearest harmonic is approximately -195 db, as compared to only Figure 13: Signal From The Cascaded Active Low-pass Filter Is Added To The 19 KHz Pilot Tone. Raw Voltage Is Shown In Yellow, And FFT Is Shown In Red. 4. CONCLUSION: A simple stereo FM baseband generator utilizing the time-division multiplexing mixing technique with PIC microcontrollers, a 4051 multiplexer, and LF351N op amps was constructed and demonstrated. It was also shown that the circuit

6 topology avoids the intermodulation interference from previously published stereo multiplexing designs. It has also been demonstrated that the circuit is modular and is extremely simple to build from ubiquitous and inexpensive integrated circuits. It is expected that this circuit could be packaged into an electronics kit that could be used by high school or university students interested in electrical engineering. Graphene has lately been subject of intense innovation and research. It is expected that graphene-based devices will analogue the functions, surpass the speed and eventually succeed siliconbased integrated circuits in the future. This paper will serve as the basis for investigation into possible radio applications of graphene-based nanoelectromechanical systems (GNEMS). REFRENCES adio_data_system&oldid= Cook, F. High Fidelity FM Stereo Modulator (Rev E2) March 2014 [cited 2014 July 4]; Available from: 4. Nilsson, J.W. and S.A. Riedel, Electric circuits. 9th ed. 2011, Boston: Prentice Hall. xxii, 794 p. 5. Cappel, R. A Simple FM Stereo Transmitter using an AVR microcontroller [cited 2014 July 4]; April 2007:[Available from: O/SIMPLE FM STEREO MULTIPLEX ENOCDER CIRCUIT.html. 6. Haykin, S.S. and B. Van Veen, Signals and systems. 2nd ed. 2002, New York: Wiley. xvii, 802 p. 1. contributors, W. FM broadcasting June 2014 [cited 2014 July 4]; Available from: le=fm_broadcasting&oldid= contributors, W. Radio Data System June 2014 [cited 2014 July 4]; Available from: 34