EE-4022 Experiment 3 Frequency Modulation (FM)

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-1 Student Objectives: EE-4022 Experiment 3 Frequency Modulation (FM) In this experiment the student will use laboratory modules including a Voltage-Controlled Oscillator (VCO) to generate an FM signal modulated by a sinusoidal message. The modules to be used are from the Telecommunications Instructional Modeling System (TIMS). The student will determine the linearity of the voltage-to-frequency conversion for the VCO. The student will achieve the following: calibrate the sensitivity of the FM modulator, compare expected and measured peak frequency deviations for an FM signal, compare expected and measured frequency spectra for FM signals, and observe the spectra of FM signals having specific peak frequency deviations. An FM demodulator is constructed and tested. The FM demodulator consists of a zero-crossing-detector that outputs a fixed-duration pulse for each detected zero-crossing having positive slope, followed by a low-pass filter. With this part the student will: test and observe the operation of a zero-crossing-detector type FM demodulator. Published Resources: TIMS-301 User Manual (Issue No. 1.6, October 2004) describes each basic TIMS module. Communication Systems Modelling with TIMS, Vol. A1 Fundamental Analog Experiments by Tim Hooper (Issue No. 4.9, 2005) Instructor s Manual to accompany Communication Systems Modelling with TIMS includes notes on the TIMS experiments Equipment Needed: TIMS system with the following modules: o Audio Oscillator module o Variable DC module o Buffer Amplifiers module o Voltage-Controlled Oscillator (VCO) module o Utilities module o Twin Pulse Generator module (for one of its two pulse generators) o Headphone Amplifier module (for its low-pass filter) o Frequency Counter module o PC-Based Instrument Inputs (earlier TIMS called this Scope Selector) if desired Oscilloscope (e.g., Agilent MSO-X-3014A oscilloscope (100 MHz, 4 GSa/s)) Multimeter (e.g., Agilent 34401A or 34405A Digital Multimeter) Prelaboratory Investigation: 1. Review information on frequency modulated (FM) and phase modulated (PM) signals, in Appendix I and Appendix II, and from EE-4022 lecture material. 2. Assume that a voltage-controlled oscillator (VCO) is to be used as an FM modulator, and operates as follows: The VCO input voltage V in determines the VCO output signal frequency as f out = f center + k f V in

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-2 where f center is the frequency out of the VCO for the case when V in = 0, and k f is the sensitivity of the VCO in units of Hertz per volt (Hz/V). Assume that the VCO input accepts a message signal and the FM signal has a peak voltage of 1V. (a) If the unmodulated carrier frequency for the FM modulator is expected to be 10 khz, then what should be the value of f center? (b) If a 2 V p-p message signal is to result in a 1-kHz peak frequency deviation from the 10-kHz carrier (in each direction), then what should be the value of the sensitivity, k f, in Hz/V? 3. Assume that a 500-Hz sine-wave signal is used as a message input to the VCO-based FM modulator described in the previous step. The message signal has an amplitude of 2 V p-p, resulting in a peak frequency deviation of 1 khz. (a) Determine the highest instantaneous frequency and the lowest instantaneous frequency out of the FM modulator. (b) Determine β, the FM modulation index (also called the FM deviation ratio). (c) Determine and plot the frequency spectrum of the FM signal (show a normalized plot that assumes the component at the carrier frequency has a level of 0 dbv, and shows the relative levels of all other significant components in units of dbv). Assume that a component is significant if it has an rms voltage level that is at least 10% (that is, within 20 db) of the level of the highest-amplitude component. (d) What is the bandwidth of the FM signal (i.e., the bandwidth of the significant components)? 4. (a) Assuming the same 500 Hz message signal, determine the FM deviation ratio β that will result in an FM signal bandwidth of 5 khz (instead of the bandwidth determined in the previous step). (b) What is the peak frequency deviation for this β? (c) To achieve this peak frequency deviation, what voltage (p-p) must the 500-Hz message have at the input to the VCO (use the known value of k f)? (d) Determine and plot the theoretical frequency spectrum of this FM signal (again show a normalized plot). (e) What is the bandwidth of the FM signal as determined by the significant components on your plot? Laboratory Investigation: 1. Calibrate the FM modulator sensitivity and record data that characterize the VCO frequency-outversus-voltage-in characteristic using the following suggested steps. a. Note that the mean frequency (also called center frequency) out of the VCO is set with the front panel control on the VCO module. b. Note: A Buffer Amplifier with an adjustable gain control will be placed between the message signal and the input to the VCO. The adjustable buffer gain provides additional control of the amplitude of the signal going into the VCO when calibrating the sensitivity of the VCO as an FM modulator. As shown on Figure 1, a DC voltage instead of the message signal will be connected to the Buffer Amplifier input to calibrate the VCO sensitivity. c. Set the VCO module on-board mode switch to VCO. Set the VCO front panel switch to LO. Set the VCO front panel gain control fully counter-clockwise (so that the VCO input V in has no effect on the VCO output frequency). d. Connect the system as shown on Figure 1, for calibrating the VCO sensitivity. e. Use the Frequency Counter to monitor the VCO output frequency, and adjust the VCO front panel f 0 control to set the center frequency to 10 khz. f. Set the Variable DC module output to about + 2 volts. With the +2V at the input to the Buffer Amplifier, adjust the Buffer Amplifier gain control to result in -1.0V at its output. g. Now adjust the VCO gain control until the VCO output frequency changes by 1 khz. Note that the direction of change will be dependent on the polarity of the DC voltage at the VCO input. The Gain control of the VCO is now set to give a 1 khz peak frequency deviation for a modulating signal of 1 volt peak at the VCO V in. To what value has the VCO sensitivity, k f, been calibrated?

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-3 h. The linearity of the modulation characteristic can be observed by measuring the VCO output frequency at each of several values of VCO DC input voltage. Use the gain control of the Buffer Amplifier to adjust the DC voltage into the VCO. Make several measurements of VCO input voltage and corresponding output frequency. If a curve is sketched as measurements are made, the region where nonlinearity occurs can be easily identified. Record a set of measurements, sufficient to reveal the onset of nonlinearity of the VCO characteristic. i. Adjust the Buffer Amplifier gain control so that the Buffer Amplifier output is again at -1.0V, and confirm that the VCO output frequency is again 1 khz from the 10-kHz center frequency. ANALOG TTL Figure 1: The FM generator with DC input for calibration 2. Generate FM signals having a 10-kHz carrier and specified peak frequency deviations using the following suggested steps. a. Note that for measurements of components in the spectrum of the FM signal, one is generally not interested in absolute amplitudes, but is usually most interested in relative amplitudes of the spectral components. b. Note: Two FM signals will be generated. The first will be generated using a 500-Hz message signal with an amplitude that results in a peak frequency deviation of 1 khz. c. Adjust the Audio Oscillator frequency to 500 Hz. In the system shown on Figure 1, disconnect the Variable DC output from the Buffer Amplifier input, and instead connect the Audio Oscillator output (sine wave) to the Buffer Amplifier input. Use the scope to measure the p-p message voltage into the VCO and adjust the Buffer Amplifier gain so that this is 2V p-p. d. Use the scope to observe the VCO output. Set the trigger level to 0V (positive edge). Be sure the horizontal position is zeroed and the horizontal zero-time reference is in the center of the display. Then adjust the scope horizontal controls to allow measuring the longest and shortest time periods using cursors as shown on Figure 2. From these periods calculate the lowest and highest frequencies and determine the measured peak frequency deviation. Figure 2 shows a representative oscilloscope display and cursors that measure the shortest time period of the FM signal. The Display controls can be used to turn on persistence, and the Run/Stop and Single (sweep) buttons can be used to obtain a display such as that shown on Figure 2. e. Measure the spectrum of the FM signal (suggest adjusting the scope horizontal control to approximately 5 ms per division. With 10 horizontal divisions (spanning 50 ms) and assuming approximately 2000 FFT points across the screen, this would result in a sampling rate for the FFT of 2000 sample points per 50 ms, or 40 ksa/s, which would be adequate because the highest frequency of interest is under 20 khz). The Agilent MSO-X-3014A oscilloscope may display a higher sampling rate when the horizontal control is set to 5 ms per division due to its oversampling features. f. Now use the Buffer Amplifier gain control to readjust the p-p message voltage into the VCO, to the value determined in the prelaboratory investigation for an FM signal having a bandwidth of 5 khz, and repeat steps d and e above.

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-4 Figure 2: Superimposed traces of FM signal with varying instantaneous frequency 3. Follow and perform the following steps to build and test an FM demodulator. a. A simple FM demodulator that reproduces the original message signal will be built and tested to provide further confirmation that the VCO output is indeed an FM signal. A scheme for achieving this result the zero-crossing-detector demodulator is described in Appendix II, and is modeled as shown below on Figure 3. USED AS LOW-PASS FILTER (LPF) Figure 3: An FM demodulator using a zero-crossing detector b. Note: The Twin Pulse Generator module is used to produce a pulse at each positive-going zerocrossing of the FM signal. To achieve this, the FM signal is converted to a TTL signal by the Comparator on the Utilities module, and this drives the Twin Pulse Generator. The input signal to

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-5 the low-pass filter (LPF) on the Headphone Amplifier module is at TTL level. It is common practice with TIMS equipment not to connect a TTL signal to an analog input. If you prefer you can use the analog output (yellow connector) from the Twin Pulse Generator. This is an ACcoupled version of the TTL signal. c. Before plugging in the Twin Pulse Generator, set the on-board MODE switch SW1 to SINGLE. Connect the demodulator shown on Figure 3. d. Use the gain control on the Buffer Amplifier to set the frequency deviation of the FM generator to zero, and connect the VCO output to the demodulator input. e. Using the WIDTH control of the Twin Pulse Generator module, adjust the output pulses at this module s output to achieve a mark/space ratio of 1:1, or as close to this as the control allows. f. Observe the demodulator output on the scope. If you have chosen to take the TTL output from the Twin Pulse Generator, there should be a DC voltage present. Why? Notice by adjusting the WIDTH control that the DC level at the demodulator output is proportional to the width of the pulses into the LPF of the Headphone Amplifier. g. Now use the gain control on the Buffer Amplifier to introduce some modulation at the VCO. Observe on the scope the output of the LPF on the Headphone Amplifier module. Measure its frequency and compare this with the frequency of the original message. Observe the original message (use the VCO input) on one scope channel, the modulated signal put of the VCO on a second scope channel, and the demodulator message output on a third scope channel. Comment on differences between the original message and the recovered message out of the demodulator. h. Observe that the amplitude of the message output from the demodulator: - varies with the message amplitude of the VCO. Is this a linear variation? - remains constant when the frequency of the message into the VCO is changed. Does this confirm that the VCO is producing FM, and not PM?

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-6 APPENDIX I. Background: Analysis of the FM Spectrum Introduction It is important to understand the distinctions between phase-modulated (PM) and frequency-modulated (FM) signals. This appendix defines the angle modulated signal, of which PM and FM are special cases. FM, under well defined conditions, offers certain features, including a method of trading bandwidth for signal-to-noise ratio. This appendix does not present signal-to-noise properties, but instead concentrates on analyzing the spectral properties of the FM signal. Definition of modulation Consider the signal: This signal has, by definition: y(t) = A cos[θ(t)] = A cos[ω C t + φ(t)] (1) an amplitude, A a total phase, θ(t) = ω C t + φ(t) an instantaneous frequency defined as the time rate of change of total phase Any one of these three parameters may be modulated by a message. We will assume that the message is a sinusoid, A M cos ω M t. Whichever of the three parameters is chosen to vary according to the message, then, by definition, the rate of variation of the chosen parameter should be directly proportional to the rate of variation of the message alone, that is, proportional to the rate of A M cos ω M t, and the amount of variation of the chosen parameter should be directly proportional to the value of the message alone, that is, it is proportional to A M cos ω M t. Other parameters may vary at the same time, as will be seen in what follows, but these variations will not in general be varying directly in accordance with the message signal. Phase modulation (PM) - definition According to the above, if a sinusoidal carrier is phase modulated by a sinusoidal message A M cos ω M t, then: total phase = θ(t) = ω C t + Δφ cos ω M t (2) and the constant Δφ is linearly proportional to A M, the message amplitude. The last term in equation (2) represents a phase variation that is proportional to the message A M cos ω M t. Note that Δφ is the peak phase deviation from that of the unmodulated carrier. The last term in equation (2) is often expressed as a phasedeviation constant k P multiplied by the message signal, and therefore Δφ = k P A M. Hence, y PM (t) A cos(ω C t k P A M cos ω M t) (3) is a phase modulated signal. Note that, for PM, the instantaneous frequency is the time-derivative of the total phase:

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-7 instantaneous frequency = ω C - k P A M ω M sin ω M t (4) Although the frequency is also varying with the message, the variation is not directly proportional to the message A M cos ω M t. Hence, by definition, this is not frequency modulation. Frequency modulation (FM) - definition According to the above, if a sinusoidal carrier is frequency modulated by a sinusoidal message A M cos ω M t, then: instantaneous frequency = ω C + Δω cos ω M t (5) and the constant Δω is linearly proportional to A M, the message amplitude. The last term in equation (5) represents a frequency variation that is proportional to the message A M cos ω M t. Note that Δω is the peak frequency deviation, and Δω = (2π) Δf. The total phase is obtained by integration of the instantaneous frequency, and thus the signal itself must be: y FM(t) A cos(ω C t Δω /ω M) sin ω M t) (6) The last term in equation (5) is often expressed as a frequency-deviation constant k f multiplied by the message signal, and therefore Δω = k f A M. Hence, y FM(t) A cos(ω C t k f A M /ω M) sin ω M t) Although the phase is also varying with the message, the variation is not directly proportional to the message A M cos ω M t. Hence, by definition, this is not phase modulation. Angle modulation - general form The defining equation, for both PM and FM, can be written in the form: y(t) = A cos(ω C t β sin (ω M t + θ)) (7) One can choose β and θto represent either PM or FM as the case may be, and according to the definitions above. Thus: for PM, β= Δφ= k P A M, the peak phase deviation, and θ = 90, (8) and for FM, β= Δω/ω M = Δf/f M, and θ = 0. (9) The parameter βis often called the deviation ratio. For a sinusoidal message at frequency f M, the deviation ratio is equal to β= Δf/f M. For a non-sinusoidal message signal having bandwidth B, the deviation ratio is β= Δf/B. Both PM and FM fall into a class known as angle modulated signals.

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-8 Receivers Demodulators for angle-modulated signals are needed to recover the message from the modulated signal. The demodulator in a PM receiver responds in a linear manner to the variations in phase of the PM signal, and the receiver output is ideally a copy of the original message. Likewise the demodulator in an FM receiver responds in a linear manner to the instantaneous frequency variations of the FM signal. If an FM signal is processed by a PM receiver, or if a PM signal is processed by an FM receiver, the receiver will output a recovered signal that is related to the original message signal but will not be directly proportional to the original message signal. For a PM signal, observing equations (1) and (3) above, the output of the PM receiver will be proportional to the phase of the modulated signal, that is proportional to φ(t) = k P A M cos ω M t. For an FM signal, observing equations (1) and (6) above, the output of the FM receiver will be proportional to the instantaneous frequency deviation from the carrier frequency ω C, where frequency is the derivative of the total phase. Therefore the FM receiver output will be proportional to dφ(t)/dt = d[δω / ω M) sin ω M t)]/dt = Δω cos ω M t. APPENDIX II. FM Modulator and Demodulator Circuits FM modulator using a VCO This experiment has been written to illustrate FM modulation using a voltage-controlled oscillator (VCO) function. A VCO is typically packaged within an integrated circuit. The VCO, as a low-cost integrated circuit (IC), can have impressive performance (for example, very good linearity). The VCO IC is generally based on a bistable flip-flop, or multi-vibrator type of circuit. Thus its output waveform is a rectangular wave. However, VCO ICs that convert this to a sinusoid are available. The mean frequency (or center frequency) of the VCO is typically determined by an RC circuit external to the VCO IC. The controllable part of the VCO is its frequency, which may be varied about a mean by an external control voltage. The variation of frequency in accordance with the control voltage is ideally linear over a large portion of the allowed input signal range. This then suggests that it would be ideal as an FM modulator. Unfortunately such is not the case because another factor, the relative instability of the center frequency of these VCOs, renders them unacceptable for modern day communication circuits. The uncertainty of the center frequency does not give rise to problems at the receiver, which may be implemented to track the drifting carrier (typically using a phase locked loop - PLL). The problem is that spectrum regulatory authorities insist, and with good reason, that communication transmitters maintain their (mean) carrier frequencies within close limits, typically within one part per million or better. It is possible to stabilize the frequency of an oscillator, relative to some fixed reference, with automatic frequency control circuitry. But in the case of a VCO which is being frequency modulated there is a conflict, with the result that the control circuitry is complex, and consequently expensive. For applications where close frequency control is not mandatory, the VCO is appropriate as an FM modulator.

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-9 This experiment is an introduction to the FM signal. A wideband FM signal is appropriate for studying some of the properties of the FM spectrum. In this experiment, two examples of an FM signal are examined, corresponding to cases described in the prelaboratory. FM demodulator using a zero-crossing-detector A simple yet effective FM demodulator is one which takes a time average of the zero crossings of the FM signal. Figure 4 suggests the principle. Figure 4: an FM signal, and a train of pulses from FM-signal zero-crossings Each pulse in the pulse train is of fixed width, and is located at a zero crossing of the FM signal (only positive-going zero crossings are detected in this example implementation). The output of the zerocrossing-detector (the second signal shown on Figure 4) is a pulse-repetition-rate modulated signal. If this pulse train is passed through a low-pass filter (LPF), the filter will perform an averaging operation. The average value of the LPF output will be high when the frequency of the original FM signal is high, and the average value of the LPF output will be lower when the frequency of the original FM signal is lower. Therefore, the zero-crossing-detector followed by a LPF performs an FM demodulation function. This zero-crossing-detector type demodulator (also called the zero-crossing counter) is tested in the latter part of the experiment. The phase locked loop (PLL) is the basis of a different FM demodulator in common use.

EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 3-10 APPENDIX III. Table of Bessel function values Source: Paul Tobin School of Electronics and Communications Engineering (http://www.electronics.dit.ie/staff/ptobin/bessel.pdf accessed Oct. 8, 2008)