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PHASE -LOCKED LOOP AND FM DEMODULATION
1 P RINCE OF S ONGKLA U NIVERSITY D EPARTMENT OF E LECTRICAL E NGINEERING 210-302 Third-Year Electronics Laboratory: E1 P HASE -L OCKED L OOP AND FM D EMODULATION In this lab you will investigate phase lock loop (PLL) operation and its application for FM demodulation using the CMOS 4046 integrated circuit. The IC contains two different phase detectors and a VCO. It also includes a zener diode reference for power supply regulation and a buffer for the demodulator output. The user must supply a loop filter in a close-loop to operate the PLL. The high input impedances and low output impedances of the 4046 make it easy to select external components. Notes 1. This lab is fairly complicated. Be sure that you understand how the circuits are supposed to work before coming into the lab. Do not try to build something that you have not fully understood and analyzed. Read this entire document before beginning to work on it. 2. Students are strongly recommended to read supplementary handouts (see references) to comprehend a theoretical background of PLL operation as well as internal circuit building blocks within the 4046 IC. 3. Handle the 4046 with care. CMOS integrated circuits are easily destroyed. Avoid static discharges. Use a 10k- resistor to couple the signal generator to the PLL. Avoid shorting the outputs to ground or the supply. A TTL gate can withstand this kind of abuse, but CMOS cannot (be careful of loose wires). CMOS does not have the output strength to drive capacitive loads. VSS should be connected to ground, VDD should be connected to 5V, and pin 5 should be connected to ground (otherwise the VCO is inhibited). 4. Answer all questions (marked by underlines) with scientific/engineering analysis and discussion when writing up the lab report. 2 1. Phase-Locked Loop Concepts Phase-locked loop is a feedback loop where a voltage-controlled oscillator (VCO) can be automatically synchronized (“locked”) to a periodic input signal. The locking property of the PLL has numerous applications in communication systems (such as frequency, amplitude, or phase modulation/demodulation- analog or digital), tone decoding, clock and data recovery, self-tunable filters, frequency synthesis, motor speed control, etc. The basic PLL has three components connected in a feedback loop, as shown in the block diagram of Figure 1: a voltage-controlled oscillator (VCO), a phase detector (PD) or phase comparator, and a low-pass loop filter (LPF). Figure 1: Block diagram of a basic phase-locked loop (PLL) The VCO is an oscillator whose frequency f osc is proportional to input voltage v o (= V vcoin ). The voltage at the input of the VCO determines the frequency f osc of the periodic signal v osc at the output of the VCO. The output of the VCO, v osc , and a periodic incoming signal v i are inputs to the phase detector. When the loop is locked on the incoming signal v i , the frequency f osc of the VCO output v osc is exactly equal to the frequency f i of the periodic signal v i , f osc = f i ( 1) It is also said that the PLL is in the locked condition. The phase detector produces a signal proportional to the phase difference between the incoming signal and the VCO output signal. The output of the phase detector is filtered by a low-pass loop filter. The loop is closed by connecting the filter output to the input of the VCO. Therefore, the filter output voltage v o controls the frequency of the VCO. A basic property of the PLL is that it attempts to maintain the frequency lock ( f osc = f i ) between v osc and v i even if the frequency f i of the incoming signal varies in time. Suppose that the PLL is in a locked condition, and the frequency f i of the incoming signal increases slightly. The phase difference between the VCO signal and the incoming signal will begin to increase in time. 3 As a result, the filter output voltage v o increases, and the VCO output frequency f osc increases until it matches f i , thus keeping the PLL in a locked condition. The range of frequencies from f i = f min to f i = f max where the locked PLL remains in the locked condition is called the lock range of the PLL. If the PLL is initially locked, and f i becomes smaller than f min , or if f i exceeds f max , the PLL fails to keep f osc equal to f i , and the PLL becomes unlocked, f osc ≠ f i . When the PLL is unlocked, the VCO oscillates at the frequency f o called the centre frequency, or the free-running frequency of the VCO. The lock can be established again if the incoming signal frequency f i gets close enough to f o . The range of frequencies f i = f o – f c to f i = f o + f c such that the initially unlocked PLL becomes locked is called the capture range of the PLL. Make sure you understand and can distinguish the definitions of lock range and capture range! – it will become more obvious when you manage to run the PLL successfully. The lock range is wider than the capture range. So, if the VCO output frequency f osc is plotted against the incoming frequency f i , we obtain the PLL steady-state characteristic shown in Figure 2. The characteristic simply shows that f osc = f i in the locked condition, and that f osc = f o = constant when the PLL is out-of-locked (unlocked). A hysteresis can be observed in the f osc ( f i ) characteristic because the capture range is smaller than the lock range. Figure 2: Steady-state f osc (f i ) characteristic of the basic PLL. From this point, students need to carefully study a brief theory of the PLL in the supplementary handout [1, 2]. Make sure you understand the PLL concept and locking mechanism. Furthermore, it is essential to clearly understand a mathematical sense of the PLL in a locked condition (section 10.4.2) using s-domain analysis and try to relate the whole concept to the feedback control theory. As mentioned above, when the PLL is in a locked condition the input frequency f i will be equal to the frequency of the signal from the VCO, f osc – so why is it called Phase-Locked Loop instead of Frequency-Locked Loop? What is the real meaning of Phase? Should we 4 employ frequency comparator instead of phase comparator since we want to track the input frequency? While the PLL of Figure 1 is in a locked condition, it can effectively be modelled by the block diagram as depicted in Figure 3. The loop low-pass filter is represented by a transfer function F(s) where the integration 1/s block is needed to convert an angular frequency from the VCO ω osc into the corresponding phase Φ osc . Identify the building block that represents the phase detector? Instead of using phase detector, can we replace it with a frequency comparator? Note that K O is the VCO proportional constant and K D is the phase comparator’s “gain”. Σ Low-pass filter F(s) Voltage-Controlled Oscillator K O rad/s V 1/s K D V/rad Φ i Φ osc ω osc Φ ε V O Figure 3: Block diagram (in s-domain) of the PLL in Figure 1. Transfer functions between V O / Φ i or V O / ω i ( ω i being an input frequency in rad/s and it is related to phase by dt d i i Φ = ω or in s-domain ω i = s Φ i ) can be derived from Figure 3 to be )( )( )( sFKKs sFsK s V OD D i O + = Φ (2) )( )( )( sFKKs sFK s V OD D i O + = ω (3) In this experiment Eq.(3) will be used extensively in the design for different cases of filter transfer function F(s). 2. The 4046 Integrated Circuit Phase-Locked Loop A block diagram of the 4046 PLL is shown in Figure 4. The large rectangle indicates the 4046 boundary and the rests are external circuit components that may be connected to the IC to render specific functions. Read carefully through the data sheet before starting to build any circuit. Try to understand functionalities of each pin. It will help you carry out the experiment smoothly. The CD4046BC 1 micropower phase-locked loop (PLL) consists of a low power, linear, voltage-controlled oscillator (VCO), a source follower, a zener diode, and two 1 HEF4046 can also be used 5 phase comparators. The two phase comparators have a common signal input and a common comparator input. The signal input can be directly coupled for a large voltage signal, or capacitively coupled to the self-biasing amplifier at the signal input for a small voltage signal. Phase comparator I, an exclusive OR gate, provides a digital error signal (phase comp. I Out) and maintains 90° phase shifts at the VCO center frequency. Between signal input and comparator input (both at 50% duty cycle), it may lock onto the signal input frequencies that are close to harmonics of the VCO center frequency. Phase comparator II is an edge-controlled digital memory network. It provides a digital error signal (phase comp. II Out) and lock-in signal (phase pulses) to indicate a locked condition and maintains a 0° phase shift between signal input and comparator input. The linear voltage-controlled oscillator (VCO) produces an output signal (VCO Out) whose frequency is determined by the voltage at the VCO IN input, and the capacitor and resistors connected to pin C1A, C1B, R1 and R2. The source follower output of the VCOIN (demodulator Out) is used with an external resistor of 10 kΩ or more. The INHIBIT input, when high, disables the VCO and source follower to minimize standby power consumption. The zener diode is provided for power supply regulation, if necessary. Figure 4: Block diagram showing an internal structure of 4046 PLL. A single positive supply voltage is needed for the chip. The positive supply voltage VDD is connected to pin 16 and the ground is connected to pin 8. In this experiment we will employ VDD = +5V. The incoming signal v i goes to the input of an internal 6 amplifier at the pin 14 of the chip. The internal amplifier has the input biased at about VDD/2; therefore, the incoming signal should be capacitively coupled to the input. The incoming ac signal v i of about one volt peak-to-peak is sufficient for proper operation. The ac coupling capacitor C i together with the input resistance R i ≈ 100kΩ at the pin 14 form a high-pass filter. C i should be selected so that v i is in the pass-band of the filter, i.e., so that the input frequency f i > 1/(2πR i C i ) for the lowest expected frequency f i of the incoming signal. The output of the internal amplifier is internally connected to one of the two inputs of the two phase detectors inside the chip. 3. Voltage-Controlled Oscillator The voltage-controlled oscillator (VCO) on the 4046 produces a square wave on pin 4 whose frequency varies with the input voltage (pin 9). The VCO characteristics are user-adjustable by three external components: R1, R2 and C1. • Basing upon the graphs in 4046 datasheet, design the VCO with a supply voltage VDD of 5V to render a center frequency (f 0 ) approximately at 200kHz and being able to tune roughly between 100kHz (f min ) and 300kHz (f max ). • Sketch the output signal from the VCO for f min , f max , f 0 , (f min + f max )/2 and when VCO IN =VDD/2 and plot the output frequency (f osc ) versus VCO’s DC input voltage (VCO IN ) with VCO IN from 0V to VDD (=5V). From this graph, calculate the VCO constant K O (in radians/sec-volt), which is the ratio of the change in operating frequency versus the input voltage. Note that the loop filter is not needed in this part. It is important to determine K O experimentally because its value will be needed for the design of the PLL loop filter in the subsequent parts of the experiment. 4. Phase Comparator I The phase comparator I on the 4046 is simply an XOR logic gate (exclusive-OR), with logic low output (v Φ = 0V) when the two inputs are both high or both low, and the logic high output (v Φ = VDD) otherwise. Figure 5 illustrates the operation of the XOR phase detector when the PLL is in the locked condition. V i2 (the amplified of input v i ) and v osc (the VCO output) are two phase-shifted periodic square-wave signals at the same frequency f osc = f i = 1/T i , and with 50% duty ratios. The output of the phase detector is a periodic pulse signal v Φ (t) at the frequency of 2 f i , and with the duty ratio D Φ which depends on the phase difference ∆ Φ (in radians) between v i and v osc , D Φ = ∆ Φ/π ( 4) 7 Figure 5: Operation of the 4046’s phase comparator I (XOR gate). The periodic signal v Φ (t) at the output of the XOR phase detector can be expressed by Fourier series: ( )( ) ki k k kP tfkvVtv θπ φ −+= ∑ ∞→ = 4sin)( 1 (5) where V P is the DC component of v Φ (t), and v k is the amplitude of the k th harmonic at the frequency 2k f i . Prove that V P is equal to V DD ⋅∆ Φ/π ? Plot V P against ∆ Φ for 0 ≤ ∆ Φ ≤ π . What is the K D of this particular XOR-gate phase comparator? Analysis of a more complicated phase comparator II is beyond the scope of this experiment, in later part of the experiment we will use phase comparator II just to see its functionality without obtaining the corresponding K D value. 5. Loop Filter Design The loop filter is placed between one of the phase detector’s output (either pin 2 or pin 13) and the VCO input (pin 9). This filter attenuates the high frequency harmonics present in the phase detector output. It also significantly controls the PLL loop dynamics. The output v Φ (t) of the phase detector is filtered by an external low-pass filter before being fed into the VCO. In Figure 4, the loop filter is a simple passive RC filter. The purpose of the low-pass filter is to pass the dc and low-frequency portions of v Φ (t) and to attenuate high-frequency ac components at frequencies 2kf i . The simple RC filter has the transfer function: p s CsR sF ω + = + = 1 1 1 1 )( 23 (6) with 8 23 2 1 2 CR f p p ππ ω == (7) is the cut-off frequency of the filter. If f p << 2f i , i.e., the cut-off frequency of the filter is much smaller than twice of the incoming-signal frequency f i , the output of the filter is approximately equal to the dc component V P of the phase detector’s output. In practice, the high-frequency components are not completely eliminated and can be observed as high-frequency ac ripple around the dc or slowly-varying v o . With F(s) described by a simple first-order low-pass filter of Eq.(7), the PLL closed- loop transfer function of Eq.(3) can be re-arranged into a standard form of the second- order transfer function, that is ++ = 1 2 11 )( 2 2 s s K s V n n Oi O ω ξ ω ω (8) Prove that: pDOn KK ωω = (9) and DO p KK ω ξ 2 1 = (10) For a second-order system, it generally requires to have a damping factor ξ to be 1/√2 for an optimal operation (Find out why?). (5.1) Using information for K O and K D obtained from previous sections to design the low-pass filter such that the damping factor ξ = 1/√2. Calculate the corresponding low-pass filter’s bandwidth and the bandwidth of the closed-loop response! Is it possible to design a low-pass filter that renders independent values between the filter’s bandwidth (and closed-loop bandwidth) and the damping factor? With the design you have got, you can now build up a complete PLL circuitry using a phase comparator I (XOR gate) as the phase detector and your circuit should look similar to that in Figure 6, noting that values of R1, R2 and C1 have been previously designed in section 3. 9 Figure 6: The basic PLL with an XOR gate as a phase detector and a simple lowpass filter as a loop filter. (5.2) If there is no incoming input signal, v i = 0, observe the signals at pin 2 and VCO’s output (pin 4) and input (pin 9). Explain what is happening!? Measure the free-running frequency f o . (5.3) Apply a 1Vp-p square wave as an incoming input signal v i at frequency f i – adjust f i to be sufficiently close to the free-running frequency f o . Use a dual-trace oscilloscope to monitor v i and VCO output v osc . When the PLL operates in a locked condition, you should be able to simultaneously view signals from both channels of the oscilloscope (two signals are at the same frequency), otherwise one of the waveform on the scope screen is blurred or is moving with respect to the other. By changing f i of the incoming signal, measure the actual lock range and capture range of the PLL. Determine the minimum peak-to-peak amplitude of the incoming signal v i such that the PLL remains locked. Does this particular PLL lock on harmonics? Record the waveforms v i , v osc , output from the phase detector ( v Φ ), and input of the VCO ( v o ) for the PLL in the locked condition at three different frequencies: (a) f i = f o ; (b) f i = the lowest frequency of the lock range (c) f i = the highest frequency of the lock range Analyse what you have measured! Compare the phase difference between v i and v osc to the theoretical prediction for the three frequencies of the incoming signal. Plot the hysteresis characteristic (similar to Figure 2) of your PLL. Also sketch the waveforms v osc , v Φ , and v o when the PLL is NOT in the locked condition, explain what you see. Employ Phase Comparator II as the PLL’s phase detector and re-do the whole of this section. Compare the results to those obtained with the Phase Comparator I. 10 (5.4) Re-design your low-pass filter with two new bandwidths ( ω p ) of ten times higher and lower than originally obtained from section (5.1), calculate the corresponding new values of ξ . With these two new filters, re-do the whole of section (5.3) using both types of phase comparators. Compare the results to what have been obtained in section (5.3). Analyse your results! What are the advantages and disadvantages of the PLL employing a simple first-order low-pass filter? 6. Lead-Lag Filter as a Loop Filter A disadvantage of the second-order loop PLL system designed in section 5 is that the bandwidth of the loop is basically dictated by loop gain K O K D . In general, the loop gain also sets the lock range, so that with the simple filter used above these two parameters are constrained to be comparable. Situations do arise in phase-locked communications in which a wide lock range is desired for tracking large signal- frequency variations, yet a narrow loop bandwidth is desired for rejecting out-of-band signals. Using a very small ω p would accomplish this were it not for the fact that this also produces underdamped loop response. By adding a zero to the loop filter, the loop filter pole can be made small while still maintaining good loop damping. This can be accomplished by employing a lead-lag filter in Figure 7 as a loop filter instead of a simple low-pass filter. R4 R5 C3 IN OUT Figure 7: Lead-lag filter. Transfer function F(s) of the lead-lag filter can be arranged in a form of p z s s sF ω ω ′ + + = 1 1 )( (11) Express ω z and ω ' p in terms of R4, R5 and C3. Show that the closed-loop transfer function of the PLL in Figure 3 can be found to be: ++ + = 1 2 1 1 )( 2 2 s s s K s V n n z Oi O ω ξ ω ω ω (12) when the lead-lag filter in Figure 7 is employed as a loop filter, where [...]... ω′p=16krad/s and use phase comparator II as a phase detector) Here, the PLL is being employed as an FM demodulator Have you managed to recover the 1kHz modulating signal Explain the operation of the entire system (FM modulator and demodulator) Sketch the demodulated signal and compare it with the modulating on the same scope screen What happens if phase comparator I (XOR gate) is employed instead of phase. .. the corresponding closed -loop bandwidth ωn) with a damping factor ξ=1/√2 With the design you have, carry out the same experiment as in section (5.3) Analyse the results you measure Try to increase ω′p to 160krad/s while maintaining ξ at 1/√2 and explain what you see 7 FM Modulation and Demodulation In this part of the experiment, we investigate the application of PLL for FM demodulation Students are... on FM demodulation technique using PLL [4] (7.1) Another 4046 IC is needed to generate an FM modulated signal Use the design information from section 3 to generate FM carrier signal at frequency f0 (150kHz) and modulate it with 1kHz sinusoidal signal Hint: you will only need the VCO on 4046 to build this FM modulator Observe the output signal of the VCO, what do you see? (7.2) Inject the modulated FM. .. theoretical analysis and scientific discussion are meaningless and carry no marks! References: [1] B Razavi, Design of Analog CMOS Integrated Circuits, Chapter 15, McGrawHill, 2001 [2] P R Gray and R G Meyer, Analysis and Design of Analog Integrated Circuits, Chapter 10, 3rd ed., Jonh Wiley & Sons, 1993 (or latest edition) [3] Fairchild Semiconductor, CD4046BC Micropower Phase- Locked Loop, 2002 Downloadable... the results you have obtained and conclude the experiment [Optional] Try injecting MP3 music to the input of the modulator and see if you can manage to recover and hear the original sound from your demodulator You definitely need a speaker for this! [Optional] Use Matlab-Simulink, Orcad-PSPICE to perform system simulation and verify functionalities of your FM modulation /demodulation system • Specifically,... simulation and verify functionalities of your FM modulation /demodulation system • Specifically, inspect spectrum of the FM signal when the carrier has been modulated by a 1-kHz sinusoidal signal – compare your results with theoretical predictions 11 • Carry out experiment to examine the phase- locking transient dynamic of your system with respect to classical feedback control theoretical concept (overshoot,... ed., Jonh Wiley & Sons, 1993 (or latest edition) [3] Fairchild Semiconductor, CD4046BC Micropower Phase- Locked Loop, 2002 Downloadable from http://www.fairchildsemi.com/pf/CD/CD4046BC.html [4] J Dunlop and D G Smith, Telecommunications Engineering, 3rd Ed., Chapman & Hall, pp68-70, 1994 [5] N S Nise, Control Systems Engineering, 4th Ed., John Wiley & Sons, 2004 September, 2009 12