MT-086 tutorial fundamentals of phase locked loops (plls) fundamental phase locked loop architecture a phase-locked loop is a feedback system combining a voltage c ontrolled oscillator (vco) and a phase comparator so connected that the oscillato r maintains a constant pha se angle relative to a reference signal. phase-locked loops can be use d, for example, to generate stable output high frequency signals from a fi xed low-frequency signal. figure 1a shows the basic model for a pll. the pll can be analyzed as a negative feedback system using laplace transform theory with a fo rward gain term, g(s), and a feedback term, h(s), as shown in figure 1b. the usual equa tions for a negative feedback system apply. (b) standard negative feedback control system model (a) pll model error detector loop filter vco feedback divider phase detector charge pump f o = n f ref (a) pll model error detector loop filter vco feedback divider phase detector charge pump f o = n f ref figure 1: basic phase locked loop (pll) model the basic blocks of the pll are the error detector (composed of a phase frequency detector and a charge pump ), loop filter , vco , and a feedback divider . negative feedback forces the error signal, e(s), to approach zero at which point the feedback di vider output and the reference frequency are in phase a nd frequency lock, and f o = n fref . referring to figure 1, a system for using a pll to generate higher frequencies than the input, the vco oscillates at an angular frequency of o . a portion of this signal is fed back to the error detector, via a frequency divider with a ratio 1/n. this divided down frequency is fed to one input of the error detector. the ot her input in this example is a fixed reference signal. the error detector compares the signals at both inputs. when the two signal inputs are equal in phase and frequency, the error will be constant and the l oop is said to be in a ?locked? condition. rev.0, 10/08, wk page 1 of 10
MT-086 phase frequency detector (pfd) figure 2 shows a popular implementation of a phase frequency detector (pfd), basically consisting of two d-type flip flops. one q output enables a positive current source; and the other q output enables a negative current source. assuming that, in this design, the d-type flip flop is positive-edge triggered, the possible states are shown in the logic table. d1 q1 clr1 clr2 d2 q2 v+ v ? hi hi +in ? in delay up down cp out i i u1 u2 u3 pfd cp d1 q1 clr1 clr2 d2 q2 v+ v ? hi hi +in ? in delay up down cp out i i u1 u2 u3 pfd cp (a) out of frequency lock and phase lock (b) in frequency lock, but slightly out of phase lock 0 +i +i 0 (a) out of frequency lock and phase lock (b) in frequency lock, but slightly out of phase lock 0 +i +i 0 up 1 0 0 down 0 1 0 cp out + i ? i 0 up 1 0 0 down 0 1 0 cp out + i ? i 0 +in ? in out 0 +i ? i (c) in frequency lock and phase lock figure 2: phase/frequency detector (pfd) driving charge pump (cp) consider now how the circuit beha ves if the system is out of lo ck and the frequency at +in is much higher than the frequency at ?in, as show n in figure 2a. since th e frequency at +in is much higher than that at ?in, the up output spe nds most of its time in the high state. the first rising edge on +in sends the output high and this is maintained unt il the first rising edge occurs on ?in. in a practical system this means that the output, and thus the input to the vco, is driven higher, resulting in an increase in frequency at ?in. this is exactly what is desired. if the frequency on +in were much lower than on ?in, the opposite eff ect would occur. the output at out would spend most of its time in the low c ondition. this would have the effect of driving the vco in the negative direction and again bring the frequency at ?in much closer to that at +in, to approach the locked condition. figure 2b shows the waveforms wh en the inputs are frequency-lo cked and close to phase-lock. since +in is leading ?in, the output is a series of positive current pulses. these pulses will tend to drive the vco so that the ?in signal become phase-aligned with that on +in. when this occurs, if there were no delay element between u3 and the clr inputs of u1 and u2, it would be possible for the output to be in high-imped ance mode, producing neither positive nor negative current pulses. this would not be a good situation. page 2 of 10
MT-086 the vco would drift until a significant phase error developed and started producing either positive or negative current pulses once again. over a relatively long period of time, the effect of this cycling would be for the outpu t of the charge pump to be m odulated by a signal that is a sub- harmonic of the pfd input reference frequency. si nce this could be a low frequency signal, it would not be attenuated by the loop filter and would result in very significant spurs in the vco output spectrum, a phenomenon known as the "backlash" or "dead zone" effect. the delay element between the output of u3 and the clr inputs of u1 and u2 ensures that it does not happen. with the delay element, even when the +in and ?in are perfectly phase- aligned, there will still be a current pulse generated at the charge pump output as shown in figure 2c. the duration of this delay is equal to the delay inserted at the output of u3 and is known as the anti-backlash pulse width. note that if the +in frequency is lower than the ? in frequency and/or the +in phase lags the ? in phase, then the output of the charge pump will be a series of negative current pulses?the reverse of the condition shown in (a) and (b) in figure 2. prescalers in the classical integer-n synthesizer, the resolu tion of the output frequency is determined by the reference frequency applied to the phase dete ctor. so, for example, if 200 khz spacing is required (as in gsm phones), then the reference frequency must be 200 khz. however, getting a stable 200 khz frequency source is not easy. a sens ible approach is to take a good crystal-based high frequency source and divide it down. for exam ple, the desired frequency spacing could be achieved by starting with a 10 mhz frequency reference and dividing it down by 50. this approach is shown in figure 3a. (a) (b) reference divider y r reference divider y r prescaler y p figure 3: adding an input reference di vider and a prescaler to the basic pll page 3 of 10
MT-086 the "n counter," also known as the n divider, is the programmable element that sets the relationship between the input an d output frequencies in the pll. the complexity of the n counter has grown over the years. in addition to a straightforward n count er, it has evolved to include a prescaler , which can have a dual modulus . this structure has grow n as a solution to the problems inherent in using the basic divide-by-n structure to feed back to the phase detector when very high-frequency outputs are required. for example, let?s assume that a 900 mhz output is required with 10 hz spacing. a 10 mhz reference frequency might be used, with the r- divider set at 1000. then, the n-va lue in the feedback would need to be of the order of 90,000. this would mean at least a 17-b it counter capable of dealing w ith an input frequency of 900 mhz. to handle this range, it makes sense to precede the programmable counter with a fixed counter element to bring the very high input fre quency down to a range at which standard cmos will operate. this counter, called a prescaler , is shown in figure 3b. however, note that using a standard prescaler as shown reduces the system resolution to f1 p. this issue can be addressed by using a dual-modulus prescaler which has the advantages of a standard prescaler, but without lo ss of resolution. a dual-modulus prescaler is a counter whose division ratio can be switched from one value to another by an external cont rol signal. it's use is described shown in figure 4. = = , therefore dual modulus prescaler ;- p / p + 1 figure 4: adding a dual m odulus prescaler to the pll by using the dual-modulus prescaler with an a and b counter, one can still maintain output resolution of f1. however, the following conditions must be met: 1. the output signals of both counters are hi gh if the counters have not timed out. 2. when the b counter times out, its output goes low, and it immediately loads both counters to their preset values. page 4 of 10
MT-086 3. the value loaded to the b counter must alwa ys be greater than that loaded to the a counter. assume that the b counter has just timed out a nd both counters have been reloaded with the values a and b. let?s find the number of vco cycl es necessary to get to the same state again. as long as the a counter has not timed out, the prescaler is dividing down by p + 1. so, both the a and b counters will count down by 1 every time th e prescaler counts (p + 1) vco cycles. this means the a counter will time out after ((p + 1) a) vco cycles. at this point the prescaler is switched to divide-by- p. it is also possible to say that at this time the b counter still has (b ? a) cycles to go before it times out. how long will it take to do this: ((b ? a) p). the system is now back to the initial condition where we started. the total number of vco cycles needed for this to happen is : n = [a (p + 1)] + [(b ? a) p] = ap + a + bp ? ap = bp + a. therefore, f out = (f ref /r) (bp + a), as in figure 4. there are many specifications to consider when designing a pll. the input rf frequency range and the channel spacing determine the value of the r and n counter and the prescaler parameters. the loop bandwidth determines the frequency and phase lock time. since the pll is a negative feedback system, phase margin and stability issues must be considered. spectral purity of the pll output is specified by the phase noise and the level of the reference- related spurs. many of these parameters are interactive; for in stance, lower values of loop bandwidth lead to reduced levels of phase noise and reference spur s, but at the expense of longer lock times and less phase margin. because of the many tradeoffs involved, the use of a pll desi gn program such as the analog devices' adisimpll? allows these tradeoffs to be evaluated and the various parameters adjusted to fit the required specifications. the progr am not only assists in the theoretical design, but also aids in parts selection and determines component values. oscillator/pll phase noise a pll is a type of oscillator, and in any oscill ator design, frequency st ability is of critical importance. we are interested in both long-term and short-term stability. long-term frequency page 5 of 10
MT-086 stability is concerned with how the output signal varies over a long period of time (hours, days, or months). it is usually specified as the ratio, f/f for a given period of time, expressed as a percentage or in db. short-term stability, on the other hand, is concer ned with variations that occur over a period of seconds or less. these variations can be random or periodic. a spectrum anal yzer can be used to examine the short-term stability of a signal. fi gure 5 shows a typical spectrum, with random and discrete frequency components causing a broad skirt and spurious peaks. phase noise (dbc/hz) f o f "close-in" phase noise broadband phase noise 1hz bw f m = offset frequency spurs output frequency figure 5: oscillator phase noise and spurs the discrete spurious components could be caused by known clock frequencies in the signal source, power line interference, and mixer pr oducts. the broadening caused by random noise fluctuation is due to phase noise. it can be the result of thermal noise, shot noise, and/or flicker noise in active and passive devices. the phase noise spectrum of an oscillator sh ows the noise power in a 1 hz bandwidth as a function of frequency. phase noise is defined as the ratio of the noise in a 1 hz bandwidth at a specified frequency offset, fm, to the oscillator signal amplitude at frequency f o . it is customary to characterize an oscillator in terms of its single-sideba nd phase noise as shown in figure 6, where the phase noise in dbc/hz is plotted as a function of frequency offset, f m , with the frequency axis on a log scale. note the actu al curve is approximated by a number of regions, each having a slope of 1/f x , where x = 0 corresponds to the "w hite" phase noise region (slope = 0 db/decade), and x = 1, corresponds to the "flicker" phase noise region (slope = ?20 db/decade). there are also regions where x = 2, 3, 4, and thes e regions occur progressively closer to the carrier frequency. page 6 of 10
MT-086 phase noise (dbc/hz) frequency offset, f m , (log scale) 1 f 1 f 2 1 f 3 "white" phase noise (broadband) "flicker" phase noise 1 f corner frequency integrate phase noise over bandwidth to get rms time jitter f output figure 6: phase noise in dbc/hz versus fr equency offset from output frequency note that the phase noise curve is somewhat anal ogous to the input voltage noise spectral density of an amplifier. like amplifie r voltage noise, low 1/f corner fr equencies are highly desirable in an oscillator. in some cases, it is useful to convert phase noise into time jitter. this can be done by basically integrating the phase noise plot over the desired frequency range. (see tutorial mt-008, converting oscillator phase noise to time jitter ). the ability to perform this conversion between phase noise and time jitter is especially useful when using the pll output to drive an adc sampling clock. once the time jitter is known, its effect on the overall adc snr can be evaluated. the adisimpll? program (to be discussed shor tly) performs the conversion between phase noise and time jitter. fractional-n phase locked loops fractional-n plls have been ut ilized since the 1970s. as has been discussed, the resolution at the output of an integer-n pll is limited to step s of the pfd input frequency as shown in figure 7a, where the pfd input is 0.2 mhz. fractional-n allows the resolution at the pll output to be reduced to small fractions of the pfd frequency as shown in figure 7b, where the pfd input frequency is 1 mh z. it is possible to generate output frequencies with resolutions of 100s of hz, while maintaining a high pfd frequency. as a result the n-value is si gnificantly less than for integer-n. page 7 of 10
MT-086 ref divider r pfd filter vco n counter f ref f 1 f out 10mhz r =50 0.2mhz n = 4501 900.2mhz ref divider r pfd filter vco "n" counter f ref f 1 f out 10mhz r =10 1mhz 900.2mhz n =900.2 "n" = n integer + n fraction n modulus = 900 + n fraction 5 f out = f ref (n/r) (a) integer n (b) fractional n figure 7: integer-n compared to fractional-n synthesizer since noise at the charge pump is multiplied up to the output at a rate of 20logn, significant improvements in phase noise are possible. for a gsm900 system, the fractional-n adf4252 offers phase noise performance of ?103 db c/hz, compared with ?93 dbc/hz for the adf4106 integer-n pll. also offering a significant advantage is the lo ck-time improvement made possible by fractional- n. the pfd frequency set to 20 mhz and loop bandwidth of 150 khz will allow the synthesizer to jump 30 mhz in less than 30 s. current base stations require two pll blocks to ensure that los can meet the timing requirements for tran smissions. with the super-fast lock times of fractional-n, future synthesizers will have lock time specs that allow the two ?ping-pong? plls to be replaced with a single fractional-n pll block. the downside of fractional-n p lls is higher spurious levels . a fractional-n divide by 900.2 (see figure 7b) consists of the n-divider dividing by 900 80 % of the time, and by 901 20% of the time. the average division is correct, but the instantaneous division is incorrect. because of this, the pfd and charge pump ar e constantly trying to correct for instantaneous phase errors. the heavy digital activity of the sigma-delta mo dulator, which provides th e averaging function, creates spurious components at the output. the di gital noise, combined with inaccuracies in matching the hard-working charge pu mp, results in spurious levels greater than those allowable by most communications standards. only recently have fractional-n parts, such as the adf4252, made the necessary improvements in spurious perf ormance to allow designers to consider their use in traditional integer-n markets. page 8 of 10
MT-086 simplifying pll design using adisimpll? the adisimpll? software is a complete pll design package which can be downloaded from the analog devices' website. the software ha s a user-friendly graphical interface, and a complete comprehensive tutorial for first-time users. traditionally, pll synthesizer design relied on published application notes to assist in the design of the pll loop filter. it was necessary to build prototype circuits to determine key performance parameters such as lock time, phase noise, and reference spurious levels. optimization was accomplished by "tweaking" component values on the bench and repeating lengthy measurements. adisimpll both streamlines and im proves the traditional design pro cess. starting with the ?new pll wizard,? a designer constructs a pll by specify ing the frequency requirements of the pll, selecting an integer-n or fractional-n implementation, and th en choosing from a library of pll chips, library or custom vco, and a loop filte r from a range of topologi es. the program designs a loop filter and displays key parameters including phase noise, reference spurs, lock time, lock detect performance, and others. adisimpll operates with spreadsheet-like simplicity and interactivity. the full range of design parameters such as loop bandwidth, phase margin, vco sensitivity, and component values can be altered with real-time updates of the simulation results. this a llows the user to easily optimize the design for specific requirements. varying th e bandwidth, for example, enables the user to observe the tradeoff between lock time and pha se noise in real-time, and with bench- measurement accuracy. adisimpll includes accurate models for phas e noise, enabling reliab le prediction of the synthesizer closed-loop phase noise. users report excellent co rrelation between simulation and measurement. if required, the de signer can work direc tly at the component level and observe the effects of varying individual component values. the basic design process using adisimp ll can be summarized as follows: 1. choose reference frequency, output fr equency range, and channel spacing 2. select pll chip from list 3. select vco 4. select loop filter configuration 5. select loop filter bandwidth and phase margin 6. run simulation 7. evaluate time and frequency domain results 8. optimize adisimpll works for integer-n or fractional-n plls, but does not simulate fractional-n spurs. phase noise prediction for fracti onal-n devices assumes the device is operating in the "lowest phase noise" mode. page 9 of 10
page 10 of 10 MT-086 references 1. mike curtin and paul o'brien, "phase-locked loops for high-frequ ency receivers and transmitters" part 1, analog dialogue , 33-3, analog devices, 1999 part 2, analog dialogue , 33-5, analog devices, 1999 part 3, analog dialogue , 33-7, analog devices, 1999 2. roland e. best, phase locked loops, 5th edition , mcgraw-hill, 2003, isbn: 0071412018. 3. floyd m. gardner, phaselock techniques, 2nd edition , john wiley, 1979, isbn: 0471042943. 4. dean banerjee, pll performance, simulation and design, 3rd edition , dean banerjee p ublications, 2003, isbn: 0970820712 . 5. bar-giora goldberg, digital frequency synthesis demystified , newnes, 1999, isbn: 1878707477. 6. brendan daly, "comparing integer-n and fractional-n synthesizers," microwaves and rf , september 2001, pp. 210-215. 7. adrian fox, "ask the applications engineer-30 (discussion of plls)," analog dialogue , 36-3, 2002 . 8. hank zumbahlen, basic linear design , analog devices, 2006, isbn: 0-915550-28-1. also available as linear circuit design handbook , elsevier-newnes, 2008, isbn-10: 0750687037, isbn-13: 978- 0750687034. chapter 4. 9. walt kester, analog-digital conversion , analog devices, 2004, isbn 0-916550-27-3, chapter 6. also available as the data conversion handbook , elsevier/newnes, 2005, isbn 0-7506-7841-0, chapter 6. 10. walt kester, "converting oscillator phase noise to time jitter," tutorial mt-008 , analog devices 11. design tool: adisimpll , analog devices, inc. 12. analog devices pll product portfolio: http://www.analog.com/pll copyright 2009, analog devices, inc. all rights reserved. analog devices assumes no responsibility for customer product design or the use or application of customers? products or for any infringements of patents or rights of others which may result from analog devices assistance. all trad emarks and logos are property of their respective holders. information furnished by analog devices applications and development tools engineers is believed to be accurate and reliable, however no responsibility is assumed by analog devices regarding technical accuracy and topicality of the content provided in analog devices tutorials.
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