INF4420 Phase locked loops Spring 2012 Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no)
Outline "Linear" PLLs Linear analysis (phase domain) Charge pump PLLs Delay locked loops (DLLs) Applications
Introduction Phase locked loops (PLLs) are versatile building blocks found in a variety of applications Frequency multiplication Frequency synthesis Clock deskew (PLL or DLL) Clock recovery (from serial data) Demodulation...
Introduction Feedback system for aligning (a fraction of) the phase of the VCO clock with an (external) reference clock. The VCO control voltage is adjusted to achieve this.
Introduction We will analyze the PLL in terms of phase. The objective of the feedback loop, the PLL, is to keep ϕ ref - ϕ out small and constant. In this state, the PLL is said to be in lock. This implies ω ref = ω out which is what we care about in many applications.
"Linear" PLL Phase detector Loop filter We will first analyze a PLL with a simple phase detector (PD) first.
Phase detector Phase is not directly observable. We have to infer the phase difference from the output of the oscillators. An XOR gate can be used as a phase detector.
Phase detector When ϕ ref and ϕ out is 90 out of phase, the XOR output will have 50/50 duty cycle, and the average output will therefore be V dd / 2. If ϕ ref and ϕ out is at 0 or 180 phase difference, the average output will be 0 or V dd respectively.
Phase detector
PLL with XOR PD With the XOR PD, to generate the required V ctl, ϕ ref and ϕ out must be out of phase.
Loop dynamics Linear analysis of the PLL in terms of phase, H (s) = ϕ out (s) / ϕ in (s).
Second order TF Generic second order transfer function applied to the PLL: Natural frequency Damping ratio
Loop dynamics By choosing PLL parameters, K VCO, K PD, and τ LF, we can design ω n and ζ, to obtain the desired loop dynamics. Magnitude response Step response
Large signal behaviour An important point for PLLs is the large signal behaviour when the system is not in lock. When the PLL starts up, ϕ ref and ϕ out may be very different. We must make sure that the system is able to achieve lock. Another concern is whether the PLL will lock to a harmonic instead. The PLL with XOR based PD is not robust in this case. In most applications, a so called charge pump (CP) PLL is preferred.
Charge pump PLL Tracks whether the reference edge or the VCO clock edge comes first (for every period), and adjusts the VCO control voltage accordingly to keep the PLL in lock. When the PLL is in lock, out and ref will be in phase. Phase frequency detector Charge pump Loop filter
Phase Frequency Detector In the Charge Pump (CP) PLL, a more elaborate PD with state is used, a Phase Frequency Detector (PFD).
PDF/CP and loop filter The PFD generates control signals for the CP to ramp up or down the VCO control voltage.
PFD/CP gain When the PLL is in lock, a small phase difference between the VCO clock (out) and the reference clock (ref) turns on the CP for a fraction of the clock period injecting a charge proportional to the phase error to the loop filter every period. Looking at several periods, an average current flows. K PFD is the combined gain of the PFD and the CP:
CP loop filter The loop filter is driven by I avg from the PFD/CP In many cases, a second capacitor, C 2, is added in parallel to reduce glitches. C 2 is usually chosen to be approximately 10 % of C 1 or less.
Transfer function The open loop transfer function from ϕ ref to ϕ out The closed loop CP PLL transfer function
Transfer function R gives rise to a zero at -1/(RC). It is required as system would be unstable with R = 0.
Non-ideal effects in PLLs PFD/CP will exhibit zero gain when the phase difference is small because of finite rise and fall times Up/down current mismatch due to timing or current source impedance Jitter from power supply, coupling, electronic noise, reference phase noise...
Delay locked loop (DLL) A DLL is similar to a PLL, but instead the delay through a voltage controlled delay line (VCDL) is locked.
Delay locked loop (DLL) Noise (jitter) does not accumulate in the delay line like it would in a VCO. As there is no VCO, the order of the loop is one less than the PLL. Stability and settling issues are less prominent. The DLL is not the same as a PLL and only relevant for some PLL applications. DLLs are usually preferred where applicable.
Frequency multiplication Frequency multiplication is a common application for PLLs. High speed clocks can be generated from a stable and precise (but slow) reference clock. N can be programmable.
Frequency demodulation The VCO performs frequency modulation (FM). The PLL can be used to find the inverse. The VCO control voltage becomes the output.
Other PLL issues We have used a continuous time analysis for the PLL. However, the PFD samples the phase. We approximated the PFD/CP output as an average current. When the deglitching capacitor, C 2, is used, the transfer function becomes third order. Using the second order transfer function may not be appropriate.
Resources Gardner, Phaselock Techniques, Wiley, 2005 Fischette, Dennis Fischette's 1-Stop PLL Center Johns and Martin, Analog Integrated Circuit Design, Wiley, 1997