Method and system for low power, low jitter, wide range, self-adaptive multi-frequency phase locked loop

[0002] The present invention relates generally to a phase locked loop (PLL) and more particularly to a self biased multifrequency PLL.

[0003] Delay-locked loops (DLLs) and phase-locked loops (PLLs) are often used in the I/O interfaces of digital integrated circuits in order to hide clock distribution delays and to improve overall system timing. In these applications, DLLs and PLLs must closely track the input clock. However, the rising demand for high-speed I/O has created an increasingly noisy environment in which DLLs and PLLs must function. This noise, typically in the form of supply and substrate noise, tends to cause the output clocks of DLLs and PLLs to jitter from their ideal timing. With a shrinking tolerance for jitter in the decreasing period of the output clock, the design of low jitter DLLs and PLLs has become very challenging.

[0004] Achieving low jitter in PLL and DLL designs can be difficult due to a number of design tradeoffs. Consider a typical PLL which is based on a voltage controlled oscillator (VCO). The amount of input tracking jitter produced as a result of supply and substrate noise is directly related to how quickly the PLL can correct the output frequency. To reduce the jitter, the loop bandwidth should be set as high as possible. Unfortunately, the loop bandwidth is affected by many process technology factors and is constrained to be well below the lowest operating frequency for stability. These constraints can cause the PLL to have a narrow operating frequency range and poor jitter performance. Although a typical DLL is based on a delay line and thus simpler from a control perspective, it can have a limited delay range which leads to a set of problems similar to that of the PLL.

[0005] FIG. 1 illustrates a conventional phase locked loop (PLL) 10. PLL 10 comprises a phase frequency detector (PFD) 12 which receives a feedback frequency and a fixed reference frequency from typically a crystal oscillator. The phase frequency detector 12 provides two output signals, an up signal or a down signal depending on the relationship of the fixed frequency and the feedback frequency. Those signals are provided to charge pump 14 which provides an output to a low pass filter 16 and a voltage controlled oscillator (VCO) 18. The VCO 18 provides an output voltage based upon the frequency. The output voltage is fed back to a counter 20 which is typically a divide by N counter which is used to ensure loop stability. Accordingly, if the phase frequency detector 12 provides an up signal there will be a corresponding increase in the charge pump signal to the VCO 18 to cause the feedback frequency to increase to match it to the fixed frequency. Conversely, if the phase frequency detector 12 provides a down signal there will be a corresponding decrease in the charge pump signal to the VCO 18 which will cause the feedback frequency to decrease, thereby bringing it in line with the crystal.

[0006] As is well known, the open loop gain (G_OL) of the PLL can be characterized by the following equation which is shown below: $G_{\mathrm{ol}}=\frac{\mathrm{Ich}·K_0·\left(1+\mathrm{RCs}\right)}{{\mathrm{Cs}}^2}$

[0007] As is well known, the closed loop gain (G_CL) for PLL is then a second-order system as shown below: $G_{\mathrm{cl}}=\frac{G_{\mathrm{ol}}}{1+\frac{G_{\mathrm{ol}}}{N}}=\frac{N·\mathrm{Ich}·K_0·\left(1+\mathrm{RCs}\right)}{{\mathrm{NCs}}^2+\mathrm{Ich}·K_0·\left(1+\mathrm{RCs}\right)}=N·\frac{1+2·\zeta ·\left(s/w_n\right)}{1+2·\zeta ·\left(s/w_n\right)+{\left(s/w_n\right)}^2}$

[0008] The loop system can be characterized by two factors, the loop damping factor and the loop bandwidth factor.

[0009] The loop damping factor (ξ) is characterized by the equation: $\zeta =\frac{{\mathrm{RCw}}_n}{2}=\frac{R}{2}\sqrt{\frac{\mathrm{Ich}·K_0·C}{N}}$

[0010] The loop bandwidth factor (w_n) is characterized by the equation: $w_n=\sqrt{\frac{\mathrm{Ich}·K_0}{\mathrm{NC}}}$

[0011] FIG. 2 is a Bode plot which illustrates the open loop gain (G_OL) and the closed loop gain (G_CL) for stable and unstable systems respectively. The traditional stability criteria for G_OLfor the PLL is G_olcrossing 0 dB with a −20 db/decade slope so that $w_n>w_{\mathrm{RC}}=\frac{1}{\mathrm{RC}},\mathrm{then}\zeta >0·5\mathrm{because}\frac{w_n}{w_{\mathrm{RC}}}=\frac{w_c}{w_n}=2·\zeta$

[0012] The open loop gain G_OLusually has a distant pole due to parasitic capacitances. Accordingly, the PLL can be unstable if appropriate precautions are not taken. Actually, the stability criteria is more restrictive if it's deduced from differential equation (sampling) but the VCO overload criteria is usually prevailing. That is due to the instantaneous voltage drop on the loop filter.

[0013] FIG. 3 illustrates a change of Ich over time. It is known that the VCO overload limit is $R·\mathrm{Ich}<\frac{\mathrm{Fvco}}{K_0}.$

[0014] This relationship leads to the following equation: $\frac{w_n}{w_{\mathrm{ref}}}<\frac{1}{4\mathrm{\pi \zeta }}.$

[0015] Accordingly, therefore, ω_refmust be at least 2.π times away from ω_Cto ensure stability. The optimum damping factor for a critically damped system stability having a minimum settling time is 0.707. So ω_refthen must be 8.88 times away from ω_nto ensure stability. A safe value for this relationship is that ω_refis ten (10) times away from ω_n, to filter input frequency noise.

[0016] As before mentioned, achieving low jitter in PLL designs can be difficult due to a number of designs tradeoffs. To reduce peak-to-peak jitter due to VCO noise, it is advantageous to keep as high a PLL bandwidth as possible. Traditional charge-pump PLL design would keep the PLL bandwidth and damping factor sufficiently far away from stability limits under all variations of the input reference frequency, the manufacturing process, and the division ratio in the feedback path N. These constraints can cause the PLL to have a narrow operating frequency range and poor jitter performance.

[0017] Ideally, both ξ and $\frac{w_n}{w_{\mathrm{ref}}}$

[0018] should be constant so that there is no limit on the operating frequency range and the jitter performance can be improved.

[0019] A self-biased PLL design technique avoids the necessity for external biasing (bandgap) by generating internal bias voltages and currents depending on the operating conditions. FIG. 4 illustrates a conventional self-biased PLL 100. In the self-biased system of FIG. 4, there is a similar phase frequency detector 101 with two charge pumps 102 and 106, one of which (charge pump 106) provides an output directly to the VCO 105 and the other of which (charge pump 102) provides its output to a low pass filter 103 which in turn provides a signal to a bias generator 104. The bias generator 104 in turn provides an output signal Vbn to the VCO 105, while the charge pump 106 provides an input to the VCO 105 of Vbp. The output V0 of the VCO 105 is fed back to a divide by N counter 108 in a manner similar to that described with reference to FIG. 1. The self-biased PLL design achieves process technology independence, fixed damping factor, fixed bandwidth to operating frequency ratio, broad frequency range, input phase offset cancellation, high supply and substrate noise rejection. Accordingly, this system is advantageous over the system of FIG. 1. However, it does have problems which will be described hereinbelow. Principally, those problems are associated with it being only allowed to operate effectively in a fixed frequency environment.

[0020] The following three papers describe some existing self-biased PLLs:

[0021] [1] Low-jitter Process-Independent DLL and PLL Based on Self-biased Techniques, John G. Maneatis, IEEE Journal of Solid State Circuits, Vol.31, No.11, November 1996.

[0022] [2] Adaptive Bandwidth DLLs and PLLs using Regulated Supply CMOS Buffers, S.Sidiropoulos, D.Liu, J.Kim, G.Wei, M.Horowitz—Rambus Inc. and Standford University, IEEE 2000.

[0023] [3] A2-1600-MHz1.2-2.5V CMOS Clock Recovery PLL with Feedback Phase-Selection and Averaging Phase-Interpolation for Jitter Reduction, Patrick Larsson, 1999 IEEE International Solid State Circuits Conference, Vol.34, No.12, December 1999.

[0024] As before mentioned, these solutions do not affect frequency range variations associated with N. They only provide a fixed bandwidth independent of the frequency range.

[0025] Accordingly, what is needed is a system and method for providing a PLL which can operate effectively over a wide range of frequencies. The system should be easy to implement in existing systems and be cost effective. The present invention addresses such a need.

[0026] A self-adaptive method for controlling a self-biased PLL system is disclosed. The method comprises providing an application-dependent input frequency; and providing an application-dependent number N representing the ratio between the output frequency and the application-dependent input frequency to the PLL system.

[0027] In a system and method in accordance with the present invention, the bandwidth and damping factor are tracked, not only with the input frequency but with the divider ratio as well. Therefore, jitter is minimized for any operating condition (i.e., input frequency variations associated with an application-dependent number N representing the ratio between the output frequency and the application-dependent input frequency to the PLL system). The charge-pump current is made to be proportional to the VCO current ID and inversely proportional to the frequency range associated with N; and the loop filter resistor is made to be inversely proportional to the square root of the VCO current ID and proportional to N. In so doing, the bandwidth and damping factors can be tracked more comprehensively.

[0028] FIG. 1 illustrates a conventional phase locked loop.

[0029] FIG. 2 is a Bode plot which illustrates the open loop gain and the closed loop gain for stable and unstable systems.

[0030] FIG. 3 illustrates a change of Ich over time.

[0031] FIG. 4 illustrates a conventional self-biased PLL.

[0032] FIG. 5 illustrates a self-biased PLL in accordance with the present invention.

[0033] FIG. 6 is a Bode plot illustrating the tracking with N.

[0034] FIG. 7 illustrates a charge pump coupled to the diode connected loads in the resistor generator.

[0035] The present invention relates generally to a phase locked loop (PLL) and more particularly to providing a lower power low jitter multifrequency synthesizer. The following description is presented to enable one of ordinary skill in the art to make and use the invention and is provided in the context of a patent application and its requirements. Various modifications to the preferred embodiment and the generic principles and features described herein will be readily apparent to those skilled in the art. Thus, the present invention is not intended to be limited to the embodiment shown but is to be accorded the widest scope consistent with the principles and features described herein.

[0036] In a system and method in accordance with the present invention, the bandwidth and damping factor are tracked, not only with the input frequency but with the divider ratio as well. Therefore, jitter is minimized for any operating condition (i.e., input frequency variations associated with an application-dependent number N representing the ratio between the output frequency and the application-dependent input frequency to the PLL system). The charge-pump current is made to be proportional to the VCO current I_Dand inversely proportional to the frequency range associated with N; and the loop filter resistor is made to be inversely proportional to the square root of the VCO current I_Dand proportional to N. In so doing, the bandwidth and damping factors can be tracked more comprehensively.

[0037] Assume that X is the charge-pump current to VCO current ratio, and Y is the resistor to square root VCO current ratio. Accordingly, X is proportional to 1/N and Y is proportional to N.

[0038] 1. VCO Overload Limit

[0039] When the charge-pump is sinking or sourcing a current Ich, the instantaneous voltage drop at the input of the VCO should not exceed its operating range. The VCO overload limit is then $R·\mathrm{Ich}<\frac{\mathrm{Fvco}}{K_0}$

[0040] Considering [1] eq. (17)-(20), $F_{\mathrm{VCO}}=\frac{\sqrt{2·k·I_D}}{C_B},K_0=\frac{k}{C_B}$ $\mathrm{Ich}=X·\left(2·I_D\right)=\frac{\alpha }{N}·\left(2·I_D\right)$ $R=\frac{Y}{\sqrt{8·k·I_D}}=\frac{\beta ·N}{\sqrt{8·k·I_D}}$

[0041] The overload limit becomes $\frac{X·Y·2·I_D}{\sqrt{8·k·I_D}}<\frac{\sqrt{2·k·I_D}}{C_B}\times \frac{C_B}{k}\mathrm{thus},\underset{\_}{X·Y<2}$

[0042] 2. Charge-pump Current Versus Loop Filter Resistance

[0043] The loop filter resistance generator is basically designed with diode connected PMOS loads. FIG. 7 illustrates a charge pump coupled to the diode connected loads. In this type of arrangement, the PMOS load must always have a positive current I_Rflowing through it. When the charge-pump is sinking a current Ich in UP mode, I_R=I+Ich. When the charge-pump is sourcing a current Ich in DOWN mode, I_R=I−Ich. Therefore, I must be greater than Ich in any case. I is made proportional to I_Dbecause NMOS N1 is connected to VBN. Let's say I=A.I_D $R=\frac{1}{{\mathrm{gm}}_{\mathrm{P1}}}=\frac{1}{\sqrt{2·k_{\mathrm{P1}}·I_R}}=\frac{Y}{\sqrt{8·k·I_D}}$

[0044] However, when Ich=0 in steady state, PMOS P1 sources I_R=A.I_Dand VBP must remain constant and equal to its value.

[0045] Then $\frac{A·I_D}{k_{\mathrm{P1}}}=\frac{I_D}{k}\mathrm{because}{I}_D=k·\frac{W}{L}·{\left(V_{\mathrm{GS}}-V_t\right)}^2$

[0046] so V_GSis conserved.

[0047] Replacing in the above R equation also I_Rby A.I_D, $A=\frac{2}{Y}$

[0048] Therefore, Ich=X.(2.I_D)

[0049] Therefore, I has to be greater than Ich if $A·I_D>X·\left(2·I_D\right)$ $A>2·X,\mathrm{so}\underset{\_}{X·Y<1}$

[0050] FIG. 5 is a block diagram of a PLL 200 in accordance with the present invention. The PLL 200 has the same elements as that of FIG. 4 and includes a decoder 202, provides inputs to the charge pumps 102 and 106, and the counter 108. The PLL 200 also includes a resistor generator 204 coupled between charge pump 106, and VCO 105. To provide a PLL for which changes in N can be taken into account the following equations must be rewritten: $F_{\mathrm{VCO}}=\frac{\sqrt{2·k·I_D}}{C_B},K_0=\frac{k}{C_B}$ $\mathrm{Ich}=X·\left(2·I_D\right)=\frac{\alpha }{N}·\left(2·I_D\right)$ $R=\frac{Y}{\sqrt{8·k·I_D}}=\frac{\beta ·N}{\sqrt{8·k·I_D}}$

[0051] Assuming Ich=Ich_C=Ich_R

[0052] C_Bis the equivalent VCO buffer load capacitance.

[0053] k is the VCO PMOS load process transconductance.

[0054] The damping factor and loop bandwidth, $\zeta =\frac{\beta }{4}·\sqrt{\alpha }·\sqrt{\frac{C}{C_B}}$ $\frac{w_n}{w_{\mathrm{ref}}}=\frac{1}{2\pi }·\sqrt{\alpha }·\sqrt{\frac{C_B}{C}}$

[0055] Both damping factor and bandwidth to operating frequency ratio are constant with N and ω_ref.

[0056] FIG. 6 illustrates an example with $N_2>N_1,w_{\mathrm{ref2}}>w_{\mathrm{ref1}},\frac{w_{\mathrm{n2}}}{w_{\mathrm{ref2}}}=\frac{w_{\mathrm{n1}}}{w_{\mathrm{ref1}}},{\zeta }_2={\zeta }_1$

[0057] Condition Where Charge Pump Currents are Different

[0058] In the case where Ich_C≠Ich_Ris considered, then:

[0059] Open loop gain: $G_{\mathrm{ol}}=\frac{{\mathrm{Ich}}_C·K_0·\left(1+\frac{{\mathrm{Ich}}_R}{{\mathrm{Ich}}_C}\mathrm{RCs}\right)}{{\mathrm{Cs}}^2}$

[0060] The closed loop gain is then a second-order system $G_{\mathrm{cl}}=\frac{N·{\mathrm{Ich}}_C·K_0·\left(1+\frac{{\mathrm{Ich}}_R}{{\mathrm{Ich}}_C}\mathrm{RCs}\right)}{{\mathrm{NCs}}^2+{\mathrm{Ich}}_C·K_0·\left(1+\frac{{\mathrm{Ich}}_R}{{\mathrm{Ich}}_C}\mathrm{RCs}\right)}=N·\frac{1+2·\zeta ·\left(s/w_n\right)}{1+2·\zeta ·\left(s/w_n\right)+{\left(s/w_n\right)}^2}$ $\zeta =\frac{{\mathrm{RCw}}_n·\frac{{\mathrm{Ich}}_R}{{\mathrm{Ich}}_C}}{2}=\frac{R}{2}·\sqrt{\frac{{\mathrm{Ich}}_R·K_0·C}{N}}$

[0061] Loop damping factor $w_n=\sqrt{\frac{{\mathrm{Ich}}_C·K_0}{\mathrm{NC}}}$

[0062] Loop bandwidth

[0063] The traditional stability becomes $w_n>w_{\mathrm{RC}}=\frac{1}{\mathrm{RC}},\mathrm{then}\zeta >0.5\frac{{\mathrm{Ich}}_R}{{\mathrm{Ich}}_C}\mathrm{because}\frac{w_n}{w_{\mathrm{RC}}}=\frac{w_c}{w_n}=2·\zeta ·\frac{{\mathrm{Ich}}_R}{{\mathrm{Ich}}_C}$

[0064] The VCO overload limit is $R·{\mathrm{Ich}}_R<\frac{\mathrm{Fvco}}{K_0}\mathrm{that}\mathrm{leads}\mathrm{to}\frac{w_n}{w_{\mathrm{ref}}}<\frac{1}{4\mathrm{\pi \zeta }}\sqrt{\frac{{\mathrm{Ich}}_C}{{\mathrm{Ich}}_R}}$

[0065] Accordingly, $F_{\mathrm{VCO}}=\frac{\sqrt{2·k·I_D}}{C_B},K_0=\frac{k}{C_B},{\mathrm{Ich}}_C=X_C·\left(2·I_D\right)=\frac{{\alpha }_C}{N}·\left(2·I_D\right),R=\frac{Y}{\sqrt{8·k·I_D}}=\frac{\beta ·N}{\sqrt{8·k·I_D}}$ ${\mathrm{Ich}}_R=X_R·\left(2·I_D\right)=\frac{\alpha R}{N}·\left(2·I_D\right)$

[0066] VCO overload limit becomes X_R.Y<2

[0067] Charge pump current versus loop PLL or resistor design limit becomes X_R.Y<1

[0068] Accordingly, $\zeta =\frac{\beta }{4}·\sqrt{{\alpha }_R}·\sqrt{\frac{C}{C_B}}$ $\frac{w_n}{w_{\mathrm{ref}}}=\frac{1}{2\pi }·\sqrt{{\alpha }_C}·\sqrt{\frac{C_B}{C}}$

[0069] In a preferred embodiment a two bit input n into the decoder 202 would adjust the counter by 4 bits (N) to adjust the frequency range, as has been mentioned. Ich changes with N accordingly, the loop bandwidth and damping factors can be effectively tracked. Accordingly, the decoder can be programmable to align the phase of the input frequency and the output frequency to ensure stability.

[0070] Accordingly, referring back to FIG. 5, the decoder 202 receives the application-dependent number N (representing the ratio between the output frequency and the application-dependent input frequency to the PLL system 200) and then adjusts the charge pump 102 and 106, the counter 108 and the resistor generator 204 to ensure that the self-biased PLL 200 operates within the frequency range associated with N. In so doing, a self-biased PLL 200 can be operated over a range of frequencies merely by adjusting the above-identified items in a manner that ensures stability over the range.

[0071] Utilizing this system more flexibility is provided on damping and bandwidth that can vary independently from each other.

[0072] Conclusion

[0073] The present invention offers a number of advantages over conventional/prior approaches. These include wide range PLL, self-biased, self-adaptive (bandwidth and damping tracking). Both damping factor and bandwidth to operating frequency ratio are constant with N and the input frequency ω_ref. The system has low power usage: less than 4 mW at maximum frequency operation. The system facilitates easy power-down mode by turning off the integral loop filter voltage. It is easy to add more programmability if needed (bandwidth, damping). The cumbersome loop filter capacitor is fixed and its ratio to the equivalent buffer load is the only process dependency. It can be reasonably matched in layout (gate capacitances). The system is well suited for any charge-pump PLL. An additional advantage is that there is no bandgap reference.

[0074] Although the present invention has been described in accordance with the embodiments shown, one of ordinary skill in the art will readily recognize that there could be variations to the embodiments and those variations would be within the spirit and scope of the present invention. Accordingly, many modifications may be made by one of ordinary skill in the art without departing from the spirit and scope of the appended claims.