CN101841331A - Method for designing passive filter of charge pump phase-locked loop (CPPLL) - Google Patents

Abstract

The invention discloses a method for designing a passive filter of a charge pump phase-locked loop (CPPLL), which is mainly applied to second-order and third-order passive low-pass filters of the CPPLL. The method comprises the following steps of: acquiring a transmission function of each module of the CPPLL so as to deduce a gain function of the whole phase-locked loop by analyzing the ideal linear model of the CPPLL; and acquiring parameter values of an electronic component device in the third-order passive low-pass filter through deduction and calculation of a mathematical method according to the bandwidth, phase margin and other parameters of the actual phase-locked loop system. The design method has the advantage that: by directly starting from the AC characteristics of the phase-locked loop and using simple conditions for stabilizing the system, a loop filter can be designed. A fast and accurate path is provided for the behavior-scale design of the low phase-jitter and rapidly locked phase-locked loop.

Description

The method for designing that is used for the passive filter of charge pump phase lock loop

Affiliated technical field

The present invention relates to the method for designing of the passive filter in a kind of charge pump phase lock loop of in digital communicating field, using always.

Background technology

Along with the develop rapidly of digital communication and semiconductor electronic technology, communication system is progressively to digitlization, integrated direction development in recent years.PHASE-LOCKED LOOP PLL TECHNIQUE is occupied crucial status in communication system.Phase-locked loop is very important basic module in the hybrid digital-analog integrated circuit, and it is usually used in constituting circuit such as frequency synthesis, clock recovery, also can be used for suppressing the shake and the noise of signal.At present, charge pump phase lock loop is of greatest concern a kind of in all phase-locked loops

Loop filter (LPF) is the important step of charge pump phase locking loop circuit, is connected between charge pump and the voltage controlled oscillator, and the fundamental frequency characteristic of phase-locked loop is determined by loop filter.Loop filter can adopt passive filter or active filter, but, for the high-order phase-locked loop, if employing active filter, because its circuit structure complexity, the phase noise that active device is introduced is excessive, and gain makes the stability of high-order phase-locked loop become poorer with technology, variation of temperature and fluctuation range is bigger.And use that passive filter can reach that circuit structure is simple, the purpose of low noise, high stability.At present, all many for the argumentation and the design of the passive filter of low order phase-locked loop and active filter, comparative maturity relates to but really rarely have for the Design of Passive Power Filter of high-order phase-locked loop.

Summary of the invention

At the top problem of mentioning, the present invention proposes a kind of method for designing that is used for the second order and the three rank passive filters of charge pump phase lock loop.This method draws its respective phase territory ideal linearity mode at first according to the basic composition module of charge pump phase lock loop; Derive the open-loop gain of whole phase-locked loop then theoretically by the ideal linearity model; Again by its open-loop gain function,,,, just can draw the parameter value of each electronic devices and components in the passive filter by the derivation and the calculating of mathematical theory according to parameters such as the bandwidth of real system and phase margins from the stability of phase-locked loop.

Below in conjunction with accompanying drawing detailed process of the present invention is further described in detail.

Description of drawings

Fig. 1 is the composition frame chart of charge pump phase lock loop.

Fig. 2 is the ideal linearity model of charge pump phase lock loop.

Fig. 3 is the circuit diagram of second order passive low ventilating filter.

Fig. 4 is the circuit diagram of three rank passive low ventilating filters.

Embodiment

The basic composition model of charge pump phase lock loop as shown in Figure 1, its respective phase territory ideal linearity mode is as shown in Figure 2.As can be seen, the course of work of phase-locked loop is from its ideal linearity model: the input clock phase theta _iAfter feedback clock phase theta/N process phase frequency detector (PFD) processing, obtain both θ that differs _e, θ _eSize be reflected on the width of PFD output signal pulses; Through behind the charge pump, obtain and differ θ _eProportional current impulse; This current impulse is considered and is removed high fdrequency component through loop filter (LPF), and is converted to control voltage V _IN, by V _INThe output signal f of control voltage controlled oscillator _OutFrequency, output clock phase feeds back to the input of phase frequency detector through frequency divider, constitutes a feedback loop.

Definition K _dBe the gain of phase frequency detector (PFD), be the gain of voltage controlled oscillator (VCO), N is the frequency division multiple, and F (s) is the transfer function of loop filter (LPF), and the open-loop gain that can be obtained phase-locked loop by last figure is

$G\left(s\right)=K_d\·I_d\·F\left(s\right)\·\frac{K_{\mathrm{vco}}}{S}\·\frac{1}{N}---\left(1\right)$

Closed loop gain is

$H\left(s\right)=\frac{G\left(s\right)}{1+G\left(s\right)}---\left(2\right)$

By above two formulas as can be known, the open loop frequency characteristic curve of phase-locked loop should be similar with loop filter.When the corresponding open-loop gain of the minimum phase shift of phase-locked loop is 1 Frequency point, the phase margin maximum of phase-locked loop, it is best that stability reaches.At this moment, the bandwidth of phase-locked loop is ω _c, the Frequency point when promptly gain is 0dB.In the design of loop filter, mainly select the capacitance resistance parameter according to above-mentioned purpose.

The phase margin of phase-locked loop open-loop gain is typically chosen between 30 ° to 70 °, when phase margin is big, can obtain stability preferably, but response speed can be slow.Therefore to take all factors into consideration the influence of various factors, the size of choose reasonable phase margin.Generally speaking, when beginning to design, get 45 ° better.

Fig. 3 is the circuit diagram of second order passive low ventilating filter, and the transfer function of this filter is

$F\left(s\right)=\frac{s\·R_2\·C_2+1}{s^2\·R_2\·C_1\·C_2+s\·(C_1+C_2)}---\left(3\right)$

Pole and zero time corresponding constant in the definition following formula is respectively T ₁And T ₂, then have:

$T_1=R_2\·\frac{C_1\·C_2}{C_1+C_2}---\left(4\right)$

T ₂＝R ₂·C ₂ (5)

Therefore the open-loop gain of phase-locked loop can be written as:

$G{\left(s\right)}_{s=\mathrm{j\ω}}=-\frac{K_d\·I_d\·K_{\mathrm{VCO}}(1+\mathrm{j\ω}\·T_2)}{{\mathrm{\ω}}^2{C}_1\·N(1+\mathrm{j\ω}\·T_1)}\·\frac{T_1}{T_2}---\left(6\right)$

The phase margin that can obtain the phase-locked loop open-loop gain from (6) formula is:

φ _C(ω)＝π+tan ^-1(ω·T ₂)-tan ^-1(ω·T ₁) (7)

Ask phase margin to the differential of ω and to make it be 0, can obtain the frequencies omega of corresponding maximum phase nargin _cSatisfy following equation.

$\frac{T_2}{1+{(\mathrm{\ω}\·T_2)}^2}-\frac{T_1}{1+{(\mathrm{\ω}\·T_1)}^2}=0$

$\⇒{\mathrm{\ω}}_C=\frac{1}{\sqrt{T_1\·T_2}}---\left(8\right)$

The bandwidth omega of the phase-locked loop that according to design the time, provides _cWith phase margin φ _c, utilize (7) formula and (8) formula, just can obtain the time constant T of loop filter ₁And T ₂Value.

$T_1=\frac{\sec {\mathrm{\φ}}_C-\tan {\mathrm{\φ}}_C}{{\mathrm{\ω}}_C}---\left(9\right)$

$T_2=\frac{1}{{\mathrm{\ω}}_c^2\·T_1}---\left(10\right)$

Thereby just can obtain the occurrence of the resistance capacitance parameter of second-order loop filter.

What introduce above is the method for designing of second-order loop filter, it can be generalized in the passive ring filter of high-order equally.Fig. 4 is the circuit diagram of three rank passive filters, and its transfer function is

$Z\left(s\right)=\frac{1+R_2{C}_{2}s}{R_2{R}_3{C}_1{C}_2{C}_3{s}^3+[R_2{C}_1{C}_2+R_2{C}_2{C}_3+R_3{C}_3(C_1+C_2)]s^2+(C_1+C_2+C_3)s}---\left(11\right)$

Arrangement can obtain through abbreviation with following formula

$Z\left(s\right)=\frac{1+T_2\·s}{s\·(1+s\·T_1)\·(1+s\·T_3)}\·\frac{1}{C}---\left(12\right)$

Wherein, C=C ₁+ C ₂+ C ₃, time constant T ₁～T ₃Respectively as the definition of (5)～(7) formula.These time constants respectively respective filter not at two limits and zero point of initial point.A limit with respect to its increase of second order filter is for the clutter noise of decaying, so just can determine its position according to the degree of decay when designing at the beginning.It generally is lower than reference signal frequency, but must be more than five times of bandwidth, otherwise will have influence on the stability of phase-locked loop.

T ₂＝R ₂·C ₂ (13)

$\frac{T_1\·T_3}{T_2}=\frac{C_1\·C_3\·R_3}{C_1+C_2+C_3}---\left(14\right)$

$T_1+T_3=\frac{C_2\·C_3\·R_2+C_1\·C_2\·R_2+C_1\·C_3\·R_3+C_2\·C_3\·R_3}{C_1+C_2+C_3}---\left(15\right)$

The transfer function of three rank passive filters is updated to the open-loop gain that just can obtain phase-locked loop in (1) formula, is thereby just can obtain its phase margin:

φ _c(ω)＝π+tan ^-1(ω·T ₂)-tan ^-1(ω·T ₁)-tan ^-1(ω·T ₃) (16)

Ask phase margin to the differential of ω and to make it be 0, can obtain the frequencies omega of corresponding maximum phase nargin _cSatisfy following equation.

$\frac{{\mathrm{\ω}}_C\·T_2}{1+{({\mathrm{\ω}}_C\·T_2)}^2}=\frac{{\mathrm{\ω}}_C\·T_1}{1+{({\mathrm{\ω}}_C\·T_1)}^2}+\frac{{\mathrm{\ω}}_C\·T_3}{1+{({\mathrm{\ω}}_C\·T_3)}^2}---\left(17\right)$

Situation during with second order is similar, the bandwidth omega of the phase-locked loop that provides during according to design _CWith phase margin φ _C, and utilize T ₁, T ₂And T ₃Between correlation, just can obtain three time constant T ₁～T ₃Next step finds the solution component parameter exactly.Because at the bandwidth place, the gain of open-loop transfer function is 1, so have

$C=C_1+C_2+C_3=\frac{K_d\·I_d\·K_{\mathrm{VCO}}}{{\mathrm{\ω}}_C^2\·N}\·\sqrt{\frac{1+{({\mathrm{\ω}}_C\·T_2)}^2}{[1+{({\mathrm{\ω}}_C\·T_1)}^2]\·[1+{({\mathrm{\ω}}_C\·T_3)}^2]}}---\left(18\right)$

In order to find the solution, simplify (13)～(15) formula, need following four constant K of definition ₁～K ₄,

K ₁＝C ₁+C ₂+C ₃＝C (19)

K ₂＝(T ₁+T ₃)·K ₁ (20)

$K_3=\frac{T_1\·T_3\·K_1}{T_2}---\left(21\right)$

K ₄＝C ₂/C ₁ (22)

By above 4 formulas, two parameters of pruning obtain

$T_2\·(K_4+1)\·C_1^2-(K_2+K_3\·K_4)\·C_1+K_1\·K_3=0---\left(23\right)$

According to above formula, select the rational proportion constant K ₄, just can solve C ₁, and then just can obtain element C ₂, C ₃, R ₂And R ₃Value.As negative or plural number appear, just need reselect K ₄Value.

In sum, the present invention is from the stability of a system, just can design the filter that compliance with system requires by mathematical method and certain calculating, thereby provides a kind of approach fast and accurately for the design of phase-locked loop.

Claims (2)

1. method for designing that is used for the passive filter of charge pump phase lock loop is primarily characterized in that this method comprises following key step:

A. by analyzing the ideal linearity model of charge pump phase lock loop, derive the open-loop gain function of whole phase-locked loop, calculating its respective phase nargin function according to the open-loop gain function then;

B. by the differential of phase margin function, draw the relational expression that frequency satisfied of its corresponding maximum phase nargin,, just can calculate several time constants of passive filter in bandwidth and phase margin parameter according to actual phase-locked loop systems to frequency;

C. according to the time constant obtained and phase-locked loop in the open-loop gain at bandwidth place, by selecting rational proportion parameter and mathematical computations, just can obtain the parameter value of each electronic devices and components in the passive filter.

2. as right 1 described method for designing, it is characterized in that: can adopt for the second order of charge pump phase lock loop and the design of three rank passive filters.

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