Boost Charge Pump Current PLL

Transcription

1 oost Charge Pump Current PLL ormal Charge Pump f R Σ K φ oost K v oost R f O K φb oost Charge Pump C C Fig. : 3 rd -Order PLL with Current-Mode Phase-Detector and oosted Charge Pump useful functions and identities Units Constants Table of Contents I. Introduction II. Inputs III. Pole and Zero Location Sizing IV. Loop Filter Component Sizing V. Copyright and Trademark otice Introduction In a boosted charge pump PLL, the loop dynamics are changed temporarily to increase the bandwidth of the PLL to allow faster settling. When the loop is close to settling, the bandwidth is reduced for good spurious and phase noise performance. There are several ways to boost the bandwidth, with the most popular method being an increase in the charge pump current. A boost in the charge pump current increases the unity-gain bandwidth, and changes the phase margin. For design an additional constraint must be introduced so the phase margin in boost and non-boost modes are a given value. The PLL need not be overconstrained, by adding to design procedure a new variable ωp/ωu, the ratio of the non-dominant pole to unity-gain bandwidth This is normally set equal to ωu/ωz, the ratio of the unity gain bandwidth to loop zero.

2 Inputs oost 0 f step 5MHz I : 00µA MHz K v : π5 volt num: 00 f u : 0kHz Preliminary Calculations f o : f r I K φ : π : Desired frequency boost : Maximum output frequency step f o : GHz Output Frequency f r : MHz Reference frequency f acc : khz Acceptable frequency error for settling PM des : 60deg Desired phase margin in non-boost mode PM b : 50deg Desired phase margin in boost mode i :.. num ω u : πf u 0 3 Charge pump current VCO Gain umber of points for plotting Desired unity gain bandwidth Divider ratio Tri-state charge pump gain

3 Pole and Zero Location Sizing The open-loop transfer function for the PLL is GH( s) ω u ω ub + Where is the desired bandwidth boost in boost mode. ω ub ω u wu_wz s + K φ K v ω u ( C + C ) s s + ω u ow by setting the loop gain equal to unity, the unity gain bandwidth and phase margin can be solved for with the result given in the following equations: K φ K v ( ) C + C In boost mode the bandwidths and phase margin equations become: K φb K v ( ) C + C For design PM, PM b, and are given, which are used to find wu_wz and with the following routine. x is a intial guess for the root finding routine. ( ) : x 3 ωp_ωu PM, PM b, wu_wz + + ( wu_wz) + root atan tan PM + atan x atan PM b, x x ωu_ωz( PM, PM b, ) : tan PM + atan ωp_ωu( PM, PM b, ) The following figures shows the effect of pole and zero spacings verses desired phase margin. Here the boost and the non-boost phase margins are swept together. Pole Placement vs. oost & Phase Margin 40 PM atan( wu_wz) atan PM b 4 atan wu_wz ( ) atan Zero Placement vs. oost & Phase Margin wu/wp 0 wp/wu 0 We can see the pole placement plots that the required zero placement is a weak function of the bandwidth boosting, but the pole placement is a strong function of the bandwidth boosting. A quick estimate the wu_wz and wp_wz values can be found by using the same value without boosting for wu_wz and use times that value for wp_wz. : Phase Margin (deg) andwidth oost by andwidth oost by 5 andwidth oost by 0 ω ω (,, ) Phase Margin (deg) andwidth oost by andwidth oost by 5 andwidth oost by 0

4 ωu_ωz( PM, PM b, ) + ( ) : Kφb_Kφ PM, PM b, (,, oost) ( ) wu_wz : ωu_ωz PM des PM b : ωp_ωu PM des, PM b, oost Kφb_Kφ wu_wz + + As a function of the desired phase margins: ( ωu_ωz( PM, PM b, ) ) + + ωp_ωu( PM, PM b, ) We plot the current boost required for a given bandwidth boost in the next figure. An important concept to note is from the plot is that more current is required to boost the bandwidth than the ratio of the bandwidths. If a certain bandwidth is required for modulation or settling time purposes, care must be taken to overdesign the bandwidth to account for process variations, especially with respect to K v of the VCO, which can vary up to 00% ( wu_wz) + wu_wz With a given (bandwidth boost), and phase margins there is a required value for the boosted current. The following equation is the ratio of the boosted current to the un-boosted current. + Current oost Required vs. oost and PM ( ) ωp_ωu PM, PM b, Current oost 0 0 For large phase margins the boosted current approaches, the bandwidth boost. Finding andwidth oost Given Current oost Alternatively, if the boosted current is given and the boosted bandwidth is calculated, a root finder can use the previous expression to find the resulting expression: Kφb_Kφ given : Phase Margin (deg) andwidth oost by andwidth oost by 5 andwidth oost by 0 ( ) : x 4 root( Kφb_Kφ( PM des, PM b, x) Kφb_Kφ given, x) PM des, PM b, Kφb_Kφ given ( ) PM des, PM b, Kφb_Kφ given 4

5 Sizing the Loop Filter Components With the pole/unity and zero/unity bandwidth ratios, the loop filter components can also be sized, by solving the following three equations simultaneously. ω u ω u wu_wz ω u K φ K v ( ) C + C R C + C R C ( ) wu_wz + + The solution to these three equations are the following loop filter components: C : K φ K v wu_wzω u wu_wz + + C 63.9 pf C : K φ K v ( wu_wz ) wu_wzω u wu_wz + + C.686 nf R : Plugging these values back into the original transfer function yields the following expression. + wu_wz s + ω u GH( s) wu_wz + s s + ω u ω u The magnitude and phase responses of this transfer function are MagGH( f_fu) wu_wzω u K φ K v : and in boost mode + wu_wz + + wu_wz + f_fu ( wu_wzf_fu) + + f_fu + Kφb_Kφ ( wu_wzf_fu) + MagGHb( f_fu) : wu_wz + f_fu f_fu + f_fu AngleGH( f_fu) : 80deg + atan( wu_wzf_fu) atan R kω 5

6 The following movie illustrates how the poles, zeros and frequency response changes as the bandwidth boosting is changed. The zero location doesn't move that much with respect to boost to maintain stability at the low loop bandwidth. The pole location moves almost proportional to the boost and always remains a small factor larger than the boost bandwidth. The closed loop expression for the PLL with boost filter in normal mode for frequencies much greater than the unity gain bandwidth is: fo_fi( f r ) + wu_wz wu_wz + f r f u If we assume *wu_wz, and wu_wz >>, the expression simplifies to fo_fi f r ( ) f r f u wu_wz Thus a boost in bandwidth is directly results in a loss of reference spur attenuation by the same amount. This means bandwidth in the unboosted mode will have be reduced by about sqrt(), and on-chip capacitors also increased in area by the sqrt(), so one must cautious using this architecture. In another article we see some loop filter modifications that can be made to improve stabilization in boost mode. Copyright and Trademark otice All software and other materials included in this document are protected by copyright, and are owned or controlled by Circuit Sage. The routines are protected by copyright as a collective work and/or compilation, pursuant to federal copyright laws, international conventions, and other copyright laws. Any reproduction, modification, publication, transmission, transfer, sale, distribution, performance, display or exploitation of any of the routines, whether in whole or in part, without the express written permission of Circuit Sage is prohibited. 6