Double-frequency jitter in synchronous networks https://www.researchgate.net/.../Double-frequency-jitter-in-synchronous-networks.pdf...

15 downloads 0 Views 3MB Size Report
Mercer University. Macon, GA, 31207, March 4-6, 2007. Double-frequency jitter in synchronous networks. J.R.C. Piqueira', A.Z. Caligares', and L.H.A. Monteiro2' ...
146

39th Southeastern Symposium on System Theory Mercer University Macon, GA, 31207, March 4-6, 2007

MB2.5

Double-frequency jitter in synchronous networks J.R.C. Piqueira', A.Z. Caligares', and L.H.A. Monteiro2'1 1Escola Politecnica da Universidade de Sao Paulo, Sao Paulo, SP, Brazil 2Universidade Presbiteriana Mackenzie, Sao Paulo, SP, Brazil Email: [email protected]

Abstract

the maximum number of sequential nodes is ten. If the nodes were linked as a tree, the total number of nodes is limited to 60 with, at maximum, three tributary nodes connected to each main chain node. Each slave node can be implemented as a PLL (Phase-Locked Loop) that is an electronic circuit that controls an oscillator maintaining its phase as a constant related to a reference signal. This device can extract clock signals from the line with good precision and low cost [4]. PLL is composed of a Phase Detector (PD), a Low Pass Filter (F), and a voltage controlled oscillator (VCO) connected as shown in figure 1. The PD is represented by a multiplier and, consequently, generates a low-frequency signal whose amplitude is related to the phase error between the VCO and the input, added to a double-frequency term that F is supposed to eliminate [4].

In this work we study the effects of double-frequency jitter in OWMS (One Way Master-Slave) chain network for clock distribution systems. The master-slave architecture considers the slave nodes as phase-locked loops (PLL) and nonlinearity in phase detection generates the double-frequency jitter A network is modeled and simulated in order to compare the results with ITU-T standards.

1. Introduction In digital switching telecommunication networks, synchronization is an important feature to avoid long buffer memories and slipping in the information streams [1]. According to Recommendation G.810 ITU-T [2], there are two methods for synchronizing switching nodes: master-slave and mutual synchronization; and master-slave strategies are generally the most appropriated. In master-slave strategy, there is a hierarchy among nodes. The master, generally with high precision, generates the timing reference that is distributed to all other nodes (slaves) of the network. This distribution can be done with clock control signals depending only on the master signal, in the OWMS (One-Way Master-Slave) strategy, or with the clock control signals depending on signal from master and slaves, in the TWMS (Two Way Master-Slave) strategy. Control signals can be sent directly, according to a star topology, or indirectly, as in a tree topology. Our work is about OWMS-single chain clock distribution system that is a special case of a tree without ramifications. In this kind of topology, the control signal is transmitted in a single direction, and it is composed of one master clock that doesn't depend on other nodes. According to ITU-T recommendation G-812 [3]

1-4244-1051-7/07/$25.00 ©2007 IEEE.

Vd (t)

vi (t)

vo (t) vc

VC (t)

Figure 1. PLL block diagram This work is about the effect of this doublefrequency that is not totally eliminated. It appears in the VCO output signal as an oscillation around the synchronous state, here called double-frequency jitter [5]. Its main effect is the onset of oscillations in the time between two successive transitions of the clock or data signal, provoking slips and errors in the data streams. Here we model an OWMS single chain network and using simulation tools we analyze the propagation of perturbations and how double-frequency terms affect the network performance, comparing the results with ITU-T standards. Our main motivation is concentrated in the telecommunication networks and their standards developed by ITU-T, ETSI and ANSI, covering Synchronous Digital Hierarchy (SDH) and Syn-

128

147

chronous Optical Networks (SONET) [6, 1]. For local area applications, as Gigabit Ethernet, there are digital integrated circuits providing data synchronization employing cache hierarchy and pipeline algorithms, that are not considered here [7].

a first order low pass, avoiding bifurcations and chaotic behaviors for the whole loop [10]. It is implemented with one zero and one pole, as used in the main commercial integrated PLL, CD 4046, for instance [4], with transfer function represented by:

2. Dynamical model for OWMS network

H (s)

T2 -c (t) + vc (t)

expressed by: =

.

ST2 +

Vd (S)

(6)

1

Consequently, the filter output can be written as:

The master clock normally has an atomic precision pattern with high stability and accuracy and its phase is

(DM comt + T (t)

ST,u + 1

Vc (s)

=as

=

Kd [sin (Oi(t)

-

Oi (t) + 00 (t))] + rl Kd [COS (Oi(t) -

0,(t)) + sin (2opmt + o

(0) (6i(t)

-

o

(0)

+cos(2o)mt+ Oi(t)+ Oo(t))(2° + oi(t) +6o(t))], (7)

(1)

where (oM represents the free-running frequency and T(t) is a perturbation signal. The expression (1) shows that if the perturbation is a step of phase it causes a discontinuity in the master's phase and, consequently, in its frequency. This perturbation propagates along the chain and, after a time interval, slave nodes are supposed to re-acquire the synchronous state with constant spatial errors and zero frequency error [8]. Spatial phase error between a j-slave node and the (j 1) node is given by Oj Oj- and frequency error with Oj representing the phase of VCO by Oj OQ signal from node j [9]. In each slave PLL, the PD compares the phases of the input signal vi (t) and of the VCO v0 (t) and its operation can be modeled as signal multiplier with its output given by:

where Kd kd ViVV0 The output of the filter controls the phase of VCO signal, following the equation: &0(t)

=

k vc(t),

(8)

where ko is the VCO gain. Combining equations (7) and (8), we obtain the equation that represents the model for the slave PLL nodes:

-

-

1,

r26o +

expressions, given by (3) and (4), with central angular frequency (DM(t) and instantaneous phases Oi(t) and Oo(t), as following: =

Vijsin [cmt + Oi(t)]

(3)

vo (t)

=

VOcos[wMt+ e0(t)].

(4)

Using the equations (2), (3) and (4), we can express vd as:

Vd(t)

kd

Vi 2

+

VQ

sin[2wM't + Oi(t) + e0(t)]

kd ViVo sin [&Oi(t)

-e0 (t)].

[cos(0e-

o)(6 -6o)] +

(9)

_

=

vi (t)

= Gr1

where G kdkoViVo is called PLL gain. Equation (9) presents a dissipative term &o but, in the right side, there is a periodic forcing term presenting angular frequency of 2woM [1 1]. As a consequence, the long-term solution is a periodic function around the synchronous state. This periodic term is the doublefrequency jitter. Trying to model this phenomenon by using MATLAB-Simulink [12], we mounted a chain with a periodic generator as master node and each slave node obeying the dynamics expressed by expression (9). Neglecting delays, PLL gain is adjusted up to establish a better situation on synchronous state. So, due to a step variation, we generate perturbations in the master that is propagated to the whole network. We measure acquisition time T, maximum transient peak to peak frequency jitter (JM) and permanent peak to peak jitter (J), relating then with the PLL gain.

(2) kdvi(t)Vo(t), where kd is the PD gain, vi(t) and vi(t) have periodic Vd(t)

o

G,r1 [cos(2o)Mt + Oi + 00) (2oM + &i + 60)] +Gsin(i -00) + Gsin(20Mit + Oi + e0),

(5)

3. Results

Expression (5) shows that undesirable doublefrequency terms appear and the idea is to cut them off by using a low-pass filter. The filter to be considered is

We simulate a ten-slave node chain using MATLAB-Simulink [12] normalizing the free running

129

148

angular frequency as 0oM = rad/s. A step phase signal with amplitude equal to 1 rad is added as '(t) and we are not considering the signal propagation time between nodes. Filter follows equation (6) and its parameters are adjusted as '1 = 62.8s and '2 = 6280s, providing a good compromise between transient and permanent responses and a cut-off frequency about two decades below the free-running frequency. The gain (G) is considered a simulation parameter. Adjusting the gain (G), we measure the maximum peak-to-peak jitter (JM) during transient response and the peak-to-peak permanent jitter (J). Jitter is measured comparing the output of two consecutive filters after a step perturbation in the master. We also measure the acquisition time (T), i.e., time to frequency error acquire permanent response for each relative position of the node, after a step phase perturbation in the master. In spite of the values for acquisition time not being specified in ITU-T recommendations, they are strongly dependent on the node gains, as shown in figures 2 and 3, giving measures of the adaptation capacity of the network.