"Dying Gasp" from a Circuit Standpoint

Introduction

The Metro Ethernet Forum (MEF) specifies requirements for carrier-grade Ethernet services. One the features they define is the "dying gasp". A dying gasp is defined as follows:

Dying Gasp is a message (or signal) sent by the Customer Premises Equipment (CPE) to the service provider when a power outage occurs.

In most cases, the hardware does not know that the power is failing until the power is already starting to go away. The dying gasp protocol requires that three "I am dying" messages be sent before the CPE gear goes down for good, which means the CPE must stay operating for about 3 msec after the power has gone away. To accomplish this feat, we need to include some local energy storage with MEF-compliant Ethernet hardware. This post will examine how we can estimate the amount of local energy storage required.

Analysis

We will begin by assuming the power supply architecture shown in Figure 1.

Figure 1: Circuit Model for "Dying Gasp" Capacitive Backup.

There are a few points that should be made about this power supply architecture:

• The input circuit will only conduct current one way.
  We need to make sure that as the power drops away, the power we need for our Ethernet interface is not drawn out of the input. In Figure 1, I show a diode, but there are number of ways of isolating the backup capacitor from the dying power source. In most cases, FETs would be more efficient than diodes, but diodes are simpler to understand. However, all this is an implementation detail.
• The load requirements are modeled as a current source.
  In most cases, we are trying to provide backup energy for a switching power supply, which draw relatively constant power over a range of voltages.
• Energy is stored in capacitors.
  In most cases, capacitors are the cheapest and easiest way of storing backup energy. This assumes the required backup time is small (~msec). As times get longer, batteries look better.

Energy-Based Capacitance Requirement Determination

If first worked the problem from an energy standpoint. Recall from basic physics that energy stored on a capacitor is given by Equation 1.

Eq. 1

The energy needed to power our MEF-compliant device is given by Equation 2.

Eq. 2

where

• P is the power draw of our MEF-compliant device.
• T_DyingGasp is the time required to transfer the three dying gasp messages.
• V_Initial is the initial voltage on the backup capacitor. This is the voltage on the backup capacitor at the moment power drops away.
• V_Final is the final voltage on the backup capacitor and is the minimum voltage at which load input can function.
• C_Backup is the capacitance of the backup capacitor.

We can use Equation 2 to solve for C_Backup (Equation 3).

Eq. 3

Current-Based Capacitance Requirement Determination

The backup capacitance requirement is given by Equation 3, but some electrical engineers do not like energy-based arguments. They prefer arguments based on circuit parameters like voltage and current, which can be measured directly. We can obtain the same result using circuit parameters as follows.

The current drawn by the load and the current drawn from the capacitor are given by Equation 4.

Eq. 4

Equation 5 shows Equation 4 broken up into its differential form.

Eq. 5

We know can integrate both sides of Equation 5, as is illustrated in Equation 6.

Eq. 6

As we would expect, both methods yield the same result.

Empirical Example

I threw the calculations into Mathcad and put the screenshot into Figure 1.

Figure 1: Calculation Used for Actual Product.

Conclusion

One of the more difficult parts of product development is determining requirements, a process I call "The Treasure Hunt." The analysis shown here describes a very common type of analysis that is done to determine capacitor requirements for backup systems.