[SI-LIST] Re: Output Capacitor of a switching Regulator

        Hi Larry,

        Thanks for the elaborate explaination. But i have three points to
clear.

        1> You said that  the capacitor ESR should be the same as the target
impedance. As mentioned in your book and mail below, the target impedance is

            (VDD*tol)/(Iomax-Iomin). But to calculate the max ESR of the
output capacitor, we have to substract the switching controller's accuracy
against temperature and       the ouput ripple voltage from the transient
window (VDD*tol).  So isnt ESR max lesser than the target impedance?

        2> Can the below mentioned equation be used in general across
different switching controllers?

        3> Also what is the safe value of the factor mentioned in the
equation?

        Regards,
        Anand.




        From:   Larry Smith <Larry.Smith@xxxxxxx> on 08/01/2002 02:55 AM
        Please respond to Larry.Smith@xxxxxxx@SMTP@Exchange
        To:     si-list@xxxxxxxxxxxxx@SMTP@Exchange, ANAND KURIAKOSE/Apex
Data Inc/01@Apex Data Inc
        cc:      

        Subject:        [SI-LIST] Re: Output Capacitor of a switching
Regulator


        Anand - The equation that you give for the calculation of the amount
        of capacitance necessary to go with a switching regulator is valid.
        Be careful to include the appropriate parenthesis to make the units
        (and calculations) come out correctly:

                Cmin = (Iomax-Iomin) * 0.8 / (ESRmax * di/dt)
                
        The trick to this equation (and the switching regulator system 
        design) is getting the ESRmax correct.  

        I like to think in terms of a target impedance.  The target
impedance
        is easily calculated.  A system that meets target impedance will
have
        precisely the amount of voltage tolerance (and noise) as was used in
        the calculation of target impedance.  The capacitor ESR should be
the
        same as the target impedance (assuming we can neglect the DC drop
along
        the path that current takes to the consumer).

                Z_target = Vdd * tolerance / I_transient
                         = Vdd * tolerance / (I_max - I_min)
                         = 1V  * 0.05      / (100A  - 50A  )
                         = 1 mOhm
                         
                for a 1V system where 5% voltage excursions can be tolerated
                when the load draws current transients between 50 and 100
amps.
                      
        The Cmin equation can be derived by considering the amount of time
that
        the capacitor has to support the load in order for the inductor
current
        (di/dt) to ramp up to the new load current.  The voltage is allowed
to
        drop 5% of Vdd as charge in the capacitor is depleted and current is
        drawn through the ESR of the capacitor.  By substituting Z_target
into
        the Cmin equation, the following more fundamental equation is
        obtained:

                Cmin = (I_max - I_min)^2 / (Vdd * tol * di/dt)
                
        This equation needs a factor somewhere between 0.5 and 1.0; 0.8 is
used
        above.  To accurately find the factor, more details about the loop
        feedback point, adaptive voltage positioning, and the loop time
delay
        before the inductor is fully activated are all required.

        This calculation for Cmin is a good starting point.  Simulation of
the
        stability and transient response of the control loop for the
switching
        regulator should be done to get a more complete analysis of the
power
        distribution system.  If the data sheet from the regulator vendor
gives
        this equation, I would go with it.  Just make sure to correctly size
        the capacitor ESR.

        regards,
        Larry Smith
        Sun Microsystems

        > Delivered-To: si-list@xxxxxxxxxxxxx
        > X-Lotus-FromDomain: APEX DATA INC
        > From: Anand.Kuriakose@xxxxxxxxxx
        > To: si-list@xxxxxxxxxxxxx
        > Date: Tue, 30 Jul 2002 23:25:30 +0630
        > Subject: [SI-LIST] Output Capacitor of a switching Regulator
        > Mime-Version: 1.0
        > Content-Disposition: inline
        > Content-Transfer-Encoding: 8bit
        > X-archive-position: 3566
        > X-ecartis-version: Ecartis v1.0.0
        > X-original-sender: Anand.Kuriakose@xxxxxxxxxx
        > X-list: si-list
        > 
        > 
        > 
        > 
        > Hi ,
        > 
        > The datahseet of a  switching regulator controller from Analog
devices mentiones
        > of an equation to determine the min value of the capacitor at the
output filter.
        > The equation is as follows:
        > 
        > Cmin = (Iomax-Iomin) * 0.8 / ESRmax * di/dt. Where di/dt is
through the output
        > inductor, Iomax and Iomin are the max and min output currents and
ESRmax is the
        > max ESR of the output capacitor.
        > 
        > It states that the minimum capacitance should produce an initial
dv/dt which is
        > equal (but opposite in sign) to the dv/dt obtained by multiplying
the
        > di/dt in the inductor and the ESR of the capacitor:
        > 
        > Can this equation be appropriately used to determine the min value
of the output
        >  capacitor?
        > 
        > Experts opinion will be greatly appreciated and will do good to my
power supply
        > design.
        > 
        > Thanks in advance.
        > 
        > Anand.
        > 
        > 
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