[SI-LIST] Re: Output Capacitor of a switching Regulator
- From: Larry Smith <Larry.Smith@xxxxxxx>
- To: si-list@xxxxxxxxxxxxx, Anand.Kuriakose@xxxxxxxxxx
- Date: Wed, 31 Jul 2002 13:25:43 -0700 (PDT)
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
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> 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
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>
>
> 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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