[EE] theoretical performance of switching regulators...

[William Westfield]

Is there a relatively simple equation for estimating the maximum possible performance of a (buck) switching regulator?
I mean, if I have Vin, Vout, an inductor with an internal resistance of R ohms, and a switching element with a drop of Vf volts, I’m going to have an efficiency that is limited by those factors, regardless of how perfect the rest of the circuit is, right?

Thanks
Bill W

[Jason White]

Power out = Power in - Power lost.

With the help of Ohm's law you should be able to Write that out in terms of
your variables. You may need two (or more) equations and have to to solve
one in terms of the other.

Or: Power out = Efficiency * Power In
Where Efficiency = Power out / Power In

Etc. Etc.

-Jason White

Post by William Westfield
Is there a relatively simple equation for estimating the maximum possible
performance of a (buck) switching regulator?
I mean, if I have Vin, Vout, an inductor with an internal resistance of R
ohms, and a switching element with a drop of Vf volts, I’m going to have an
efficiency that is limited by those factors, regardless of how perfect the
rest of the circuit is, right?
Thanks
Bill W
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[Alan]

Bill,
Don’t forget about your diode losses. (Or synchronous switch losses)
Looking forward,
Al Shinn (Tinker)

Message: 1
Date: Wed, 21 Nov 2018 01:38:27 -0800
Subject: [EE] theoretical performance of switching regulators...
Content-Type: text/plain; charset=utf-8
Is there a relatively simple equation for estimating the maximum possible performance of a (buck) switching regulator?
I mean, if I have Vin, Vout, an inductor with an internal resistance of R ohms, and a switching element with a drop of Vf volts, I?m going to have an efficiency that is limited by those factors, regardless of how perfect the rest of the circuit is, right?
Thanks
Bill W

[peter green]

Post by William Westfield
Is there a relatively simple equation for estimating the maximum possible performance of a (buck) switching regulator?
I mean, if I have Vin, Vout, an inductor with an internal resistance of R ohms, and a switching element with a drop of Vf volts, I’m going to have an efficiency that is limited by those factors, regardless of how perfect the rest of the circuit is, right?

Lets see if we can put an upper bound on the efficiency.

Lets assume that the current in the inductor is pretty much constant (i.e. we are deep into continuous mode operation). Lets only "steady state" losses, during the two modes of operation and not switching losses as we move between the two nodes. Lets also assume that the capacitors are lossless and the input and output voltages are constant.

We have three devices to consider.

1. The inductor
2. The charge switch
3. The discharge switch (may be a diode)

Lets define some variables.

Po the output power
Pw the average wasted power
Pwc the wasted power during charging
Pwd the wasted power during discharging
Tc the proportion of time spent charging
Td the proportion of time spent discharging
Io the output current
Vo the output voltage
Vs the supply voltage
Ii the current through the inductor
Ri the resistance of the inductor
Viic the inductive component of the voltage across the inductor during charging (positive).
Viid the inductive component of the voltage across the inductor during discharging (negative).
Vir the resistive component of the votage across the inductor
Vcs the voltage drop across the charge switch
Vds the voltage drop across the discharge switch.

Ii = Io = Po / Vo
Vir = Ri * Ii

Pwc = (Vir + vcs) * Ii
Viic = Vs - Vcs - Vir - Vo

Pwd = (Vir + vds) * Ii
Viid = Vs - Vcs - Vir - Vo

Tc + Td = 1
Td = 1 - Tc
Tc*Viic + Td*Viid = 0
Tc*Viic + (1 - Tc)*Viid = 0
Tc*Viic + Viid - Tc*Viid = 0
Viid = Tc*Viid - Tc*Viic = Tc *
Tc = Viid / (Viid - Viic)

Pw = Tc*Pwc + Td * Pwd

[RussellMc]

Post by William Westfield

Post by William Westfield
Is there a relatively simple equation for estimating the maximum

possible performance of a (buck) switching regulator?

Post by William Westfield
I mean, if I have Vin, Vout, an inductor with an internal resistance of

R ohms, and a switching element with a drop of Vf volts, I’m going to have
an efficiency that is limited by those factors, regardless of how perfect
the rest of the circuit is, right?
Lets see if we can put an upper bound on the efficiency.
I was 'back of brain' considering how many factors you'd need to add

before getting into the noise.

I useful point is that in an ideal system Vin/Vout = Tout/Tin for one cycle.
or Tout = Tin x Vin/Vout
ie for a given charge time the discharge time DECREASES as Output voltage
INCREASES.

Tin = inductor charge time.
Tout = discharge time.

Then, once you add inefficiencies you need a longer Tin to supply the same
Vout.
ie effective or apparent Vout is increased by inefficiencies.
So for efficiency Z, 0 < Z < 1 you see

Tout = Tin x Vin/Vout x Z

This is useful for determining how long inductor current flows, and how
long the switch and 'rectifier' elements conduct in a cycle in a given mode.

To the basic ohmic losses consider adding various junction capacitance
charges and discharges and switching losses due to eg partial conduction
during switching and turnoff delays due to charge seepiyt times and ....
agh! :-). (And more).

Somewhere you get down into the noise.

98% is awesome no matter what.
95% is extremely good and often only for a selected part of the operating
range.
90% is often achieved for many systems using best practices.
80%+ can be hoped for from any mass market kluge.
Lower has been seen :-).

Very high Vin:Vout ratios hurts efficiency.

Very high frequencies reduce inductor sizes but demand superior switch
performance.
Very low frequencies increase core sizes and losses and are usually avoided
unless special reasons dictate.
...

E&OE.
Corrections welcomed.


Russell