Optimising yer gain bandwidth
From: Genome (genome_at_nothere.net)
Date: 08/28/04
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Date: Sat, 28 Aug 2004 19:55:31 GMT
The denizons of wisdon from Unitrode taught me all about slope matching and
such stuff but one thing they said wuz that your op-amp needed sufficient
gain bandwidth to ensure that all things would be fruity pie. I takes that
to mean that they have sufficient gain bandwidth so as the waveforms are not
corrupted at the switching frequency, perhaps I interpretate them wrong but
then one day I thought what happens if you don't have enough.
Forgive me if I've lost you already, you have to be into this rubber room
type stuff in the first place. I love loop compensation and have to take
many tablets when I can't figure out what a loop is doing.
Now..... slope compensation works for voltage mode converters as well. The
ripple current in your inductor becomes a ripple voltage across the output
capacitors ESR. Run through the sums and match the slopes and you get the
maximum gain in your VEA.
At that point the crossover frequency of your, oh it's just blown up, power
supply id Fs/2piD...... wonderful.
But then I look at my measly two switch forward converter and the bit I want
to compensate has an L of 1mH and a VOUT of 15V with a capacitor ESR of
130mR. So I do sum sums. dI/dT during the off time is 15/1m or 15,000A/s
which becomes a dV/dT or 1,5000x130m or 1950V/s
Cool. My ramp is 3V in 10uS for a dV/dT of 300,000V/s so the maximum gain in
my VEA is 300,000/1950 or about 150. If I wanted to maintain waveform purity
at 100KHz then I would need an op-amp with a gain bandwidth product in
excess of 15MHz.
Unfortunately I like LM324s with a GBW of 1MHz. What's a man to do, ay?
Stuff the waveform purity and do a bit of algebra. All I'm interested in is
what happens at crossover so the op-amps roll of shouldn't contribute too
much to things.
Let's say the op-amp rolls off at four times the frequency that the system
rolls off.
At the moment I know that
Fcos = Fs.Gopamp/150*2piD
D is 50% for my forward converter and Fs is 100KHz so that's about
Fcos = 32K*Gopamp/150
The bandwidth of my opamp is
Fopamp = GBW/Gopamp
and I want that to be four times Fcos so
GBW/Gopamp = 4*32K*Gopamp/150
Rearrange
Gopamp^2 = GBW*150/4*32K
Gopamp = SQRT(GBW*150/4*32K)
GBW is 1MHz so
Gopamp = 34
Which makes Fco 7.3KHz.
Caveat...... it's above something.
So.......... now I know.
DNA
I wear my socks in bed, saves them from getting crusty the next morning.
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