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V = Vin x (N + (N-1)) where N = number of half cycles
This is correct except for N=0. The change in the bridges output voltage is added every half cycle. The first half cycle is special, since the voltage change is from 0 to 170. For the next half cycle bridge voltage jumps from 170 to -170 so the change in bridge output voltage is 340. This leads to MMC voltages in the pattern:
0 170 510 850 1190 ...
This is only true if all the bridge power goes solely into the primary tank and the primary is lossless. Coupling to the secondary will reduce the voltage and primary current. That depends on the amount of coupling and tuning.
Excellent! Right, it doesn't work for N=0, but I'm not overly concerned about that. My goal is to make a calculator that will determine the maximum burst length a MMC can withstand without being over-volted using worst case conditions (lossless primary, no power transfer, etc). The reason behind it is for those of us looking to build a DRSSTC with a very small MMC due to budget it is important to know a ball-park value for how long of a burst is safe to run. If I hadn't come to 4HV and asked about this I'd have fired up my DRSSTC for a 50uS burst the first time when a 18uS burst is enough to over-volt the MMC!
I'm surprised a half-bridge adds 2x Vbus per half cycle when in a standard nonresonant environment the load only sees 1/2 Vbus as Vpk (or Vbus as Vp-p).
I'm surprised a half-bridge adds 2x Vbus per half cycle when in a standard nonresonant environment the load only sees 1/2 Vbus as Vpk (or Vbus as Vp-p).
I'm confused. Isn't Vp-p equal to 2*Vbus? I'm supposing that Vbus is the same as Vin. A non-resonant analogon would be an inductance charged up with a Vin DC voltage. Current would rise according to
I = V * t / L
100A are reached then in about 12us with 170V and 21uH. That's a bit shorter than the 18us for the resonant case. This is due to the intermediate drops of primary current to zero in the resonant case. When current is low there is little power transfer from the voltage source to the tank.
Well what I meant was that in a standard SSTC (or any nonresonant load) on a half bridge the primary/load sees alternating +85V and -85V, which is 170Vp-p, which is 1x the total bus voltage.
In the DRSSTC On a half bridge model described above after the first half cycle the LC circuit sees an increase of 340V per half cycle over the previous half cycle. This is 2x Vbus.
I think for a full bridge on rectified 120V mains the load sees Vp-p = 2Vbus = 340V.
So what confused me was that Vp-p across the load seems to have magically doubled by going from nonresonant to resonant load conditions.
I think I have misunderstood you all along. You wrote:
I'll be using a Half-Bridge fed by full wave rectified and filtered 120V mains
I was thinking your half bridge was switching between 2 (half wave rectified) rails of +170V and -170V. For full wave rectified 170V, switching takes place between 0 and 170V and your voltage rampup is only at half the speed, i.e. 170V per half cycle. Sorry about this.
I think I have misunderstood you all along. You wrote:
I'll be using a Half-Bridge fed by full wave rectified and filtered 120V mains
I was thinking your half bridge was switching between 2 (half wave rectified) rails of +170V and -170V. For full wave rectified 170V, switching takes place between 0 and 170V and your voltage rampup is only at half the speed, i.e. 170V per half cycle. Sorry about this.
No worries! You've still provided immense help this whole time.
So then, I should be able to amend the formula for a half bridge to: Vmmc = 1/2 Vbus * ((2N)-1)
and then for a full bridge it would be: Vmmc = Vbus * ((2N)-1)
This actually works out to my benefit as I can easily add an option to select whether a half or full bridge is used in the calculator I'm making. Also, I can have twice as long of a burst length for a half bridge.
The other formula shouldn't need any modification, right? It makes sense that it wouldn't as it describes the voltage at a certain peak current for the resonant circuit, and isn't related to the input voltage. V = Ipk * 2Pi * Lpri * Fres
So then, I should be able to amend the formula for a half bridge to: Vmmc = 1/2 Vbus * ((2N)-1)
Almost. Since the voltage swing is Vbus including the first half cycle, it's simply Vbus * N and for the full bridge Vbus * 2N.
The other formula shouldn't need any modification, right? It makes sense that it wouldn't as it describes the voltage at a certain peak current for the resonant circuit, and isn't related to the input voltage. V = Ipk * 2Pi * Lpri * Fres
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Interesting thing is that the primary current can be larger than this math suggests too. All depends on your load conditions and tuning point. I think under some conditions the secondary can back drive the primary resulting higher currents.
So then, I should be able to amend the formula for a half bridge to: Vmmc = 1/2 Vbus * ((2N)-1)
Almost. Since the voltage swing is Vbus including the first half cycle, it's simply Vbus * N and for the full bridge Vbus * 2N.
Are you sure? This is basically describing what I initially thought would happen until you stated otherwise:
Sigurthr wrote ... Based on "adding switching voltage to MMC voltage every time you switch" I originally thought: 1) Voltage first applied; MMC voltage: 0V. Time Since Start: 0uS 2) First half cycle complete. MMC voltage: 170V. Time Since Start: 3.125uS 3) Second half cycle complete. MMC voltage: 340V. Time Since Start: 6.25uS. 4) 3rd half cycle complete. MMC voltage: 510V. Time Since Start: 9.375uS. 5) 4th half cycle complete. MMC voltage: 680V. Time Since Start: 12.5uS
With each new line being a half cycle: 170 170 170 170 170 170 170 170 170 170
If that's the case it certainly simplifies things. I wish I could simply test a resonant half bridge and verify these suppositions but I'm just not equipped to do so. I have a software engineer friend doing the programming for this calculator I want to make and I'm sure I'm driving him batty with the constant revisions, haha. Though, an issue we came across in implementation was determining a good way of finding the largest N (Nmax) before the voltage across the Primary Capacitor (Vmmc) exceeds the rated voltage (VmmcMAX). The only way we came up with was setting a bound of 20,000 for N (10,000 cycles) and using a Loop that counts down from 20k until Vmmc < VmmcMAX returns true. While this brute force method works it isn't the simplest and certainly isn't efficient.
If it really is just Vmmc = Vbus * N for half-bridge then we can simply just take the integer of ((VmmcMAX / Vbus) -1) to get a conservative Nmax. I believe the code to truncate from the float N to the integer Nmax would simply be: Nmax = (int) N; and this is a whole lot faster and easier than a complicated brute force search for Nmax.
Re: larger primary currents; The only time I know of where primary currents may exceed the predicted when loading is factored is in when the drive frequency shifts away from the secondary resonance frequency resulting in lessened loading. For example if you were using secondary base feedback and had the primary tuned to exact resonance - as the Fres of the secondary drops from streamer capacitance it would take more primary current to transfer the same energy to the secondary. This is one reason why primary feedback and a lower tuned primary is often used, to compensate for this and to transfer the most energy into the arc once breakout has been achieved.
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DRSSTC Peak Primary Current formula?
