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Why does it work so well?

Started by Piotr Wyderski January 30, 2017
I have the following simple converter: CD4093 drives the power logic 
shift register's NPIC6C596A OE pin with 500kHz square wave signal with
duty cycle 40%. Both chips are powered from 5V, the shift register is
set to all ones. Hence I have 8 modulated open drain channels, 
everything works as expected. Now I connect a 1:1 transformer wound
on a PC40 6mm toroid (AL=2300), 16 turns each. The primary goes to
+8V and one of the drains. The secondary is loaded with a Shottky-based 
half-wave rectifier + a 3k3 resistor + 100n.

If the transformer arrangement is as in the flyback converter, the
thing behaves as a sloppy flyback, with huge voltage spikes on the
drain, which indicates that the flywheeling diodes/other structures
within the IC are not very fast. The efficiency is also very poor,
but for such a small load current it doesn't matter.

The curiosity appears when I swap the connections of the primary
to make this configuration resemble a forward. Now all the waveforms
look like the examples in a book, just beautiful. The kickback
voltage from stray inductance is non-existent, the edges are sharp, etc.
But the output stage has absolutely no reset circuit and there is
no flux exursion. Why is that?

I thought it might be related to some form of active clamping hidden
inside the IC, but no, exactly the same behavior occurs when I use just
a 2N7000.

	Best regards Piotr


On Monday, January 30, 2017 at 6:25:37 PM UTC+11, Piotr Wyderski wrote:
> I have the following simple converter: CD4093 drives the power logic > shift register's NPIC6C596A OE pin with 500kHz square wave signal with > duty cycle 40%. Both chips are powered from 5V, the shift register is > set to all ones. Hence I have 8 modulated open drain channels, > everything works as expected. Now I connect a 1:1 transformer wound > on a PC40 6mm toroid (AL=2300), 16 turns each. The primary goes to > +8V and one of the drains. The secondary is loaded with a Shottky-based > half-wave rectifier + a 3k3 resistor + 100n. > > If the transformer arrangement is as in the flyback converter, the > thing behaves as a sloppy flyback, with huge voltage spikes on the > drain, which indicates that the flywheeling diodes/other structures > within the IC are not very fast. The efficiency is also very poor, > but for such a small load current it doesn't matter. > > The curiosity appears when I swap the connections of the primary > to make this configuration resemble a forward. Now all the waveforms > look like the examples in a book, just beautiful. The kickback > voltage from stray inductance is non-existent, the edges are sharp, etc. > But the output stage has absolutely no reset circuit and there is > no flux exursion. Why is that?
This doesn't make any sense to me - I can't turn it into any kind of circuit diagram in my head. An LTSpice file that could be loaded into LTSpice and looked at as circuit diagram, and presumably run as a simulation, would be more accessible. In particular, what is the shift register doing for you? http://www.nxp.com/documents/data_sheet/NPIC6C596A.pdf I can imagine some interesting things that you could do, but I've got no idea what you are actually doing. -- Bill Sloman, Sydney
bill.sloman@ieee.org wrote:

> This doesn't make any sense to me - I can't turn it into any kind of circuit diagram in my head.
Just imagine a single MOSFET flyback, Bill, that's all it is. There are two manifestly different ways to connect the transformer: flyback style (right), and a mistake in wiring, which swaps the phase dots, resulting in a resetless forward coverter without a choke at the secondary side. And, surprisingly, it is the forward which appears to work perfectly. The flyback is good enough, but just good enough. > In particular, what is the shift register doing for you? Here it just acts as a regular N MOSFET with the OE pin being the gate. I wanted to do a bench test using real components before sending the PCB plans to the makers. In the final circuit it scales to 8 such MOSFETs, which can be selectively enabled by the shifted-in content, because in the open-drain configuration the OE pin is ANDed with the content. So, it provides 8 independent 500kHz-modulated current channels and all the kickback-handling circuitry with the component count of 1.
> An LTSpice file that could be loaded into LTSpice and looked at as circuit diagram,
> and presumably run as a simulation, would be more accessible. I don't have a simulation of this particular circuit, but my other simulations which include forward SMPSes consistently report rapid flux excursions and the current at the primary side to be on the order of 4.5kA or something similarly funny, in a complete disagreement with reality. Best regards, Piotr
"Piotr Wyderski" <no@mail.com> wrote in message 
news:o6mppe$kvf$1@node1.news.atman.pl...
> I have the following simple converter: CD4093 drives the power logic shift > register's NPIC6C596A OE pin with 500kHz square wave signal with > duty cycle 40%. Both chips are powered from 5V, the shift register is > set to all ones. Hence I have 8 modulated open drain channels, everything > works as expected. Now I connect a 1:1 transformer wound > on a PC40 6mm toroid (AL=2300), 16 turns each.
Well there's your first problem. You've designed the transformer ("transformer", not "coupled inductor"!!) to store almost zero energy. 16 turns is 256 times 2.3 (you didn't give units but I assume that's 2.3uH/t^2) or 588uH. That's quite a fine common mode choke, or pulse transformer, at 500kHz, but it isn't worth shit for flyback! The magnetizing current is on the order of 8V / (588uH * 2 * pi * 500kHz) = 4.3mA, so the power is 34mW. Going to guess that's about what you measured at the output? :-) Any excess you try to dump into the poor thing (say because the output /isn't/ rising to 8V+, thus the core remains saturated between cycles), goes into leakage inductance instead, which if you wound that (in the best case) as bifilar, will be on the order of 0.3uH, and if "side by side" windings, maybe 5uH. Making wide guesses here, as you didn't provide a drawing or part number for the core, or a winding schedule.
> The primary goes to > +8V and one of the drains. The secondary is loaded with a Shottky-based > half-wave rectifier + a 3k3 resistor + 100n.
Hmm, 10.6V into 3.3k is 34mW, so at least it's plausible that you weren't deeply into saturation -- 10.6V at 60% duty is more than enough reset flux. Being a closed loop ferrite, it won't fully reset, but you'll stay above B=0 (the residual is called remenance). Probably, the capacitance of the schottky diode was enough to provide reset flux, as well.
> If the transformer arrangement is as in the flyback converter, the > thing behaves as a sloppy flyback, with huge voltage spikes on the > drain, which indicates that the flywheeling diodes/other structures > within the IC are not very fast. The efficiency is also very poor, > but for such a small load current it doesn't matter.
The IC doesn't show any freewheeling structures, only clamp diodes. You left the drain completely unclamped (except for the IC's own internal protection)? What the hell?
> The curiosity appears when I swap the connections of the primary > to make this configuration resemble a forward. Now all the waveforms > look like the examples in a book, just beautiful. The kickback > voltage from stray inductance is non-existent, the edges are sharp, etc. > But the output stage has absolutely no reset circuit and there is > no flux exursion. Why is that?
It's a charge pump. It's fine, except for the monstrous inrush surge at startup, and the lack of voltage regulation... Tim -- Seven Transistor Labs, LLC Electrical Engineering Consultation and Contract Design Website: http://seventransistorlabs.com
Tim Williams wrote:

> Well there's your first problem. You've designed the transformer > ("transformer", not "coupled inductor"!!) to store almost zero energy. > > 16 turns is 256 times 2.3 (you didn't give units but I assume that's > 2.3uH/t^2) or 588uH.
The convention in Polish literature is that AL is expressed in nH/t^2, I thought that this is a worldwide habit. But yes, your assumption is correct.
> That's quite a fine common mode choke, or pulse transformer, at 500kHz, > but it isn't worth shit for flyback!
This is exactly the value the calculator suggests: http://schmidt-walter-schaltnetzteile.de/smps_e/spw_smps_e.html (for 10V/10V/4mA/500kHz => 584.1uH). At this energy level it should not matter whether the core is closed or has an air gap.
> The magnetizing current is on the order of 8V / (588uH * 2 * pi * > 500kHz) = 4.3mA, so the power is 34mW.
In full agreement with reality. :-)
> Any excess you try to dump into the poor thing (say because the output > /isn't/ rising to 8V+, thus the core remains saturated between cycles), > goes into leakage inductance instead, which if you wound that (in the > best case) as bifilar, will be on the order of 0.3uH, and if "side by > side" windings, maybe 5uH. > > Making wide guesses here, as you didn't provide a drawing or part number > for the core, or a winding schedule.
There is no part number, I have wound it myself. The core is from China, all I know are the dimensions and the material, which is PC40. It is composed of 2 coils 16 turns each, both wound with 0.25mm triple insulated wire of different colors. Due to its thick insulation (the wire is rated for 7kV) a single coil occupies the entire circumference of the core and there are two coils, one at the top of the other, both single-layer.
> Hmm, 10.6V into 3.3k is 34mW, so at least it's plausible that you > weren't deeply into saturation -- 10.6V at 60% duty is more than enough > reset flux.
But how? Where does the energy of the collapsing magnetic field go?
> Being a closed loop ferrite, it won't fully reset, but you'll stay above > B=0 (the residual is called remenance).
https://product.tdk.com/info/en/catalog/datasheets/ferrite_mn-zn_material_characteristics_en.pdf PC40 has Br=125mT and Bs=500mT, so there is a safe 4:1 margin. But I (and LTSpice) would expect that B is closer to Bs than Br, which it apparently isn't.
> Probably, the capacitance of the schottky diode was enough to provide > reset flux, as well.
OK, this is a very plausible proposal.
> The IC doesn't show any freewheeling structures, only clamp diodes.
Fig. 4. of the NXP datasheet shows an anti-parallel diode between the source and the drain of the output MOSFET, which should be fine for a flyback. Measurements show it is 2x better than that of 2N7000 (which quickly gets killed by the spikes :-)).
> You left the drain completely unclamped (except for the IC's own > internal protection)?
Yes. The chip has a built-in clamping structure engaging at 37.5V (measured and astonishingly close to the Typ breakdown voltage from the specs) and 30mJ avalanche capacity. > What the hell? In flyback mode the clamping structure activates and hence defines Vmax. In forward mode the scope shows Vmax at the drain is ~24V, i.e. 72% of the worst case from Abs. Max., the reverse voltage across the rectifier diode is hair below 20V and there are no significant Gibbs effect overshots, 1Vpp maybe. I will not show the waveforms, as they are just perfect. Seems to be super-stable and safe, I just don't understand why. :-)
> It's a charge pump. It's fine, except for the monstrous inrush surge at > startup, and the lack of voltage regulation...
It is a mockup of an insulated MOSFET gate driver (one of), where the capacitance is that of two gates, as it is intended for 50Hz AC switching in the classic configuration. The load is stable (the gate discharge resistor), the input voltage too, and the surge will not last long. Best regards, Piotr
"Piotr Wyderski" <peter.pan@neverland.mil> wrote in message 
news:o6nvrq$n5a$1@node2.news.atman.pl...
> The convention in Polish literature is that AL is expressed > in nH/t^2, I thought that this is a worldwide habit. But yes, > your assumption is correct.
I know better than to let A_L go unqualified... some use nH, some use uH, some use t^2, some use "per 100 turns"! A lot of ham resources have tables of powdered iron and ferrite cores (which are actually designations of Micrometals, and Fair-rite, respectively) in the latter format (and report the units about as often..!). So thanks for confirming. :-)
> This is exactly the value the calculator suggests: > > http://schmidt-walter-schaltnetzteile.de/smps_e/spw_smps_e.html > > (for 10V/10V/4mA/500kHz => 584.1uH). At this energy level > it should not matter whether the core is closed or has an air gap.
Oh.. so you actually are doing really teeny power. Because... thingy. Fair enough. The alternative interpretation is then that you're using way more core than you should be -- but whatever. Hand-winding more turns, on a teeny core, is worse than the cost of an oversize core. It's a valid engineering decision, eh? :^)
> There is no part number, I have wound it myself. The core is from China, > all I know are the dimensions and the material, which is PC40.
It's weird that PC40 is a TDK designation, but there's no part number or drawing to go with it. (I suppose it could be that a no-name factory bought TDK *powder*, and make their own final parts. In which case, who knows what the part really is, or if they ever wrote a datasheet for it.) Anyway, it's not hard to measure A_e and l_e of a toroid, so it's not really a big deal...
> It is composed of 2 coils 16 turns each, both wound with 0.25mm triple > insulated wire of different colors. Due to its thick insulation > (the wire is rated for 7kV) a single coil occupies the entire > circumference of the core and there are two coils, one at the > top of the other, both single-layer.
Lovely stuff, I need to pick up a few spools some time. Should be pretty good coupling then: overlapping single layer windings are /approximately/ a twisted pair. (Consider if you wound them as a bifilar twist, then untwisted them in-situ so you just had two layers, laying on top of each other in a coincidentally parallel fashion.) That puts your transmission line impedance in the ~150 ohm range, and the winding length around..... half a meter maximum, I would guess? (Normal twisted pair is more like 100-120 ohms, and for that matter, twisted *enamel magnet wire* is as low as ~60 ohms. But I'm guessing the thin center conductor and relatively thick insulation will push it up a bit higher, plus the uneven winding not being perfectly parallel.) What relevance is transmission line impedance? It handily gives the (asymptotic LF approximation equivalent) inductance and capacitance. The L manifests as leakage, while C manifests as P-S parasitic capacitance. If Z_0 is about half Z_{free space} (377 ohms), then L is about half and C about double that of their given values (i.e., L/len isn't 1.257 uH/m, but more like 0.6 uH/m, and C/len isn't 8.84pF/m, but more like 20 -- but it also gets extra because of dielectric constant, so maybe 30 instead). Sanity check: sqrt( (0.6 uH/m) / (30 pF/m) ) = 141 ohms. Close enough for a SWAG! At max 0.5 m length, that's 0.3uH and 15pF. If you recall my TLT time domain analysis, the 15pF manifests as coupling between pins (which cancels out if the circuit is differential, and has enough CMRR), and the 0.3uH manifests as leakage. Both are about at their minimum impact, if you use it at a circuit impedance around Z_0. So, if you're driving 8 volts, you'd want to draw 53mA at the same time. Or dampen it with an R+C, where the R is around 150 ohms, and C is some times more pF, maybe 50-100. If you don't provide damping, then you'll get ringing -- which may not be a [functional] problem at all, but is almost always a nuisance during testing and EMC. That also means, say you want to push around a gate, hard: you can't do it any faster than the 0.3uH limits you to. A 10nF gate has a 1/4 wave time constant of 43ns. (And an impedance of 5.5 ohms, so you'd use that much gate resistance to dampen it.) And the peak current during that event would be about 1.4A, for a 10V step. (Which is not at all a bad GDT, really. That'd be fine for an isolated inverter in the low 100s kHz!)
>> Hmm, 10.6V into 3.3k is 34mW, so at least it's plausible that you >> weren't deeply into saturation -- 10.6V at 60% duty is more than enough >> reset flux. > > But how? Where does the energy of the collapsing magnetic field go?
What little energy is stored in the core (which seems to be "most of it", since the power is so low!), is clamped by the diode and ultimately dissipated in the resistor. The 0.3uH of leakage will store whatever's left. Worst case: core saturates, and the driver draws short-circuit current, maybe 200mA. 200mA into 0.3uH is 6nJ, is 3mW at 500kHz (still not a lot, really). If clamped at 30V (37.5V - 8V, give or take), the overshoot pulse will only last for 2ns. I doubt that thing even switches that fast, so you should see very little overshoot indeed in the flyback case. So.......are you *suuuure* you checked the phase on these two conditions, correctly? Because you'll see tons of overshoot in the forward converter case -- because the reset pulse is completely unclamped, otherwise -- and hardly a few volts of overshoot from the flyback arrangement, which is nicely clamped by the diode. Related question: what was the output voltage under the two conditions? Forward should yield a bit less than the supply voltage, changing little with duty cycle; flyback will vary ~proportionally (actually goes as D / (1-D)).
>> The IC doesn't show any freewheeling structures, only clamp diodes. > > Fig. 4. of the NXP datasheet shows an anti-parallel diode between > the source and the drain of the output MOSFET, which should be fine > for a flyback. Measurements show it is 2x better than that of 2N7000 > (which quickly gets killed by the spikes :-)).
No, that's not a clamp diode, that's the intrinsic body diode. (It's redundant to draw it outside the MOSFET, anyway: that's precisely what the triangle in the middle of the MOSFET symbol is saying.) The body diode actually serves the purpose of a "damper" or "efficiency" diode, if anything. These are mostly-obsolete terms from CRT circuits. What happens here is, the flyback pulse is overly strong (or overly slow), and resembles, not so much a nice square clamped pulse, but a free ringdown of the RLC circuit (which is the flyback transformer and deflection coil in parallel, and their winding inductance and capacitance). If the ringdown is linear, and not well damped, then if the positive overshoot was, say, 500%, the subsequent negative undershoot will be, guess what, about 500% again. To stop the ringing and begin a linear horizontal scan, the negative ringdown is clamped with a diode. Which simply happens to be a diode from GND to [switching node]. Or, anything on a secondary winding that yields the same effect. (Back in the toob days, they used a secondary to generate "B+ boost", around 550V, which was used for vertical deflection and some other things.) In your circuit, you might experience a similar effect, in the forward configuration, because the flux reset pulse is quite tall: ~400% overshoot. If it rings down and clamps to ~GND, then the body diode is doing exactly this kind of job. :) Anyway, back to clamping -- the S-D "diode" isn't designed to avalanche in this case; rather, the G-D diode is made with a lower breakdown voltage, so that the transistor is turned on, dissipating the clamp energy as conduction, rather than spilling out into the semiconductor. (Avalanching a MOSFET that's part of an IC, would probably scramble the rest of the IC's internal functions. Similar reason why you want to avoid putting much bias into the input protection diodes, or why ESD events often cause latchup or reset.) But what you really want, is a clamp diode that dumps the pulse into a reservoir. Like what a ULN2003 has: a junction diode from [output pin] to [clamp pin]. In this case, you'd load the [clamp pin] with, say, a 20V zener diode, or an R || C. In one-offs, you'd just use an RCD network. This is called the peak voltage clamp snubber: C >> C_{switching junction}, so it acts as a boost converter, rectifier and filter; and R is sized to bleed off the worst-case power flow. Oh, and in this case, since the core is oversized, it's fine for flyback, but the reset pulse in forward mode delivers precisely as much energy (to the snubber) as the flyback does normally, so your efficiency will be almost exactly half! Typically you'd use a core with average permeability around 30 for flyback (better for more energy storage), and around 3000+ for forward (better for /least/ energy storage!). Since you don't have a choice here (it's the same transformer :) ), your forward mode efficiency is the pits. :-/
> In flyback mode the clamping structure activates and hence defines Vmax. > In forward mode the scope shows Vmax at the drain is ~24V, i.e. 72% > of the worst case from Abs. Max., the reverse voltage across the > rectifier diode is hair below 20V and there are no significant Gibbs > effect overshots, 1Vpp maybe. I will not show the waveforms, as they > are just perfect. Seems to be super-stable and safe, I just don't > understand why. :-)
Perhaps the above will explain why. :-) Do double-check the polarity on that one... FYI, Gibbs effect is irrelevant: it is strictly a nonphysical effect, seen when taking the Fourier transform of a nonphysical (unlimited bandwidth, piecewise-discontinuous) signal. Real signals are always continuous (not only that, but with continuous derivatives and finite bandwidth), so if you ever see something that looks sort-of like it, it's either an instrument error (DSO sinc interpolation, when implemented poorly, is an illustration of it), or a part of the real signal -- most often a parasitic network (such as here, the RLC properties of the switching loop), and therefore the amplitude and frequency of that transient are representative of real physical elements in the circuit (which means also that, we needn't throw up our hands when we see them -- they are elements under the designer's control!). I know, it's pedantic -- I clearly understood what you meant by using the term. But I think it is worth emphasizing the essence of the effect, because of its beauty: a phenomenon with interesting theoretical properties, which tests the limits of our analytical methods, and pushes us to think of ever-more diabolical circuits in case it leads to even deeper understanding. How is it that the Gibbs effect has finite overshoot, even after infinite harmonics? Bwuh?! A real signal cannot have a discontinuity... but what if we try, say, launching a shock wave down a nonlinear transmission line! What then? How sharp can we get? Tim -- Seven Transistor Labs, LLC Electrical Engineering Consultation and Contract Design Website: http://seventransistorlabs.com
On 1/30/2017 3:02 AM, bill.sloman@ieee.org wrote:
> On Monday, January 30, 2017 at 6:25:37 PM UTC+11, Piotr Wyderski wrote: >> I have the following simple converter: CD4093 drives the power logic >> shift register's NPIC6C596A OE pin with 500kHz square wave signal with >> duty cycle 40%. Both chips are powered from 5V, the shift register is >> set to all ones. Hence I have 8 modulated open drain channels, >> everything works as expected. Now I connect a 1:1 transformer wound >> on a PC40 6mm toroid (AL=2300), 16 turns each. The primary goes to >> +8V and one of the drains. The secondary is loaded with a Shottky-based >> half-wave rectifier + a 3k3 resistor + 100n. >> >> If the transformer arrangement is as in the flyback converter, the >> thing behaves as a sloppy flyback, with huge voltage spikes on the >> drain, which indicates that the flywheeling diodes/other structures >> within the IC are not very fast. The efficiency is also very poor, >> but for such a small load current it doesn't matter. >> >> The curiosity appears when I swap the connections of the primary >> to make this configuration resemble a forward. Now all the waveforms >> look like the examples in a book, just beautiful. The kickback >> voltage from stray inductance is non-existent, the edges are sharp, etc. >> But the output stage has absolutely no reset circuit and there is >> no flux exursion. Why is that? > > This doesn't make any sense to me - I can't turn it into any kind of circuit diagram in my head. An LTSpice file that could be loaded into LTSpice and looked at as circuit diagram, and presumably run as a simulation, would be more accessible. > > In particular, what is the shift register doing for you? > > http://www.nxp.com/documents/data_sheet/NPIC6C596A.pdf > > I can imagine some interesting things that you could do, but I've got no idea what you are actually doing.
He's not clocking the shift register. He's strobing the OE pin to use the outputs as open drain transistors. -- Rick C
Tim Williams wrote:

> I know better than to let A_L go unqualified... some use nH, some use > uH, some use t^2, some use "per 100 turns"!
Holy Moly, so it seems (again!) that our local conventions are much more uniform. Which is nothing to brag about, rather stunning, personally...
> The alternative interpretation is then that you're using way more core > than you should be -- but whatever. Hand-winding more turns, on a teeny > core, is worse than the cost of an oversize core. It's a valid > engineering decision, eh? :^)
The circuit has to be small enough not to dominate the PCB area, compared to the circuit it is driving. The width of a DPAK transistor + all the necessary safety margins make this 6mm core just fine. The only truly limiting factor is to have enough space to contain the windings, given their required insulation ratings. If both windings are made of TIW, and I want that to be sure that even a single insulation failure is not going to fry the control logic, the windings barely fit.
> It's weird that PC40 is a TDK designation, but there's no part number or > drawing to go with it.
It came from AliExpress in bags of 100. A lifetime supply, so I thought, now need to buy more. :-) But the lack of specs is quite typical, I have all sort of strange ferrites in quantity, including various NOS square loop rings from the old computers, in a futile attempt to sharpen my magamp-jitsu. I need to take their characteristics myself.
> Lovely stuff, I need to pick up a few spools some time.
It depends on the particular type, some of them are fine to work with, some behave like a fishing line and then manual winding satisfies all the conditions to commit manslaughter of a casual bystander.
> and the winding length around..... half a meter maximum, I would guess?
24cm each, including the PCB mounting segments.
> But I'm guessing > the thin center conductor and relatively thick insulation
The insulation thickness is consistently 0.1mm across all the diameters.
> So.......are you *suuuure* you checked the phase on these two > conditions, correctly?
Here are the waveforms: https://s30.postimg.org/fkvd1uqnl/DS1_Z_Quick_Print2.png Blue is the voltage at the drain, yellow at the output winding. The scope settings are correct, I was afraid of an inversion mode on one of the channels as an artifact of playing with the math functions during an earlier experiment. BTW, in the real circuit the f where the supply current has its minimum is ~350kHz, which is fine And now, err... uhm... I was measuring the *drain* voltage, not the *inductor* voltage, which is fully anti-correlated. The answer was in front of my eyes all the time, but I have somehow mentally locked on the inductor behavior while observing the transistor. The thingy has been a flyback from the very beginning and it is perfectly clear why it behaves so well. I believe you know how stupid I feel now, but at least the puzzle is solved...
> Because you'll see tons of overshoot
[snip] That's exactly what happens, Tim. You ARE an expert and I think I owe you a bottle of something. Ashamed, yet happy, Piotr BTW, the LED rectifier idea is so tempting... :-/
rickman wrote:

> He's not clocking the shift register. He's strobing the OE pin to use > the outputs as open drain transistors.
Exactly. Well, not quite true at the bench, because I also use the strobe clock as the data and latch clocks, as it was the simplest way to fill the register with ones, but yes, you have the idea right. Best regards, Piotr