Induction heater design - Page 1
Forum section: electronics / projects

author: Junkers
author_rank: Contributor
timestamp: June 18, 2017, 06:44:26 am
content: I've recently been working on an induction heater for interests sake, which I would like to later adopt for a small furnace build. However, I've encountered a few issues in terms of design and my own limited knowledge. I've noticed that many people adopt current transformers for their DIY builds. I understand that these provide galvanic isolation and enable higher voltages to run on the primary side of the circuit which allows for better efficiency. What I don't understand is how to correctly determine the windings ratio. Most literature in relation to this either approaches it from the perspective of stepping up/down the voltage or matching impedances. What is confusing me is how are you meant to match the impedance of a circuit that theoretically has zero impedance (neglecting negligible elements like ESR).I've simulated my circuit in LTSpice and found everything works reasonably well but doesn't align with the theory and what I observe in practice. For example, I wound 19 turns onto a set of four ferrite toroids and found that the inductance measured by my LCR meter at 10KHz (5.749mH) translates to a theoretical impedance of 466.2 Ohms (Z = sqrt(R2+ sL2) ~ sqrt(2.38R2+ 2.pi.12.841KHz*5.749mH2). In reality though, I noticed my power supply was only pulling 0.04A at 32V. This would put the impedance at around 800 Ohms. So I setup a potentiometer in series with my primary inductor and drove the circuit at 12.841KHz, adjusting the pot until voltage was a 50/50 split. The resistance of the pot was 780 Ohms which confirms the low current draw. To contrast this with what I observe in LTSpice, the primary inductor allows 8 - 8.5A to flow. I find the fact that the theory, LTSpice's simulations, and what I am observing are so far apart hard to understand. What could I be doing wrong here? Why is the inductance I measured not in accordance with the calculated impedance, and why do neither relate to what I see in practice?Below is the LTSpice schematic and the current passing through the primary inductor:http://imgur.com/a/Vb48yhttp://imgur.com/a/zBRtESo I guess in summary my questions are:#1 How should I go about determine my windings ratio when the impedance of the secondary circuit is approximately zero?#2 Why is the inductance measured by my LCR meter not reflected in the impedance I measure?#3 What could be the reason that LTSpice gives me such erroneous data?

author: fourtytwo42
author_rank: Super Contributor
timestamp: June 18, 2017, 08:07:59 am
content: I think I would get your schematic right first,L4 has a capacitive value, R5&R7 should not return to ground, there is apparently no appropriate bias supply to X1 & X2, ohh maybe its L1 / R1 hard to discern.Whats the capacitors in the CT secondary for ? Ahh its not a CT....sorryThere's a spurious junction on X1/HIN, 1N4148's are unsuitable as boost diodes, I could go on......Sometimes it's the simple things that make a simulation give unexpected results

author: T3sl4co1l
author_rank: Super Contributor
timestamp: June 18, 2017, 08:19:57 am
content: Quote from: Junkers on June 18, 2017, 06:44:26 amUnder what theory would a circuit have zero resistance?A sorely incomplete one, I hope.Since after all, without resistance, there can be no power transfer!No, it is indeed precisely the ESR that remains, which is reflected through the transformer, and matched.Where does the ESR come from? How to calculate it?The work coil is a transformer, one with poor coupling. The work is a shorted turn, except it's not really a short, it has self-inductance (the inductance of one turn around the current path) and resistance (which is of course the material resistance, factored by skin depth or material thickness, size and shape, and so on). This sets the current due to the induced voltage; the current is then reflected back into the work coil as a load.Because the transformer has poor coupling, it has a lot of leakage inductance. So a reasonably detailed model would look like an L1 || (L2 + R) circuit, where L1 is the coil's self inductance, L2 is the leakage inductance, and R is the work resistance.This still doesn't help you much, because L2 is really hard to put a number on, and R is tricky to do any better than estimate, given simple conditions (like a bunch of cylinders).I give this as background, but not as actually useful help. So what does help? Sqash it all together and call it an estimated Q factor (which at its simplest, reduces to an L + R or L || R equivalent, at a given frequency).What good is that? Two things. One, Q factor varies widely with conditions anyway, so it's not very useful knowing it precisely. Second, because of this, the power supply needs to be able to work into the same range that your load is expected to cover.A very practical example is a steel melting process, which might go from a Q of 5 (loaded with cold magnetic metal: the magnetic hysteresis loss about doubles the loss (ESR)!) to a Q of 10 or 20 (above Curie temperature, or maybe slumped into a small heel), to back down to 10 or so (with a full molten load).The Q is proportional to the ratio of areas between work coil and load. You always want to be as close to the work as possible, to keep efficiency high; if you avoid designing for very low Q (say, 1-3), that's fine -- you can always increase Q by adding an inductor (hopefully high quality, to maintain efficiency) in series with the work coil. You can't reduce it, though!The Q also varies with work resistance:Lower resistivity materials, like aluminum, bronze and copper, tend to reflect magnetic fields rather than dissipate power. The Q is higher, maybe 2-3x that of hot steel. Also, the coil losses are much larger, because the coil itself is carrying about as many amp-turns as are induced in the work, and is made of the same resistivity!Higher resistivity materials, like stainless, titanium, graphite and so on, tend to work very nicely -- as long as they are thicker than several skin depths. Simply put: as long as the field is being dissipated into the material (that's what skin effect is: the cancellation of magnetic field due to induced currents), it will be heated effectively.Clearly, at some point, resistivity can be too high, and the Q will rise again. This is true of ceramics and composites, which don't have enough bulk conductivity to do much (yet they may be excellent absorbers at microwave frequencies, say -- SiC and ferrite are good examples). A perfect insulator has no induced current at all, and therefore does not load the coil.Based on this, and given a ballpark Q range of perhaps 5 to 30, and an inverter range of 2:1, you can design the transformer and taps.30/5 = 6. 6 is almost 3 octaves (which is, so the transformer probably needs 3 or 4 taps.That is, given some work coil inductance (say 1uH nominal), and a frequency (say 50kHz), you therefore need 10uF to resonate with it, and you get a resonant impedance of 0.32 ohms. For Q = 5 to 30, you get ESR = 10 to 63 mohm.The inverter might deliver a 320Vpk square wave at 50kHz, at up to 30A RMS. That's 10kVA capacity, so you can drive a 5kW load anywhere from 1:2 to 2:1 mismatch (i.e., at 320V and 15A, or 160V and 30A -- you need some way to adjust the effective voltage, either by PWM*, or varying the supply voltage, or adjusting the driven frequency away from resonance**.*This has to be phase shift PWM in an H bridge. (The reactive currents don't work out if you PWM anything else, like a half bridge -- try it.)**This saves on power conversion stages, but has an ominous side effect: the control loop is almost impossible to stabilize. The "plant" has a complex pole pair, where the Q factor of that pole is (more or less) equal to the work coil Q (so, it's very peaky when the Q is high), and the pole frequency is equal to the difference between resonant frequency and driven frequency. Which in turn depends on the control state..... so, yeah.You can guard band it, but you end up with a ponderously slow control, which can be dangerous for the inverter's health. (Say if the control doesn't respond quick enough, and it dips below setpoint, hits resonance, and current builds up 2-3x what it should be, and...) A DSP could be designed to solve for this and change the controller's time constant accordingly, but geez, that's a lot of work. (It might be simpler to apply a state space solution, simply cranking through a pile of linear algebra every cycle. You'd end up with something that doesn't quite look like PWM or PID control, and would have the advantage of being the most agile possible control.)Anyway, the example inverter has load impedance range of 160/30 = 5.3 to 21.3 ohms (a factor of +/- 2, so to speak), which needs to be matched to a 10-60 mohm load. A ratio of 23:1 to 18:1 is minimal (i.e., 2 taps).But that's only at one inductance, and one frequency. For each of these, you get a proportional spread in load impedance. A practical design might consider work coils 1-10uH, at frequencies 20-80kHz, matched with one capacitor of 5uF, or a selection of capacitors somewhere from 0.4uF to 63uF. This gives a huge spread of impedances, so you'll likely compromise by cutting off certain combinations: large and small inductances, at high and low frequencies, respectively. This gives a sort of tilted prism, in the L-Freq-Q operating space.Anyway, whatever the compromise made, you'll likely want to settle with a transformer around, say, 4:1 tap range. Pile up the ferrite and you can manage this with only a few secondary turns -- convenient as they'll need to be water cooled.Note that leakage inductance, in the transformer, needs to be small. The secondary should fit closely around the primary. It's fine to wrap the cores with the primary, then assemble the secondary  into it. Even better is using a single tube (as large as possible) down the center, and a huge tube around the outside, with the tubes joined at the top and bottom so you get one big shorted turn, except one end isn't actually shorted, but the inner and outer connect to separate plates that go to the capacitor and work coil. (For this one, you'd probably close and flood the center, and wrap the outer with cooling tubes, or flood the whole thing, primary and all, which is nice for cooling the primary and cores, but not so nice for insulation.)(Can you tell I've done this before?)Tim

author: Junkers
author_rank: Contributor
timestamp: October 10, 2017, 09:40:59 am
content: Thanks for your input Tim. I went away and did a little reading / thinking / tinkering and have managed to put together a driver which can manage around 700W. When I start to push beyond this point things get a little dicey however...In the waveform capture below you can see the voltage from one of the outputs of the H bridge and the current waveform on the primary side of the transformer. Everything seems to be playing along somewhat nicely.https://ibb.co/nfkf1GExcept for one thing... The current waveform isn't crossing the zero volt line where it appears it should be. When I try to align the two by lowering the frequency into the driver I get this:https://ibb.co/cgpUvbNoise. Something isn't happy and I have no idea what. I'm not certain the first waveform is entirely wrong either. Even though the current waveform is skewed and suggests that the circuit isn't at resonance, the primary side resistance factored against the number of windings on the primary side of the transformer corresponds roughly to the ESR of the tank. ((59V / 16A) / (8^2) = 0.065 Ohms ~ I measured the components individually with an LCR meter). My only guess is that the Q factor is too high and by running the tank just outside of the resonant frequency the level of resistance produced by the series tank circuit increases and compensates Q given that Q = sqrt(L/C) / R. ( L = 3uH, C = 40uF ). Can anyone suggest what might cause noise like that illustrated?I would be happy to run more power through the system with the tank running just outside of the resonant frequency but the driver isn't having a bar of it. If you look at the first image you will notice the sine wave isn't perfectly symmetrical. It distorts at the point where the output node on the H bridge switches off (illustrated in red) to the point where the opposite arm switches on (can't be seen in the capture). There's a dwell period of 2% between each commutation and while the current waveform lags the voltage waveform, it creates chaos at higher orders of power. I realize the current is looking for a path out of the circuit but given the order of power that's trying to escape I can't rely on snubbers alone. This is why I want the tank to run at resonance, so I can achieve ZVS switching. But that's not going to happen until I can figure out the source of this noise...Oh, here's a picture for pictures sake... (Excuse the mess)https://ibb.co/kX2oow

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 10, 2017, 04:32:38 pm
content: Looks about right, given how loose the switching loop is. First of all, note what the output voltage is doing: when at resonance, when it switches off, the voltage is floating (zero current)! When the next transistor switches on, it quickly shorts out that floating voltage. Which means there's an RLC loop there, with some initial voltage and zero current, then the transistor switches on and discharges that voltage, giving a peak current, and ringing.Whereas just above resonance, it's in soft switching (ZVS turn-on). You've already achieved ZVS, don't worry about that.Zoom in on the ringing, and measure the resonant frequency. Connect a capacitor across the high side transistor, maybe 1nF, and measure it again. Use this calculator to find L and C:https://www.seventransistorlabs.com/Calc/RLC.html#cxReflect on what L and C might be present in the circuit, and how you might address them (reduce L, dampen with R or R+C or R||L).By the looks of it, the probed half of the H-bridge should be around 100nH. Which is really high for this!The other half if the H-bridge should be much less, maybe 20-30nH (and it can be better still). Reflect on what the difference might be.Tim

author: Etesla
author_rank: Regular Contributor
timestamp: October 12, 2017, 07:47:03 pm
content: Have you looked into zvs induction heaters? I made a couple of those way back and they always ran cool and powerful.

author: Junkers
author_rank: Contributor
timestamp: October 15, 2017, 10:05:09 am
content: Thanks for the link. I measured the ringing frequency to be 4.348MHz unloaded and 2.94MHz with a 1nF capacitor across one of the high side drivers. The tool states the capacitance is 8.43e-10 F. I calculated the parasitic inductance to be 1.59e-6 H based on what I found here:https://www.digikey.co.nz/en/articles/techzone/2014/aug/resistor-capacitor-rc-snubber-design-for-power-switches.Using Digikey's formula I should only require a capacitor of an equal capacitance to that found across the high side driver and a 43 Ohm resistor. I used the closest I had on hand which was 1.0e-9 F and 39 Ohms. This didn't produce the desired result though. I ended up trailing a few different values and found 47nF and 6.8 Ohms to be a good compromise between power dissipation and dampening. Here is a capture of the snubbers in effect (left vs right arms of the bridge):On closer inspection things aren't so pretty...These current spikes I measured with my current clamp are also interesting...I believe they are artefacts though as even when I don't have the clamp around any wire I get thisThis is with the probe set to 1x and the voltage/current scale being set to 1mV/100mA so I guess noise coupling into the output isn't that surprising. Should I be concerned or is this par for the course?All of this has been done at relatively low power, using a lab power supply (max 30V 3A). I've yet to put it through its paces so nothing is final or conclusive yet. The one upshot is that I've been able to run this at 14.80KHz which is much closer to hard switching than before (15.34KHz).Quote from: Etesla on October 12, 2017, 07:47:03 pmI have looked into these. I bought one of the generic 1000W units off ebay a long time ago. Apparently this topology does not do well beyond 60V - 70V according to this blog here:http://adammunich.com/zvs-driver/. I'd like to achieve at least 2Kw and at those power levels I don't think it would be practical in terms of efficiency let alone having to accommodate a power source like that.

author: strawberry
author_rank: Super Contributor
timestamp: October 15, 2017, 01:13:16 pm
content: https://www.eevblog.com/forum/projects/zvs-induction-heater-2000w/How about pulse skipping power control?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 15, 2017, 06:04:43 pm
content: Wow, 1.6uH, you might want to get rid of that rather than trying to dampen it out.Did you notice the L is different for the two halves of the H-bridge? Why is that?Tim

author: Junkers
author_rank: Contributor
timestamp: October 21, 2017, 08:01:13 am
content: Quote from: strawberry on October 15, 2017, 01:13:16 pmThat looks great. Certainly pushing the upper bound. I'd like to push well past 2KW if I can...Quote from: T3sl4co1l on October 15, 2017, 06:04:43 pmThis turned out to be a salient point. That 1.6uH was largely due to the lab supply wires, 1.22uH of it anyway. The other 0.33uH is due to the 30cm power cables soldered to the board and the remnants are parasitic. Directly connecting the board to the lab supply helped clear a lot of the noise captured previously. A 10MHz ringing was still present so I performed the same test as I previously mentioned. Using a small ceramic capacitor (680pF) and a 33 Ohm resistor I managed to snub out most of the noise on either side of the bridge. However, as you pointed out, things aren't balanced in terms of inductance so it seems I have to play each side off against one another by shifting the frequency. I think the imbalance in inductance is due to the slight asymmetry of the board's traces. I'm also using heaped solder on the traces to increase the boards ability to handle power. I would've thought increasing the current carrying capacity of the traces would help lower inductance but since it's solder I don't know this for a fact. (Is it impure? Does that create an inductance of its own?).I've also placed a 470uF capacitor between the power rails on the board as this helped further smooth out the remaining noise while running the inverter on my lab supply. I tried to power this unit up on my 1Kw SMPS but the current limiter kept triggering. I suspect that will be due to the aforementioned DC link capacitor.I also have an isolation transformer, variac, rectifier, and 10 000uF capacitor which has now taken over the role of my SMPS, allowing me to ease the power on.So with all of that said and done things aren't running too badly. I pushed the unit up to about 1100W for a few brief moments before easing the power back down to a steady 700W. As the crucible began to get warm (300C ish) it became more difficult to keep the noise balanced between either arm of the h bridge. Anyway, here's a clearer picture....Crucible at room temperature:Offset against the other arm. You can see the effect of the imbalance of inductance and the consequence using the same snubber values on either side.If I increase the frequency to resolve whatever is occurring in the previous capture then...VersusThe obvious answer is to redress the imbalance by changing the snubber values on the effected arm. However, I'd like to know what could be causing the type of noise occurring in 2nd capture as when the crucible gets warm the noise becomes increasing like that shown. Here's what it looks like:I know that as graphite heats its resistance drops so I presume the change in noise characteristics has something to do with a change in impedance but that doesn't quite complete the picture. I've varied the number of turns on the current transformer and in effect changed the impedance, I've never seen waveforms like that though. Any thoughts on what may lead to waveforms like that?I didn't get much of an opportunity to play with it beyond this point as the function generator I have has a bad habit of momentarily pausing between each frequency change, inducing a big current spike. Might see if I can salvage some FETs and get back out there tomorrow.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 21, 2017, 05:56:28 pm
content: Huh, in the picture, there was a big fat electrolytic on one side, apparently across the DC bus. What happened to that?Indeed, you need one on each side, connected across each pair of transistors. The required value is not massive, it only needs a low enough impedance to maintain the supply voltage give or take some ripple, at the switching frequency and load current. It looks like you've figured this out, which is excellent.Here's one I did (half bridge, two in parallel each side),And the waveform,Using IGBTs so the voltage was higher, and risetime pretty fast.Those are only 0.1uF film caps at the transistors, and 2.2uF banked together to the bottom. The results were fine, as you can see.Tim

author: Junkers
author_rank: Contributor
timestamp: October 22, 2017, 08:43:12 am
content: Quote from: T3sl4co1l on October 21, 2017, 05:56:28 pmI ended up removing it as it appeared to be originally contributing to the noise. I then brought it back to help quench the remaining noise but it was getting rather warm. It's ESR is quite high so I've substituted it with a couple of 560pF capacitors in the meantime, one on either side. There's a slight oscillation coupled into the square wave due to the values of the DC link capacitors but I don't think it's particularly threatening. I've also redesigned the snubbers to account for the differing levels in inductance on either arm of the bridge. Things seem to be working well now.Another waveform capture... because I know you can't get enough of them. Notice the ringing in the current clamp's waveform is mostly gone. It can be removed completely with a little frequency adjustment.I didn't push it past 1Kw today as I need to get the fans running on the heat sinks. That's yet to come.Was the use of a ferrite bead necessary there?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 22, 2017, 08:49:22 am
content: Hot from ESR, that means you need more, not less!pF? Really? Surely those are nF? pF ain't gonna do jack at this level...Tim

author: Junkers
author_rank: Contributor
timestamp: October 22, 2017, 08:51:15 am
content: Ah yes! nF is correct. I've been playing around with the snubbers for a little too long I think

author: calexanian
author_rank: Super Contributor
timestamp: October 23, 2017, 05:00:49 am
content: My induction heater went bang today. I was hooking up a new coil and water recirculating supply and i think something bent over and touched, or got short enough to arc. One of the power devices went bang. IRFP260N to be exact. I ordered another whole unit off eBay. They are only $32. I will get a couple replacement parts from mouser with my next order to them. I like the design. Its simple. No regard to overload protection though.

author: Junkers
author_rank: Contributor
timestamp: October 23, 2017, 08:19:53 am
content: Quote from: calexanian on October 23, 2017, 05:00:49 amThose units can't be beaten for value. Can buy 20 IRFP260Ns for $12 USAdded some cooling today. Runs much better, capable of sustaining reasonable power now. The capacitor nearest to the coil is the next culprit. I had the crucible up to 450C before I had to kill it, the tank capacitor was at 90C. I have these waiting in the wings:Just need to get hold of a brazing torch so I can mate the copper plate with the tubing.I also captured some footage today, mainly to illustrate how loud my variac is. It's intimidating... I'm not sure how normal this is and was hoping to get some feedback. Unfortunately the mic on my phone doesn't really do it justice. To give you an idea though, the dust and debris on the variac will bounce around when it's under load. I've adjusted the carbon brush so it's quite tight but I'm not sure what else I can do.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 23, 2017, 09:10:35 am
content: Hmm, look for loose metal bits on and around the variac core?If it varies with load, it may be loose windings. The force on the copper wire depends on current, while the force on the steel laminations depends on input voltage.Tim

author: Junkers
author_rank: Contributor
timestamp: November 30, 2017, 11:25:00 am
content: So I've been doing a little more work here and there since I last posted. I ended up building a concrete kiln from refractory cement with mixed results. The engineer who sold it to me said the cement was not conductive, Alumina oxide or some such... but I'm questioning that as I haven't been able to push past 400W. You can see it in the background of this picture.I've made a couple of changes to the circuit itself also. It now has 4 separate PWM channels synchronized with each other so I can control high side's duty cycle independently of the low side. This made quite an impact on the level of ringing present, I think mainly due to the low side being active for longer and allowing more residual energy to escape through a more friendly means (not the high side flyback). That's speculation though. I'm using an arduino in the meantime and have a CPLD on the way. The arduino can be a little temperamental, losing alignment on odd occasions. Perhaps it's my coding but I happen to like CPLDs/FPGAs a lot more anyway.One of the other changes I've made was to change the type of transistor. The IRFP260Ns were just a bad fit. I thought it may be due to them being knock offs but no, even the authentic ones presented the same issues. I switched to IGBTs and tried a variety of brands and ratings. All of them seem to operate extremely well in comparison. The IGBTs I tested were NGTB35N65FL2WG, STGW40NC60V, and IHW25N120E1XKSA1 for reference.I also found the source of my strange current waveform distortions near the zero crossing point, it was just a matter of impedance matching. I think the original crucible requires more turns than I have wire so for the meantime being I will use my smaller crucible. Works well as you can see in the video below. I later did a run at 960W and achieved 900C. More watts to come...The last issue to solve is to do with my bigger power supply (the variac) as when I power the induction heater from it the peak voltage/current isn't stable. It tends to 'flicker' around a lot, particularly at higher loads. I think it's due to the capacitor not handling the ripple current (supposedly capable of 23A) or some form of resonance occurring between the circuit and the DC link capacitor. What I don't understand is that if it is due to excessive ripple current, why does a 10000uF capacitor fail where as the much smaller capacitor inside my SMPS sustain such heavy ripple current without so much as a quiver in the final waveform. Here's a shot of the issue I managed to capture on a much older scope (I wanted to make a comparison between my new scope vs old). The peak of the square wave appears shaded when in actual fact it's just fluctuating rapidly. Any thoughts on this?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: November 30, 2017, 11:33:51 am
content: Quote from: Junkers on November 30, 2017, 11:25:00 amIf it were resonance, what is the resonant frequency? What values of inductance and capacitance would be necessary to create that?(This becomes a much more interesting question in closed loop operation, but it sounds like you're still running open loop? So that's N/A.)QuoteAt what rate does it fluctuate? What does that tell you about the source of the fluctuation?Looks like a classic symptom of insufficient mains filtering. Rule of thumb is 2000uF per amp at 12V. So if you were doing 20A and 24V, you'd use 20 times more and 2 times less than 2000, or 20,000uF.Tim

author: strawberry
author_rank: Super Contributor
timestamp: February 19, 2024, 08:53:17 pm
content: what will happen with Q<2 ? will LC stop working (hard switching)

author: David Hess
author_rank: Super Contributor
timestamp: February 20, 2024, 01:38:11 am
content: Quote from: Junkers on June 18, 2017, 06:44:26 amAt low voltages and high currents, losses are primarily proportional to the current squared, so it is advantageous to use a transformer to raise the primary side impedance for greater efficiency.QuoteThe procedure is the same when designing the impedance transformation at the output of a power RF amplifier. It is *not* about impedance matching for maximum power transfer, because if the impedance was matched, then half of the power would be dissipated in the source leading to 50% efficiency. For better than 50% efficiency, the source impedance after the transformation is lower than the load impedance.Starting with the output power and impedance of the load, the impedance transformation is selected to allow the maximum output voltage swing of the power output device, and then the current required from the output device can be calculated.The load for an induction heater is poorly defined by hysteresis and eddy current losses in the part being heated, but it could be measured, or estimated, and then the impedance transformation to a lower impedance to drive the secondary winding could be made. Since the load will vary over a considerable range, the primary side control circuits must have some way to limit the power, typically by limiting the voltage and current.If the output impedance is too low for the secondary winding, then too much power will be transferred to the secondary winding itself, so that could be used as a way to find the maximum impedance transformation from the transformer.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: February 20, 2024, 08:43:57 am
content: Quote from: strawberry on February 19, 2024, 08:53:17 pmWhat was this in response to, and was it pressing enough to necropost--?Tim