Resonant LCR with signal generator

[klugesmith]

Tired of waiting for overdue toy "ZVS Induction heaters" from ebay, I made a practice coil and measured it on the bench.

With an ordinary benchtop signal generator I was pleased to get tank circuit ringing with more than 10 amps RMS at 126 kHz.  49 volt-amps, from a 50 ohm function  generator that can put out up to about 0.6 watts.  Here are the details.

For lecture hall and SPICE simulations, I wanted to start with 1 uF and 1 uH, to get time constant 1 us (Fres = 159 kHz) and characteristic Z = 1 ohm.  The blue capacitor, which helped me blink a neon glow lamp more than 50 years ago, was just measured to be 1.001 uF!   The coil was wound today, starting a bit on the large side. Tank resonance at 126 kHz implies L = 1.6 uH.

Connections are made with BNC cables and a BNC tee at oscilloscope input. Scope input is high-Z, and the transmission lines are negligible at this frequency.
With LC tank unconnected, maximum output sinusoid was measured by scope to be 31 V peak-to-peak and 10.94 volts RMS.  If source impedance were nominal then we could drive 5.47 V into 50 ohms, for 0.60 watts.
After connecting LC tank and adjusting frequency for maximum voltage, I recorded 4.70 volts RMS at 125.5 kHz.   Computed current amplitudes are 10.5 A RMS in both L and C.  Review of my arithmetic would be welcome.   Don't know if capacitor would become warm.   Power lost in tank can't be exceeding 0.6 W.

Next steps are to measure change in resonance with repeatable ferrous & nonferrous loads in coil.  Or for Solhi's interest, measure B at center of coil using a small sense coil.

[edit] Has anyone seen evidence of volt-amp ratings on IH's or IH capacitors? It seems natural that the value would be product of RMS voltage and RMS current in the tank circuit.  A very generous upper bound on heating power.

[davekni]

After connecting LC tank and adjusting frequency for maximum voltage, I recorded 4.70 volts RMS at 125.5 kHz.   Computed current amplitudes are 10.5 A RMS in both L and C.  Review of my arithmetic would be welcome.

I'm getting:  1 / (1.001uF * 2 * PI * 125.5kHz) = 1.2669 ohms.  4.70V / 1.2694 ohms = 3.710Arms.  Coil current should be the same.

[edit] Has anyone seen evidence of volt-amp ratings on IH's or IH capacitors? It seems natural that the value would be product of RMS voltage and RMS current in the tank circuit.  A very generous upper bound on heating power.

Haven't seen a VA rating.  Often curves of RMS current and/or voltage vs. frequency.

[klugesmith]

Right you are, Dave. Thanks for spotting me.
I'd tabulated peak-to-peak voltages, then used that to figure currents, which were wrongly high by factor of 2.828 when presented as RMS.
Corrected value is 3.7 amps RMS, like you said, and 17.4 volt-amps.

My spreadsheet figure for Z was already 1.27 ohms, and I'd been too tired and eager to publish to reconcile that with high current value.
Haven't yet figured the Q value and associated ESR.
Here are Bode plots of measured voltage and computed currents (blue for iC, orange for iL).

And similar from a rough SPICE model.   

LTSpice standard L model includes a parasitic R parameter -- how do we get that value to appear in schematic-view, other than as a plain text note?
How do we set trace colors, or suppress the phase curves in AC analysis result chart?  Thanks!

[Anders Mikkelsen]

Nice work! Capacitors for inductive heating and other HF high-VAR applications are usually specified in max voltage (dielectric limit), max current (foil limit) and max VAR (dissipation limit, dielectric temperature). I think the thermal limit should be V^2 + I^2, foil + dielectric dissipation, but V*I is simpler and close enough.

[klugesmith]

Thank you, Anders.
My toy ZVS heater modules just arrived.   Looks like a distinctive design, with the warning "Is strictly -prohibited" etched in metal.
Billed as 12 to 30 V, 20 A, 1000 W. No other documentation.
Package sticker says G1915-US26-0023, and has a QR code that says the same thing.

Has anyone here traced, or seen posted, a schematic diagram for this part? 
No work coil is included.   How about if I aim for 100 kHz, or would 50 kHz be a better first step?

[edit] Of course if nobody speaks up, I will make and post a proper schematic, edited from one of the many IH schematics previously posted around here.
The capacitors say 0.3 uF 630 VAC 50 kHz.   Do they look like a typical style found in IH consumer products?

Speaking of products for consumption, I found IH devices here https://www.koilboi.com/induction-heaters
apparently for evolving vapor or smoke out of some kind of botanical material in bud form.

[davekni]

Has anyone here traced, or seen posted, a schematic diagram for this part?

I'm 99% certain it's the standard basic ZVS oscillator circuit.  Has exactly the right set of parts.

I'd suggest lifting the supply end of the two gate pull-up resistors (large 470-ohm parts) and wiring them separately to your incoming supply voltage.  Powering those gate pull-up resistors first before applying power to inductors will make startup much more smooth.  Avoids need for fast supply ramp-up and minimizes FET voltage transient that occurs at turn-on.  Depending on FET parts (Vds spec.), might allow running above 30V input.  Feed gate resistors from a 30V supply or through another external power resistor to your input voltage.

Do they look like a typical style found in IH consumer products?

Yes, those are almost certainly the standard cooktop resonant capacitors.  I use those (0.33uF version) for my DRSSTC MMC and other projects.  Been quite happy with them, including results of destructive testing (to +-2.1kV at 80kHz 1% duty cycle).

How about if I aim for 100 kHz, or would 50 kHz be a better first step?

Either is likely fine.  Low limit will be inductor saturation and resulting high FET current.  Upper limit may be FET gate charging time given 470ohm pull-up resistor current rather than capacitor temperature.

[klugesmith]

Thanks. I'll start a new thread for measurements with the ZVS driver.

Came back here to share a bit of analytic insight that I acquired while figuring Q to be about 27 for the tank in OP, using fractional bandwidth method. Need a correction factor because of finite driver impedance.

Consider a tank with L = 1 uH and C = 1 uF, so "Z0" = 1 ohm and radian frequency is 1e6 per second. F0 = 159 kHz.
Let's add enough damping for Q = 50, using 0.02 ohms (Z0/Q) in series or 50 ohms (Z0 * Q) in parallel.
In one case the R bears the whole tank current, in the other it bears the whole tank voltage.
Either way, average power loss (or drive power to sustain oscillation) is 1/50 of tank energy per radian time.

I drew it both ways in LTSpice schematic editor, with 50-ohm-impedance source as pictured in OP.
A third instance has a current source (infinite source impedance), for simple measurement of parallel-LCR impedance.


The L and C impedances in Bode plot intersect at Z0 (1 ohm), but combined LCR tank impedance rises to peak of 50 ohms at resonance frequency. Source amplitudes (2 volts and 0.02 amps) were chosen to get 1 volt (and 1 amp) in tank at resonance. 

We see that as frequency moves away from resonance, voltage with the finite-impedance source (green and blue curves) falls off more slowly than the impedance magnitude (red curve).

I confirmed this with spreadsheet computation of voltage divider with complex impedance on low leg.  Graphically the "vector view" , with reactive impedance or conductance on vertical axis, makes it clear what is going on.
 
The impedance magnitude is down 3 dB at 0.99 and 1.01 times f_res, for fractional bandwidth = 0.02 (1/50 = 1/Q).

The voltage magnitude with 50 ohm source (as in OP) is down 3 dB at 0.98 and 1.02 times f_res. We could say the fractional bandwidth of this circuit is 0.04.  But its reciprocal, 25, is only half of the tank's Q. Need correction factor of 2.

The case in OP is intermediate, with source impedance apparently 36% higher than tank at resonance. Spreadsheet analysis puts the 3 dB points at 0.9828 and 1.0175, a separation of 0.0347 times f_res. Correction factor is 1.735 (but that's probably valid only for the Q=50 tank).
Scope sweep in OP showed lower and upper 3 dB points about 8 kHz apart, which is 1/15.7 of the center frequency.
So I bet the true Q is less than 31.4, maybe around 27.  Analysis and raw data could use improvement.

An alternate approach can get Q without tuning frequency up and down.  From capacitor nameplate and F_res we can get L, Z0, etc.   The tank impedance at f_res is real, and we can try figuring it from drive voltage, current, and/or impedance measurements.  In the OP case, tank appears to reach 73% of function generator output impedance.  That would be 36.7 ohms, which is 28.9 times the calculated Z0.

[Anders Mikkelsen]

For more accurate measurements of resonant tanks, it can be useful to put a resistor in series with the output of your signal generator, and measure the voltage before and after the resistor. This allows you to use a resistance with usually better precision than the signal generator Zo, and you can also chose a resistance value other than 50 ohms to get a more precise measurement.

[klugesmith]

+1 on Anders's last point.   Here's an example with the purchased module. 

Initial bench measurements were to observe the output port, with no work coil and no power.
The 2 built-in toroidal chokes, with built-in 0.6-uF capacitor, form a built-in resonator.

DC resistance is about 51 milliohms.
The OP's signal generator and scope show a narrow impedance peak at 15.7 kHz.

I figure total L = 172 uH, or 86 uH per toroid.   "Z0" = 17 ohms.
Maximum test voltage is about +/- 260 mV, so semiconductor components are not expected to interfere.

It's hard to accurately figure the resonant impedance of that built-in tank, because it's on the order of 1000 ohms.
Observed voltage is about 95% of the signal generator voltage with no load.
As Anders suggested, a known resistor (perhaps 950 or 1000 ohms) in series with source will allow more accurate measurement.

[klugesmith]

Got more electrical measurements to report, using the "12 to 30 volt" inexpensive ZVS IH module pictured above.   It may have been harsh to call it a toy, but construction quality is poor. 

The toroidal chokes have no mechanical attachment other than their lead wires, so in a real industrial or consumer product they would fail the vibration stress test.

Before any power, we measured internal DC resistance to be 51 milliohms, and built-in inductance to be 174 uH, resonating with built in capacitor at 15.7 kHz.

As Dave guessed, the board has "standard" Mazilli / Marko ZVS circuit topology and components.  FETs are IRFP250N.   Tank cap is 2 x 0.3 uF. 

I made a work coil with 12 AWG (2 mm diameter) Cu magnet wire, aiming for 4.2 uH, getting about 5.0 uH, for observed resonance at 92 kHz.

Did not yet modify the gate resistor Vcc connections for power sequencing, but did use a lab supply with meters, adjustable current limiting, and output on/off switch.  With supply set to 14 V, max current 6 A, sometimes the unit fails to start when switched on. 
When it does start, idle DC current at 14 V is 1.0 A.  After a while the work coil gets hot to touch. The wire's AC resistance is 2.6 times its DC value because of skin effect.  Proper current or voltage measurement will follow.

Before touching scope to the equipment under test, I connected it to a small sense coil for measuring magnetic field strength.   Four turns of insulated 30 AWG wire on a 15 mm glass tube; outside of coil is 16 mm diameter.  When placed near center of work coil, it produced 5 volts peak-to-peak at 92 kHz.  0.44 volts RMS per turn.  Unreviewed calculation says the B field in loop is +/- 5.7 mT (5700 gausses).
A FEMM simulation of the coil shows field about that strong at peak current of 15 amps, but that model also puts coil inductance at be 4 uH instead of 5 uH.

It's easy to heat things and watch DC current increase, while monitoring frequency and magnetic flux with the hand-held sense coil.   Brass modeler's tubing gets perceptibly warm.  Acid brush handle is smoking hot in seconds.   Straightened paper clip wire gets red hot in 15 seconds, with less power draw because it's so small.


[edit] The problem of sometimes not starting may have been caused by power supply current limit set to only 6 A.  ZVS has started on every try after setpoint was turned up to 9 A.

At Vcc = 22 V, with a section of acid brush handle present at the start, initial DC draw is 7.5 A.   In less than 10 seconds that drops below 5 A, as the work reaches incandescence and Curie point temperature.   Sense coil voltage was 22 V at 80 kHz, indicating max B of 29 mT (averaged over the sense area, which includes the workpiece).   I tried posting a mp4 video directly, size-reduced to 715 kilobytes by MMS to email, but the forum software woudn't take it.

My first real tank current measurement is figured from voltage/Z0.  If the tank capacitance is nominal, then Z = 2.89 ohms.   Scope probing showed the voltage across work coil to be a sinusoid with peak amplitude 39 volts.   Work coil current was 13.5 A peak, 9.5 A RMS, when DC input was 13.5 V and 0.9 A.  Coil got warm, but not too hot to touch. 
A next step is to determine the tank circuit Q value.

[klugesmith]

Acid brush handles are proposed as a good workpiece for impressing lecture hall audiences, comparing coil and frequency options, or doing low level modeling.  Made of mild steel, very thin, good geometry for eddy currents, and ubiquitous and cheap. Will they heat more slowly with a longitudinal slot in place of the tube seam?

I uploaded a video with all the action in 10 seconds.  Forum is not showing a teaser image, so I must paste one in.
https://www.youtube.com/shorts/9A_o3SL09o0


If you prefer time lapse views of wire bending, soldering, and other "making things" steps, this guy carries the IH concept one step too far.
Pumps water through thin steel tubular workpiece, and a radiator, to heat the room. Solhi please take note.

/>Applause for his use of a telescoping antenna to get a thin "seamless" steel tube.

[klugesmith]

Pete's video about experimental coils made from solid copper wire (for very short duty cycles)
got me thinking about system parameters, perhaps fancier than input DC voltage and current,
that are 1) not hard for amateurs to measure or calculate
and 2) might usefully correlate with practical heating power,
and 3) allow comparison with commercial systems and technical literature.

Tank frequency (much discussed) and volt-amps seems like a good starting point.  Tank energy is not hard.  Magnetic field strength will be proportional to square root of tank energy per unit of coil volume, the factor being independent of size and frequency, and slightly dependent on coil aspect ratio.

Anders wrote, in up-thread post with pictures of substantial high frequency capacitors:
>> I think the thermal limit should be V^2 + I^2, foil + dielectric dissipation, but V*I is simpler and close enough.

Agreed. Same could be said for kVA nameplate on power transformers.   At full load there's substantial heat from core loss (proportional to V^2) and copper loss (proportional to I^2).   Transformer doesn't much care about the V-I phase relationship (what fraction of the kVA is reactive) or the ratio between V and I magnitudes;  both are fixed in IH capacitors.

Anders's post includes V, I, kVAr chart from datasheet of a 6.3 uF capacitor. 
It's very telling, and easy to replicate in a spreadsheet.
The green curve has a flat section where we are kVA limited.
For example, at 35.1 kHz, capacitor can handle up to 600 Vrms and 833 Arms (product = 500,000).
As frequency goes down, allowable voltage goes up and current down by square root of f ratio, until we hit 700 Vrms datasheet limit at 25.8 kHz and 714 Arms. At lower frequencies, max I and VA go down in proportion to f. 
As frequency goes up, VA limit allows less voltage and more current until 50.5 kHz, where we reach 1000 Arms limit (and 500 Vrms for this value of C).  Above that frequency, allowable V and VA go down in proportion to 1/f.
Here's the same general story in an industrial reference:  https://www.celem.com/faq

In an LC tank, we can get tank energy from VA = Vrms x Arms, divided by radian frequency.  Numerically the same as C * Vpeak^2 / 2,  or L * Ipeak^2 / 2.
* For that capacitor in datasheet , max E is 3.1 joules in voltage limited region, dropping progressively to 1.57 J in the VA limited region.
* My exemplary 1uF-1uH tank, with 1 Vrms and 1 Arms at resonance (for 1 VA), has 1 microjoule sloshing between C and L twice per cycle, and has 0.02 watts of loss if Q = 50. Operating more usefully at 100 Vrms and 100 Arms (for 10 kVA) there would be 0.01 joule of tank energy and 200 watts of loss.
* In my "toy ZVZ IH", on 22.8 VDC (the setting in video), idle tank is estimated to have about 47 Vrms, 16 Arms, 0.75 kVA, and 1.3 mJ of energy at 92 kHz.    The 12 AWG coil and traces on board get hot pretty quickly.   
Who's got a datasheet for the consumer IH capacitors? I'll look in other threads for hints about the maker and product series. The nameplate 0.3 uF, 630 VAC, and 50 kHz can't apply to a single operating point, which would have 59 amps and 37 kVA in one capacitor! IMUS (in my unreviewed spreadsheet).

[davekni]

The nameplate 0.3 uF, 630 VAC, and 50 kHz can't apply to a single operating point, which would have 59 amps and 37 kVA in one capacitor!

Yes, certainly true.  I have one imprecise data point for my very-similar 330nF 630Vac 1200Vdc 50kHz capacitors:  With a small computer cooling fan blowing on a cap from 150mm away, 16C temperature rise at 32kHz 270Vrms 18Arms.  Ran that test for a total of 33 hours.  Started at 14C rise at 1 hour, increasing to 16C by 5 hours and staying there.  Not sure if the increase from 14C to 16C is significant (indication of tiny bit of self-healing) or some other cause of drift in measured temperatures.