# Re: Series-resonant primary topology

```Hi all,
I can clear this matter up quite easily:

> Original Poster: "Marco Denicolai" <Marco.Denicolai-at-tellabs.fi>
>
> Tesla List <tesla-at-pupman-dot-com> on 26.11.99 20:28:41
>
> To:   tesla-at-pupman-dot-com
> cc:    (bcc: Marco Denicolai/MARTIS)
> Subject:  Series-resonant primary topology
>
>
>
> Original Poster: Kennan C Herrick <kcha1-at-juno-dot-com>
>
> >To Marco Denicolai (and all):
>
> >Whiling away a quiet morning I was thinking about series-resonant
> >t.c. drive.  I note on your Web page that you cite series L-C
> >impedance as being =SQRT(L/C)...but I recall it as being =wL-(1/wC),
> >where w=2*pi*f; or =Xl-Xc where X=the reactance at f.  At resonance,
> >Xl=Xc and Z=0.
>
> Right. Also I find from my books Z=Xl-Xc, but all the articles about
> resonant power supplies mention Z=SQRT(L/C). I must confess I haven't
> had time to investigate were it comes from. But I must tell you that I
> have measured the current in the real circuit and, believe me, Z was
> really SQRT(L/C)! By the way, that is the equation for the
> "characteristic impedance" of a line (or cable, or whatever), were L
> is inductance/inch and C is capacitance/inch. It not dependent on the
> frequency.

Technically, Z includes both SQRT(L/C) and any ESR present in the
circuit in vectorial combination. We quite often ignore ESR in high
Q resonant circuits and are left with a figure for the lossless surge
impedance.  Derived by:

With a tuned circuit at resonance, Xl = wL = Xc = 1/wC

for the lossless case, let Z = Xl = Xc    (NB - Xl-Xc = 0 at resonance)

hence, Z^2 = Xl.Xc
= wL/wC
= L/C
=> Z = SQRT(L/C)

Regards,
Malcolm

> >I seem to perceive that the series-resonant topology is a handy way
> >to implement a low-loss >coupling< between a voltage source on the
> >one hand and a current sink on the other.  By operating it suitably
> >>off resonance<, one can obtain any current one wants from a voltage
> >source;
>
> You should be safe operating it at frequencies < 1/2 of the LC
> resonance frequency, to avoid resonant rise already at the LC primary
> circuit.
>
> >But if the Q of the L-C circuit were at all decent, one would have to
> >maintain the excitation frequency fairly closely in order to stay at
> >the right point on that slope.  Otherwise the current would vary
> >excessively.
> > Do I have this right?  If so, it might not do for driving a t.c.
> > with
> >that excitation frequency--especially one like mine where the
> >frequency is kept dead-on with the secondary's resonance.
>
> If you have got MicroSim (demo version, no charge) you can take my
> simple circuit and simulate it. It works with no hassles (converges
> well) and the waveforms you get are really like what I get from the
> actual circuit. Now, if you simulate my power supply H-bridge together
> with the TC model from Terry Fritz, can't you already get a good
> picture of its functionality?
>
> >But wait...since the secondary's resonance is pretty sharp, and if
> >the slope of the driving L-C circuit's resonance curve were
> >relatively low compared to that, perhaps the series-resonant scheme
> >is worth more thought.  Tune for secondary resonance and let the
> >drive current fall where it may, within acceptable limits.
>
> I must admit I have been investigating this switching topology as much
> as needed to build a working device: my final target is to build a
> medium-size TC, not to become a SMPS guru. I have already spent one
> year doing it... That's why I am not qualified to understand/explain
> 100% of this topology. Sorry guys.
>
> But MicroSim is great is you have time / interest to check the
> functionality of the solution above.
>
> Regards
>
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