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Finding peak lamp current in electronic CFL ballast

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Jun 22, 2008
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I am trying to find out how to find the maximum current that will occur for the LRES inductor in this CFL schematic.

Please could I be assisted to do this.?

CFL Schematic

I must know this so I can ensure that this inductor does not saturate.

Mains = 265VAC
LRES = 2.3mH
CRES = 6.8nF
Flourescent Tube ON’ resistance, R = 228 Ohms.

iL(t) = inductor current at time t
iR(t) = Resistor current at time t
iC(t) = Capcitor current at time t

vL(t) = inductor voltage at time t
vR(t) = Resistor voltage at time t
vC(t) = Capcitor voltage at time t

V = Step input voltage of 188V at t=0
Z = impedance of L in series with parallel RC.

To cut a long story short………

…..this problem boils down to an inductor (LRES) in series with a parallel RC (where R = 227.8R and C= 6.8nF)………

That is, this circuit here
LRC circuit

A voltage of 188V appears across this LRC network at t = 0 (C initially uncharged and I(L) = 0 at t = 0.

…so here is the situation on LTSpice, with the step input of 188V, and the rising inductor current…….


It is then needed to solve (by calculation, not simulation) for what current appears in the inductor (LRES) at t=16us.

(This is due to 16us being the bridge half period time at the ‘RUN’ frequency)

Here is the circuit to be solved as above…..

L in series with parallel RC Circuit

I believe the quickest way to do this is to use Laplace Transforms.

The differential equation to start with is………

(Using Kirchoffs Laws…….iL(t) = iR(t) + iC(t)

…….iL(t) = vC(t) / R + C * dvC(t) / dt

differentiating both sides with respect to t and rearranging……

[V - vc(t)] / L = C * [d^2]vc(t)/[dt]^2 + (1)


V/L = C * [d^2]vc(t)/[dt]^2 + + vc(t)/L (2)

This is then converted to the S domain…………

V/sL = C( [s^2]Vc(S) ) + s Vc(S) + Vc(S) / L (3)


Vc(S) = V / { s * (CL[s^2] + sL + 1) } (4)

I have somehow got to convert the above equation (4) to a standard Laplace Transform so that I can convert back to one of the time-domain solutions as given in standard Laplace tables.

Unfortunately I am struggling with this.

I believe I must use Partial Fractions to help, but the ……………

“s * (CL[s^2] + sL + 1) “

…..term in the denominator of (4) appears to defy all the partial fraction forms given in my maths book.

Any help to get equation (4) into a standard Laplace Transform much appreciated.

When I have solved equation (4) I will have an expression for vC(t). (Cap voltage)

-I will then be able to do Q = C * vC(t) to find the Q (i.e. charge) in the cap at time t .

the current in the capacitor will be iC(t) = dQ/dt

current in the resistor will be iR(t) = vC(t)/R

then the required inductor current , iL(t) will be iR(t) + iC(t)
Anyway, I have not been able to convert equation (4) to the time domain so ,


-HERE is ANOTHER method to find the inductor current at time t = 16us.:-
(again I am not sure if it is right so please could you check?

First of all

iL(t) = iC(t) + iR(t) (5) …..Kirchoff’s Law


iL(t) = V / Z (6)

where V = 188V ,
and Z = sL + { [R * 1/sC] / [R + 1/sC ] } (7)

rearranging (7)

Z = sL + { R / (sCR + 1) } (8)

Putting (8) and (6) into (5)…………..

V / sL + [ R / (sCR + 1) ] = iC(t) + iR(t) (9)

But: = iC(t) = C*dvC(t)/dt (10)

And : iR(t) = vC(t)/R (11)

So: V / {sL + [ R / (sCR + 1) ] } = C*dvC(t)/dt + vC(t)/R (12)

Converting LHS of (12) to S domain……

: V / {sL + [ R / (sCR + 1) ] } = sC Vc(S) + Vc(S)/R (13)

Rearranging (13)

Vc(s) = (V/R) / ( s^2 .LCR + sL + R) (14)

And again, (14) is not in any standard Laplace form.

Please does any reader know how to get (14) into a standard Laplace form so I can convert it to time domain and find vC(t) at t = 16us as part of the “journey” of getting the inductor current, iL(t) at t = 16us ?

Tables of partial fractions don’t appear to help in factorisong the denominator of (14).

To mention a simple fact that invalidates your calculation, the CFL characteristic is actually far from resistive behaviour.

It's rather a typical electric arc/gas discharge characteristic with a constant voltage drop plus some negative inner resistance.

See a measurement of a mains operated 36W/120cm fluorescent lamp for reference. In addition to the said basic arc characteristic,
a periodic reignition occurs.

I guess, you won't continue to try an analytic laplace solution with the said characteristic and change to numerical analysis/SPICE simulation instead.


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