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Re: Ideal Magnifier Model - PSPICE (Antonio?)
Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
Tesla list wrote:
>
> Original poster: Rob Maas <robm-at-nikhef.nl>
> Recently there was some discussion in this group, related to the
announcement
> of the 'Green Monster', about coupling values (k_12) between L1 and L2.
> A high coupling speeds up energy transfer between C1 and C3, but can only
> be realized by close proximity of L1 and L2. This causes serious isolation
> problems. So the practical value of k_12 has to be a compromise; most
> practical
> values seem to be in the region 0.35 < k_12 < 0.50 .
> In order to get a feeling what that means, I wrote a small program that
> basically just calculates eq's (5), (4) and (8) of your paper "Designing a
> Tesla Magnifier"; the list is ordered in ascending order of k12, and
discards
> C3/C2 values smaller than a chosen input value:
Ok. Too low C3/C2 means that a lumped C2 must be added.
>...
> The relation between L2 and L3 does not seem to be problematic:
> L3 is 3-7 times larger than L2; since L scales with turns squared,
> this is easily accomplished.
Note that (eq. 7) k12=sqrt(1/(1+L3/L2)), or L3/L2=1/k12^2-1.
> But for most of the given k12-values,
> C3 is significantly smaller than C2. Suppose we write
>
> (1) C3 = R*C2
>
> splitting C3 in a 'Medhurst' part C3(M), and a topload part C3(T),
> and C2 in its 'own' Medhurst part and the part of C3 (as you explained
> above), and neglecting the transmission line contribution, we get
>
> C3(M) + C3(T) = R*(C2(M) + C3(M))
>
> for a small 30cm x 10 cm topload, C3(T) = 14 pF, and for a
> small 10 cm x 40 coil C3(M) = 6 pF, so rewriting (1):
>
> (2) 20 = R*(C2(M) + 6)
>
> Even for an R-value of 1 (a full table reveals that most R-values
> are smaller than 1), one still needs C2(M) = 14 pF
> (corresponding to an L2 of 30cm diameter, height 45 cm).
> In case R = 0.5, C2(M) = 34 pF, which makes a secundary of 70 cm
> diameter and more than a metre high. Moreover, these larger R-values
> only occur for high mode numbers.
Evidently, in these cases some extra C2 capacitance must be added.
Corona rings, or relatively small toroids, at the top of L2 and at
the bottom of L3, and the transmission line, can add substantial
capacitance. To reduce C2, it's always possible to increase the
third mode multiplier, m. With m=infinity, C2=0. This case is
unrealistic, however. A design can be made iteractively by fixing
the two first multipliers (k,l), and then by increasing the third,
m, and recalculating the capacitances until a value is reached
where just a small correction in C2 is necessary. As C2 is not
critical, a system designed in this way will work well even without
further adjustment of C2.
> >From the above list, only mode 3:4:9 seems attractive;
> modes (5:6:15,17) and (4:5:12,14,16) also produce reasonable
> C3/C2 ratios and realistic values for k12.
Note that these modes are always in the form k:k+1:k+n, n>>2.
These are the modes that tend to a regular Tesla coil operation,
but with a high-frequency oscillation appearing at the base of
the third coil (useful?).
> Aloowing k12 to be larger, gives more possibilities:
>
> -------------------------------------------------------------------
> table for k12-values between 0.500 and 0.600
>
> and C3/C2-values > 0.500
>
> k12( 8:11:22) = 0.500 L3/L2 = 2.994 C3/C2 = 0.707
> k12( 3: 4:11) = 0.502 L3/L2 = 2.963 C3/C2 = 1.436
> k12( 3: 4:13) = 0.510 L3/L2 = 2.840 C3/C2 = 2.092
> k12( 3: 4:15) = 0.515 L3/L2 = 2.768 C3/C2 = 2.857
> k12( 7:10:19) = 0.523 L3/L2 = 2.658 C3/C2 = 0.666
> k12( 7:10:21) = 0.536 L3/L2 = 2.485 C3/C2 = 0.870
> k12(10:15:26) = 0.542 L3/L2 = 2.398 C3/C2 = 0.557
> k12( 6: 9:16) = 0.547 L3/L2 = 2.341 C3/C2 = 0.600
> k12( 2: 3: 6) = 0.565 L3/L2 = 2.133 C3/C2 = 0.833
> k12( 6: 9:18) = 0.565 L3/L2 = 2.133 C3/C2 = 0.833
> k12( 9:14:25) = 0.572 L3/L2 = 2.052 C3/C2 = 0.642
> k12( 6: 9:20) = 0.577 L3/L2 = 2.006 C3/C2 = 1.094
> k12( 8:13:22) = 0.590 L3/L2 = 1.873 C3/C2 = 0.579
> k12( 2: 3: 8) = 0.591 L3/L2 = 1.862 C3/C2 = 1.698
> k12( 5: 8:15) = 0.599 L3/L2 = 1.792 C3/C2 = 0.766
> --------------------------------------------------------------------
Note that now the faster modes 2:3:m and 3:4:m appear too. The others
are essentially multiples of them, some with "imperfect" first notches.
> but the oscillator part is probably very difficult to build.
Yes. It's difficult to reach the modes 3:4:m and below.
> The conclusion seems to be that C3 should not become too large in
> order to avoid a huge L2-C2 system - unless a 'lumped' capacitor
> is added to the L2-C2 system, but I don't know whether this is really
> practical due to the high voltages - or am I missing something here?
C2 is always proportional to C3, for a given mode. A lumped C2 can
be built, maybe as a high-voltage MMC, as Terry tried some time ago.
But it appears now that the best magnifiers operate in modes that
don't need a too large C2. It's just convenient, and always possible,
to design the system so the distributed C2 is such that complete
energy transfer continues to occur. The output voltage waveforms
for the modes k:k+1:k+n, n>>2, also have greater rms values than
in the faster modes k:k+1:k+2. You can see the waveforms using my
program mrn6 (http://www.coe.ufrj.br/~acmq/programs (probably
down until tomorrow)).
> I have also a question about k12: is k12 independant from the
> presence of L3-C3. What I mean is this: suppose one has a magnifier
> design, with a particular k12 = k12(k:l:m) value. Is it sufficient
> to model (e.g. using your Inca program) the L1-L2 system for that
> particular value of coupling?
Yes. The formulas assume that there is no magnetic coupling between
L2 and L3. It seems to be possible to design the system with all
the three coils coupled too, but of course the design formulas
would be somewhat different.
Antonio Carlos M. de Queiroz