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Re: Ideal Magnifier Model - PSPICE (Antonio?)



Original poster: Rob Maas <robm-at-nikhef.nl> 

 > > Why is the "self capacitance of L3" included in C2:
 >
 >We usually model a coil that has distributed capacitance and one side
 >grounded as a grounded coil in parallel with a "self-capacitance",
 >grounded too.
 >In a magnifier, the third coil has both ends floating. If we assume that
 >the capacitances from both ends of the coil to ground are identical,
 >the simplest model for a floating coil has then a capacitor to ground at
 >each end:
 >
 >+--L3--+
 >|      |
 >C3a    C3b
 >|      |
 >+------+-o ground
 >
 >If one end of the coil is grounded, if we assume that the
 >capacitances don't change due to this, the two capacitors must be
 >each identical to the "self-capacitance" of the coil.
 >And really, a measurement (or calculation) of the free-space
 >capacitance of a cylinder results in a capacitance that is quite
 >close to twice the Medhurst capacitance for a coil with the
 >shape of the cylinder.
 >Example: A coil with 32 cm of length and 4.4 cm of radius has a
 >Medhurst capacitance of 5.55 pF.
 >The free-space capacitance of an open cylinder with these dimensions
 >results as 10.15 pF.
 >
 > > Isn't C3 = 'self capacitance of L3' + 'capacitance of topload' on top of
 >L3 ?
 >
 >Yes, it is, using the "normal" copy of the self-capacitance at the
 >output side of L3.
 >
 >Antonio Carlos M. de Queiroz

Antonio,

Thanks for the above explanation.

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:

--------------------------------------------------------------------------
      table for k12-values between  0.350 and  0.500

                           and C3/C2-values >  0.500


k12( 6: 7:16) =   0.357    L3/L2 =   6.849     C3/C2 =   0.560
k12( 6: 7:18) =   0.365    L3/L2 =   6.525     C3/C2 =   0.744
k12( 5: 6:13) =   0.384    L3/L2 =   5.776     C3/C2 =   0.564
k12( 5: 6:15) =   0.395    L3/L2 =   5.411     C3/C2 =   0.802
k12( 5: 6:17) =   0.402    L3/L2 =   5.192     C3/C2 =   1.074
k12( 4: 5:10) =   0.417    L3/L2 =   4.741     C3/C2 =   0.540
k12( 4: 5:12) =   0.434    L3/L2 =   4.303     C3/C2 =   0.857
k12( 4: 5:14) =   0.444    L3/L2 =   4.075     C3/C2 =   1.231
k12( 4: 5:16) =   0.450    L3/L2 =   3.940     C3/C2 =   1.663
k12( 9:12:23) =   0.470    L3/L2 =   3.533     C3/C2 =   0.585
k12( 8:11:20) =   0.487    L3/L2 =   3.220     C3/C2 =   0.543
k12( 3: 4: 9) =   0.488    L3/L2 =   3.204     C3/C2 =   0.889
------------------------------------------------------------------

The three items in the list, k12, L3/L2 and C3/C2 depend only on
the the three mode numbers k:l:m, as given as 'argument' of k12.

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. 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.

 >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.

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
--------------------------------------------------------------------

but the oscillator part is probably very difficult to build.

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?

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?

Any comment about this is appreciated.


best regards,   Rob Maas