# Re: Couples Therapy

```Tesla List wrote:
>
> Original Poster: "Ruud de Graaf" <rdegraaf-at-daxis.nl>

> Thank you for your comprehensive answer. At first I was a little surprised
> with your first comment: 'I don't see any relation between the theory of
> coupled bandpass filters and Tesla
> transformers.', but apparently you didn't meant it like it sounded. I
> understand the need for resistor(s) in a bandpass filter to make it suitable
> for its job, but do you mean with 'this condition' the moment of critical
> coupling? I don't think resistors can have any influence on the moment a
> bandpass filter has the transition from one peak to two peaks in the dB/f
> graph.

Hi Rudd:

The resistors determine totally if there are two peaks or just one.
Without them the bandpass has always two peaks, ideally of infinite
amplitude, or limited only by losses in a real circuit (except if the
coupling coefficient between the coils is exactly 1, what is impossible
in practice). A Tesla coil operates in this condition.

Imagine, for example, what happens in the filter with just one resistor:
k
o------C1--+   +--+--+---o
+          |   |  |  |   +
Vin         L1  L2 C2 R  Vout
-          |   |  |  |   -
o----------+   +--+--+---o

If R is large, the circuit is almost lossless, resonates at two
different frequencies, and there are two sharp peaks in the frequency
response.
If R is small, it practically short-circuits C2 and L2, taking them
out of the circuit, but leaves C1 connected to an almost purely
inductive impedance seen at the input of the transformer. The
remaining circuit has only one resonance frequency and the
frequency response has only one peak, sharp too.
Try this circuit in a simulator:

C1=C2=1/sqrt(2)
L1=2*sqrt(2)
L2=sqrt(2)
k=1/sqrt(2)
R=1

This is a normalized Butterworth design, with a passband geometrically
centered at 1 rad/s, with 1 rad/s of bandwidth, and unity gain. It is
exactly at the limit between one and two peaks. R>1 produces two peaks.
R<1 just one. (sqrt=square root.)

Antonio Carlos M. de Queiroz

```