Hi All,
Please look at this in fixed font.
I'm looking for understanding of a series to parallel conversion for
antenna matching.
I'm pretty sure I'm missing something, so point it out to me.
This is in regard to a crystal radio, so the match is for a low impedance
antenna to a high impedance tank circuit.
The antenna: R=58 ohms C=1072 ohms at 1Mhz.
The tank: L=240uh C=106pf Q = 1000
Tank Z =~1.5 Mohms
Here's my understanding of what I think I'm reading.
I put a matching capacitor in series with the antenna.
Antenna-- -----R-----C--------Match cap-----tank------ground.
and this is supposed to transform the circuit to this.
( Maybe better said, equivalent to this)

l------------l
l l
Antenna--- R C LC---Tank
l l
l------------l
^
Ground

I calculate an 18.5pf cap for the match, making the antenna look like 58R
and 17pf.

So this; Antenna-- -----58R-----270pf--------Match
cap18.5pf-----1.5Mohms------ground.
This converts to;
l-----------------l
l l
Antenna---58R 17pf 1.5M---LC Tank at
l l Resonance
l-----------------l
^
Ground

And I now have a 1.5 Mohms source feeding a 1.5 Mohm load.
The purpose of which is to cause minimal loading of the tank by the antenna.
I don't understand how adding a series capacitor makes a parallel
conversion.
What do I misunderstand or do just need to believe the numbers.
Thanks, Mikek

Ahh....1 should have said Series to Parallel Conversion.
Mikek

On Thu, 13 Jan 2011 11:05:38 -0600, "amdx" wrote:

This is in regard to a crystal radio, so the match is for a low impedance
antenna to a high impedance tank circuit.
The antenna: R=58 ohms C=1072 ohms at 1Mhz.

Hi Mike,

Is this a fantasy antenna?

For the 58 Ohm resistive value, it would have to be about 300 feet
tall - not the size of operation one usually comes to expect for a
Xtal radio aficionado.

If it is that tall, it would exhibit 200 Ohms Inductive reactance (one
fifth of what you report, and the opposite sign).

Something doesn't wash here.

I calculate an 18.5pf cap for the match, making the antenna look like 58R
and 17pf.

58±j17 Ohms is still a complex impedance, and says nothing of match
which can only be expressed in terms of the expected load R.

And I now have a 1.5 Mohms source feeding a 1.5 Mohm load.

How that is arrived at is something of a mystery. By the numbers, you
describe a 26000:1 mismatch.

The purpose of which is to cause minimal loading of the tank by the antenna.

Well, what you have described is sufficient mismatch to insure that.
The English reading of your sentence also is instructive: the tank is
isolated from the antenna, i.e. no signal is passed to it. This seems
to be counterproductive in regards to detection.

I don't understand how adding a series capacitor makes a parallel
conversion.

Haven't we been down this road some months ago?

73's
Richard Clark, KB7QHC

Richard Clark wrote:

For the 58 Ohm resistive value, it would have to be about 300 feet
tall - not the size of operation one usually comes to expect for a
Xtal radio aficionado.

If it is that tall, it would exhibit 200 Ohms Inductive reactance (one
fifth of what you report, and the opposite sign).

Something doesn't wash here.

Perhaps it's a longwire antenna, of crappy wire, parallel to
the ground?

"Richard Clark" wrote in message
...
On Thu, 13 Jan 2011 11:05:38 -0600, "amdx" wrote:

This is in regard to a crystal radio, so the match is for a low impedance
antenna to a high impedance tank circuit.
The antenna: R=58 ohms C=1072 ohms at 1Mhz.

Hi Mike,

Is this a fantasy antenna?

It's an example from an article, I don't like the number either, seems like
maybe
2 to 12 ohms would be more realistic. I think the capacitance is ok.

For the 58 Ohm resistive value, it would have to be about 300 feet
tall - not the size of operation one usually comes to expect for a
Xtal radio aficionado.

If it is that tall, it would exhibit 200 Ohms Inductive reactance (one
fifth of what you report, and the opposite sign).

Something doesn't wash here.

Ok, how about just working with the concept.

I calculate an 18.5pf cap for the match, making the antenna look like 58R
and 17pf.

58±j17 Ohms is still a complex impedance, and says nothing of match
which can only be expressed in terms of the expected load R.

Sorry, I missed a math step, the R was converted to 1.5M.
see formula below.

And I now have a 1.5 Mohms source feeding a 1.5 Mohm load.

How that is arrived at is something of a mystery. By the numbers, you
describe a 26000:1 mismatch.


Here's what is stated in the article:
" The concept is that at any given frequency, a parallel RC network has an
equivalent
series RC network, and vise versa. We can use this property to transform the
real component
of an impedance to a much higher or lower value.
As long as Xc series R series.
Xc (parallel) = Xc (series)
R (parallel) = XC^2 (series) / R (series)
The Xc of a 17pf at 1Mhz is 9368 Ohms.
To rewrite Rp= 9368^2 / R = 1.513 Mohms

The article then goes on to say,
The utility of this equivalence can be seen by choosing a sufficiently small
value of C series
(a large Xc series) A "small" resistance can then be transformed into a
"large" value.

The purpose of which is to cause minimal loading of the tank by the
antenna.

Mikek

On Jan 13, 9:05*am, "amdx" wrote:
Hi All,
*Please look at this in fixed font.
*I'm looking for understanding of a series to parallel conversion for
antenna matching.
I'm pretty sure I'm missing something, so point it out to me.
This is in regard to a crystal radio, so the match is for a low impedance
antenna to a high impedance tank circuit.
*The antenna: R=58 ohms C=1072 ohms at 1Mhz.
*The tank: L=240uh C=106pf Q = 1000
*Tank Z =~1.5 Mohms
Here's my understanding of what I think I'm reading.
I put a matching capacitor in series with the antenna.
Antenna-- -----R-----C--------Match cap-----tank------ground.
and this is supposed to transform the circuit to this.
( Maybe better said, equivalent to this)

* * * * * * * * * * * l------------l
* * * * * * * * * * * l * * * * * *l
Antenna--- *R C * * * *LC---Tank
* * * * * * * * * * * l * * * * * *l
* * * * * * * * * * * l------------l
* * * * * * * * * * * * * *^
* * * * * * * * * * * Ground

I calculate an 18.5pf cap for the match, making the antenna look like 58R
and 17pf.

So this; *Antenna-- -----58R-----270pf--------Match
cap18.5pf-----1.5Mohms------ground.
This converts to;
* * * * * * * * * * * * l-----------------l
* * * * * * * * * * * * l * * * * * * * * l
Antenna---58R 17pf * * * *1.5M---LC Tank at
* * * * * * * * * * * * l * * * * * * * * l * * * *Resonance
* * * * * * * * * * * * l-----------------l
* * * * * * * * * * * * * * * *^
* * * * * * * * * * * * * Ground

And I now have a 1.5 Mohms source feeding a 1.5 Mohm load.
The purpose of which is to cause minimal loading of the tank by the antenna.
*I don't understand how adding a series capacitor makes a parallel
conversion.
What do I misunderstand or do just need to believe the numbers.
* * * * * * * * * * * * * * * * * *Thanks, Mikek

Seems like it doesn't much matter whether the antenna is real or
imagined; the point is rather what's going on when you couple a low
impedance source to a parallel-resonant tank through a small
capacitance...

Perhaps it will help you to think first about a low impedance source,
let's say 50 ohms at 1.591MHz (1e7 radians/sec), that you want to
couple to an (imaginary) inductor, 2.5mH with Qu=500 at that
frequency, and maximize the energy transfer to the inductor. The
inductance and Q implies that the effective series resistance of the
inductor is 50 ohms. That means all we need to do is cancel out the
inductive reactance, and we can do that with a series capacitance--
that happens to be 4pF. That assumes the ESR of the capacitance is
zero, or essentially zero.

But what if the inductor has 1/4 as much inductance, 0.625mH, same
Qu? Then its effective series resistance is 1/4 as much, or 12.5
ohms, and to get the same energy dissipated in it, you need the
current through it to be 2 times as large as before (constant R*I^2).
The total capacitance to resonate the tank is 4 times as much: 16pF.
If you divide that into two 8pF caps, one directly across the inductor
and the other in series with the 50 ohm source, (very close to) half
the tank's circulating current flows in each capacitor. For the same
energy delivered to the coil, the voltage at the top of the inductor
must be half as much as before. Since the coupling capacitor to the
source is twice as large as it was before, the load impedance the
source sees must be the same as before (50 ohms, as required for max
energy transfer).

Carry that another step, to an inductor with 1/16 the original
inductance and the same Qu=500, and you need 64pF to resonate it and
16pF to couple to it from the low impedance source. Now you divide up
the total capacitance with 3/4 of it (48pF) directly across the
inductor and 1/4 of it to the source. 3/4 of the tank's circulating
current flows in the 48pF capacitor, and 1/4 of it in the 16pF to the
source; the source once again sees a 50 ohm load (because the voltage
at the top of the inductor is 1/4 of the original, and the capacitor
coupling to the source is 4 times as large -- with the current in the
source unchanged).

The key to understanding this coupling, to me, is the division of the
tank's circulating current between the two capacitances, one directly
across the coil and one in series with the source. The smaller the
inductance (at constant Q), the more circulating current required for
the same energy dissipation, and the smaller
_percentage_of_total_resonating_capacitance_ for coupling to the
(constant impedance) source.

Cheers,
Tom

On 1/13/2011 11:05 AM, amdx wrote:
Hi All,
Please look at this in fixed font.
I'm looking for understanding of a series to parallel conversion for
antenna matching.
I'm pretty sure I'm missing something, so point it out to me.
This is in regard to a crystal radio, so the match is for a low impedance
antenna to a high impedance tank circuit.
The antenna: R=58 ohms C=1072 ohms at 1Mhz.
The tank: L=240uh C=106pf Q = 1000
Tank Z =~1.5 Mohms
Here's my understanding of what I think I'm reading.
I put a matching capacitor in series with the antenna.
Antenna-- -----R-----C--------Match cap-----tank------ground.
and this is supposed to transform the circuit to this.
( Maybe better said, equivalent to this)

l------------l
l l
Antenna--- R C LC---Tank
l l
l------------l
^
Ground

I calculate an 18.5pf cap for the match, making the antenna look like 58R
and 17pf.

So this; Antenna-- -----58R-----270pf--------Match
cap18.5pf-----1.5Mohms------ground.
This converts to;
l-----------------l
l l
Antenna---58R 17pf 1.5M---LC Tank at
l l Resonance
l-----------------l
^
Ground

And I now have a 1.5 Mohms source feeding a 1.5 Mohm load.
The purpose of which is to cause minimal loading of the tank by the antenna.
I don't understand how adding a series capacitor makes a parallel
conversion.
What do I misunderstand or do just need to believe the numbers.
Thanks, Mikek


At resonance, the LC tank disappears and you are left with a 1.5 Meg
equivalent of the tank losses.

Adding a small capacitance in series with your antenna gives you,
effectively, an antenna that looks like a 58R in series with a 17 pF
capacitor.

So now your circuit looks like:

58R---17pF-----|
|
1.5M
|
|
----
GND

I don't see any conversion at all.

John

On 1/13/2011 11:05 AM, amdx wrote:
Hi All,
Please look at this in fixed font.
I'm looking for understanding of a series to parallel conversion for
antenna matching.
I'm pretty sure I'm missing something, so point it out to me.
This is in regard to a crystal radio, so the match is for a low impedance
antenna to a high impedance tank circuit.
The antenna: R=58 ohms C=1072 ohms at 1Mhz.
The tank: L=240uh C=106pf Q = 1000
Tank Z =~1.5 Mohms
Here's my understanding of what I think I'm reading.
I put a matching capacitor in series with the antenna.
Antenna-- -----R-----C--------Match cap-----tank------ground.
and this is supposed to transform the circuit to this.
( Maybe better said, equivalent to this)

l------------l
l l
Antenna--- R C LC---Tank
l l
l------------l
^
Ground

I calculate an 18.5pf cap for the match, making the antenna look like 58R
and 17pf.

So this; Antenna-- -----58R-----270pf--------Match
cap18.5pf-----1.5Mohms------ground.
This converts to;
l-----------------l
l l
Antenna---58R 17pf 1.5M---LC Tank at
l l Resonance
l-----------------l
^
Ground

And I now have a 1.5 Mohms source feeding a 1.5 Mohm load.
The purpose of which is to cause minimal loading of the tank by the antenna.
I don't understand how adding a series capacitor makes a parallel
conversion.
What do I misunderstand or do just need to believe the numbers.
Thanks, Mikek


Ah! After studying this for a while, I think I understand what you are
driving at.

Convert series 58R and 17 pF to a parallel equivalent. That is, take the
reciprocal of Z = 58 - 9368j to get Y = 661e-9 + 106.8e-6.

Now, what is the reciprocal of the real part of Y? That's 1/661e-9 or
about 1.5 Meg. So, the real part of the parallel equivalent now looks
like the resistance you are interested in.

Does this help?

Cheers,
John

On Thu, 13 Jan 2011 13:30:52 -0500, "Greg Neill"
wrote:

Richard Clark wrote:

For the 58 Ohm resistive value, it would have to be about 300 feet
tall - not the size of operation one usually comes to expect for a
Xtal radio aficionado.

If it is that tall, it would exhibit 200 Ohms Inductive reactance (one
fifth of what you report, and the opposite sign).

Something doesn't wash here.

Perhaps it's a longwire antenna, of crappy wire, parallel to
the ground?


Hi Greg,

No, that would more likely result in a characteristic Z of 600 Ohms.
If by being close to ground you mean the 58 Ohms finds itself invested
in the dirt, well, yes that might be the case.

The long and short of it means that to investigate the problems of an
antenna "loading" a tank coil means that you really must understand
the antenna - not a simple thing as this thread will undoubtedly
reveal.

73's
Richard Clark, KB7QHC

On Thu, 13 Jan 2011 12:42:01 -0600, "amdx" wrote:


"Richard Clark" wrote in message
.. .
On Thu, 13 Jan 2011 11:05:38 -0600, "amdx" wrote:

This is in regard to a crystal radio, so the match is for a low impedance
antenna to a high impedance tank circuit.
The antenna: R=58 ohms C=1072 ohms at 1Mhz.

Hi Mike,

Is this a fantasy antenna?

It's an example from an article, I don't like the number either, seems like
maybe
2 to 12 ohms would be more realistic. I think the capacitance is ok.

Hi Mike,

Then your intuition is firing on all cylinders, great.

Here's what is stated in the article:
" The concept is that at any given frequency, a parallel RC network has an
equivalent
series RC network, and vise versa.

This is classically true. The frill of "at any given frequency" can
be discarded.

We can use this property to transform the
real component
of an impedance to a much higher or lower value.

This concept is not a "property," however; more a transformation (as
should be apparent in the original statement). In other words
concept
equivalent
property
transform
use four words to describe one thing - transform (plain and simple).

As long as Xc series R series.
Xc (parallel) = Xc (series)
R (parallel) = XC^2 (series) / R (series)
The Xc of a 17pf at 1Mhz is 9368 Ohms.
To rewrite Rp= 9368^2 / R = 1.513 Mohms

Well, what looks like hand-waving is probably close to the numbers one
could expect.

The article then goes on to say,
The utility of this equivalence can be seen by choosing a sufficiently small
value of C series
(a large Xc series) A "small" resistance can then be transformed into a
"large" value.

The reason why I say hand-waving (and this is probably your gut
reaction as to "why") is that the five lines of operations you quote
starts with a presumed requirement and then proves it has been met.

What happens if Xc series R series?
What happens if Xc series R series?
What happens if Xc series = R series?
What happens if Xc series R series?

This somewhat clouds the mystery for you of understanding Parallel to
Series conversion. I wonder too. Are we dropping in a new component
and stepping back with a wave and Voila! to find the Parallel circuit
has suddenly been transformed? Yeah, that WOULD be a mystery.

And what is this Xc(parallel) and Xc(series) stuff?

Xc is stricty a function of pi, capacitance, and frequency.

And what is this R(parallel) and R(series) stuff?

R is a function of its, well, resistance. No variables to be found.

No doubt there is more to be extracted from this article.

73's
Richard Clark, KB7QHC