Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

As promised.

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

And the author was a student at the time -- impressive.

Hmm... I wonder what he's up to these days? Good chance he's still alive!

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

On Wed, 10 Oct 2007 19:57:29 -0700, The Phantom
wrote:

As promised.

Cool; thanks.

Here are a couple of sims. RCboost2 is the one I accidentally
discovered ca 1975, when a thing oscillated that wasn't supposed to.

John

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

On Wed, 10 Oct 2007 21:34:47 -0700, John Larkin
wrote:

On Wed, 10 Oct 2007 19:57:29 -0700, The Phantom
wrote:

As promised.

Cool; thanks.

Here are a couple of sims. RCboost2 is the one I accidentally
discovered ca 1975, when a thing oscillated that wasn't supposed to.

Your first example is identical in topology to the first example in
Vorperian's paper. Your resistors even have the same values he uses.

Joel, Vorperian has a footnote referenced in the first sentence of
section 7.2 that didn't get included in your scan. What is it, please?


John

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

On Thu, 11 Oct 2007 05:16:03 -0700, The Phantom
wrote:

On Wed, 10 Oct 2007 21:34:47 -0700, John Larkin
wrote:

On Wed, 10 Oct 2007 19:57:29 -0700, The Phantom
wrote:

As promised.

Cool; thanks.

Here are a couple of sims. RCboost2 is the one I accidentally
discovered ca 1975, when a thing oscillated that wasn't supposed to.

Your first example is identical in topology to the first example in
Vorperian's paper. Your resistors even have the same values he uses.

I picked that up somewhere else on the web, no doubt propagated from
his original. My second circuit is based on my accidental topology,
with the same values plugged in for convenience. The actual circuit,
part of an intercom/cargo winch control system for the C5A, had
different values, which I can't remember, and oscillated around 40 Hz.

John

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

Hi Phantom,

"The Phantom" wrote in message
...
Joel, Vorperian has a footnote referenced in the first sentence of
section 7.2 that didn't get included in your scan. What is it, please?

Ref. 1 is:

J. Holbrock, "Laplace Transform for Electronic Engineers," Pergamon Press,
Oxford, 1966.

Kind of an odd reference given the supporting text ("The possibility of
obtaining any voltage or current gain...") -- must be a book that's heavy on
theory (I don't have a copy).

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

"The Phantom" wrote in message
...
As promised.


[Useful reading. But yes, there's caveats with the 'x2' limit.]

Attached, a contrived, LTspice structure, giving 2 gain.

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

On Fri, 12 Oct 2007 01:55:12 +0100, "john jardine"
wrote:


"The Phantom" wrote in message
.. .
As promised.


[Useful reading. But yes, there's caveats with the 'x2' limit.]

Attached, a contrived, LTspice structure, giving 2 gain.

In the Epstein paper, he says that the gain is 2 if the network is a
general ladder network. At the end of the paper, he admits he has now
formal proof.

The example you've given would seem to indicate that, using ideal
components with mathematically unlimited values, the gain obtainable is
unbounded.

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

On Fri, 12 Oct 2007 01:55:12 +0100, "john jardine"
wrote:


"The Phantom" wrote in message
.. .
As promised.


[Useful reading. But yes, there's caveats with the 'x2' limit.]

Attached, a contrived, LTspice structure, giving 2 gain.


Cool. It did seem like cascading could be done without theoretical
limit. The voltage looks like it's increasing exponentially with stage
count.

I'll check Mouser for those parts.

John

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

On Fri, 12 Oct 2007 02:06:53 -0700, The Phantom wrote:

On Fri, 12 Oct 2007 01:55:12 +0100, "john jardine"
wrote:


"The Phantom" wrote in message
. ..
As promised.


[Useful reading. But yes, there's caveats with the 'x2' limit.]

Attached, a contrived, LTspice structure, giving 2 gain.

In the Epstein paper, he says that the gain is 2 if the network is a
general ladder network. At the end of the paper, he admits he has now

Jeeesh . What an awkward typo. This should say "...he admits he has NO
formal poof."

formal proof.

The example you've given would seem to indicate that, using ideal
components with mathematically unlimited values, the gain obtainable is
unbounded.

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

On Fri, 12 Oct 2007 11:24:17 -0700, John Larkin
wrote:

On Fri, 12 Oct 2007 01:55:12 +0100, "john jardine"
wrote:


"The Phantom" wrote in message
. ..
As promised.


[Useful reading. But yes, there's caveats with the 'x2' limit.]

Attached, a contrived, LTspice structure, giving 2 gain.


Cool. It did seem like cascading could be done without theoretical
limit. The voltage looks like it's increasing exponentially with stage
count.

I simulated it too. John has 3 orders of magnitude increase in impedance
level per stage. With only two orders increase, the gain was around 1.8
after 7 stages. With one order increase in impedance level per stage, the
gain was decreasing with each stage except for the last stage (which is
unloaded), where the gain does increase.


I'll check Mouser for those parts.

John

Epstein paper - Synthesis of Passive RC Networks with Gains Greater than Unity.pdf
 

On Fri, 12 Oct 2007 13:19:59 -0700, The Phantom
wrote:

On Fri, 12 Oct 2007 11:24:17 -0700, John Larkin
wrote:

On Fri, 12 Oct 2007 01:55:12 +0100, "john jardine"
wrote:


"The Phantom" wrote in message
...
As promised.


[Useful reading. But yes, there's caveats with the 'x2' limit.]

Attached, a contrived, LTspice structure, giving 2 gain.


Cool. It did seem like cascading could be done without theoretical
limit. The voltage looks like it's increasing exponentially with stage
count.

I simulated it too. John has 3 orders of magnitude increase in impedance
level per stage. With only two orders increase, the gain was around 1.8
after 7 stages. With one order increase in impedance level per stage, the
gain was decreasing with each stage except for the last stage (which is
unloaded), where the gain does increase.


The within-stage parts ratios, currently 100:1, could also probably be
optimized for the cascade situation. A lower ratio might give a little
less boost per stage, but might make the cascading situation better,
so the stage-stage impedance ratios might come down.

Complex!

John