[SI-LIST] Re: Open Termination - Sandor
- From: Bill Wurst <billw@xxxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Fri, 17 Sep 2004 14:11:59 -0400
Sitar,
The answer to your first question:
>My question is why there are no more superpositions to make it 3V, 4V etc.
>even though the driver is continuously pumping a constant V and more and more
>E field guys approaching the open end.
>
is that it depends on the characteristics of the generator (voltage
source and source impedance). Assume that the source generated a 2V
step and has an impedance (resistive) of 50 Ohms. The transmission line
in this example also has a characteristic impedance of 50 Ohms and is
lossless. Initially at the instant of the step, the transmission line
(TL) appears as a 50 Ohm resistor and by the voltage divider formed with
the TL and the source, only 1V propagates down the TL. When the
wavefront reaches the open, the 1V reflecting wave is superimposed on 1V
arriving wave and 2V appears at the open. As the reflecting wave
propagates back and finally reaches the source, it finds a load that
matches the characteristic impedance of the TL and no additional
reflections occur (note that the source now "sees" an open circuit and
no current flows in the TL any longer, and there are no wavefronts to
propagate).
Now, let's assume that the source has an impedance of 5kOhms. Again, by
voltage divider action, only ~20mV propagates down the TL initially. It
reaches the open and doubles (now ~40mV) and the ~20mV reflected wave
propagates back to the source. This time, however, when it arrives at
the source it sees close to an open circuit (5kOhms >> Z0). The voltage
at the source is now ~40mV and a new wavefront of /almost /20mV (not as
much as the first wavefront because the /difference /between the source
(2V) and the node voltage at the source end of the TL (~40mV) is now
scaled by voltage divider action) begins to propagate toward the open.
This goes on forever as the voltage at both ends of the line
asymptotically approach (in step-wise fashion) 2V. In this example, the
open transmission line behaves similar to a capacitor.
Now on to your second question:
>What happens if we make the source end also open (by yanking the source) the
>instant the voltage at the load end turned 2V?
>
Again, lets assume a voltage source that initially supplies 2V and has a
resistive source impedance of 50Ohms. Keep in mind that at the instant
before the source was disconnected, it was still supplying 1V and 20mA
to the TL. At the instant after the disconnection, current no longer
flows into the line and a negative wave front of 0V minus 1V (-1V)
propagates toward the open while the reflected wave begins propagating
back toward the generator (source) end. This sets up an oscillating
condition much like a lossless LC tank circuit but in this example it's
a square wave with a period equal to twice the length of the line.
Perhaps your best bet to achieve a greater understanding of some of
these concepts is to obtain an inexpensive SPICE simulator and
experiment. Another thing to keep in mind is that conservation of
charge, and generally conservation of energy, apply.
Hope this helps.
-Bill
==========================
Sitar Moniker wrote:
>>From your explanation in previous mail, what I understand is the E field
>>(though you called it energy wave) rolls down the line happily and suddenly
>>finds itself standing in a situation where it can't jump out into the air
>>(infinite impedance discontinuity) nor just sit there and roadblock junior E
>>fields rushing from behind. The clever E field turns around (reflection) and
>>hugs the oncoming E field (superposition). Thus, we have total voltage at the
>>open equal to 2V and a E field standing there corresponding to 2V.
>By now, the E field guy standing at the open end prefers to stand looking
>toward source end(reflection mode) and use superposition to his advantage. My
>question is why there are no more superpositions to make it 3V, 4V etc. even
>though the driver is continuously pumping a constant V and more and more E
>field guys approaching the open end.
>
>What happens if we make the source end also open (by yanking the source) the
>instant the voltage at the load end turned 2V?
>
>Open end case is as ideal as it gets. So, let us keep everything else related
>to this as ideal as they could be. The answers may be trivial to the experts
>but I don't know how to get a hang of these concepts.
>
>
>Sandor Daranyi <sandord@xxxxxxxxxxxxx> wrote:If you imagine the wave reflected
>at the open end, the
>direction of travel may be reversed but it still sees
>the same line impedance, so the voltage amplitude
>won't change. After superposition, 1+1=3D2. In real life
>of course, there are always losses, so it will be
>less, but the reflection (or rather its effect on the
>signal) is something that is really easy to observe
>with an oscilloscope. As always, in real life it's a
>bit more complicated because there may be some ringing
>on the signal and perhaps several reflections, due to
>other "imperfections" beside an unterminated line.
>These imperfections are anything that can make the
>transmission line nonideal. E.g. when it has
>stubs/branches hanging off it, finite impedances
>connected to it (a device inputs perhaps) somewhere
>along the line, line geometry changes etc. In general:
>impedance variations.
>
>Now you could say, yes, but what happens when the
>wavefront reaches the beginning of the transmission
>line and gets reflected again, wouldn't that result in
>a higher voltage on the line? Well, the thing to note
>here is that there is a driver hanging off the source
>end. In ideal case, the driver will be a voltage
>source or maybe a current source. If it's a current
>source, it has infinite impedance and you do have a
>reflection again, so you end up with higher and higher
>voltages but going back to looking at the energy, it
>is not surprising, since the current source will keep
>pumping energy in there! If you have an ideal voltage
>source driving, it'll have zero impedance. Just like
>infinite impedance, zero impedance can not "swallow"
>energy, so it will be reflected back, but the
>difference is that voltage is reflected back with the
>opposite phase in this case.
>
>If you are interested in a more practical case, the
>basic things to consider are that real life drivers
>have finite source impedances, they have
>nonlinearities and limited V & I ranges. =20
>
>So, with all the signal integrity problems they can
>cause, are reflections always bad? Not necessarily.
>For example PCI uses reflected wave switching which
>allows the use of relatively weak drivers.
>
>Cheers,
>
>Sandor
>
>-----Original Message-----
>From: Sitar Moniker [mailto:si_monkey2@xxxxxxxxx]=20
>Sent: Friday, 17 September 2004 5:04
>To: sandord@xxxxxxxxxxxxx
>Cc: si-list@xxxxxxxxxxxxx
>Subject: Re: [SI-LIST] Re: Open Termination
>
>Thank you. It definitely helps to understand in terms of energy. As you men=
>tioned, due to voltage superposition, the voltage at the open end gets do=
>ubled. Extending this idea, will there be an occasion (ideal or otherwise=
>) when the open end voltage becomes 3X or 4X. If so, under what condition=
>s? If not, what limits this from happening?
>
>Sandor Daranyi wrote:
>Hello Sitar,
>
>Others have already given good information regarding your questions but sin=
>=3D
>ce you asked for something intuitive, maybe I can add something worthwhil=
>=3D
>e. The warning is that intuitive explanations can often be oversimplific=3D
>ations.
>
>
>
>>-----Original Message-----
>>From: Sitar Moniker
>>Sent: Wednesday, 15 September 2004 7:48
>>To: si-list@xxxxxxxxxxxxx
>>Subject: [SI-LIST] Open Termination
>>=3D20
>>In SI and HSDD books, they assume that open termination offers infinite
>>impedance. My understanding is open end line is exposed to air which has
>>about 377 ohms.
>>=3D20
>>1) How do you get infinite impedance for unterminated line?
>>
>>
>
>The easiest way to see what happens is in terms of energy. (Looking at what=
>=3D
>happens to energy is a very useful techni que when trying to understand s=
>=3D
>omething like this.) The driver pumps energy into the transmission line. =
>=3D
>The resulting energy wave travels down the line at close to the speed of =
>=3D
>light and eventually reaches the end. The energy COULD continue to travel=
>=3D
>in air but you would need a coupling mechanism between the transmission =3D
>line and free air. If there is no coupling, it is irrelevant what would h=
>=3D
>appen in air, or indeed that it's 377ohms. If energy can't be transferred=
>=3D
>, then by definition the impedance must be infinite. If it weren't, there=
>=3D
>would be a finite impedance and energy could be transferred.
>
>Nothing is perfect in the real world, so there can be some little coupling =
>=3D
>e.g. due to losses and radiation from the transmission line, so the menti=
>=3D
>oned infinite impedance is only an approximation, but for most practical =
>=3D
>cases, quite a valid one.
>
>Of course, if you have an antenna at the end of the transmission line, sudd=
>=3D
>enly you do have a coupling mechanism and the story changes. Everything g=
>=3D
>ets a bit trickier though, because now you would have things like radiati=
>=3D
>on efficiency and the antenna itself would behave like an impedance trans=
>=3D
>former between the transmission line and free air.
>
>
>
>>2) Is there any intuitive way to show that voltage at the open end
>>doubles- other than using math: ref. coeft. =3D3D +1?
>>
>>
>
>>From the previous answer, you may already see what happens here. When the f=
>=3D
>ace of the energy wavefront reaches the end of the transmission line and =
>=3D
>more energy still keeps arriving, it won't jump into air and it won't pil=
>=3D
>e up there, either. Instead, it will get reflected and the reflected wave=
>=3D
>will get superimposed on the arriving part of the wave. Why twice the vo=3D
>ltage? Due to voltage superposition, which should sound familiar from bas=
>=3D
>ic electronic theory (a quick "voltage superposition" google search threw=
>=3D
>up: http://www.allaboutcircuits.com/vol_1/chpt_10/6.html).
>
>Sandor
>
>------
>Sandor Daranyi
>Snr Design Engineer
>
>
>
>
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-Bill
billw@xxxxxxxxxxx <mailto:billw@xxxxxxxxxxx>
*/Advanced Electronic Concepts, LLC/*
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