# [SI-LIST] Re: Diode Termination

*From*: "Howard Johnson" <howie03@xxxxxxxxxx>*To*: <si-list@xxxxxxxxxxxxx>*Date*: Thu, 13 Dec 2007 22:47:51 -0800

Dear Ria, I sense you are looking for a precise answer here, so I shall endeavor to create one. Prelude: (1) When you talk about an amplitude level on a transmission line, you must specify whether your amplitude is a "voltage" or a "current" amplitude. For most digital PCB transmission structures we take the shortcut of assuming that the characteristic impedance zc(f) is pretty flat over the frequency band that interests us, so we just assign zc(f) a constant real value, like 50 ohms, which we give the name z0. We further assume only two modes, one going this-a-way and one going the opposite direction (that-a-way). In that simplified case, we can talk about voltage waveforms v1(t) and i1(t) representing a forward-moving mode of waveform propagation and make the statement that v1(t,x)/i1(t,x)=z0 at any point x. The same is true for the reverse-moving waveform number described by (v2,i2) but for one exception -- since it goes the opposite direction is has an opposite sense of current, so at any particular point x we write v2(t,x)/i2(t,x)=-z0. (2) I presume that much is familiar to you. (3) If you wish to determine the total voltage at any given point x you must sum the voltage amplitudes of the forward and reverse-travelling waves at that point. For example, the total voltate (call it vt) at the endpoint of a transmission line would be the sum of the forward wave v1(t,x) plus the reflected wave, v2(t,x) at the point x=end-of-line. (4) In the terminology of the article you cite, "Diode Terminations", www.sigcon.com/Pubs/news/2_19.htm , the forward wave measured at the endpoint I call "I" (for incident), the reverse-travelling wave measured at the endpoint I call "R" (the reflection), and the sum of both voltages "T" is the total voltage measured across the endpoint. (5) It is tempting to think of the total voltage at the endpoint as somehow "exiting" the line, because it is the voltage you measure at across the end terminals. Probably that's not very good language, though, as it seems to have confused you. (6) Now I want to throw you a curve. What if I want to know the output CURRENT (iout) flowing through the termination? That would be the sum of currents, i1(t,x)+i2(t,x), which you can derive from the voltages like this: iout(t)=[v1(t,endpoint) - v2(t,endpoint)]/z0. (7) If I give you an incident signal v1(t) (arriving at the endpoint), and ask you to tell me the size of the reflected signal you'd probably whip out the reflection formula G=(zL-z0)/(zL+z0), where G (gamma) represents the reflection coefficient, and where zL is the terminating impedance at the endpoint. Then you'd say that the reflected signal equals v1(t,endpoint)*G. Pretty good. (8) How about the current exiting the line? (Output current actually does "exit" the structure, which is where I picked up the "exit" word). Well, according to (4) you can calculate the exiting current from the voltages, like this: iout(t)=[v1(t,endpoint) - v2(t,endpoint)]/z0. (9) But, we know a value for v2(t,endpoint), calculated using G, so use it: iout(t)=[v1(t,endpoint) - v1(t,endpoint)*G]/z0. (10) Simplify: iout(t)=v1(t,endpoint)[1-G]/z0. (11) Plugging in your value for G you get this: iout(t)=v1(t,endpoint)*2/(zL+z0) (12) Check: when zL equals infinity you get no current. When zL=0 you get a current equal to v1(t,endpoint)*2/z0 (that's correct). (13) I brought up this whole discussion so you could see the relation of the endpoint voltage to the incoming and reflected VOLTAGE amplitudes: T = I + R (14) If you re-arrange the terms, you get the relation in the article, R = T - I. This is just a mathematical re-arrangement. If (14) is true, then so is this. (15) Sometimes I'm a little slippery with the details as to whether the symbols R, T and I represent particular voltages, or they represent "coefficients". I've never much cared to go into the difference. I find that as long as I stick with a convenient voltage amplitude, like 1V, it hardly matters. If we are being complete, however, I should state that (13) and (14) work if you consider each of R,T and I to be voltage waveforms. If you want to work strictly with reflection coefficients, you can do this: T/I = 1.00 + R/I In this case we interpret "R/I" to be the voltage reflection coefficient at the end of the line (I called it G earlier), and "T/I" to be another sort of coefficient. It tells you the ratio of (A) what size VOLTAGE signal comes out of the end of the line (there goes my bad terminology again -- I mean what size VOLTAGE signal is measurable as the apparent voltage across the load) to (B) the VOLTAGE of the incident wave. THAT I find to be one of the more interesting points of the "Diode Termination" article. Sometimes I'm not sure how far to go with an answer. You asked a very good question. Did I make things better or worse for you? Best regards, Dr. Howard Johnson, Signal Consulting Inc., tel +1 509-997-0505, howie03@xxxxxxxxxx www.sigcon.com -- High-Speed Digital Design seminars, publications and films -----Original Message----- From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On Behalf Of Ria R Sent: Thursday, December 13, 2007 8:21 PM To: si-list@xxxxxxxxxxxxx Subject: [SI-LIST] Diode Termination All, I have a question on something I read about diode termination. Howard Johnson in one of his answers to a diode termination question says the following: One equation of interest regarding the theory of diode terminations is the relation between the incident signal amplitude traveling down a transmission line (I), the amplitude of the signal reflected at the end of a line (R), and the amplitude of the signal that exits the line and is apparent at the load (T). I am clear about "I" and "R". But what does "T" mean? I thought there was just signal incident and signal reflected. Is there a signal "Exiting"?? Also, if this is explained, the next question is, what does he mean by: In English, the signal at the end of the line is the superposition of whatever came in, plus whatever bounced back toward the driver. This same equation may be re-written to express "R" as a function of "T" and "I": R = T - I Can someone please clarify the above equation?? Thanks in advance. Regards, Ria. ____________________________________________________________________________ ________ Never miss a thing. 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**References**:**[SI-LIST] Diode Termination***From:*Ria R

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