Dear Peter Zhu, Regarding the reflections formula, suppose a wave of unit amplitude propagates towards the right end of a long cable. The cable impedance is Z0. The impedance loading the end of the cable is ZL. The incident waveform arrives with voltage vi(t) and current ii(t) = vi(t)/Z0. That ratio of voltage to current does not match what the load requires, because in the load you must have vload(t)/iload(t) = ZL. What happens at the load is that a reflection entity is created. The reflection has voltage vr(t) and current ir(t)=vr(t)/Z0. Note carefully that current in the incident wave moves to the right (assuming a positive voltage vr), while current in the reflected wave moves to the left. The current in the load must therefore be the superposition of these two currents like this, iload(t) = ii(t) - ir(t). This is the "current balance equation". The voltage at the load equals the supoerposition of the incident and reflected waveforms on the cable, like this: vload(t) = vi(t) + vr(t). This is the "voltage balance equation" >From these basic equations you can derive both formulas 4.52 and 4.53. To make the derivation, first substitute into the current balance equation the expressions for current, as a function of voltage. I have dropped the time-based arguments to simplify the notation. vload/ZL = vi/Z0 - vr/Z0 Now substitue on the left side what we know from the voltage balance equation about vload, to get this: (vi + vr)/ZL = vi/Z0 - vr/Z0 Multiply through both sides by ZL*Z0 and collect like terms: vi(Z0 - ZL) = -vr(Z0 + ZL) Express vr as a function of vi vr = vi*(ZL - Z0)/(ZL + Z0) this is the reflection formula. now compute the voltage at the load vload = vi + vr = vi*( 1 + (ZL - Z0)/(ZL + Z0)) = vi * (2*ZL / (ZL + Z0)) Perhaps you are wondering why it is that a reflection entity must be created? The cable supports only two modes of propagation -- to the right, and to the left. With in each mode, the equations of propagation are quite strict, specifying the velocity of propagation, the attentuation, and the rule that the ratio of voltage to current within each mode is fixed and equal to Z0. The creation of a reflected entity is the only possibility allowed by the equations of propagation on a transmission media. Lastly, I note that in some of your correspondence you have referred to the equation T(w) = 2*ZL/(Z0 + ZL) as representing the signal "absorbed by the load". This is not quite correct, as loads absorb "power", not "signal amplitude", therefore we must change your statment to say that the voltage apparent across the equals vload(w) = vi(w)xT(w), and the power absorbed by the load equals PowerAbsorbedByLoad(w) = [vload(w)] x [vload(w)*] / zload where the symbol vload(w)* denotes the complex conjugate of vload(w) I hope these brief comments are helpful to you. Best regards, Dr. Howard Johnson, Signal Consulting Inc., tel +1 509-997-0505, HYPERLINK "mailto:howie03@xxxxxxxxxx"howie03@xxxxxxxxxx http:\\sigcon.com -- High-Speed Digital Design seminars, books, and articles P.S., My business manager asks that I encourage you to sign up for my all-new course based on my latest book, High-Speed Signal Propagation. Check out the web site for times/dates of public venues. The classes are a great way to interact personally and get all your questions answered. If you've already been, please tell a friend... -----Original Message----- From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Peter Zhu Sent: Tuesday, April 19, 2005 6:57 PM To: ray jiang; si-list@xxxxxxxxxxxxx Subject: [SI-LIST] Re: Question about the Equation in Handbook of Black Magic Ray: The 4.53 is the reflection at the terminal, so it is (Zl-Z0)/(Zl+Z0), WHY? Why do you think (Zl-Z0)/(Zl+Z0) has been reflect back to source? Thanks Peter -----Original Message----- From: ray jiang [mailto:jlray2000@xxxxxxxxx]=20 Sent: Wednesday, April 20, 2005 12:26 AM To: Peter Zhu; si-list@xxxxxxxxxxxxx Subject: Re: [SI-LIST] Question about the Equation in Handbook of Black Magic Peter,=20 I have some idea on this question. The 4.53 is the reflection at the terminal, so it is (Zl-Z0)/(Zl+Z0). The deduce can be found in any books about transmition line theroy. As 4.52, i agree with you that it is the fraction of propagating signal that is absorbed by the load, which should be 1-R2(w) =3D 2Z0/(Zl+Z0). If this deduce is right, i think the book has made a mistake. Best Regards, Ray Jiang On 4/19/05, Peter Zhu <peter.zhu@xxxxxxxxxx> wrote: > All: >=20 > One question in Dr. Howard Johnson-High Speed Digital Design: >=20 > How to understand the Equation 4.52 and 4.53 >=20 > I believe the T(W) is the fraction of propagating signal that is > absorbed by the load, and the R2(W) is the fraction of propagating > signal that reflects back toward the source. >=20 > But where do the two equations come from? How to deduce it? I think it's > the base to fully understand the signal reflection. >=20 > Thanks in advance. >=20 > Peter >=20 > UTStarcom >=20 > ---------------------------------------------------------- -------- > To unsubscribe from si-list: > si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field >=20 > or to administer your membership from a web page, go to: > //www.freelists.org/webpage/si-list >=20 > For help: > si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field >=20 > List FAQ wiki page is located at: > http://si-list.org/wiki/wiki.pl?Si-List_FAQ >=20 > List technical documents are available at: > http://www.si-list.org >=20 > List archives are viewable at: > //www.freelists.org/archives/si-list > or at our remote archives: > http://groups.yahoo.com/group/si-list/messages > Old (prior to June 6, 2001) list archives are viewable at: > http://www.qsl.net/wb6tpu >=20 > ------------------------------------------------------------ ------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List FAQ wiki page is located at: http://si-list.org/wiki/wiki.pl?Si-List_FAQ List technical documents are available at: http://www.si-list.org List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List FAQ wiki page is located at: http://si-list.org/wiki/wiki.pl?Si-List_FAQ List technical documents are available at: http://www.si-list.org List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu