This is a nice explanation but still a bit puzzling. Especially

confusing is the fact that

Vswing has a different definition in the cases of LCM and HCM.

The definition is the same and the difference between HCM and LCM is

that HCM powers the channel drivers from the logic level power supply,

Vdd, and LCM powers its drivers from a low voltage power supply on the

order of Vswing.

Also,

according to the paper, the signaling power is that dissipated by the

termination and the lossy transmission line. If Vswing stands for the

voltage measured at the output pin of the transmitter and the line is

lossless, wouldn't the power always be Vswing^2/Z0 ?

Lossless or not, the transmitter puts Vswing across the line at its

output, so the power into the line will be Vswing^2/Zo is correct.

Also, in the case of HCM, Vdd is not really the voltage `across the

channel' so the product V*I is not really the power dissipated by the

channel+termination.

V*I is the generic calculation of the power *supplied* by the circuit DC

power source. If the line draws current Vswing/Zo from the driver, then

the DC supply, Vdd, must provide Vswing/Zo amperes to the driver, making

the power provided by the DC supply Vdd*Vswing/Zo. The paper is

interested in computing the power supply requirements as well as the

driver circuit internal dissipation requirements as a function of data rate.

If I have two equal resistances in a series and

put V volts across both resistors and try to measure the power

dissipated by the bottom one, it will not be V*V(across R)/R=V^2/2R

but rather V^2/4R. Why is this not an accurate model of the HCM

transmitter? Or is the load resistor not considered part of the

driver? Or (more likely) they just use their expression because it has

the dimension of power and is related to the actual power dissipated

at the receiving end?

They break the total power drawn from the DC power supply into two

components: the power dissipated by the line and its termination; and

the power dissipated by the driver electronics and whatever internal

source termination it uses. The receiver Vrx, the line loss H(f), and

the characteristic impedance Zo, are all that are necessary to compute

the power required by the line and its termination at a particular

Nyquist frequency f. The driver internal dissipation is not so

straightforward and must be computed on a case by case basis as a

function of CMOS process and circuit topology.

Finally, their analysis does not really care about the 2 in the

denominator (or any other constants for that matter) but does care

about the power of H(f) there. I can belive the fact that LCM is more

sensitive to the frequency response since the HCM transmitter is a

current source and therefore in V*I, the I part does not depend on

H(f) (as noone looses current along the way in a transmission line).

Is this the idea of their analysis (greatly simplified, of course)?

Yes, it is all very straightforward. Once again:

for the HCM case:

the receiver requires Vrx at its input,

this means the transmitter must place Vrx/H(f) at its side of the line,

Vrx/H(f) across the line input requires (Vrx/H(f))/Zo amperes,

the (Vrx/H(f))/Zo amperes supplied by the driver, into the line,

ultimately is supplied by the DC power supply Vdd to the driver,

so the DC power supply Vdd is providing Vdd*(Vrx/H(f))/Zo watts to make

just the line portion of the bit transmission happen.

The LCM case is similar.

In any case, thanks for the explanation. I would appreciate any

clarification on the questions above.

This part is somewhat unclear to me. Regardless of what happens at the

receiver end, wouldn't it always be that

I*Z0=Vout and Vrx=H(f)*Vout so I*Z0=Vrx/H(f) (provided the load looks

resistive and that's essentially what equalization will achieve)?

Essentially, equalization will just make the reactive component of the

load `invisible' to the reciever but this is already assumed in all

the models above, so how does this relate to the factor of 2 in

equation (2) in the paper?

First of all, the I at the receiver end is not the same as the I at the

transmitter end. A transmission line does not obey the laws of lumped

element circuit analysis because it is entails energy transmission by

wave propagation. In both LCM and HCM, you have (Vrx/H(f))/Zo amperes

must be injected into the line at the transmitter side. One difference

is that for HCM, Vswing=Vrx/H(f), and for LCM, Vswing/2=Vrx/H(f). The

second difference is that for HCM, the DC voltage supply for the circuit

is Vdd, and for LCM, DC voltage supply for the circuit is Vswing. The

resulting power required of the DC supply for HCM and LCM are then

Vdd*Vrx/(H(f)*Zo), and Vswing*Vrx/(H(f)*Zo), respectively. But because

Vswing/2=Vrx/H(f) in the LCM case, Vswing=2*Vrx/H(f), making the power

in terms of Vrx, 2*(Vrx/H(f))^2/Zo watts, and not (Vrx/H(f))^2/(2*Zo) as

they state in the paper.