S21 can have value at 0 GHz?
I think that S21 generally applies to high frequency signals because it relates to wave reflection etc. If it applies to DC, only resister should be cared about. When I get the following table from an on line tutorial, I am puzzled about the S21 0GHz column.
The paper also has the following explanations:
Figure 2 shows a set of 13 SerDes channel characteristics in the frequency domain that is typical for a SerDes system. For discussion in this article, the data used with these channels has a 100 psec bit time (10 Gbps bit rate). The figure y-axis is in dB units.
This set of curves is representative of any set of frequency domain channel characteristics. Most practical systems have characteristics that include a lot of irregularity due to system mismatches and signal ****-outs. This simplified set of curves is for discussion purposes in this article.
The table in Figure 2 shows the list of 13 channels referenced by ?Index? number along with the channel DC (0 GHz) gain, gain at 5 GHz which is the Nyquist frequency for the 10 Gbps data stream, and gain at 10 GHz. The channel attenuation at 5 GHz varies from -16.4 dB to -32.7 dB, with about -1 to -2 dB change per step in Index value. This high frequency attenuation needs to be restored to a flat response within the Nyquist frequency band (0 ? 5 GHz) to achieve low data bit error rates in the SerDes system.
Can you help me on this question, i.e. S21_0GHz has such values difficult to understand to me?
Thanks,
If your device/cable has any resistance, there is some insertion loss at 0Hz and S21 is <0dB.
If you have difficulty to interpret S21 at 0Hz, you can also convert the S-parameters to Z-parameters.
Because the S21_0GHz column has variable data, it is not only resistor obviously. Thus, it can be thought as low frequency measurement (how low?), even though it is not shown the measurement frequency?
It is not obvious to me. I would think the different "channels" have different paths length, and resistance as well as high frequency insertion loss varies with length.
That is one possibility. We sometimes extrapolate measurements down to DC. Low enough frequency is where the path length is << wavelength.
I think not. S parameters involve the concept of Forward and Backward travelling waves. The lowest frequency I have seen talking about electrical standing waves at low frequency was for 60 hz power grid analysis, and those lines were tens of kilometers long.
In other media, you can see lower frequency, such as in ocean waves, but once again, even though they might be at 0.1 Hz, they require a forward and backward wave.
So at DC, there is no such thing. I suppose you could just use a voltage divider equation to estimate the S21 transfer to a load at DC, and maybe deduce what S11 would have been if there were an actual reflected wave.
biff, you are right about the wave concept, but we can of course calculate S-parameters from Y/Z-parameters at any frequency, including DC. S-parameters down to 0Hz are widely used in wideband simulations (e.g. RFIC) to ensure proper DC response.
interesting, never knew that
S-parameters can be calculated by a formal transformation from terminal currents and voltages. The travelling waves are more a visual interpretation of the numbers.
There's however a special property of DC S-parameters, they are purely real values.
The Thevenin/Norton maximum power transfer theorem initially was developed for DC.
The maximum amount of power will be dissipated by a load resistance when that load resistance is equal to the source resistance of the network supplying the power.
If the load resistance is lower (or higher) than the source resistance, its dissipated power will be less than maximum, so the reflected power back to the source will be higher.
From the ratio of powers (or currents and voltages as was stated above) can calculate S-parameters at DC.
yes but there is no actual "reflected power". Its not like there is an actual 50 ohm resistor in the source that heats up with reflected power. The power delivered to the load is just diminished...its just not as an efficient generator as it could be. Not sure what S11 means then.
Don't look at the meaning, just at the mathematics.
Strictly speaking, the description only apllies to a generator with circulator. In steady state, the load impedance is transformed to the source reference plane. A load short (S11 = -1) will appear as any impedance with |S11'| = 1 at the generator. If S11'=1, no power is dissipated in the source impedance.