The reflection coefficient of any device (S11), can it be greater than one?
Please note that the definition of s-parameters assumes that each port is hooked up to a terminated transmission line of a characteristic system impedance, usually 50 ohms. This means that all ports are terminated at Zo + 0j. s11 larger than 1 means that the system performs amplification and external energy is being supplied to the device under test. For a steady state passive network the magnitude of s11 must always be less than 1 or conservation of energy would be violated. I can not see that this is possible.
The internal reflections between the ports can of course have very large amplitudes such as in any high Q resonator. But the voltage seen by the ports at Zo will directly translate to energy absorbed by the corresponding line terminations.
You can of course have reflection coefficients larger than one if You allow line impedance to vary and the system is not terminated.
Yes, it can. For example, if you are measuring S11 for an antenna without an anechoic chamber, the antenna could be receiving some signal from the enviroment that could be interpreted as a reflection coefficient larger than 1. You must interpret carefully and think twice about what you are measuring because in some cases numerical results can be misleading.
Can you please explain a bit more, like if we are measuring the reflection coefficient and its value is found to be greater than one, what interpretation can we make and what are the possible conclusions and inferences that can be made.
Under particular circumstances the power that goes back into the port 1 is the superposition of the reflected power + other contributions (such as the antenna received power) is greater than the power transmitted by the VNA to the port 1. That situation could cause a S11>1. On conclusion is that you can be measuring an active device. Other conclusión is that your device is coupling power form the enviroment and that some portion of that power is propagating back to the port 1, which is a likely situation if you are measuring an antenna without a shielded room or an anechoic chamber..
You can measure S11>1 if you are dealing with an active device. One other possible is the characteristic impedance of your system. If you choose a complex characteristic impedance, it is possible to measure S11>1 for passive devices too.
Dealing with a passive device, S111 in such devices, it can be due to a bad calibration or a bad definition of S parameters.
Yes S11>1 is possible particularly in active devices. Gunn diodes can be configured by adjusting the bias to give a negative resistance to microwave frequencies. This will make ZLnegative in the general reflection coefficient equation that will lead the reflection coefficient to be bigger than one. It is also possible in devices that have only magnetic biasing such as some ferrite devices. Under particular conditions this can also lead to negative resistance. This can be used in frequency doubler s but tends the be an electrically noisy way to do it. If you have no electrical or magnetic bias (alternative source of energy) then look at calibration.
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6312388
It can be higher than one even for completely passive characteristic impedances and passive loads. E.g take Zo = 50-50j, Zl = 50+60j, you will get an magnitude of Gamma equal to 1.0945. The question is how is that interpreted?
The simple answer is for passive devices, no and for active devices such as amplifiers, yes. This is assuming single frequency and linear transmission lines.
Conservation of energy can not be broken.
Non stationary signals are different. But then it is a matter of how You define the reflection coefficient. For instance, a high Q system, a reflected pulse summing network or similar systems able to "store" energy can momentarily give s11>1 for non stationary signals even in passive networks when the amplitude of the input varies or in pulsed systems. For pulsed systems such as TDR this is even true for a simple open transmissionlines, but that is stretching definitions a bit to far...
@John I am interested to learn what magnetically biased devices You refer to in case You still read this thread...
Gerasimos is correct.
It is possible to have a reflection coefficient greater than 1 without violating any passivity conditions. This happens when you have a lossy transmission line with a complex termination. Check out the literature as this is explained in more details. However, you can convince yourself of this using simple graphical methods.
Omar
@ Erik Isberg
"a high Q system, a reflected pulse summing network or similar systems able to "store" energy can momentarily give s11>1 for non stationary signals even in passive networks when the amplitude of the input varies or in pulsed systems."
First: what is Stationary signal ?
Second: does S11 definition apply to time domain or it's just a representation of steady-state behavior ?
@Ahmad Deel
That´s is good question without a good answer. There are several established definitions of stationarity in mathematics and other disciplines as well. A stationary ergodic process is usually defined as having a constant mean and variance over time, having a constant probability distribution. In theory this is always a matter of definition, since theoretically the point can be made that a true stationary process can not exist since it has to start and stop at some finite times...
In practical work I think a workable definition is that the spectrum of the signal should be reasonably constant over time. White noise and periodic signals would be clear cases. Shot noise and other transient depend on the time scale You chose to use for analysis. This essentially boils down to the bandwidths of Your measurements.
S parameters are simply defined as reflection and transmission ratios and can be used in any context. TDR and steady state network analyzer results will usually be very similar at comparable bw,
S11 being higher than one doe snot violate anything we know at all. Lossy transmission lines, if terminated with certain impedances, can easily give you s11 higher than one. Now, please do remember that (s11)**2 does not always correlate to power. it is E X H(conjugate) that does. In the case of lossy transmission line, E and H have a phase difference that depends on the loss in the line, so they will give a product (with H conjugated, of course) that is less than 1, so this makes very body happy, most important of which is Mr. Poynting!
Please note that the definition of s-parameters assumes that each port is hooked up to a terminated transmission line of a characteristic system impedance, usually 50 ohms. This means that all ports are terminated at Zo + 0j. s11 larger than 1 means that the system performs amplification and external energy is being supplied to the device under test. For a steady state passive network the magnitude of s11 must always be less than 1 or conservation of energy would be violated. I can not see that this is possible.
The internal reflections between the ports can of course have very large amplitudes such as in any high Q resonator. But the voltage seen by the ports at Zo will directly translate to energy absorbed by the corresponding line terminations.
You can of course have reflection coefficients larger than one if You allow line impedance to vary and the system is not terminated.
Hello, I want to ask a question about measuring the S parameters for a parallel plate transmission lines between 1 MHz-100MHz. After calibration step (coax cable1 and coax cable 2 which connected to the DUT), I need to connect the VNA to the parallel plate . However, it cen be possible with using non-coaxial cables. Thus, it causes some mistakes for measurements such that the connected transmission line acts an active device (confusing S parameters! when calculating characteristic impedance) Additionally, I can not manage de-embedding of the non-coaxial parts due to the fact that Idon't know their S parameters or electrical circuit parameters. How is the best connecting procedure for this type measurements? Thanks
The coaxiaial cables from a VNA are unbalanced transmission lines, so if You need to characterize a balanced system such as You describe, You need to use balluns or broad band transformers. Dual source VNA:s can also be used. This MJ article from last Year describes some of the problems:
http://www.microwavejournal.com/articles/print/22555-isolated-baluns-eliminate-tradeoffs-in-differential-measurements
It also helps to calculate the characteristic input impedances approximately in Your test setup and try to match the ports. I do not understand what You mean by the connecting coax lines acting as active devices. You should be able to calibrate everything to Your test setup reference planes using reference components at the ballun ports, not the coaxial line ports. Then You will measure the balanced ports of Your DUT correctly. You may have to make up Your own reference components for special cases like this. This is usually fairly easy for such low frequencies.
Hope this helps.
Dear Sir,
I think no.
T+R = 1
T - Transmission with S - Parameter
R - Rflection with S Parameter
And the definition is, that T+R as a sum not be greather than 1.
All the best
F. Gräbner
There is a whole area of oscillator design that uses the region outside the normal Smith chart, i.e. with reflection coefficient greater tan 1 (The circles keep on going!). A Gunn diode has a reflection coefficient greater than 1.
https://www.researchgate.net/figure/278401927_fig4_Measured-reflection-coefficient-of-a-31-m-m-length-Gunn-diode-for-different-DC-voltages
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Electromagnetics
- Electromagnetic Fields