Very informative inputs have been made by all the contributors regarding the intrinsic nature of [S]. I will just make a small addition regarding measurement. [S] of active devices especially transistors are tabulated for specific set of bias conditions and will change if bias conditions are changed. I found this to be a common oversight by students when I teach courses related to microwave engineering.

Hello Noaman, The S-parameter calculations remain the same regardless of the type of circuit being measured/modeled. Think of them as characterization parameters of any N-port network. Moreover, one notable highlight for passives is that the magnitude of S -parameters for passives is always less than 1 else it signifies the results are wrong (Since passives do not add power).

Thank you!

Hi Noaman. To add a little more detail to Aditya's correct answer, the S-parameter matrix of a passive network must be positive semi-definite --- meaning that all of its eigenvalues are non-negative. This essentially guarantees the "no added power" condition for any possible set of inputs on its ports.

But yes, the definition of the s-parameters and methods of calculating them are exactly the same, in principle. (With some practical caveats --- you may have difficulty keeping an active device stable during your measurement, for example.)

Oops, I mis-spoke. I meant to say that for passive devices, the matrix I-S*S must be positive semi-definite, not the S-matrix itself. Note that I-S*S is Hermitian, so its eigenvalues are real.

Sorry for the confusion.

thanks a lot Matthew an d Aditya :-)

The properties and rules of the S-matrix for passive devices are very well defined. There exist active one ports (reflection amplifiers) .In particular there is no symmetric passive, lossless and reciprocal 3 port matched on all ports

Fritz Caspers yes you are right the rule of S-parameters for passive are well define, I am exploring S-parameters and reflection coefficient for non reciprocal devices. İn some literature it is stated that in nonreciprocal system just phase of S21 is different from S12. In non reciprocal case do we have to use the same relation which is used for reciprocal network to calculate reflection parameters by using Scattering matrix.

Difference between active and passive S matrix parameter from an RF engineer point of view could be better understood for multi-port devices like, for example, antenna arrays, power combiners/splitters, etc. Passive S-parameters are measured by a regular VNA in "passive" mode. In this mode, one port transmits and the rest receive to measure the incident power. This forms a column/row of passive S matrix. Each Sij element is just a ratio of received power at port "i" to transmitted power at port "j". The full matrix is formed when all ports operate consequently as transmitters. In active mode, more than one port or all ports transmit and all ports receive. This changes, of course, amount of incident power at each port compared to passive scenarios. As a consequence, passive Sii could be of poor values for impedance matching while active Sii could be much better suited for broadband impedance matching. Mathematically active S matrix is derived from passive S multiplied by a given/arbitrary complex excitation vector. E.g., in antenna arrays, such vectors present different magnitudes and phases of signals at ports to form ans steer beams. Note active S matrix is defined only for Sii self- terms and active Sij off-diagonal terms do not make any physical sense.

Very informative inputs have been made by all the contributors regarding the intrinsic nature of [S]. I will just make a small addition regarding measurement. [S] of active devices especially transistors are tabulated for specific set of bias conditions and will change if bias conditions are changed. I found this to be a common oversight by students when I teach courses related to microwave engineering.

Two small additions.

1. S matrix can be used to describe devices in which there is a transformation of wave types.

2. For passive devices, the poles of the elements S matrix are located in one half-plane of complex frequencies, and for active devices this limitation is absent.

Best wishes.

Denis you means that the difference between the S-parameters of active and passive RF devices is of the same nature as the difference between a scholar or researcher who share his knowledge and experience with other and the one who do not

When doing measurements of S-parameters with a vector network analyzer there is no basic difference between the S-parameters of active or passive DUTs. OF course different rules for the elements of the s-matrix apply. And caution is advised not to overload the inputs of the VNA when measuring amplifiers.A tricky point are nonlinear elements (so far we have assumed that the DUT is linear) There are ways to take this into account (in general via X-parameters) and one can also do measurements on certain nonlinear elements (e.g. mixers ) in the frequency offset mode. In certain cases one may like to use a time domain approach (i.e. taking really data in then time domain and then FFT to frequency domain).