They just both couple like they did when only one was on, but both the couplings happen at once, e.g. S21 and S12, so each antenna's return loss is added to the coupling from the other antenna, which may make it better or worse, and will change if you vary the phase between the antennas, to scan their beam for instance.

Hi Irfan Ali Tunio,

Scattering parameters define what waves are "scattered" out of a system on a given port, under the assumption of a wave incident on any given port. Thus, S12 or S21 evaluate how much "coupling" you have between your antennas, or how much power (voltage) comes out of one antenna, assuming the other antenna is excited.

The thing about such systems is that they are assumed to be linear. This has several implications, the first of which is that the coupling is independent of input power. For example, it is assumed that if the power coupled between the antennas is 10% of the incident power (S21/S12 = -10dB), then if one antenna has an incident power of 1W, 0.1W will scatter out of the second antenna, or if 100 W is incident on one antenna, 10W will scatter out the other.

Secondly, linear systems allow superposition to be applied. This means that the coupling of the two antennas will not change, regardless of which antennas are being excited (or both!). By definition, your scattering parameters remain unchanged. So for example, if one antenna has 10W incident on it, and the other has 20W incident on it, the first antenna will couple 2W back towards its source, and the second will couple back 1W.

The question was about coupling between two antennae...what was said in the comments above is correct but one should keep in mind that depending on the geometrical position of the two antennae (e.g. two horn antennas side by side for close range "radar "' in say geological applications) that there is also coupling via the near field and not only in the far field. This is basically all contained in the S-parameters .Of course for a simple microwave link and communication in the far field only one barely can see the effect of the other antenna in S11 or S22 respectively.

In antenna arrays, S-parameters are measured when each port i=1,...,n is driven one at a time. Such S-parameters are often called "passive". The "passive" S matrix allows to assess "active" S-parameters when all ports are excited with certain complex weights w_i. Then, the "active" return loss ("active S_ii") for any i=1...n is just a weighted sum of the i-th S- matrix row:

S_ai = S_i1*w_1 + S_i2*w_2+...+S_ii*w_i+...+S_nn*w_n (i=1,..., n)

Note only "active self-terms" makes sense. Physical outcomes from this simple math can be very rich to bring insights on array operation and features. For example, "active" S-parameters show what happens when array scan being excited with the weights w_i that includes a phase taper to steer radiation beams. Also, impedance matching typically should be much better in properly designed arrays compared to their single elements, viz. S_ai_dB < (

Thank you very much for all your scholarly feedbacks. Since antenna array theory is really interesting in terms of so many assumptions that we take to evaluate certain parameters like radiation pattern, impedance etc, I would like to know more about the last comment given by Dr Anatoliy Boryssenko where it has been considered that the array theory would imply the same effect on receiving/tranmitting array antennas (infact ANTENNA RECIPROCITY).Well, we know that when it comes to single antenna , the theory of reciprocity makes sense but since in antenna arrays due to the effect of mutual coupling(closely packed arrays) is different on receiving and transmitting arrays then how come is it possible to have the theory of reciprocity valid for mutually coupled R/T antenna arrays ?

Some effects of mutual coupling is different in TX and RX arrays, for instance in a TX the mutual coupling will change the TX power being reflected back to the power source(s), and the power radiated, whereas in RX it changes the power being reflected into space, and the power received, but its effect on gain and other parameters is the same. I don't know what you have read but either it is wrong or you have misunderstood it.

TX and RX performance of antennas are often calculated and used differently but they are reciprocal if the arrays are identical. Antenna parameters are calculated treating the antenna as if it is in TX or RX whichever is more convenient, and then the results applied in whichever (TX or RX) is required.

hi, generally when the designer decide to calculate mutual coupling between two antenna elements in an array (s12 or s21), one of elements should be connected to match load(50 ohm) and the other element is excited. this kind of mutual coupling is passive. on the other hand in active phased array antennas, when all of the array elements are excited for beam steering, active S-parameters should be used in calculations. HFSS software is powerful for calculating active S-parameters in such cases.

It might be useful for you to check the concept of active reflection coefficient

Just to illustrate some of my previous points on effect of mutual coupling in arrays and role that the S-matrix plays in such assessments, this slide shows how the concept of "active" S-matrix works at practice. Additionally, the slides reveals also the edge truncation effect which happens in finite arrays when elements have different active reflection (impedances) depends on their location within the array. E.g., the elements in the center tends to operate like in infinite array while those close to edges and corners are more distributed especially at the lower frequency. The single element impedance is not good as in arrays and so on.

Actually what Stuart Barth said above is totally correct; the scattering parameters define what waves are "scattered" out of a system on a given port with considering the wave incident on other ports. So, S21 & S12 evaluate how much "coupling" between both antennas is there, assuming the other antenna is excited and this does not changed if the other antenna is not excited.