S-Parameters playlist.
https://www.youtube.com/watch?v=_p0efFhCt6I&list=PLFxhgwM1F4yyAu86pAYE5KTppq0xZ8NFr
What is Scattering or S Parameters. S11, S12, S21 & S22. History & Properties.
What is Scattering S-Parameters: S11, S12, S21, S22 RF Microwave Engineering.
Scattering Parameters Explained - S11, S12, S21, S22 in Microwave Engineering.
The first published description of S Parameter was in the thesis of Vitold Belevitch in 1945.
S Parameter is also called S Matrix or Scattering Parameter and it describes the relationship of input and output ports of an electrical system.
Beside S Parameter, we used Z, Y, H, T and ABCD Parameters to analysis the electrical system. S Parameter does not use open or short circuit to characterize a linear electrical network. Instead, matched loads are used. At high frequency, we can’t have a perfect short circuit (0 Ω) or open circuit (∞ Ω) anymore. Therefore, at high frequency, we will prefer to use S Parameter over others.
From the S Parameter matrix, we can obtain the characteristics of linear networks such as 1) Gain, 2) Loss, 3) Impedance, 4) Phase group delay and 5) Voltage Standing Wave Ratio (VSWR).
In the 1960s, Hewlett Packard (HP) introduced the first microwave network analyzer. The vector network analyzer measures the amplitude and phase of voltage traveling wave phasors.
The Scattering S-Parameters is a mathematical representation widely used in electrical engineering, particularly in the field of RF (Radio Frequency) and microwave engineering, to describe the behavior of electrical networks in response to input signals. The S-parameters characterize how RF power is transmitted, reflected, or absorbed by a system, such as a transmission line, antenna, or circuit.
S Parameter changes with frequency, so frequency must be specified for any S Parameter measurements. At the test frequency each element or S-parameter is represented by a unitless complex number that represents magnitude and angle, i.e. amplitude and phase. The complex number may either be expressed in rectangular form or, more commonly, in polar form.
Reciprocity
A network is reciprocal if it is passive and contains only reciprocal materials that influence the transmitted signal. For example, attenuators, cables, splitters and combiners are all reciprocal networks, where Smn = Snm in each case, meaning the S-parameter matrix is equal to its transpose. Networks that include non-reciprocal materials in the transmission medium, such as magnetically biased ferrite components, are non-reciprocal. An amplifier is another example of a non-reciprocal network.
Lossless Network
A lossless network is one that does not dissipate any power. Mathematically, this is expressed as:
This means that the sum of the incident powers at all ports is equal to the sum of the outgoing (e.g., reflected) powers at all ports. This implies that the S-parameter matrix is unitary, which can be expressed as:
(S)H (S) = (I)
Lossy networks
A lossy passive network is one in which the sum of the incident powers at all ports is greater than the sum of the outgoing (e.g. 'reflected') powers at all ports. It therefore dissipates power:
Complex linear gain
This represents the linear ratio of the output reflected power wave to the input incident power wave, with all values expressed as complex quantities. For lossy networks, it is sub-unitary, while for active networks, |G| is more 1. It will equal the voltage gain only when the device has equal input and output impedances.
where (S)H is the conjugate transpose of (S) and (I) is the identity matrix.
Scalar linear gain
This represents the gain magnitude (absolute value), defined as the ratio of the output power wave to the input power wave, and is equal to the square root of the power gain. It is a real-valued (or scalar) quantity, with phase information omitted.
Scalar logarithmic gain
This represents the gain magnitude (absolute value), which is the ratio of the output power wave to the input. This measure is more commonly used than scalar linear gain. A positive quantity is generally understood as "gain," while a negative quantity is referred to as "negative gain" (or "loss"), equivalent to its magnitude in dB. For example, at 100 MHz, 10 m length of cable may exhibit a gain of −1 dB, equivalent to a loss of 1 dB.
Insertion loss
In case the two measurement ports use the same reference impedance, the insertion loss (IL) is the reciprocal of the magnitude of the transmission coefficient |S21| expressed in decibels.
Input Return Loss (IRL) is a measure of how effectively a system or component (such as an antenna, filter, or amplifier) matches its impedance to the connected transmission line or source. It quantifies the amount of input signal reflected back due to impedance mismatch, essentially indicating the efficiency with which the system receives power from the source.