4 Radio-Frequency Parameters
This section introduces some of the most common Radio-Frequency (RF) parameters used in the field of EMC:
Reflection Coefficient Γ.
We speak of matched impedances in case the load impedance Zload is the complex conjugate of the source impedance Zsource. In radiated emission and immunity EMC testing, it is important to understand the term matching and how to quantify it. All receiver and/or transmitter antennas must be matched to their receiver and/or transmitter equipment impedance (typical Z0 = 50Ω).
The reflection coefficient Γ (=s11 in case of 1-port networks!) is defined as [4.4]:
All variables are complex numbers. Vforward is the forward voltage wave to the load and Vreflection is the reflected voltage wave by the load. Zsource is the complex source impedance and Zload is the complex load impedance. Zsource is typically the characteristic impedance Z0 or the transmission line impedance. The reflection coefficient Γ is often given in [dB]:
VSWR.
VSWR means Voltage Standing Wave Ratio. The VSWR expresses the ratio of the maximum voltage Vmax [V] of a standing voltage wave pattern and the minimum voltage of a standing wave pattern Vmin [V] on a transmission line. A VSWR value of 1.0 means perfectly matched. A VSWR value of infinity means complete mismatch (100% of the forward wave is reflected). The VSWR can be calculated by using the reflection coefficient from above [4.5]:
Return Loss.
The return loss [dB] is the dB-value of the loss of power in the signal reflected (Preflected) by a discontinuity in a transmission line or due to an impedance mismatch. A low RL value indicates that not much power is transferred to the load and is reflected instead. Return loss [dB] is the negative value of the reflection coefficient Γ in [dB] [4.6].
Insertion Loss [dB].
The term Insertion Loss (IL) is generally used for describing the amount of power loss due to the insertion of one or several of the following components (passive 2-port networks):
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Transmission Line (cable, PCB trace)
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Connector
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Passive Filter
The insertion loss (IL) represents the power ratio in [dB] of the power P1 and the power P2 of the picture above. P1 is the power, which would be transferred to the load in case the source is directly connected to the load. The power P2 represents the power which is transferred to the load in case the Passive 2-Port Network is inserted between the source and the load [4.2], [4.3].
Scattering Parameters (S-Parameters).
Scattering Parameters} - also called S-parameters - are commonly used in high-frequency or microwave engineering to characterize a two-port circuit (see the picture below). The scattering parameters describe the relation of the power wave parts a1, b1, a2, and b2 that are transferred and reflected from a two-ports input and output. The physical dimension for the incident a and reflected b power waves is not Watt, it is √Watt.
Generally speaking, the S-parameter sij is determined by driving port j with an incident wave of voltage Vj+ and measuring the outgoing voltage wave Vi- at port i. Considering the picture above, the four scattering parameters can be computed as follows:
Impedance Matching Summary.
The table below shows how to convert between VSWR [1], return loss [dB] and the reflection coefficient [1]. Z0 is the "system impedance" (typical Z0 = 50Ω or Z0 = 75Ω).
In order to give you an idea what a good match means in terms of VSWR, reflection coefficient or return loss: we summarized all the values in this table below.
References:
[4.2] Mark van Helvoort, Mathieu Melenhorst. EMC for Installers - Electromagnetic Compatibility of Systems and Installations. CRC Press, 2019, p.141