The magical use of S-parameters in high-frequency measurement
After the personal computer platform entered the GHz stage, from the computer's central processor, display interface, memory bus to I / O interface, all entered the country of high-frequency transmission, so the measurement of high-frequency parameters appeared on the table. Generally, the basic items that must be considered for high-frequency measurement include the following:
◆ Impedance─Characteristic impedance. Our common cables / signal lines have different impedances such as 50, 75, and 100 ohms. The impedance referred to here is not DC resistance, but the so-called characteristic impedance, which is the impedance faced by each signal transmission through the station .
◆ S-Parameters——S parameters (S11, S21, S12, S22)
◆ PropagaTIon Delay——Propagation delay
â—† SWR-Standing Wave Ratio
◆ Crosstalk——crosstalk
The computing speed of information electronic products and the amount of information transmitted have been greatly increased, and the high-frequency characteristics of related electronic components have become increasingly important. In the past, components such as PCBs, cables, connectors, etc., which were regarded as purely bridging functions, in order to meet the needs of high-frequency applications, existing specifications gradually incorporate attenuation, characteristic impedance, crosstalk, transmission delay, transmission delay time Items with high frequency characteristics such as isolation effects and signal jitter. This article will mainly introduce the application of S-parameters in high-frequency measurement.
In high-speed transmission operation, the quality of signal transmission is very important. In order to obtain maximum transmission efficiency, various high-frequency parameters will become an important reference basis for design, debugging and improvement, and practical application. Special attention must be paid to Impedance Matching problems, signal delay time (PropagaTIon Delay), time lag (PropagaTIon Skew), noise (Noise), signal loss (Loss) and signal attenuation (AttenuaTIon) and other topics. However, these parameters are not easy to calculate and measure, and must rely on high-precision instruments to assist in obtaining accurate values. Generally speaking, the instruments used in high-frequency testing are roughly “Time Domain Reflectometry†and “Network Analyzerâ€.
For engineering personnel, the S parameter is an important indicator. The original name of the S parameter is "Scattering-Parameter". Electromagnetic energy is transmitted in the form of electromagnetic waves in a medium or conductor such as air. The electromagnetic waves will cause signal reflection due to the mismatch of the characteristic impedance of the loop. When there are countless signals reflected in the loop, the changes in electromagnetic energy distribution and time seem quite complicated.
When the frequency is low, the size of the component is small compared with the wavelength of the signal waveform. The influence of the reflected wave withdraws from the signal change time in a short time, so it shows a stable state. Therefore, the impedance of the voltage-current ratio can be used to express the inherent characteristics of the device. It is generally viewed as a "centralized fixed number" loop. Some people call it a node (Lump) circuit. The basic characteristics of its loop device are:
â—† Resistance: energy loss (heat generation)
â—† Capacitance: electrostatic energy
â—† Inductance: electromagnetic energy
However, for high-frequency components and circuits, the size of the components cannot be ignored relative to the internal electromagnetic wave transmission speed of the components. After all, the interference of the proceeding and reflected waves of electromagnetic waves inside the parts loses consistency, and the inherent characteristics of the steady state of the voltage-current ratio are no longer applicable. Instead, the concept of characteristic impedance of "distributed fixed number" is used. Some people also use distribution ( Distributed) circuit to call it. Therefore, the elements considered for the distribution of fixed loop components are the elements based on the transmission and reflection of electromagnetic waves, namely:
â—† Reflection coefficient
â—† Attenuation coefficient
â—† Delay time of transmission
The above considerations are the basic source of the S-parameter concept.
The low-frequency transmission line can adopt the voltage and current relationship of the bottom two-port (2 Port) loop to show the characteristics of the loop. Please note that the network mentioned here refers to a circuit, not a server network or the Internet.
The various parameters commonly used include nothing more than Z parameters, Y parameters and F parameters. The performance of F parameters (image parameters) is as follows:
[V1] [AB] [V2]
[] = [] []
[I1] [CD] [I2] ............. (1)
The performance of the Z parameter (open-circuit impedance parameters) is as follows:
[V1] [Z11 Z12] [I1]
[] = [] []
[V2] [Z21 Z22] [I2] .......... (2)
The Y parameter (short-circuit admittance parameters) behaves as follows:
[I1] [Y11 Y12] [V1]
[] = [] []
[I2] [Y21 Y22] [V2] ............ (3)
Please note that no matter which of the above-mentioned parameters, you can use the simple measurement method of terminal short circuit or terminal open circuit. The following uses Y parameter as an example to illustrate.
I1 = Y11V1 + Y12V2
I2 = Y21V1 + Y22V2
When the terminal is short-circuited, that is, when V2 = 0, Y21 = I2 / V1. In the case of transistors, the h parameter can be derived by mixing the Z parameter and the Y parameter.
However, the leap into the high-frequency country, the influence of the inductance of the lead wire and the capacitance of the end point cannot be ignored. It cannot be achieved simply by the terminal short circuit state (impedance is zero) or the terminal open circuit state (impedance is infinite). For example, the determination of Z11, the policy of making I2 zero, the measurement using 100% reflection becomes unreasonable.
For this reason, S-parameters with the concept of proceeding wave and back-measurement wave can describe the characteristics of high frequency. In Figure 3, the incident wave (Incident Wave) is a1 and a2, and the reflected wave (Reflected Wave) is represented by b1 and b2. The relationship between the incident wave and the reflected wave can be represented by the following mathematical formula:
[b1] [S11 S12] [a1]
[] = [] []
[b2] [S21 S22] [a2] ......... (4)
If the mathematical expression is expanded, it can be expressed by the following two expressions:
b1 = S11 × a1 + S12 × a2 ............ (5)
b2 = S21 × a1 + S22 × a2 ............. (6)
S11, S12, S21, S22 are S parameters. It can be measured using a non-reflective terminal. This means that when Z1 = Z0, a2 is equal to zero, so S11 = b1 / a1.
In general, S-parameters can be measured using a network analyzer. S11 and S22 are related to the voltage reflection coefficient and can be calculated by measuring the impedance. S21 and S12 are related to transmission characteristics, such as attenuation or phase characteristics, which can also be measured by the combination of oscillators and oscilloscopes. As for the loop calculation method using S-parameters, please refer to Figure 4 first, and try to calculate b2 as an example.
If both the sending end and the receiving end are considered based on the transmission characteristics of the terminal, according to the previous S parameters (5) and (6), if the reflection coefficient of the load is expressed by Γl, then it is
a2 = Γl × b2
Bring this formula into (6), you can find:
b2 = S21 × a1 / (1 S22 × Γl) ......... (7)
For the same reason, the reflection coefficient of the sending end is expressed by Γs, then:
bs = Vs × sqrt (Z0) / (Zs + Z0)
Since a1 = bs + Γs × b1, bring this formula into formula (5), you can find:
a1 = bs + Γs × (S11 × a1 + S12 × Γs × b2) ....................................... .(8)
Combining (7) and (8), the transmission characteristics can be obtained:
b2 = S21 × bs / ((1-Γs × S11) × (1-S22 × Γl)-Γs × Γl × S12 × S21)) ... (9)
Γl = (Zl-Z0) / (Zl + Z0) Γs = (Zs-Z0) / (Zs + Z0)
Z0 is the characteristic impedance of the network.
From the above description, it is not difficult to see that the calculation using the S parameter does not use voltage or current, but the reflection coefficient of the connection point is used.
If the signal flow graph (Signal Flow Graph) is used to display the loop, the following transformation rules can be used to achieve:
â—† Variables of incident wave and reflected wave are converted into contacts
â—† S parameter becomes branched
â—† The branch is from the independent variable node into the dependent variable node
The magical use of S-parameters
There is no doubt that the S parameter is an effective way to judge the characteristics of the system in the Frequency Domain.
If you observe the S-parameters and light waves, there are quite different meanings.
Think again, S11 is TDR (Time Domain Reflection), and S21 is TDT (Time Domain Transmission), so there is an interpretable relationship between TDR / TDT and single-ended S parameters. S21's TDT means Insertion Loss, and S11's TDR is Return Loss. However, in the case of high-speed transmission, the differential transmission (Differential) mode is used. Therefore, the S parameter in the differential mode (also called mixed mode) is also a part of the necessary recognition. To meet the differential transmission, a 4-port (4 Port) loop must be introduced. In the above presentation, among them, Sghij's interpretation meaning is S (output mode) (input mode) (output port) (input port).
The following will take Maxim's MAX3950 10Gbps deserializer (de-serializer) as an example to explain the magical use of S-parameters. As far as S11 presents Return Loss, it is necessary to set up the measurement first. Fig. 11 is the measurement result of the return loss (Return Loss) of the single-ended connection type, and the return loss (Return Loss) of the differential type can also be obtained.
In the application of USB 2.0 interface, in order to overcome the problem of electromagnetic noise, a common mode filter component CMF (Common Mode Filter) will be introduced. It is generally a good method to evaluate SMF components with S-parameters. CMF is equivalent to a 4-port component, in other words, equal to 16 parameters.
[S11 S12 S13 S14]
[S21 S22 S23 S24]
S = [S31 S32 S33 S34]
[S41 S42 S43 S44]
Since there will be common mode input and reflection, differential input and reflection, after proper conversion, it can be converted into the following parameters:
[Scc11 Scc12 Scd11 Scd12]
[Scc21 Scc22 Scd21 Scd22]
S = [Sdc11 Sdc12 Sdd11 Sdd12]
[Sdc21 Sdc22 Sdd21 Sdd22]
For the same reason, the USB 2.0 cable can also use the same thinking and use S parameters to evaluate its noise characteristics. In short, the S-parameter (scattering-parameter) is a type of terminal parameter. The four-terminal circuit is expressed by connecting the impedance-corrected power reflection coefficient and the pass coefficient. Of course, the measurement of the circuit characteristics is sufficient to reflect this problem. s-parameter calculation / s-parameter calculator.
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