**Introduction to S-parameters**

S (scattering) parameters are used to characterize electrical properties using matched impedancesThe internet. Scattering here is the way current or voltage is affected in the event of a transmission line interruption. use. S-parameters can treat a device as a “black box” with inputs and corresponding outputs, so that the system can be modeled without concern for the intricate details of its actual structure.

todayintegrated circuitThe bandwidth of the devices continues to increase and their performance must be characterized over a wide frequency range.Traditional low frequency parameters such as resistance, capacitance and gain may be frequency dependent and therefore may not be fully describedICperformance at the target frequency. Furthermore, characterizing every parameter of a complex IC over the entire frequency range may not be achievable, while system-level characterization using S-parameters can provide better data.

You can use a simpleRFrelayto demonstrate high-frequency model validation techniques.As shown in Figure 1, an RF relay can be thought of as a three-port device: an input port, an output port, and a port forswitchThe control port of the circuit. If the device performance is independent of the control side, once set, the relay can be reduced to a two-port device. Therefore, the device can be fully characterized by observing the behavior of the input and output.

Figure 1. RF Relay Model

To understand the concept of S-parameters, it is necessary to know some transmission line theory.Similar to the familiar DC theory, at high frequencies, the maximum transmissionpowerandpower supplyThe impedance is related to the impedance of the load. Voltage, current, and power from a source of impedance ZS, travel as waves to a load of impedance ZL, along a transmission line of impedance Z0, . If ZL = Z0, all power is transferred from the source to the load. If ZL ≠ Z0, some power is reflected from the load back to the source and maximum power transfer does not occur. The relationship between the incident and reflected waves is represented by the reflection coefficient Γ, which is a complex number that contains information about the amplitude and phase of the signal.

If Z0 and ZL match exactly, no reflections will occur, Γ = 0. If ZL i is open or shorted, Γ = 1, indicating a complete mismatch, and all power is reflected back to ZS. In most passive systems, ZL is not exactly equal to Z0, so 0 < Γ < 1.To make Γ greater than 1, the system must contain a gainelement, but the RF relay example will not take this into account. The reflection coefficient can be expressed as a function of the associated impedance, so Γ can be calculated by:

(1) → (2)

Assume that the transmission line is a two-port network, as shown in Figure 2. In this representation, it can be seen that each traveling wave consists of two parts. The portion of the total traveling wave flowing from the output of the two-port device to the load, b2, is actually composed of a portion of a2 reflected from the output of the two-port device and a portion of a1 of the transmitted device.Conversely, the total traveling wave b1 that flows from the input of the device back to the power supply is composed of a portion of a1 reflected from the input and a portion of a2 that returns to the device.

Figure 2. S-parameter model

From the above description, the formula used to determine the value of the reflected wave can be listed using the S-parameter. The calculation formulas of the reflected wave and the transmitted wave are shown in Equation 3 and Equation 4, respectively.

(3)

(4)

If ZS = Z0 (impedance of two-port input), no reflections will occur, a1 = 0. If ZL = Z0 (impedance of two-port output), no reflections will occur, a2 = 0. Therefore, we can match Conditions define S-parameters as follows:

(5)

(6)

(7)

(8)

in:

S11 = Input reflection coefficient

S12 = reverse transmission coefficient

S21 = Forward Transmission Coefficient

S22 = back reflection coefficient

Any two-port system can be completely described by these formulas, the forward and reverse gains are characterized by S21 and S12, respectively, and the forward and reverse reflected powers are characterized by S11 and S22, respectively.

To solve for the above parameters in a real system, ZS, Z0, and ZL must match. For most systems, this is easily achieved over a wide frequency range.

**design andMeasurementTransmission Line Impedance**

To ensure a two-port system has matched impedance, ZS, Z0, and ZL must be measured. Most RF systems operate in a 50 Ω environment. ZS and ZL are generally affected by the vector usedNetwork Analyzer (VNA), but Z0 can be designed to match the VNA impedance.

**Transmission Line Design**

The impedance of the transmission line is determined by theinductanceand capacitance ratio setting. Figure 3 shows a simple transmission line model.

Figure 3. Lumped Element Model of Transmission Line

Using the formula for calculating the complex impedance at the frequency of interest, determine the values of L and C required to obtain a specific impedance. The way to adjust L and C depends on the type of transmission line model, the most commonly used models are microstrip line and coplanar waveguide. Model.Utilize physical parameters such as distance from trace to ground, trace width, andPCBSubstrate dielectric constant, etc., can balance inductance and capacitance to provide the desired impedance. The easiest way to design the impedance of a transmission line is to use an impedance design program, of which there are many.

**Measuring Impedance**

After the transmission line is designed and produced, its impedance must be measured to verify the design and implementation. One way to measure impedance is to use time domain reflectometry (TDR) measurements that reflect the signal integrity of PCB traces. TDR sends a fast pulse along the signal line, records the reflection, and uses the reflection information to calculate the path impedance at a specific length from the signal source. Use impedance information to find open or short circuits in the signal path, or to analyze the impedance of a transmission line at a specific point.

TDR works on the principle that for a mismatched system, at different points in the signal path, reflections will add or subtract from the signal source (constructive and destructive interference). If the system (in this case, the transmission line) is matched to 50 Ω, no emissions will occur on the signal path and the signal will remain the same. However, if the signal encounters an open circuit, the reflections will add to the signal, doubling it; if the signal encounters a short circuit, the reflections will cancel it out by subtracting it.

If the signal encounters a termination resistor with a value slightly above the correct matched impedance, a bump will be seen in the TDR response; if the termination resistor value is slightly below the matched impedance, a bump will be seen in the TDR response sunken. A similar response will be seen for capacitive or inductive termination, as the capacitor is shorted at high frequencies and the Inductor is open at high frequencies.

Of all the factors that affect the accuracy of the TDR response, the most important is the rise time of the TDR pulses sent along the signal path. The faster the rise time of the pulse, the smaller the features the TDR can resolve.

According to the rise time set by the TDR equipment, the shortest spatial distance between two discontinuities that the system can detect is:

(9)

in:

lmin = shortest spatial distance from source to discontinuity

c0 = speed of light in vacuum

trise = rise time of the system

εeff = effective permittivity of the medium in which the wave travels

A rise time of 20 ps to 30 ps is sufficient for detecting relatively long transmission lines, but a much faster rise time is required for detecting the impedance of an integrated circuit device.

Recording TDR impedance measurements can help resolve various issues in transmission line design, such as incorrect impedance,ConnectorDiscontinuities caused by junctions and welding related problems, etc.

**Accurately record S-parameters**

Once the PCB and system are designed and fabricated, the S-parameters must be recorded using the VNA at a set power and a range of frequencies; the VNA should be calibrated to ensure accurate recording. The choice of calibration technique depends on factors such as the target frequency range and the reference plane required by the device under test (DUT).

**Calibration technology**

Figure 4showA complete 12-term error model for a two-port system and its systematic effects and sources of error are presented. The measurement frequency range affects the calibration choice: the higher the frequency, the greater the calibration error. As more error terms become significant, calibration techniques must be changed to accommodate high frequency effects.

Figure 4. Complete two-port 12-term error model

A widely used VNA calibration technique is SOLT(Short, Open, Load, Transmission) calibration, also known as TOSM (Transmission, Open, Short, Match) calibration. It is easy to implement, requiring only a known set of standard components and measuring in both forward and reverse conditions. Standard components can be purchased with the VNA or from other manufacturers. Once the standard element is measured, the difference between the measured response and the known response can be determined to calculate the systematic error.

SOLT calibration locates the reference plane for VNA measurements at the end of the coaxial cable used during calibration. The downside of SOLT calibration is that any interconnects between reference planes, including SMA connectors and PCB traces, etc., can affect the measurement; these become larger sources of error as the measurement frequency increases. SOLT calibration can only remove the six error terms shown in Figure 4, but it provides accurate results for low-frequency measurements with the advantage of being easy to implement.

Another useful VNA calibration technique is TRL (transmission, reflection, line) calibration. This technique is based only on the characteristic impedance of short transmission lines. Using two sets of two-port measurements and two sets of reflection measurements where the two transmission lines differ from each other by a short length, a complete 12-term error model can be determined.A TRL calibration kit can be designed on the DUT’s PCB in order to utilize this calibration technique to eliminate errors caused by transmission line design and interconnects, and to transfer the measured reference plane from the coaxial cable.moveto the DUT pins.

Both calibration techniques have their own advantages, but TRL can eliminate more sources of error and thus provide higher accuracy for high-frequency measurements. However, TRL requires precise transmission line design and accurate TRL standard components at the target frequency, making it more difficult to implement. SOLT implementation is relatively simple, as most VNAs come with a SOLT standard kit that can be used over a wide frequency range.

**PCB Design and Implementation**

To properly calibrate a VNA, proper PCB design is critical. Techniques such as TRL can compensate for errors in PCB design, but cannot completely eliminate them. For example, when designing a PCB with TRL calibration, the value of S21 (such as the insertion loss of RF relays, etc.) must be very low. In order to accurately measure S-parameters, it is necessary to consider the return loss of transmission standards (S11, S22). Return loss refers to the impedance difference Matching results in input power reflected back to the source. No matter how well designed the PCB traces are, there will always be some level of mismatch. Most PCB manufacturers can only guarantee an impedance matching accuracy of 5%, and even reaching this accuracy is difficult. This return loss can cause the VNA to indicate a larger insertion loss than actually exists because the VNA “thinks” it is sending more power to the DUT than it actually is.

As the required level of insertion loss decreases, it will be necessary to reduce the amount of return loss that the transmission standard contributes to the calibration. And the higher the measurement frequency, the more difficult it is to do this.

To reduce the return loss of the calibration standard designed by TRL, there are several points that need special attention. First, transmission line design is very important and requires close coordination with the PCB manufacturer to ensure that the correct design, materials and processes are used to achieve the desired impedance versus frequency profile. The choice of connecting device is critical and must be able to operate satisfactorily within the relevant range. After selecting the connection device, it is also necessary to ensure that the junction between the connector and the PCB is well designed, otherwise it may destroy the required 50 Ω impedance between the coaxial cable and the PCB transmission line, resulting in increased system return loss. big. Many connector manufacturers provide proper layout drawings for high-frequency connectors, as well as pre-engineered transmission line designs and PCB stack-ups. Finding a PCB manufacturer that can produce this design can greatly simplify PCB design work.

Secondly, it is important to consider the junction between the PCB assembly connector and the PCB transmission line, so the soldering of the connector will have a significant impact on the transition. A poorly connected or misaligned connector can disrupt the delicate balance between inductance and capacitance, affecting the impedance of the junction. Figure 5 is an example of a poorly soldered connector junction.

Figure 5. Poorly connected SMA

If the design procedure does not take into account the dielectric constant of the solder mask coating, it can also adversely affect the impedance of the transmission line. In low frequency PCBs, this is not a huge problem, but as frequencies increase, solder mask can be a problem.

To ensure that the return loss of the transmission trace is acceptable, it is necessary to measure the return loss with the VNA. Since the reference plane of the system is from connector to connector, SOLT calibration should be sufficient to measure transmission traces. Once the return loss performance of a transmission trace is determined, defects can be monitored by performing TDR on the trace. TDR shows the areas where the system deviates the most from the target impedance.

On the TDR curve, it should be possible to mark the specific part of the system that contributes the most to the deviation. Figure 6 shows a transmission line trace and its corresponding TDR curve. The impedance of certain sections can be located on the TDR curve to see which sections are causing the greatest return loss. As can be seen from the figure, the junction between the SMA and the transmission line deviates from 50 Ω, and the impedance of the transmission line itself is not very close to 50 Ω. In order to improve the performance of this PCB, some of the measures mentioned above need to be taken.

Figure 6. PCB vs TDR curve

**Using S-parameters**

S-parameters can provide many benefits when characterizing a DUT over a certain frequency range. In addition to showing gain, loss, or impedance matching at a certain frequency, S-parameters can be replaced by other forms such as Y-parameters (admittance parameters) to calculate physical parameters such as capacitance. The only difference between the Y-parameters and the S-parameters is that the former are derived with the target pin shorted (0 Ω) (Equations 5 to 8), while the latter are derived with a matched 50 Ω termination impedance. A practical measurement of the Y-parameter is possible, but it is more difficult to record than the S-parameter because it is very difficult to create a true short over a wide frequency range. Since broadband 50 Ω matching is easier to do, a better approach is to record the S-parameters and then convert the S-parameters to Y-parameters. This is possible with most modern RF software packages.

**Calculate physical parameters**

As an example of using S-parameters to calculate capacitance over a target frequency range, consider the RF relay shown in Figure 1. In order to calculate the capacitance of the relay to ground when the relay is open (ie, open), the S-parameter records must first be converted to Y-parameters, that is, the data in the 50 Ω environment is converted to the data in the short-terminated case. It is obvious from the physical structure of the relay that when the output port is grounded and the switch is open, the capacitance to ground can be known by checking the Y11 parameter, which measures the amount of power sent back to the signal source. When the switch is open, all power should be reflected back to the source, but in reality, some power goes to the output port that is grounded (required by the Y parameter), and this power is transferred to ground through the capacitor. Therefore, divide the imaginary part of the Y11 parameter by 2πf to get the capacitance of the RF relay to ground at the target frequency.

To calculate the inductance of an RF relay, a similar method can be used, but this time the Y parameter needs to be replaced by the Z (impedance) parameter. The Z parameter is similar to the S and Y parameters, but instead of using impedance matching or shorts, an open circuit is used to define the termination. With a little thought, this method can be applied to all devices to calculate many different physical parameters.

**matching network**

Another application of S-parameters is the design of matching networks. Many applications require impedance matching to ensure optimal power transfer at a certain frequency. Using S-parameters, the input and output impedance of the device can be measured, and the S-parameters can then be displayed on a Smith chart and an appropriate matching network can be designed.

**Provide models to customers**

As mentioned above, because S-parameters are widely applicable, S-parameter files can be used to provide users with input and output information of linear circuits and fully characterize devices over a wide frequency range without disclosing complex or proprietary designs. Customers can use S-parameters to build device models in their systems in a similar way as described above.

**concluding remarks**

S-parameters are a useful tool for creating and validating high-frequency models over a wide bandwidth. Once recorded, S-parameters can be used to calculate many other circuit characteristics, as well as create matching networks. However, there are some necessary considerations that must be taken into account when designing a measurement system, the most important of which are the choice of calibration method and PCB design. Some potential problems can be avoided by taking the measures described in this article.

references

Rako, Paul. “TDR: taking the pulse of signal integrity.” EDN, September 3, 2007.

Bowick, Chris, John Blyler, and Cheryl Ajluni. RF Circuit Design. Newnes. 2007.

About the Author

Joseph Creech ［[email protected]］ Graduated from University of Cork in Ireland in 2005 with a bachelor’s degree in engineering. He has worked for 6 years in the design evaluation department of the RPS group at Analog Devices.

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