The concept of the S-parameter is the most intuitive approach to the microwave attributes of the interconnect or system, providing the most intuitive way to describe crosstalk from the application of the audio range to millimeter wave frequency range. The S-parameter is used in the measurement of RF components such as filters, amplifiers, mixers, antennas, isolators, and transmission lines. The measurement results determine that the radio frequency device is reflected and transmitted in a plurality of values (amplitude and phase) when transmitting signals forward and reverse. They fully describe the linear characteristics of the radio frequency element.
First, introduction
In serial data link analysis and evaluation using high-speed communication environments, applications require application, perform modeling, measurement, and simulation on real-time waveforms of real-time oscilloscopes. These applications are set to allow the user to load the circuit model for the test measuring fixture and instrument used to collect waveforms in the measurement device. Figure 1 shows a block diagram instance of such a link.
Figure 1. Schematic diagram of serial data link system modeling can be used using S parameter modeling.
The S parameter model is usually used in these systems. This paper discusses the problem involving the S parameter level, which provides an algorithm for preventing pseudo-signal and typical zero-filled interpolation possible insertion additional pulses.
Second, S parameter measurement
When you measure a S parameter set using a VNA or a Vector Network Analyzer, a sine wave incident signal is placed on a port. In order to obtain the reflection coefficient, the reflected sinusoidal amplitude and phase will be measured. All other ports must be used for reference impedance. The ratio of the reflected signal to the incident signal is represented as S11, S22, S33 ... until the total number of ports. Complete this operation with multiple frequencies. For transmission items, such as S21 in some configurations, a sine wave is placed on port 1, and measurements on port 2, the ratio of the reflected signal to the incident signal becomes S21. For coupling items and other transmission items, All other combinations of ports to port measurements. This applies to all other ports that use reference impedance termination, and reference impedance is usually 50 ohms. When this requires measurement, the sine wave is stable after all reflection and transmission stabilization.
You can also use the TDR step generator, the time domain reflectometer, or the time domain transmission TDT, and the S parameters are measured and calculated in the time domain. The step contains frequencies that are applied simultaneously to the measured device. The lower SNR is related to TDR / TDT compared to sweep sinusoidal measurement. This is mainly at higher frequencies, and the step signal has a smaller harmonic.
Frequency interval and time response cycle:
The frequency interval of being tested S-parameter data determines the number of samples until the desired sample rate of the time domain waveform is indicated in the system model environment. The smaller the frequency interval, the more the number of samples, the longer the S-parameter set. If the frequency interval is too large, the time interval is too short, the response has not been stable, then a false signal will occur. This can cause time domain signals to be reversed to incorrect position. Frequency domain amplitude response performance is correct, but the frequency domain phase response also displays a false signal. Determine the formula of the time interval is as follows:
Where: T is the time interval of the S-parameter set coverage, ΔF is the frequency interval. This reciprocal relationship indicates that the longer the covered interval t, the smaller the Δf. This causes the frequency resolution to be more refined, causing the number of frequency domain samples to increase until the desired sample rate frequency.
The parameter fs represents a sampling rate. Covering DC until the number of frequency domain samples in the FS range is equal to calculating the number of time domain samples when IFFT gets time domain responses. Therefore, when the sampling rate is constant, the smaller the Δf, the longer the time interval.
Cascaded S parameters and false signals:
The S parameter module level is a critical operation in the serial data link emulation and analysis environment. To understand multiple problems involved, look at the cascade shown in Figure 5, where three module levels are connected together. The model of the model in each module is represented by a S-parameter set of 1.69 m. To calculate the transfer letter of the system test point, it is necessary to combine multiple cascading modules into one module. In the 3 modules, the S parameter of each module is the same. In addition, we assume that the switch to each S parameter set in the time domain is fully stable in the time domain.
If there is no S-parameter interpolation, then the time interval T covered by the last cascade S-parameter set will be the same as each module. Therefore, if the total latency of the 3 cascade is larger than the time interval covered by each module, the false signal will occur. In the time domain, the false signal causes the pulse response characteristic to occur at the time position of the error, and the timing may reverse. This is derived from the phase fake signal in the time domain, where the phase vector is less than two samples per rotation.
Cascaded S parameter example:
To explain the problem in more detail, look at the 2-port S parameter model with loss, a uniform 1.69 m cable, where 40 ohms are produced on the circuit emulator. The S-parameters spacing at 50 MHz until 25 GHz are saved to a file. According to the formula (1), this interval corresponds to the time interval of 20 ns.
Figure 2. Schematic diagram of the Z0 characteristic impedance of 40 ohms 1.69 m.
Figure 3. S11 and S21 S parameter diagram of a single 1.69 m cable model. Amplitude (DB) to the frequency (GHz).
The frequency sound diagram of this model 2 port S parameter set is shown. Note that the attenuation of S21 at 25 GHz is about -6 dB. Therefore, if the three uniform cable levels are connected, the resulting attenuation is -18 dB at 25 GHz.
Now, we transform the S parameter vector to time domain, as shown in Figure 4 below. This is to create a resolved conjugate portion from Nequist to the sampling rate, and use the S parameter data of the riist value when the Sample value is used from DC until 1/2 sampling rate, and then calculates when the IFFT.2 port S parameter is calculated. The domain version will be represented as T11, T12, T21, and T22.
Figure 4. Single 1.69 M cable model S parameter set T11 and T21 time domain diagrams. Amplitude to time (NS).
Note that in the T21 diagram, the delay of a cable can be seen. The delay is 7.971 ns. There are multiple round-back reflection to the port 2, but it is too small, it can't see it. The 50MHz interval of the S parameter of this cable results in a total interval T of 20 ns. This is enough when the 7.971 NS insertion of the cable is inserted.
Since the resistance value of the cable Z0 is 40 ohms, the reference impedance of the S parameter is 50 ohms, so there will be a reflection at the beginning and end of the cable, and there will be several other back-reflexed reflection. For T11, the reflection time is at the beginning of the record, and therefore reflects when the signal is transferred back and forth, and when the time is twice the multiple times, the reflection will occur. Therefore, the first place to reflect in 15.94 ns. Other returns are very small, so I can't see it. In this example, 20 ns time T is very long enough to support this first back reflection transfer time.
Figure 5. Schematic diagram of the circuit emulator that is three-line-upless circuit emulators that is exactly the same 1.69 m cable model.
Another thing to pay attention is that due to the 50 ohm reference impedance and the 40 ohm characteristic impedance of the cable does not match, there is also a reflection at the cable input at time zero. Since the S-parameter is converted to the leakage and cycle characteristics of the IFFT, the part of this pulse is reversed to the end of the time recording. This is an important detail when the S-parameter set is performed, and when using zero filling in the time domain.
Now look at these three exact S-parameter collars, assuming that the frequency interval is still 50 MHz to 25 GHz, the total time T is 20 ns. This circuit is obtained from the circuit emulator shown above. The frequency domain amplitude map shown in Figure 6 is consistent with the expected, and the S21 of the three cables is -18 dB at 25 GHz, and a cable is -6 dB.
Cascaded S parameter sets are transformed into time domain, as shown in Figure 7. These figures show the influence of the phase hypotaxial signal, resulting in a time domain pulse is not in the correct time position. A cable has a delay of 7.971 ns, so the latency of the three cable levels should be 23.9 ns, and since this delay is longer than the time T of the S-parameter set 20 ns, a false signal will occur. This can be seen in the T21 curve, and the impulse response is at 3.918 ns, not 23.9 ns. Look at T11, it can also be seen that the anti-influence signal is offset to the position of ~ 7.8 NS, and its position should be at ~ 47.8 ns. This is the time transmitted from the port 1 to the port 2, and then transmits back to the time used.
Third, S parameter interpolation algorithm
The respective S parameters of each module must be re-sampling to provide a smaller frequency interval, gain a higher time interval for combined S parameters.
Figure 6. The three cascading cable modules are combined with S11 and S21 S parameters. Amplitude (DB) to the frequency (GHz).
You can take a variety of ways to perform another way. For example, one way is to perform an interpolation in the frequency domain. This can be done by the interpolation real part and the imaginary part, or by the interpolation amplitude component and the phase component. This can be implemented using a linear interpolation, but will result in significant errors, unless the frequency interval is sufficiently small. Use higher order interpolation to improve higher frequencies, but may introduce transient errors in the start frequency and end frequency, in the start frequency and end frequency, there is no continuous point in the data set.
The following procedures provide certain advantages for performing interpolation and re-sampling algorithms:
1. If there is no DC value of the S parameter, all S parameter data vector will be inferred. There is no DC value from the S parameter measured from the VNA. The S parameter measured using TDR / TDT has a DC value.
Figure 7. Integrate 3 Class Cable Modules to a T11 and T22 Timeabata of the S-Parameter Set. Note that the pulse offset in T21 is removed to a delayed position of 3.918 NS, which should be in 23.9 ns.
2. Determine all the common maximum frequencies of all S parameter sets. This value can be the maximum frequency of all S parameter sets in cascading. The set of each S parameter is inferred to the frequency exceeding the maximum common frequency.
3. Use the IFFT to convert the inferred frequency domain S parameter to obtain the time domain pulse response.
4. Determine the actual public sampling cycle between pulse responses. The actual public sampling cycle can be obtained as the minimum sampling period of the pulse response. Then sampling the pulse so that it has the same sample rate.
5. The correct position is zero filling pulse response, as described below, a higher time interval. Improved time intervals can be determined as the sum of all time intervals indicated by each S parameter set. This requires that each S parameter set in the cascade does not have a false signal.
Radio frequency
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