EMC concepts explained
Capacitor Impedance Evaluation from S-Parameter Measurements
Part 1: S11 One-Port Shunt, Two-Port Shunt and Two-Port Series Methods
T
his is the first of two articles devoted to the topic of capacitor impedance evaluation from the s parameter measurements using a network analyzer. Part 1 describes the impedance measurements and calculations from the s11 parameter using the one-port shunt method, two-port shunt, and two-port series methods. Part 2 will discuss impedance measurements and calculations using the s21 parameter with two-port shunt and two-port series methods.
Configurations, Circuit Models, S11 – Impedance Relationships
One-Port Shunt Method
Note: The one-port shunt method is also called a (one-port) reflection method [1]. One-port configuration for a two-terminal DUT is shown in Figure 1.
Figure 1: One-port shunt configuration
Figure 2 shows the transmission line circuit model at Port 1.
Figure 2: Transmission line circuit model of one-port shunt configuration
The network analyzer sends the incident waves (at different frequencies) to Port 1, terminated with Zx (interconnects are taken out of the measurements through the calibration process).
Upon the arrival at load Zx, the incident waves get reflected (unless the load impedance Zx equals Z0). The reflected voltage waves, vr, are related to incident voltage waves, vi, by the load reflection coefficient, Γ, defined as
This load reflection coefficient equals the s11 parameter and can be computed from [2],
Eq. (1) is used to obtain the DUT impedance in terms of s11 parameter, as follows
Resulting in the DUT impedance in terms of the s11 parameter as [1],
Two-Port Shunt Method
The two-port shunt configuration for a two-terminal DUT is shown in Figure 3.
Figure 3: Two-port shunt configuration
The simplified circuit model of this shunt configuration is shown in Figure 4.
Figure 4: Transmission line circuit model of two-port shunt configuration
Note that the DUT impedance Zx is in parallel with the Port 2 impedance Z0, resulting in an equivalent load impedance of
The s11 parameter equals the load reflection coefficient and can be computed from
Utilizing Eq. (8) in Eq. (9) we get
or
which simplifies to
Eq. (13) is now solved for Zx in terms of s11.
or
resulting in
Two-Port Series Method
The two-port series configuration for a two-terminal DUT is shown in Figure 5.
Figure 5: Two-port series configuration
The simplified circuit model of this series configuration is shown in Figure 6.
Figure 6: Transmission line circuit model of two-port series configuration
Note that the DUT impedance Zx is in series with the Port 2 impedance Z0, resulting in an equivalent load impedance of
The s11 parameter equals the load reflection coefficient and can be computed from
Utilizing Eq. (18) in Eq. (19) we get
or
Eq. (21) is now solved for Zx in terms of s11.
or
resulting in
Impedance Measurement Setup and Results
The impedance measurement setup and the PCB boards are shown in Figure 7. The boards were populated with Murata X7R ceramic capacitors, GCM188R71H472KA37, GCM188R71H473KA55, GCM188R71C474KA55, of the values 4.7 nF, 47 nF, and 470 nF, respectively.
Figure 7: Measurement setup and PCBs
Impedance curves for a 47 nF capacitor are shown in Figures 8 and 9. Figure 8 compares the results between the one-port shunt and two-port shunt configurations, while Figure 9 compares the two-port series and two-port shunt configurations.
Figure 8: S11-based impedance curves – one-port shunt (Eq. 7) vs. two-port shunt (Eq. 17)
Figure 9: S11-based impedance curves – two-port series (Eq. 26) vs. two-port shunt (Eq. 17)
Clearly, the two-port series measurement is not reliable. Figure 10 shows the capacitor impedance curve obtained from the Murata Design Support Software “SimSurfing” [3].
Figure 10: Murata “SimSurfing” impedance curve for 47 nF capacitor
The one-port shunt, two-port shunt and Murata measurements at 0 dB and at self-resonant frequencies are shown in Table 1.
Table 1: Impedances at 0 dB and self-resonant frequencies
Clearly, the one-port shunt and two-port shunt measurements do not agree with the Murata values. The measurement results for the other two capacitors (4.7 nF, 470 nF), not presented here, showed similar trends.
The overall conclusion is that the capacitor impedance evaluation from s11 parameter measurements is not accurate. The next article will discuss the capacitor impedance estimation from s21 parameters and show its superiority over the s11-based methods.
References
- Microwaves & RF Application Note, Make Accurate Impedance Measurements Using a VNA. https://www.mwrf.com/technologies/test-measurement/article/21849791/copper-mountain-technologies-make-accurate-impedance-measurements-using-a-vna
- Keysight Application Note, Impedance Measurements of EMC Components with DC Bias Current. https://www.keysight.com/us/en/assets/7018-01969/application-notes/5989-9887.pdf
- Murata Design Support Software “SimSurfing.” https://ds.murata.co.jp/simsurfing/index.html?lcid=en-us
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Dr. Bogdan Adamczyk is professor and director of the EMC Center at Grand Valley State University (http://www.gvsu.edu/emccenter) where he performs EMC educational research and regularly teaches EM/EMC courses and EMC certificate courses for industry. He is an iNARTE-certified EMC Master Design Engineer. He is the author of two textbooks, “Foundations of Electromagnetic Compatibility with Practical Applications” (Wiley, 2017) and “Principles of Electromagnetic Compatibility: Laboratory Exercises and Lectures” (Wiley, 2024). He has been writing “EMC Concepts Explained” monthly since January 2017. He can be reached at adamczyb@gvsu.edu.
Patrick Cribbins is pursuing his Bachelor of Science in Electrical Engineering at Grand Valley State University. He currently works full time as an Electromagnetic Compatibility Engineering co-op student at E3 Compliance, which specializes in EMC and high-speed design, pre-compliance testing and diagnostics. He can be reached at patrick.cribbins@e3compliance.com.
Khalil Chame is pursuing his Bachelor of Science in Electrical Engineering at Grand Valley State University. He currently works full time as an Electromagnetic Compatibility Engineer co-op student at E3 Compliance, which specializes in EMC and high-speed design, pre-compliance and diagnostics. He can be reached at khalil.chame@e3compliance.com.