Characterization of Circuit Components Using S-Parameters

1. Characterization of Circuit Components Using S-Parameters Chapter 1

2. Topic • S-Parameters • S1P • S2P • Y-Parameters • Components • Wires • Inductors • Resistors • Capacitors • S-parameter Extraction

3. One-Port S-Parameter Incident wave (V1+) is Vin/2 (as if Zin=RS) Voltage at the input of the receiver is Zin/(Zin+RS)Vin Vin=V1-+V1+ V1-=Vin -V1+ V1-= Zin/(Zin+RS)Vin- Vin/2 =(Zin-RS)/[2(Zin+RS)]Vin V1-/ V1+ =(Zin-RS)/(Zin+RS)

4. One-Port S-Parameter Series RLC with resonant frequency at Resistance at resonant frequency: RL

5. Design a Series RLC Resonant Circuit RL=50 Ω L1=2.4 mH RS=50 Ω fres=1 MHz What is C1?

6. Design a Series RLC Resonant Circuit RL=50 Ω L1=2.4 mH RS=50 Ω fres=1 MHz What is C1? C1=1/(Lω2res)

7. One-Port S-parameter Power reflected to the source Power delivered to the load

8. Two-Port S-parameter Incident wave into the output port or wave reflected from RL Incident Wave generated by Vin Reflected wave Actual voltage measured at the input of the two-port network: V1++V1- Actual voltage measured at the output of the two-port network: V2++V2-

9. S11

10. S11

11. S12

12. S12

13. S22

14. S22

15. S21

16. S21

17. Y-Parameters Yo=1/Zo

18. Calculate Y-Parameters Using ADS

19. Wires • In the AWG system, the diameter of a wire will roughly double every six wire gauges. E.g.

20. Skin Effect (Eddy Current)

21. Skin Depth The skin depth is thus defined as the depth below the surface of the conductor at which the current density has fallen to about 37% of its surface current density.

22. Inductance of a Straight Wire • breadboard wire: 22 AWG or 25.3 mils in diameter. • Each mil =25.4 um or 0.0643 cm. • 5 cm of a No. 22 copper wire produce about 50 nH of inductance.

23. Resistors • Carbon-composition resistor • Wirewound resistor • Carbon-film resistor

24. Carbon-Composition Resistors Carbon composition resistors consist of a solid cylindrical resistive element with embedded wire leads. The resistive element is made from a mixture of finely ground (powdered) carbon and an insulating material (usually ceramic). The resistance is determined by the ratio of the fill material (the powdered ceramic) to the carbon. Higher concentrations of carbon, a good conductor, result in lower resistance. The parasitic capacitance arises out small capacitance between carbon fill. More expensive than carbon film resistor.

25. Wirewound Resistors • Wirewoundresistors are commonly made by winding a metal wire around a ceramic core. • The inductance is much larger than a carbon composition resistor • Poor temperature drift coefficient • Too much L and C to be useable at high frequencies

26. Carbon Film Resistor • Less expensive than carbon-composition resistors • Can drift with temperature and vibration • A carbon film is deposited on an insulating substrate, and a helix is cut in it to create a long, narrow resistive path. (Partially exposed)

27. Generic Resistor Model

28. Example 8.7 nH 8.7 nH 10K 0.3 pF Impedance associated inductor is negligible At 200 MHz A 10 Kohm resistor looks like a 2564.3 resistor at 200 MHz.

29. Insert an Equation in ADS

30. Impedance at 200 MHz 10 Kohm At DC

31. Extract Resistance from Y11 R=1/(0.0001) =10 KΩ

32. Extract Capacitance (1) Slope is constant!

33. Extract Capacitance (2) C=Y11imag_deriv/2/π=1.88 pF/2/3.1416=0.2992 pF

34. Generic Equivalent Circuit for a Capacitor L: inductance of the leads Rp: account for leakage current

35. Quality Factor of a Simplified Capacitance Model Quality factor= Im[Z]/Re[Z] =1/(ωRC)

36. Generic Equivalent Circuit for an Inductor Series resistance +skin resistance

37. Extraction Example

38. Parasitic Resistance of an Inductor R=1/0.033=30.3 Ω

39. Inductance Extraction L=R/(2πfL) =29.73 nH

40. Parasitic Capacitance of an Inductor Capacitance: 117.14 fF

41. Quality Factor of a Simplified Inductor Circuit Model Q=Quality factor= Im[Z]/Re[Z] =(ωL) /(R) Larger Q, better inductor

42. Additional Slides

43. Metal Film Resistor

44. Thin-Film Chip Resistor