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

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Characterization of Circuit Components Using S-Parameters Chapter 1

Topic S-Parameters – S1P – S2P Y-Parameters Components – Wires – Inductors – Resistors – Capacitors – S-parameter Extraction

One-Port S-Parameter Incident wave (V 1 + ) is V in /2 (as if Z in =R S ) Voltage at the input of the receiver is Z in /(Z in +R S )V in V in =V 1 - +V 1 + V 1 - =V in -V 1 + V 1 - = Z in /(Z in +R S )V in - V in /2 =(Z in- R S )/[2(Z in +R S )]Vin V 1 - / V 1 + =(Z in- R S )/(Z in +R S )

One-Port S-Parameter Series RLC with resonant frequency at Resistance at resonant frequency: R L

Design a Series RLC Resonant Circuit R L =50 Ω L1=2.4 mH R S =50 Ω f res =1 MHz What is C1 ?

Design a Series RLC Resonant Circuit R L =50 Ω L 1 =2.4 mH R S =50 Ω f res =1 MHz What is C 1 ? C 1 =1/(Lω 2 res )

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

Two-Port S-parameter Reflected wave Incident Wave generated by Vin Actual voltage measured at the input of the two-port network: V 1 + +V 1 - Actual voltage measured at the output of the two-port network: V 2 + +V 2 - Incident wave into the output port or wave reflected from R L

S11

S12

S22

S21

Y-Parameters Y o =1/Z o

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

Skin Effect (Eddy Current)

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.

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.

Resistors Carbon-composition resistor Wirewound resistor Carbon-film resistor

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.

Wirewound Resistors Wirewound resistors 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

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.helix (Partially exposed)

Generic Resistor Model

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

Impedance at 200 MHz 10 Kohm At DC

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

Extract Capacitance (1) Slope is constant!

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

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

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

Generic Equivalent Circuit for an Inductor Series resistance +skin resistance

Extraction Example

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

Inductance Extraction L=R/(2πf L ) =29.73 nH

Parasitic Capacitance of an Inductor Capacitance: 117.14 fF

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