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 (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)]VinV1

-/ V1+ =(Zin-RS)/(Zin+RS)

One-Port S-Parameter

Series RLC with resonant frequency at

Resistance at resonant frequency: RL

Design a Series RLC Resonant Circuit

RL=50 ΩL1=2.4 mHRS=50 Ωfres=1 MHz

What is C1?

Design a Series RLC Resonant Circuit

RL=50 ΩL1=2.4 mHRS=50 Ωfres=1 MHz

What is C1?C1=1/(Lω2

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: V1

++V1-

Actual voltage measured at the output of the two-port network: V2

++V2-

Incident wave into the output port or wave reflected from RL

S11

S11

S12

S12

S22

S22

S21

S21

Y-Parameters

Yo=1/Zo

Calculate Y-Parameters Using ADS

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 finelyground (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 arisesout 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.

(Partially exposed)

Generic Resistor Model

Example8.7 nH 8.7 nH10K

0.3 pF

At 200 MHz

Impedance associated inductor is negligible

A 10 Kohm resistor looks like a 2564.3 resistor at 200 MHz.

Insert an Equation in ADS

Impedance at 200 MHz

10 KohmAt 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 leadsRp: 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/(2πfL) =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

Additional Slides

Metal Film Resistor

Thin-Film Chip Resistor