### S2P, Parameter extraction

```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)]Vin
V1-/ 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 Ω
L1=2.4 mH
RS=50 Ω
fres=1 MHz
What is C1?
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)
One-Port S-parameter
Power reflected
to the source
Power delivered
Two-Port S-parameter
Incident
Wave generated by Vin
Incident
wave into the output
port or wave reflected
from RL
Reflected
wave
Actual voltage measured at
the input of the two-port network: V1++V1Actual voltage measured at
the output of the two-port network: V2++V2-
S11
S11
S12
S12
S22
S22
S21
S21
Y-Parameters
Yo=1/Zo
Calculate Y-Parameters Using
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.
(Partially exposed)
Generic Resistor Model
Example
8.7 nH
10K
8.7 nH
0.3 pF
Impedance
associated
inductor is negligible
At 200 MHz
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
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/(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