1. Smith Chart & Matching
Anurag Nigam

2. NatTel Microsystems Pvt. Ltd.
Tutorial 4
Day1
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3. NatTel Microsystems Pvt. Ltd.
Lab Objectives
In this lab exercise we will
Modify UMS PH15 Process Substrate to accommodate Air Bridge and Open Substrate at the bottom to simulate distributed ground condition.
Simulate single and two via inductances
Design a small signal tuned gain stage with effect of via inductance included in performance
Design 50Ω and Non 50Ω Planar Lines
Visualize Currents in Planar Lines
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4. NatTel Microsystems Pvt. Ltd.
Telegraph Equations
Passive Structures used for transmission of Microwave Signals in Microwave Circuits are called Transmission Lines.
Various Forms of Transmission Lines are Microstrip, Strip & Slot Lines, Coplanar Waveguides, Twisted Pair Wire and Coaxial Lines.
Equations governing Voltage and Current Relationship at any point on Transmission Line are called Telegraph Equation.
R Series Resistance of both the conductors per unit length (/m)
L Series Inductance of both the conductors per unit length (H/m)
G Shunt Conductance between two conductors per unit length (S/m)
C Shunt Capacitance between two conductors per unit length (C/m)
z Small section of transmission line (m)
For Sinusoidal Voltage and Current
Writing Kirchhoff's Voltage and Current Equations for the L-Section
Using both equations &
Solution
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5. Electrical Characteristics of Transmission Line
Characteristic Impedance
Phase Constant
Attenuation Constant
Phase Velocity
For a Lossless Line R=0 & G=0
Wavelength
Cut-off Frequency
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6. Characteristic Impedance of a Transmission Line
Characteristic Impedance of a Line is impedance, termination into which at the load side results in same impedance looking into the line at the source side.
Transmission Line
Characteristic Impedance
In case of Termination of Line into non-characteristic impedance load, Power gets partially reflected and transmitted at the interface.
If then
z=0
Transmission Line1
Transmission Line2
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7. Incident, Reflected & Transmitted Waves
Transmission Line1
Transmission Line2
z=0 z
Ratio of Reflected Voltage to Incident Voltage at the Reflection Plane is Reflection Coefficient
Ratio of Transmitted Voltage to Incident Voltage at the Interface is Transmission Coefficient
z=0 z
Voltage Waveform
Current Waveform
Incident Waveform
Reflected Waveform
Transmitted Waveform
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8. Incident Reflected & Transmitted Power
z=0
Return Loss
Insertion Loss
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9. Introduction to Smith Chart
Let be load impedance into which transmission line with Characteristic Impedance is terminated.
Load Impedance normalized to Characteristic Impedance of the line is given by
Constant Resistance Circles
Equating real & imaginary parts as
Reflection Coefficient
Impedance & Admittance Chart
Constant Reactance Circles
Normalized Load Impedance
Admittance Chart for Shunt Elements
Impedance Chart for Series Elements
Constant shunt Capacitance Circles
Constant series Inductance Circles
Constant shunt Resistance Circles
Constant series Resistance Circles
Constant shunt Inductance Circles
Constant series Capacitance Circles
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10. Voltage Standing Wave Ratio (VSWR)
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