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# 654_ch1 - ECE 654 Solid State Devices II Prof S Mohammadi 1...

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Unformatted text preview: ECE 654 Solid State Devices II Prof. S. Mohammadi - 1 - ECE 654: Solid State Devices II Chapter I Power Gains, and Stability Analysis of Microwave Transistors Introduction We start our discussion by introducing Smith Chart which is the plot of reflection coefficient in the complex plain. Then we will discuss the importance of interconnects and the parasitics they introduce on the performance of a microwave transistor. Finally we will discuss various gain definitions as well as the concept of stability, device cut off frequency and maximum oscillation frequency. Smith Chart normalized impedance characteristic impedance 1 1 1 1 Z Z L L +- = +- = +- = Γ nL nL L L Z Z Z Z Z Z Z Z rt ω Smith chart is the plot of in complex plane Γ relationship between and Z is a bilinear transformation Γ circle remain circle when they are mapped Impedance Plane ( ) Z Im ( ) Z Re Γ- Plane ( ) Γ Im ( ) Γ Re mapping of constant resistance until circle corresponds with imaging axis in impedance plane with respect to Note: Γ (the reflection coefficient) is defined as the ratio of reflected to incident signals. ECE 654 Solid State Devices II Prof. S. Mohammadi - 2 - mapping of constant reactance 3 = χ 1 = χ 3 1 = χ = χ 3- = χ 1- = χ 3 1- = χ 3 = χ 1 = χ 3 1 = χ = χ 3- = χ ( ) Im = Z arc of circle ( ) Γ Im ( ) Γ Re ( ) Z Im ( ) Z Re Smith Chart 1- = Γ short circuit inductive capacitive ( m a t c h e d ) ⇒ = Γ 1 open circuit orthogonal unit circle-½ ½ Note that for Γ =0, there is no reflected wave (matching condition to Z ). For an impedance Smith chart, the bottom half of the circle represents capacitive impedances while the top half is associated with inductive impedances. Positive real values of impedance (positive resistances) reside inside the unity circle while negative resistances go outside of the circle. It is also possible to draw Smith chart for admittances. In this case the locations of open and short and capacitive and inductive areas are reversed. ECE 654 Solid State Devices II Prof. S. Mohammadi - 3 - Smith chart can be used to calculate impedance transformation You can graphically find the transformed impedance d d Z , L Z in Z ) ( d Γ to do so in nin in L j L nL nL L Z to it convert Z find find to d length electrical the twice by rotate clockwise e identify chart smith the on Z locate Z Z rt Z normalize * * ) 2 ( ) ( * * * ) ( * Γ Γ Γ = Γ- β ω θ ( ) length electrical d e d e x d j L x L : ) ( ) ( 2 2 β β γ-- Γ = Γ Γ = Γ loss less * example Ω + = 60 30 j Z L connected to 50 TRL impedance Ω TRL : 2cm length @ 2GHz assume phase velocity 50% of the speed of light ( ) Ω- = Γ- Γ + = ⋅ =-- = Γ = Γ ° = = = = = = = Γ ⋅ = + = + +- + = +- = Γ °--- ° 7 . 26 7 . 14 1 1 4 . 55 . 32 ....
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654_ch1 - ECE 654 Solid State Devices II Prof S Mohammadi 1...

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