Notes4_Sparams - ECE145A/218A Notes Set#4 1 2Port...

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ECE145A/218A Notes Set #4 1 Rev.11/07 Prof. S. Long/ECE/UCSB 2–Port Parameters Two-ways of describing device:A. Equivalent - Circuit-Model Physically based Includes bias dependenceIncludes frequency dependenceIncludes size dependence - scalabilityIdeal for IC designWeakness: Model necessarily simplified; some errors. Thus, weak for highly resonant designsB. 2–Port Model Matrix of tabular data vs. frequencyNeed one matrix for each bias point and device sizeClumsy – huge data sets requiredTraditional microwave methodExact2 Port descriptionsThese are black box (mathematical) descriptions. I1I2V2V1++port 1port 2Inside might be a transistor, a FET, a transmission line, or just about anything. The terminal characteristics are V1V2I1& I2– there are 2degrees of freedom.
ECE145A/218A Notes Set #4 2 Rev.11/07 Prof. S. Long/ECE/UCSB Admittance Parameters I1I2=Y11Y12Y21Y22V1V2Example: Simple FET Model CgdgmVgsVgsRdsCgs+By inspection: Y=jωCgs+jωCgdjωCgdgmjωCgdGds+jωCgdEasy! 111112120021VVIIYYVV====
ECE145A/218A Notes Set #4 3 Rev.11/07 Prof. S. Long/ECE/UCSB Impedance Parameters V1V2=Z11Z12Z21Z22I1I2Example R1R3R2By inspectionZ=R1+R3R3R3R2+R3121121110022IIVVZZII====But, y, z, and hparameters are not suitable for high frequency measurement. Problem: How can you get a true open or short at the circuit terminals? Any real short is inductive. Any real open is capacitive. To make matters worse, if you are trying to measure a high freq. active device, a short or open can make it oscillate! Solution: Use termination in Z0instead! Broadband. Not very sensitive to parasitic L,C Kills reflections. Redefine parameters to use fwd. and rev. voltage waves. Measurement can use directional couplers.
ECE145A/218A Notes Set #4 4 Rev.11/07 Prof. S. Long/ECE/UCSB S–Parameters input reflection coeffrev. transm. gainfwd transm. gainoutputa1=0a2=0a2=0Γa1=0b1b2=S11S12S21S22a1a2Note that Z0must be defined. We don’t really need transmission lines. Our objective now is to de-mystify S-parameters – they are easy!Recall V(x)=V+(x)+V(x) phasor quantities.I(x)=V+(x)Z0V(x)Z0amplitude, not rms values.We can normalize the amplitude of waves to Z0: a(x)=V+(x)Z0forward waveb(x)=V(x)Z0reverse waveWhy? So that 12a(x)a*(x)=power in forward wave. if a=1.414then power in wave is 1 watt. (or arms=1) Z0Z0a1a2b2b1z=0z=0ZoZoZ0Z0a1a2b2b1z=0z=0ZoZo
ECE145A/218A Notes Set #4 5 Rev.11/07 Prof. S. Long/ECE/UCSB likewise, b(x)b*(x)/2 is the power in the reverse wave So, in terms of total voltage V(x) and current I(x), v x( )=V x( )Z0=a x( )+b x( )i x( )=Z0I x( )=a x( )b x( )or, [][][][])()(21)()(21

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