lecture29_lumpedvsdistributed

7/17/2019 Lecture29_LumpedVsDistributed

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Lumped Versus Distribut

Circuit Elements



Lumped Circuit Elements

resistor

capacitor

inductor

independent sources

dependent sources

Lumped Vs Distributed



Lumped Circuit Element Models

Lumped circuitelements are defined

by ordinary, linear ,

constant-coefficient

differential equations.


L +

-

v(t)

i(t)

d

di Lt v

)( =



Circuit Analysis for Lumped Circuits

The differential equations obtained for thusing KVL and/or KCL (i.e., loop or noda

analysis in!ol!e only one !ariable" time.

#e are really assuming that the entire ci

at a single point in space, or equi!alentlythe tra!el time of the electric signal is neg




Distributed Circuit Elemen

$ distributed circuit is one for %hictra!el time of the electric signal be

the components cannot be neglec

The !oltages and currents in suchcircuit are functions of position as %

as time.




Lumped Versus Distributed Circuit Eleme

&oints of !ie% for determining %hethecircuit should be considered 'lumpe

'distributed"

)ise time !ersus tra!el time &eriod !ersus tra!el time

Component si*e !ersus %a!elength




Rise time ( RT ) is the time requiredthe signal to change from +- to

of its final !alue.

Travel time or delay time (TD) is thone%ay propagation delay throu

signal path.

Rise Time Versus Travel T





TD = l/v p %here l is the length of thesignal path and v p is the !elocity of

propagation.

)ule of thumb" RT/TD > 10 ⇒ definitely lumped

RT/TD < 1 ⇒ definitely distributed





The spatial e0tent of the +--time is gi!en by

1f d < l , %e definitely need to model

circuit as distributed.


pv RT d ⋅=





1 nsTD =



Period Versus Travel Time

The period (T ) of a sinusoidal signal is gi!en by

%here f is its frequency.

)uleofthumb"

TD/T < 0.01 ⇒ definitely lumped

TD/T > 0.1 ⇒

definitely distributed

This ruleofthumb is only useful for narro% band pass signals %ith

a %elldefined carrier frequency %hose period can be used in its

application.




Component Size Versus avele

)ule of thumb"

l/ λ < 0.01 ⇒ definitely lumped

l/ λ > 0.1 ⇒ definitely distributed

%here l is the largest dimension of the compone

=c/f is the %a!elength

This ruleofthumb is only useful for narro% band pass signals %ith

a %elldefined carrier frequency %hose %a!elength can be used in

its application.




Electroma!netic Compon

Lumped components %ith all dimensions much smaller than λ.

resistors, capacitors, inductors

Distributed components %ith one dimension either comparable t

than λ, and other dimensions much smaller than λ.

coa0ial cables, hollo% %a!eguides

Distributed components %ith dimensions on the order of λ

most antennas Distributed components %ith all dimensions much greater than λ

graded inde0 optical fibers, reflector antennas


lecture29_lumpedvsdistributed

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