Tutorial 7 Transfer Functions

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University of Miami *

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Electrical Engineering

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Oct 30, 2023

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Tutorial 7 Transfer functions 𝑍𝑍𝑍 + 𝑍𝑍𝑍 = 𝑍 + 𝑍 𝑆𝑆 = 𝑆𝑆 + 𝑍 𝑆𝑆 Z3 and Z4 are in parallel… Z1 and Z2 are in series… 1 1 1 1 1 1 1 1 1 1 1 1 4 1 3 1 1 + = + = + = + = S ZT S ZT S ZT Z Z ZT Develop output equation
Vin s s s s Vout Vin Z Z Z Vout . 1 1 1 1 1 . 2 1 2 + + + + = + = Simplify denominator ) 1 ( 1 3 ) 1 ( 1 ) 1 )( 1 ( 2 + + + = + + + + s s s s s s s s s 1 3 1 . 1 3 . 1 3 ) 1 ( . 1 1 . ) 1 ( 1 3 1 1 2 2 2 2 + + = = + + = + + + + = + + + + = ∴ s s Vin Vout s Vin as Vin s s s Vout Vin s s s s s Vout Vin s s s s s Vout
A thermometer is used to measure the temperature of an industrial oven. The thermometer temperature (τ) has a 2s time delay and the oven temperature (V oven ) is set to ramp at a rate of 3 o 𝑠𝑠 −1 The system can be modelled by the following. oven m m V V dt dV = + τ Where τ is the thermometer temperature V m is the current oven temperature V oven is the final oven temperature Develop an s-domain transfer function for the system What do you know? If V m = 0, τ = 2 seconds From look-up tables, a ramp input is 𝑎𝑎 𝑠𝑠 2 2 3 ) ( ) ( 2 s s V s sV m m = + 2 3 ] 1 2 )[ ( s s s V m = + ) 1 2 ( 3 ) ( 2 + = s s s V m ) 2 1 ( 2 3 ) ( 2 + = s s s V m ) 2 1 ( 5 . 1 ) ( 2 + = s s s V m
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