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Unformatted text preview: Electronic Instrumentation Quiz 1 Review Op Amps (Continued) Notes ◗ Test is TOMORROW 6:00 p.m.8:00 p.m. DCC 308 ◗ If you’ve just started Project 1 you are a week behind ! (Get to open shop this weekend) ◗ Make sure to find the studio attendance sheet if it doesn’t make it around to you Review Topics Quiz Review Tally 10 20 30 40 50 60 70 80 Transfer Functions Resonant Frequency (Filters) Transformer Circuit Analysis Pspice Topics Arb. Units Transfer Functions and Phasors ◗ Apply the voltage divider equation and parallel and series combination rules to find transfer functions using complex impedance expressions ◗ Simplify the transfer function to find a function which governs behavior at low and high frequencies. ◗ Find an expression (or value) for the magnitude and phase of the simplified transfer function at the corner or resonant frequency ◗ Find Vout or Vin from the transfer function (magnitude and phase) Crib Sheet Highlighter Crib Sheet Highlighter Crib Sheet Highlighter Transfer Functions and Phasors 1) Find the transfer function for the above circuit. Write in terms of Z impedance first Transfer Functions and Phasors C j Z R Z C R ϖ 1 = = 1) Transfer function for the above circuit. a) Combine Impedances: Find Z R2C1 b) Use voltage divider to find H=V out /V 1 c) Substitute component values d) Simplify Z Z Z H j ϖ ( 29 j ϖ R 2 C 1 ⋅ 1 + j ϖ C 1 R 1 R 2 + ( 29 1 + Transfer Functions and Phasors 2) Assume R 1 =R 2 =1KΩ and C 1 =1μF, evaluate the magnitude of the transfer function at ω=0 and ω=∞ . a) Magnitude of the transfer function at ω=0 For low frequencies, the lowest power dominates H j ϖ ( 29 j ϖ R 2 C 1 ⋅ 1 + j ϖ C 1 R 1 R 2 + ( 29 1 + ϖ H j ϖ ( 29 1 1 lim → Transfer Functions and Phasors 2) Assume R 1 =R 2 =1KΩ and C 1 =1μF, evaluate the magnitude of the transfer function at ω=0 and ω=∞ . b) Magnitude of the transfer function at ω= ∞ For high frequencies, the highest power dominates H j ϖ ( 29 j ϖ R 2 C 1 ⋅ 1 + j ϖ C 1 R 1 R 2 + ( 29 1 + ∞ ϖ H j ϖ ( 29 1 2 lim → Transfer Functions and Phasors 3) See crib sheet When doing analysis ωt will eventually drop out so just θ is used V 1 → A e j ϖ t θ + ( 29 ⋅ V 1 → 5 e j π 4 ⋅ V 1 → 5 e j 0.79 ( ) ⋅ Transfer Functions and Phasors 4 Given R1=1K Ω , R2=1K Ω , and C1=1 μ F, what is the output phasor V out → ϖ 2 π 1 ⋅ KHz H j ϖ ( 29 j ϖ R 2 C 1 ⋅ 1 + j ϖ C 1 R 1 R 2 + ( 29 1 + H j ϖ ( 29 ϖ R 2 C 1 ⋅ ( 29 2 1 2 + ϖ C 1 R 1 R 2 + ( 29 ( 29 2 1 2 + 6.283 2 1 2 + 12.566 2 1 2 + 0.505 = Need both Magnitude and Phase from the transfer function. Magnitude Transfer Functions and Phasors Need both Magnitude and Phase from the transfer function....
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This note was uploaded on 10/16/2008 for the course ENGR 4300 taught by Professor Kraft during the Spring '08 term at Rensselaer Polytechnic Institute.
 Spring '08
 KRAFT
 Instrumentation

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