Frequency Transfer Function of a Solenoid What is

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Frequency Transfer Function of a Solenoid What is the Frequency Transfer Function Bode Plots

Frequency Transfer Function of a Solenoid What is the Frequency Transfer Function Bode Plots for some simple circuits Tests Performed Magnitude and Phase data Analysis Emmanuele Ravaioli Kevin Sperin MPE-PE 21 -02 -2013

What is the Frequency Transfer Function? u(t) System y(t) Provided all initial conditions are

What is the Frequency Transfer Function? u(t) System y(t) Provided all initial conditions are zero, taking the Laplace transform gives: Factoring out Y(s) and U(s) gives: U(s) H(s) Y(s) Where H(s) is the transfer function 2

What is the Frequency Transfer Function? By applying a known input to the system

What is the Frequency Transfer Function? By applying a known input to the system and measuring the output the transfer function can be determined experimentally. This is repeated for each frequency of interest. U(s) H(s) Understanding how the transfer function affects the input, we can then investigate the internal dynamics that govern the system. Y(s) 3

Bode plots for some simple circuits Courtesy of Emmanuele Ravaioli 4

Bode plots for some simple circuits Courtesy of Emmanuele Ravaioli 4

Tests Performed Solenoid is made up of 10 coils. The inner layer consists of

Tests Performed Solenoid is made up of 10 coils. The inner layer consists of 6 coils. The outer layer consists of 4 coils. Main tests: • Total solenoid - Frequency 1 Hz – 20 k. Hz • 6 inner coils only - Frequency 1 Hz – 20 k. Hz • 4 outer coils only - Frequency 1 Hz – 20 k. Hz To highlight the resonance peak: • Total solenoid - Frequency 4 k. Hz – 6 k. Hz • 6 inner coils only - Frequency 4 Hz – 6 k. Hz • 4 outer coils only - Frequency 3 Hz – 6 k. Hz 5

Magnitude of Solenoid With Increasing Frequency 120 Magnitude (d. B) 100 80 60 40

Magnitude of Solenoid With Increasing Frequency 120 Magnitude (d. B) 100 80 60 40 20 0 1, 00 E+01 1, 00 E+02 1, 00 E+03 Frequency (Hz) 1, 00 E+04 1, 00 E+05 6

Magnitude of Solenoid With Increasing Frequency 120 100 Magnitude (d. B) 80 f(high) ~

Magnitude of Solenoid With Increasing Frequency 120 100 Magnitude (d. B) 80 f(high) ~ C d. B Mag - Both f(medium) ~ L 60 d. B Mag - Inner d. B Mag - Outer f(low) ~ R Sum of Inner & Outer 40 Rs+L 20 0 1, 00 E+01 1, 00 E+02 1, 00 E+03 Frequency (Hz) 1, 00 E+04 1, 00 E+05 7

Phase of Solenoid With Increasing Frequency 100 80 60 Phase (Degrees) 40 20 0

Phase of Solenoid With Increasing Frequency 100 80 60 Phase (Degrees) 40 20 0 1, 00 E+00 Phase - Both 1, 00 E+01 1, 00 E+02 1, 00 E+03 1, 00 E+04 1, 00 E+05 Phase - Inner Phase - Outer -20 -40 -60 -80 -100 Frequency (Hz) 8

Total Inductance L Capacitance Resonance C Frequency f 0 Rs 1 Rs 2 Total

Total Inductance L Capacitance Resonance C Frequency f 0 Rs 1 Rs 2 Total 0. 460 H 4. 723 k. Hz 30. 8 Ω ~100 kΩ 6 Inner Coils 0. 141 H 4. 463 k. Hz 18. 4 Ω ~50 kΩ 4 Outer Coils 0. 067 H 3. 870 k. Hz 12. 65 Ω ~50 kΩ 9

Thank you for listening Any Questions? 10

Thank you for listening Any Questions? 10