Lab 5 RS

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LC Resonance circuits

The LC cicuit

TF EIM Lab5 LC.png ==Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use [math]L[/math] = 10 - 100 [math]\mu H[/math], R = 1k [math]\Omega[/math]==

[math]\omega_0=\frac{1}{\sqrt{\mbox{LC}}}[/math]

I choose the following values for [math]\mbox{R}[/math] and [math]\mbox{C}[/math]:

[math]R=aaa\ \Omega[/math]
[math]C=bbb\ \mu F[/math]

So the resonance frequency is [math]\omega_0=\frac{1}{\sqrt{aaa\ \Omega\ bbb\ \mu F }} = ccc\ \frac{\mbox{rad}}{\mbox{sec}}[/math]

Or [math]f=\frac{\omega_0}{2\pi} = ddd\ \mbox{kHz}[/math]


Let's estimate:

L4 LC.png


Construct the LC circuit using a non-polar capacitor

Measure the Gain [math]\equiv \frac{V_{out}}{V_{in}}[/math] as a function of frequency. (25 pnts)

#Compare the measured and theoretical values of the resonance frequency ([math]\omega_{L}[/math]) (10 pnts)

Questions

  1. Is there a value of [math]R[/math] in which [math]V_{out} \approx V_{in}[/math] at resonance. What is the value?(5 pnts)

The RLC cicuit

TF EIM Lab5 RLC.png

  1. Design and construct a series LRC circuit.
  2. Measure and Graph the Gain as a function of the oscillating input voltage frequency. (25 pnts)
  3. Measure and Graph the Phase Shift as a function of the oscillating input voltage frequency. (25 pnts)

Questions

  1. What is the current [math]I[/math] at resonance? (5 pnts)
  2. What is the current as [math]\nu \rightarrow \infty[/math]? (5 pnts)




LC Resonance circuits

The LC cicuit

TF EIM Lab5 LC.png

Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use [math]L[/math] = 10 - 100 [math]\mu H[/math].

[math]\omega_0=\frac{1}{\sqrt{\mbox{LC}}}[/math]

I choose the following values for [math]\mbox{R}[/math] and [math]\mbox{C}[/math]:

[math]R=aaa\ \Omega[/math]
[math]C=bbb\ \mu F[/math]

So the resonance frequency is [math]\omega_0=\frac{1}{\sqrt{aaa\ \Omega\ bbb\ \mu F }} = ccc\ \frac{\mbox{rad}}{\mbox{sec}}[/math]

Or [math]f=\frac{\omega_0}{2\pi} = ddd\ \mbox{kHz}[/math]


Let's estimate:

L4 LC.png

Construct the LC circuit using a non-polar capacitor

Measure the Gain [math]\equiv \frac{V_{out}}{V_{in}}[/math] as a function of frequency. (20 pnts)

Measure the Gain when an external resistance approximately equals to the inherent resistance of the rf choke [math]R_{L}[/math]. (20 pnts)

Compare the measured and theoretical values from the resonance frequency ([math]\omega_{L}[/math]) and the Quality factor [math]Q \equiv 2 \pi \frac{W_S}{W_L} = 2 \pi \frac{\mbox{Energy Stored}}{\mbox{Energy Lost}}[/math] value for each case; [math]W = \frac{1}{2}LI^2[/math]. (10 pnts)

Questions

  1. If r=0, show that [math]Q = \frac{1}{\omega_0 R_L C}[/math]. (10 pnts)
  2. Show that at resonance[math] Z_{AB} \approx Q \omega_0 L[/math]. (10 pnts)

The LRC cicuit

TF EIM Lab5 RLC.png

  1. Design and construct a series LRC circuit.
  2. Measure and Graph the Gain as a function of the oscillating input voltage frequency. (20 pnts)

Questions

  1. What is the current [math]I[/math] at resonance? (5 pnts)
  2. What is the current as [math]\nu \rightarrow \infty[/math]? (5 pnts)


Forest_Electronic_Instrumentation_and_Measurement

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