Lab 5 TF EIM

LC Resonance circuits

The LC cicuit

1. Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use [math]\displaystyle{ L }[/math] = 10 - 100 [math]\displaystyle{ \mu H }[/math], R = 1k [math]\displaystyle{ \Omega }[/math] .
2. Construct the LC circuit using a non-polar capacitor
3. Measure the Gain [math]\displaystyle{ \equiv \frac{V_{out}}{V_{in}} }[/math] as a function of frequency. (25 pnts)
4. Compare the measured and theoretical values of the resonance frequency ([math]\displaystyle{ \omega_{L} }[/math]) (10 pnts)

Questions

1. What is the bandwidth of the above circuit? (5 pnts)

From the plot above we have [math]\displaystyle{ \left(\frac{V_{out}}{_{Vin}} \right)_{max} = 0.0138 }[/math]

The bandwidth defined as the width from [math]\displaystyle{ \omega_1 }[/math] to [math]\displaystyle{ \omega_2 }[/math] where the amplitude of signal drop down to [math]\displaystyle{ \frac{1}{\sqrt{2}} }[/math].

At this point [math]\displaystyle{ \left(\frac{V_{out}}{V_{in}} \right) = \frac{0.0138}{\sqrt{2}} = 0.00976 }[/math]. Let's plot this line and calculate the bandwidth.

The RLC cicuit

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

Forest_Electronic_Instrumentation_and_Measurement