Lab 7:  RLC Resonant Circuits

In this lab you will use the function generator and the oscilloscope to measure the voltage and phase in a resonant parallel and series RLC network.  The measurements you will perform are very similar to those you did for the steady-state RC network lab.  However unlike RC networks, RLC networks can be resonant.  Unlike the RC Networks lab, the focus is to measure the center frequency and Q of the circuits rather than to take data over the entire frequency range. 

In order to do this lab you need to understand:  

1) the characteristics of band-pass and notch filters,
2) how to find the 3 dB points, and
3) how to measure frequency and phase.

Reading  Ch 2.28-30 + lecture notes. 

The RLC network.  For these measurements we will construct series and parallel RLC networks on your breadboard.  Your will apply a sine wave using your function generator and make the measurements using your oscilloscope.  Use the following values:  R = 1 K; L = 10 mH, and C = 0.01 μF. 

The four networks you will construct are shown bellow.  Two of them should be band-pass filters and the other two should be notch filters.

Calculate the resonant frequency you expect based on the labeled component values ().  Now measure the resistance of R and of your L (R_L) using your DMM and record it in your notebook.  Measure the capacitance of your capacitor with the capacitance meter and record that in your notebook.  Later you will model the circuit using these values (maybe).

Function generator set up.  Connect the function generator to your circuit.  Use a BNC Tee to also connect the function generator to channel 2 of your scope.  Set the function generator to output a 100 Hz sine wave with a 2 Vp-p amplitude and zero DC offset.  Use the sync signal from the function generator for the external trigger of the scope as you have done before.

Oscilloscope probes.  Obtain a 1X or 10X scope probe and connect it to channel 1. 

Scope set up.  Set up the scope so you can see the traces of both channels.  Connect the probe to V_in.  Verify that this voltage is and should be the same as observed in channel 2. 

Set up and plan your measurements.  We want to measure the magnitude and the phase of the voltage V_out at 3 frequency points for each filter.  The point at the center frequency (resonance frequency) and a data point at each of the 3dB points (V_out/V_max  = 1/√2). 

3dB points.  Be careful!  The 3 dB points are defined with respect to the maximum of the V_out/V_in.  For the band-pass filter 3 dB is measured from maximum of V_out/V_in at the center frequency.  For the notch filter 3 dB is measured from maximum of V_out/V_in far away from the notch.  The 3dB point is measured with respect V_max, not V_in.  You will adjust the frequency of your function generator so that V_out/V_max  = 1/√2.  You will need to measure all three frequencies.

Make the measurements of V_out.  Set up the trace V_out and V_in on the scope so that you can observe one complete cycle.  For each frequency your will need three measurements:  The period, the magnitude of the voltage V_out, and the time delay of V_out with respect to V_in.  Prepare a table in your notebook to record these values.  You will have one table for each of the four circuits.

FILTER	period (for frequency)		Vout				Vin
measurement	div	scale time/div	time delay (for phase)		amplitude Vp-p		amplitude Vp-p
			div	scale time/div	div	scale (V/div)	div	scale (V/div)
center freq		DO NOT RECORD YOUR DATA HERE. PLEASE USE YOUR LABORATORY NOTEBOOK.
upper 3 dB
lower 3 dB

The Quality Factor.  The quality factor of the resonance is Q = f₀/Δf, where Δf is the width at the 3 dB point and f₀ is the resonant frequency.  This width is often referred to as the full width at half power maximum (FWHM).  Calculate Q for your network (see the lecture notes and the text).

RLC Resonant Circuits Lab (50pts)  NAME  ________________________________

section ______                          Lab Partner ________________________________

Data work up:  Fill in the tables (after completing the calculations ion your notebook)

• Note the type of filter:  band-pass or notch.
• Show the schematic in your table so we can tell that you know which circuit you measured.

filter type:	measurement	freq (Hz)	Vout/Vin (dB)	phase (deg)
schematic (sketch below)
	center freq
	upper 3 dB
	lower 3 dB
	Q =

filter type:	measurement	freq (Hz)	Vout/Vin (dB)	phase (deg)
schematic (sketch below)
	center freq
	upper 3 dB
	lower 3 dB
	Q =

Summary

filter type:	band pass		notch
	parallel	series	parallel	series
Q measured
Q calculated
fcenter (measured)
fcenter (calculated)

Reference (you do not need to answer questions in this section).

Function Generator Sync out and Scope External Trigger.  Your function generator also has another output, usually labeled sync out, trigger out, TTL out, etc.  Plug this output into channel 1.  Observe the waveform and sketch it in your notes.  Change the amplitude and frequency of the function generator output.  This waveform has the same frequency as the sine wave output, but its amplitude does not change.  It is also a square wave or other waveform with sharp transitions that are good for triggering other events, such as the oscilloscope trace. 

Having explored the characteristics of the sync signal, disconnect it from channel 1 and connect it to the channel marked ext (the external trigger).  Set the scope to trigger from the external source.  Verify that you are triggering from the external source by disconnecting the external source.  The channel 2 sine wave trace should roll across the screen.  Reconnect the sync.  Notice that you can lower the amplitude of the function generator output (going to channel 2) to its minimum and the scope trace will remain synchronized!

This paragraph is repeated from an earlier lab for your convenience.  If you are unfamiliar with scope probes, your instructor will help you.  Scope probes come in two common flavors, 1X and 10X.  The 10X probe divides the voltage by a factor of ten.  The 1X probe does not change the voltage.  Some of the probes in the lab have a switch to change flavors.  Check to see if yours has a switch.  Test your probe by touching it to the test port of the scope.  This is a small gold plated contact near the focus controls of your scope.  The test port has a 1 kHz 0.5 Vp-p voltage for testing your probe.  What variety of probe do you have?  Is it a 1X or 10X?  Can it be switched?  Is your probe functioning correctly?  It does not matter which flavor you have as long as you know which it is.

Measuring frequency.  Measuring the period on one or more cycles does this.  You will need to do this for each frequency you use.

Measuring phase.  Phase is always a relative measurement.  That it is measured with respect to some reference point.  In this measurement we are comparing the phase shift of the sine wave V with respect to V₀.  This V₀ is the phase reference.  Measuring the time difference between a reference point on the V₀ sine wave and the same point on the V sine wave best does this. 

The phase shift in degrees is then obtained knowing the period of the wave and that one period is 360 degrees.