1.0 IntroIn this lab, you will build both a low-pass and high-pass filter. First, you will simulate the circuit using the analysis program Multsim. Then, you will build the circuit on the breadboard.

2.0 Low-Pass Filter2.1 Simulated CircuitMultisim is a simple program which allows the user to create and analyze circuits. We will be building the first order low-pass RC circuit shown in Figure 1.

Figure 1: Low-pass RC Circuit

Instructions:1) Open Multisim: Start >> Engineering >> NationalInstruments >>Multisim 10.12) On the far right panel, locate the NI Instrument menu and select the NI Function Generator.

Place the Function Generator on the schematic

3) In the same menu, locate and place the NI Oscilloscope. Double-click on the icon to bring up the scope, which looks exactly like the one we have used for the ELVIS II.

4) On the top menu, go to Place >> Component. Select “Basic” from the Group menu. Find the “Resistor” tab. Choose the 10k resistor. Place this component

5) In the same menu, locate the “Capacitor” tab, and select a 100 nF capacitor. Place this component.

6) In the same menu, change the Group to “Sources.” Under the “Power_Sources” tab, choose “Ground.” Place this component

7) Wire the diagram to create the low pass RC circuit.

Now, we will do some circuit analysis. First, input a square wave to your circuit. Observe the output waveform for low frequencies, say under 100 Hz. Notice how the signal rises and falls exponentially?

Determine the rising and falling time constant of the system. The time constant is defined as the time it takes for the signal to reach 63% of its peak voltage.

For an RC circuit, the time constant should be equal to 1/RC. Calculate this value and compare it to your experimental time constant. How close were you?

2.2 Construct an actual circuitYou will need 4 wires, a 10k resistor, and a 100nF capacitor. Make the following connections on the breadboard:

1) Wire FGEN to AI0+2) Resistor from FGEN to intermediary node on breadboard3) Capacitor from intermediary node to AI Ground4) Wire intermediary node to AI1+5) Wire AI0- to AI Ground6) Wire AI1- to AI Ground

This setup will allow you to use the Bode plotting instrument. Open up this tool from the NI Instrument launcher.

Falling time constant

Rising time constant

Change the start frequency to 10 Hz. Run the device.

Try to locate the corner frequency. This is defined as the point where the gain is 1/√2 times the original gain. Recall that decibels (dB) is a measure of signal ratio given by

dB=20 logV o

V iwhere Vo/Vi is the gain. Solve this equation for dB = 1/√2 . Now, find the point on the gain portion of the Bode plot where this occurs. To check your answer, this should correspond to a phase response of -45°.

Finally, this circuit should display a gain response which falls off 20dB per decade. Confirm this is true manually in the time domain. To do so, close the Bode plot and open the Oscilloscope. Run the function generator at one tenth the corner frequency, the corner frequency, and ten times the corner frequency. Determine the gain in each case by observing the amplitude of the input and output waveforms. Determine if the 20 dB per decade rule applies.

3.0 High Pass FilterThe high pass RC circuit is shown below. Repeat all the above steps (Multisim analysis, building the actual circuit, Bode plot, and Oscilloscope testing) using this new circuit.