BioNB 440: Lab 2

Voltage, Current, and Frequency

Introduction.

This assignment will cover some of the aspects of AC circuits. We will be measuring voltage and current in circuits consisting of resistors and capacitors, as a function of the frequency of the input voltage. We will also be starting to motivate the idea that any waveform may be made up of the sum of sinewaves.

Download the following EWB circuits by right-clicking on the link and choosing the Save Link as option. You may need to add the ewb extension to the filename in the dialog box:

• VandI.ewb Voltage and current through resistors and capacitors. Schematic
• kirchoffc.ewb Kirchhoff's laws applied to capacitors. Schematic 1, Schematic 2, Schematic 3
• bodedemo.ewb Demonstration of phase/magnitude measurement. Schematic
• fourier2.ewb Syntheisis of squarewave from sinewaves. Schematic

Note that in this and every lab assignment the verb build means to construct a circuit on the protoype board whith actual parts. The verb simulate means use Electronics Workbench mathematically simulate the circuit.

Whenever possible you should attempt to fit your measured results to the theoretical equations given in class. Simulate the following:

1. Using VandI.ewb, measure the phase and magnitude of the current through the resistor and capacitor as a function of frequency. The current through the resistor should be independent of frequency, while the current through the capacitor should be linear with frequency.

2. Show that the currents in circuits (1) and (2) of the kirchoffc program are proportional to frequency. Show that the two voltage traces displayed on the oscilloscope in circuit (3) sum to the input squarewave.

3. Using the expanded oscilloscope display in the bodedemo circuit, measure the phase and magnitude of the output sinewave with respect to the input sinewave. Reverse the positions in the circuit of the resistor and capacitor and repeat the measurement. Note that the Bode Plot instrument does the measurement for you.

4. Modify the circuit in bodedemo to the following:
   Meaure the phase and magnitude of the output sinewave with respect to the input.

5. The fourier2.ewb circuit produces a squarewave by summing several sinewaves. The squarewave is then lowpass filtered by an RC circuit. A second branch of the circuit then synthesizes the lowpassed squarewave directly. In general, the effect of any linear circuit can be produced by modifying the phase and magnutude of the sinewaves which make up the signal. Modify the circuit to produce a triangle wave. Each frequency component has a relative amplitude proportional to 1/frequency² and phase alternating between 0 and 180 degrees.

6. Simulate a model axon which includes membrane capacitance. The circuit might look like the following:
   Measure the risetime and amplitude of the waveform as a function of distance.