BME 310 Lab 2 Circuits, John G. Webster1/29/00

Introduction

This lab introduces the resistor, capacitor, and operational amplifier (op-amp), and shows how they can be used to build filters and other biomedical-related circuits. It also introduces laboratory equipment used to build and test circuits.

Resistors and capacitors are circuit elements that impede current flow. Ohm’s law is v = iR, and says that the voltage across something is equal to the current through that thing times its resistance (or impedance). Current can be direct current (dc), which has a frequency of 0 Hz, or it can be alternating current (ac) with a frequency of >0 to  Hz. Resistors impede current flow the same amount for any frequency. Their value of impedance is always R (ohms). The impedance of a capacitor is dependent on the frequency of current through it. Its value of impedance is 1/(jC), where C is the capacitance value expressed in farads (F) and  = 2f is the frequency in radians/s whereas f is the frequency in cycles/s (Hz). Because a capacitor’s impedance varies with frequency, we can use it to make a filter. A filter is a circuit that minimizes unwanted frequencies. Filters built with resistors and capacitors are called passive filters.

The op amp is an integrated circuit consisting of many transistors, resistors, and capacitors and is used to amplify signals. It is drawn as a triangle with + (noninverting) and – (inverting) terminals on it. Op amps are useful because they have gain—they can take an input and amplify it by some amount controlled by the person building the circuit. We use them in biomedical instrumentation to measure small signals from the body (on the order of microvolts to millivolts) and amplify them to the 1 to 2 V range, so that they can be more easily observed. Filters built with op amps are called active filters.

Before the lab: Read material about electronics from J. G. Webster (ed.), Bioinstrumentation, Chapter 2 at the coursepage

More detailed information is in Horowitz, P. and W. Hill, The Art of Electronics, 2nd ed. Cambridge: Cambridge University Press, 1998.

Laboratory Equipment

Resistors, capacitors, op amps
Bread board
HP 33120A signal generator
HP 54600B oscilloscope
HP 34401A digital multimeter
HP E3630A dc power supply

Procedure

A.Lab Equipment

Turn on dc power supply and digital multimeter (DMM).
Adjust the power supply to 15 V using the knob labeled 20 V.
Press the DC V button on the DMM. Plug one end of one cable into the COM port on the power supply and the other end into the GND port on the DMM. Plug one end of the other cable into the +20 V port on the power supply and the other end into the top right port of the DMM. Record the voltage and verify that the voltage displayed is close to +15 V.
Remove the cable from the +20 V port on the power supply and plug it into the –20 V port. Record the voltage and verify that the voltage displayed on the DMM is close to –15 V.
Turn dc power supply off.
Unplug both cables from the dc power supply.
Press the 2W button on the DMM. This will allow us to measure resistance.
Measure the resistances of the resistors in front of you and record their values.
Turn on the oscilloscope and waveform generator.
Connect probe 1 to the waveform generator. Make sure channel 1 is selected on the oscilloscope. Press the AUTO-SCALE button.
Press the VOLTAGE button on the oscilloscope and then press the button at the bottom of the display under V P-P. Record the peak-to-peak voltage of the waveform on the screen.
Press the TIME button on the oscilloscope and then press the button at the bottom of the display under FREQ. Record the frequency of the waveform on the display.
Verify that the voltage and frequency shown on the oscilloscope are the same as shown by the waveform generator.
Change the frequency and voltage of the waveform generator by pressing the FREQUENCY and AMPLITUDE buttons, respectively, and adjusting the knob accordingly. The values can also be changed by keying in the actual numerical values desired. Record the effects of changing the frequency and amplitude of the waveform.

B.Voltage Divider and Filter

1.Construct the voltage divider circuit below, setting the input signal to 10 Hz and 1 V peak to peak.

2.Calculate the voltage value you expect across resistor B.

3.Record the voltage across resistor B.

Change the frequency to 50, 100, 500, 1000 Hz and record the voltage across resistor B each time.
Remove resistor B and replace it with the capacitor.
Record voltage measurements at 10, 50, 100, 500, 1000 Hz across the capacitor.
Interchange the positions of the resistor and capacitor.
Record voltage measurements across the resistor at 10, 50, 100, 500, 1000 Hz.

C.Operational Amplifier

Construct the circuit shown below.

Calculate the gain for this circuit.
For your input signal, use 1 V dc from the power supply. Record what you observe on the oscilloscope.
Remove the dc power supply as your input and use the waveform generator. Use a 1 V peak-to-peak input signal at 10 Hz.
Wire the output from the signal generator into one channel on the oscilloscope. Put the output from the circuit on the other channel. Display both at the same time. Record what you observe. Press AUTO-SCALE if necessary.
Turn the amplitude of the waveform generator up to 10 V peak-to-peak. Press AUTO-SCALE on the oscilloscope. Record what you observe.
Turn the amplitude on the waveform generator back down to 1 V peak-to-peak. Record the output for the frequencies 10, 50, 100, 500, 1000 Hz.
Construct the circuit shown below.

Record the output for the frequencies 10, 50, 100, 500, 1000 Hz.

Results

In B4, describe how the voltage changed with frequency. Explain your results.
In B, once the capacitor was inserted to replace resistor B, did the circuit become a high-pass or low-pass filter? Explain.
Explain why we need filters.
In C6, record what you observed. Explain the cause of your observation.
In C8, record the gain of the circuit. Explain how the gain depends on frequency.