ES 3: Introduction to Electrical Systems



ES 3: Introduction to Electrical Systems

Laboratory 4: Amplification, Impedance, and Frequency Response

I. GOALS:

In this laboratory, you will build an audio amplifier using an LM386 integrated circuit. The amplifier will increase the voltage of a very weak signal, and the output of the amplifier will drive an audio speaker. This is an example of a complete electrical system.

You will be asked to determine the Thevenin equivalent resistance of the amplifier chip, as a way of reviewing the material covered in Lab #3. In addition, you will use the oscilloscope to measure the amount by which the amplifier increases the weak input signal (the gain). Finally, you will measure the gain for a wide range of input signal frequencies. From this data, you can report the frequency response of the amplifier circuit by constructing a Bode plot using Excel.

After the laboratory, you will perform a theoretical analysis of the amplifier circuit.

II. PRE-LAB QUESTIONS:

Read the laboratory manual in its entirety and be certain that you understand the experiments that need to be completed. In this lab, you will use a breadboard to prototype a somewhat more complicated circuit. Review the use of the breadboard (Lab #3).

What is the impedance (in ohms) of a 0.01 μF capacitor at the following frequencies?

10 Hz = 62.8 rad/sec

100 Hz

1 kHz

10 kHz

III. EXPERIMENTS:

In this laboratory, you will build an audio amplifier and measure its gain and frequency response. The voltage gain of an amplifier is simply the ratio of the output signal voltage to the input signal voltage:

[pic] Eq. 1

In electrical engineering, gain is often expressed in decibels (dB). The gain in dB is found by taking log10 of the ratio in Eq. 1 and multiplying by 20:

[pic] Eq. 2

Notice that if vout=vin, then the gain is AV = 1 (v/v) = 0 dB. If the output signal is 100 times larger than the input signal, then the gain is AV= 100 v/v or 20log10(100) = 40 dB.

Ideally, a perfect amplifier would have the same voltage gain for every conceivable input signal. In reality, however, the gain of an amplifier always drops to zero for very high frequency signals. Many amplifiers also exhibit poor gain at low frequency. The variation of gain as a function of frequency is called the frequency response: AV(f) vs. f.

The first task of this experiment is to build an audio amplifier using the LM386 integrated circuit (IC). This IC contains approximately 25 circuit elements such as resistors, transistors and diodes (see Section V.3 for the internal circuit). It is difficult to miniaturize capacitors, so the amplifier circuit shown in Figure 1 requires three external capacitors in addition to the LM386 chip.

[pic]

Figure 1. An amplifier circuit that uses the LM386 chip

The circuit symbol for an amplifier is a triangle. The input(s) to an amplifier are drawn on the broad side of the triangle (pins 2 and 3), and the output is drawn at the vertex of the triangle (pin 5). All amplifiers require an external power source. This power supply is applied to pins 6 and 4 of the LM386. We will use a 9 volt battery as the power source.

Note: Pins 1, 7, and 8 are not used in this particular circuit.

Amplifiers increase the voltage (or current, or power) of a weak input signal. Examples of devices that produce weak signals requiring amplification include microphones, strain gauges, pH sensors, and antennas. In this experiment, we will replace the signal device by a function generator. This substitution will allow you to apply a well-behaved input signal to the amplifier. The function generator is connected to the amplifier’s input (pin 3) through a coupling capacitor CC. The coupling capacitor blocks unwanted DC voltages (ω=0) from entering the amplifier because the impedance of a capacitor is infinity as ω(0 (i.e., an open circuit):

[pic] Eq. 3

The 100μF capacitor connected to the output of the amplifier chip (pin 5) performs the same function as CC: it blocks unwanted DC voltage from reaching the speaker. Why would we want to block DC voltages? DC voltages do not produce any sound; only time-varying signals produce audible sound. A constant voltage applied to the speaker will dissipate power, however, and this power is simply wasted because no sound is produced.

Figure 1 shows the amplifier circuit in an abbreviated style. This style is used to simplify the appearance of the schematic, but it can be tricky to understand at first. Figure 2 shows the same circuit drawn in a more complete and familiar fashion.

Of particular importance is the numbering of the pins of the IC. The IC has a small mark either near pin 1 or at the top of the chip. These two marks are shown on the LM386 in Figure 2. The pins are then numbered sequentially in a counter-clockwise direction.

You should now build the amplifier circuit on a breadboard. Use a coupling capacitor with CC=0.01μF. Connect the battery last, after you have double-checked that the circuit is correctly wired. Make certain that the IC straddles the deep groove in the breadboard such that pins 1-4 are connected to the tie points to the left of the groove and pins 5-8 are connected to the tie points to the right of the groove.

Please refer to the photographs of the circuit in Section V if you require additional help.

[pic]

Figure 2. A complete schematic of the amplifier circuit shown in Fig. 1

Measure and record the resistance or capacitance for all of the components used in the amplifier circuit: R10=____Ω; CC=____μF; C100=____μF; C047=____μF; Rspkr=____Ω

In this experiment, the function generator needs to produce a very small voltage. This requires pressing the [ATT-20dB] button and gently pulling the AMPL knob out. Each of these actions reduces the output voltage by 20dB for a total attenuation of -40dB. In this experiment you should set the function generator to produce a 1000 Hz sinusoid with a peak-to-peak amplitude of 50 mV:

vin(t) = 0.025sin(2π.1000t) volts Eq. 4

Voltage Gain

Using the two channels of the oscilloscope, measure vin and vout as shown in Figure 2. Report the measured values in your lab report and calculate the voltage gain of the amplifier using both (v/v) and (dB).

Check: The LM386 should have a voltage gain of approximately 20 v/v.

Next, find the Thevenin equivalent resistance of the LM386 amplifier (f =1kHz) by measuring the output voltage of the amplifier with the speaker disconnected (this is the open circuit voltage). Repeat the measurement of vout with the speaker re-connected. Report these two measurements. In your lab report, calculate RTH of this amplifier using the methodology that you learned in Laboratory #3.

VOC = ______vp-p

Vspkr = ______vp-p

RTH(amp)=___________Ω

Note: RTH(amp)Chart>> “XY scatter”. Then select the Data Range to include the Frequency data and both columns containing the Gain data (outlined by clicking and dragging the mouse).

[pic]

Figure B2. Excel Spreadsheet showing Gain vs. Frequency data selected for insertion into a chart

Next, insert Titles and axis labels, including the units, as shown in Figure C2.

[pic]

Figure C2. Excel Spreadsheet showing the selection of chart titles and axis labels

Notice how the low frequency data is crowded together. To fix this problem, a Bode plot uses a logarithmic frequency axis. To create this axis, Double-click the Frequency axis of the chart and change the scale to logarithmic as shown in Figure D2.

[pic]

Figure D2. Excel Spreadsheet showing the conversion of the frequency axis from LINEAR to LOGARITHMIC

Finally, clean up the appearance of the graph by double clicking the Gain axis and resetting the Value (X) axis crosses to -10 (dB).

[pic]

Figure E2. Excel Spreadsheet showing Gain vs. Frequency as a Bode Plot

Please remember to label each data set with the value of the coupling capacitor by inserting an appropriate Legend into the plot: Cc = 0.01uF and Cc = 0.02uF.

Include this Bode plot of the amplifier’s frequency response in your lab report.

V.3. Internal circuit of the LM386 audio amplifier chip

[pic]

VI. PARTS LIST:

LM386 audio amplifier chip

100μF non polarized electrolytic capacitor

0.047μF or 0.05 μF capacitor

0.01 μF capacitors (2 per group)

10 Ω resistor

16 ohm speaker with soldered wires

9 volt battery with battery clip

Breadboard for prototyping circuits

Function Generator (Instek, GFG-8250A)

Oscilloscope (Tektronix TDS 2012, or equivalent) with 2 probes

LCR meter (Stanford Research Systems Model 715), one unit per room.

Test Leads: BNC-to-Alligator clips (1)

Wires with Alligator clips (2)

Banana plug-to-Alligator clips (2)

Hook-up wire for breadboards

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[1] Although, if this capacitor is small and the speaker resistance is small there is a significant additional attenuation of the low frequency gain.

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Scope

Function Gen.

This column contains all of the ground connections

To 9v (+)

To spkr

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