ELEC 241 Lab

Experiment 3.1

Resistive Voltage Dividers

Part 1: Measuring AC Voltage with the DMM

Equipment

Components



Step 1:

 Connect your BNC T connector to CH1 of the scope.

Step 2:

 Use a BNC patch cord to connect one end of the T to the function generator output. Connect a BNC clip lead to the other end of the T.


Step 3:

 Set the function generator to produce a 2 V p-p (i.e. 1 V peak), 100 Hz sine wave.

Step 4:

 Set the DMM to AC Volts and connect the probes to the clip leads. What is the voltage reading on the DMM?

Step 5:

 Set the function generator to produce a square wave. Readjust the Amplitude control if necessary to maintain the 2 V p-p amplitude. What is the voltage reading on the DMM?

Step 6:

 Reset the function generator to sine wave. Note the reading on the DMM at 5 Hz, 50 Hz, 500 Hz, 5 kHz, and 50 kHz.

Question 1:

 What is the useful frequency range of the DMM for measuring AC signals?

Diversion:

 The AC voltage function of the DMM is calibrated to read (approximately) the RMS value of the waveform. RMS stands for root-mean-square i.e. the square root of the mean value of the square of the function:
$\displaystyle V_{RMS} = \sqrt{\frac{1}{T}\int_0^T v^2(t)dt}$

We'll see the importance of this when we study power. For now, just remember that for a sine wave, $V_{RMS} = 0.707 V_{Peak}$ .

Part 2: The Basic Voltage Divider



Note
The rest of the circuits in this Lab should be wired on your breadboard. You could use either BNC clip leads or BNC patch cords to the interface board to connect the circuits to the function generator and scope. Using the interface board should be more efficient since you can leave the instruments connected and change the circuit by just pulling out the old components and plugging in the new ones (remember they're all voltage dividers). The instructions will assume you are using the interface board with the following connections: Oscilloscope CH1 to J1-1, CH2 to J1-2, and function generator to J1-3.


Step 1:

 Wire the following circuit, using 10k$\Omega$ (brown-black-orange) resistors for both $R_1$ and $R_2$ :
\includegraphics[scale=0.650000]{ckt3.1.1.ps}

What should the divider ratio ($v_{out}/v_s$ ) be?

Step 2:

 Set the function generator to produce a 2 V p-p sine wave.

Step 3:

 Using the oscilloscope, measure $V_{out}$ . Is it what you expect?

Step 4:

 Without disturbing the function generator settings, replace the two 10k$\Omega$ resistors with two 47$\Omega$ (yellow-violet-black) resistors. What is the output voltage now?

Step 5:

 Again leaving the function generator alone, replace both resistors with 1M$\Omega$ (you're on your own for this one) resistors. Measure the output voltage.

Moral:

 No circuit exists in isolation. To be useful its input or output (or both) must be connected to some other circuit. Unfortunately, the interaction between the circuit and a non-ideal source or load causes it to behave differently than it would in an idealized situation. With careful design, this interaction can be minimized or accounted for. If ignored it can reduce the performance of the system, or keep it from working altogether.

For example, for the measurements we made in this part, we would have the following model for the complete system including circuit, source, and load:

\includegraphics[scale=0.400000]{ckt3.1.2.ps}


Question 2:

 Based on your measurements and the above model, what are the output resistance ($R_S$ ) of the function generator and the input resistance ($R_L$ ) of the scope?

Part 3: The Potentiometer (Volume Control)

A potentiometer (or pot for short) is a fixed value resistor with a third, movable contact or slider which may be positioned anywhere along the resistive element. If we represent the position of the slider by $\alpha$ , where $\alpha$ varies between 0 (fully counterclockwise) and 1 (fully clockwise), then the resistance between the lower end of the resistor and the slider will be $\alpha R$ and between the slider and the upper end will be $(1-\alpha) R$ , where $R$ is the total resistance of the potentiometer.

If we connect the two fixed contacts to a voltage source and measure the output between the movable contact and one fixed contact, we get a variable voltage divider:

\includegraphics[scale=0.650000]{pot1.ps}

Then the output is

$\displaystyle v_{out} = \frac{R_2}{R_1 + R_2} v_{in} = \frac{\alpha R}{(1-\alpha)R + \alpha R} v_{in}= \alpha v_{in}$


Step 1:

 Select a 10k$\Omega$ potentiometer from your parts kit. It will have three short wires sticking out the bottom in a triangular pattern. The center terminal is the slider contact and the two outer terminals are the fixed contacts.


Note
Figuring out the value of a pot can be tricky. Some pots are labeled directly with the value (e.g. "100" or "10K"). Others are labeled using the same code as for fixed resistors, except that numbers, rather than colors, are used. For example, a 10k$\Omega$ resistor would have the bands brown-black-orange. The values of these colors are 1, 0, and 3, so a 10k$\Omega$ pot would have the label "103"


Step 2:

 Wire the following circuit:
\includegraphics[scale=0.650000]{ckt3.1.3.ps}


Step 3:

 Set the function generator to produce a 2 V p-p 100 Hz sine wave.

Step 4:

 Set the potentiometer adjustment screw to mid scale and measure $v_{out}$ .

Step 5:

 The potentiometer has a scale divided into 10 equal divisions, presumably representing 10 equal divisions of resistance. Set the potentiometer to each of these 10 divisions and measure $v_{out}$ . Is this presumption correct?

Part 4: Resistive Transducers

In Lab 2 we looked at active or generating transducers, i.e. they converted acoustical or optical energy to electrical energy and produced a voltage (or current) directly. Some transducers are passive, they don't produce voltage directly, but vary some electrical parameter (e.g. resistance) and must be connected to an external source to produce an output.

If in the volume control circuit above, $v_{in}$ were fixed at $V_0$ and $\alpha$ varied with time, we would have $v_{out}(t) = V_0 \alpha(t)$ , i.e. we would have a resistive transducer. More common is where we have just a single resistor with $R = f(x)$ , where $x$ is the physical parameter being measured.

For example, if $p(t)$ represents the acoustical pressure in a sound wave and we have a resistance which varies with pressure, $R=R_0 + kp$ , then in the following circuit we would have $v_{out}(t) = I_0R(t) = I_0 R_0 + I_0 k p(t) = V_0 + I_0 k p(t) = V_0 + K p(t)$ , where $K = I_0 k$ .

\includegraphics[scale=0.650000]{ckt3.1.4a.ps}

The output consists of the desired signal, $K p(t)$ , superimposed on a constant DC offset, $V_0$ . We saw this last week with the photodiode, and we know how to deal with this offset: just switch the scope to AC.


Step 1:

 Unscrew the cover from the mouthpiece of the telephone handset. Carefully remove the microphone cartridge.
Measure the resistance between the two contacts on the back of the microphone. This is $R_0$ of microphone.

Step 2:

 Shake or tap the microphone and measure $R_0$ again. Hold the microphone in a vertical position and measure again. How consistent is the resistance?

Step 3:

 Replace the microphone in the handset and replace the cover.

Diversion 1:

 Since we don't have any current sources in the lab, we'll have to build an approximate current source the way we talked about in class: by connecting a voltage source in series with a large resistor. When we do, we get the following circuit (which looks suspiciously like a voltage divider):
\includegraphics[scale=0.650000]{ckt3.1.4b.ps}


Diversion 2:

 In the last two Labs we used the 0-6V half of the power supply as a signal source. We will be using the other half ($\pm 20 \rm V$ ) as a source of power for our circuits. Since we will need to have the power voltages (and ground) available at many points in the circuit, it will be convenient to connect them to the bus strips that run through the breadboard.

Step 4:

 Connect the GND and +15V connector blocks to two rows on the top bus strip. Connect the gaps at the center of the bus strip to form two full width power buses.

You now have a power and ground bus that looks like this:

\includegraphics[scale=0.650000]{pwr_bus1.ps}


Step 5:

 Set the Meter Selector switch on the power supply to +20V. Adjust the 0 to 20V voltage control to product 10 volts.

Step 6:

 Use a red banana patch cord to connect the 0 to +20V terminal of the power supply to the red banana jack on the breadboard. With a green cord, connect the Common terminal to the green banana jack.

Step 7:

 Plug one end of a handset coil cord into the handset and the other end into J1-7 of the interface board.

Step 8:

 Connect one side of the microphone to ground by connecting pin 13 (mic2) of the interface board socket strip to pin 14 (gnd). Plug the other side of the microphone (pin 12) into a hole in the breadboard socket strip.

Step 9:

 Into another hole in the same column, plug one end of a 4.7 k$\Omega$ resistor. Plug the other end of the resistor into the positive bus strip.

Step 10:

 We now should have wired the circuit shown in the figure above. Connect CH1 of the oscilloscope to $v_{out}$ .


Step 11:

 Speak into microphone and observe $v_{out}$ . What are the DC offset and the peak to peak signal amplitude?

Question 3:

 How does the signal amplitude of the carbon microphone compare with that of the microphone we used last week? Could we connect this directly to the speaker or handset earpiece and produce an audible sound?