ECEN 1400 - Introduction to Digital and Analog Electronics

Peter Mathys, Spring 2014


Lab 2: Soldering and Basic Capacitor Properties

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Goals of this Lab


Prelab

P1. Soldering. To get a headstart about soldering, look at this video about soldering (5 min) and read the instructions below. Make sure to bring solder to the lab (available for purchase in the e-store ECEE 1B10).

  1. Tools
  2. Soldering

P2. Capacitor Charge/Discharge. Consider the following schematic of a voltage source with constant voltage vS, a resistor with resistance R, and a capacitor with capacitance C.

Schematic for charging/discharging C

By selecting different values for vS and for the initial capacitor voltage vC(0) at t = 0 sec, this circuit can be used to study how a capacitor is charged and discharged through a resistor. For the capacitor voltage vC(t) we find for t > 0

Charge/Discharge formula for vC(t)

A derivation of this formula is given in the Notes for Capacitors.

Capacitor Charge. Starting from a discharged capacitor with initial voltage at time t = 0 sec of vC(0) = 0 V, and applying a nonzero voltage vS through resistor R, we find

Charging capacitor C

Thus, the voltage gap between vS and vC(t) decreases exponentially in time. The speed of the decrease is controlled by the time constant Tc = R*C (with R in ohms and C in farads). If Tc is larger it will take longer to charge the capacitor and if Tc is smaller the capacitor will be charged faster. The time constant Tc can be estimated from a graph of vC(t) by noticing that at time t = R*C the capacitor voltage is (1-e-1) * vS (approximately 0.632 * vS).

Capacitor Discharge. Starting from a charged capacitor with nonzero initial voltage of vC(0) at t = 0 sec, and setting vS = 0 V so that the capacitor is discharged through R, we find

Discharging capacitor C

That is, the voltage vC(t) decreases exponentially and the speed of the decrease is controlled by the time constant Tc = R*C. The time constant can be estimated from the graph of vC(t) by noticing that at time t = R*C the capacitor voltage is e-1 * vC(0) (approximately 0.368 * vC(0)).

Use the following setup in Multisim to display the charge/discharge waveform of the voltage across capacitor C1.

Multisim setup for charging/discharging capacitor C

Adjust the settings of the waveform generator so that you obtain the following readout on the oscilloscope. In your lab report write down the settings that you used.

Charging/discharging waveform for capacitor C in Multisim

From the display of the oscilloscope estimate the time constant Tc and compare it with the actual value of R*C. Note that this can be used to determine C for an unknown capacitor if R is known. Use this to design a setup for determining the value of the equivalent capacitance Ceq of the following circuit.

Circuit with unknown equivalent capacitance

Show your setup and show how you computed Ceq from the measured waveforms.

P3. RC Lowpass and Highpass Filters. Capacitor "resistance" for sinusoidal voltages decreases as the frequency increases since the impedance ZC of the capacitor is ZC = 1/(j*2*pi*f*C). Thus, the RC circuit shown in the Multisim setup below should pass low frequencies and attenuate high frequencies.

Multisim setup for measuring RC lowpass filter

A filter that is passing low frequencies and attenuating high frequencies is called a lowpass filter (LPF). Use the Multisim setup shown above to measure the amplitude VS of the sinusoid generated by the waveform generator and the amplitude VC of the voltage across the capacitor. The ratio G = VC/VS is called the (magnitude of) the gain of the filter (since this is a passive filter G will be less or equal to 1).

Measure the gain G for the following frequencies: f = 15, 30, 90, 150, 270, 750, 1500 Hz. Set the amplitude of the waveform generator to 1 Vpp and measure VS and VC as peak-to-peak voltages with the oscilloscope. Plot G versus f to verify that this is indeed a LPF.

For a highpass filter (HPF) that is passing sinusoidal waveforms with high frequencies and attenuating sinusoidal waveforms with low frequencies we need to exchange the roles of the resistor and capacitor as shown in the Multisim setup below.

Multisim setup for measuring RC highpass filter

Repeat the measurements you did for the LPF (at the same frequencies) for the RC HPF shown below. This time G = VR/VS, where VR is the voltage across the resistor. Measure VS and VR as peak-to-peak voltages with the oscilloscope. Plot G versus f to verify that this is indeed a HPF.


Lab Experiments

E1. Soldering Test Probes. Good measurement practice and refined debugging skills begin with the right equipment! Suppose you have to measure the voltage at a particular pin of an IC (integrated circuit), e.g., and LM386 as shown in the picture below.

Measurement Probes on an 8-DIP IC

The alligator clips from your lab kit are too clumsy for the job and the red mini test clip on the left is clearly much better suited. The goal of this experiment is to practice soldering while producing something useful, namely two test leads with banana plugs on one end and mini test clips on the other end as shown next.

Two test leads with mini test clips

Both, the test clips and the banana plugs need to be soldered to the test lead wire. Strip off the insulation from the test lead wire at both ends, about 3/16" on one end (the banana plug end) and a little more than 1/16" on the other end (the test clip end). Twist each of the stripped ends and use the soldering iron to pre-tin the wires. Remove the caps from the test clips and feed the test lead through the hole in the cap before soldering. Handle the test clips carefully, they are somewhat fragile, especially with the caps off. The following picture shows a mini test clip with the cap taken off and the test lead wire with the pre-tinned end.

Mini test clip with cap off

Note that there are two sides to the test clip, the front side where the end of the hook sticks out and the backside with no protrusion for the hook. The next picture shows the test lead pulled through the hole in the cap, just before soldering the wire to the clip.

Mini test clip with wire through hole in cap

Now you are ready to solder the test lead wire to the (copper colored) metal end of the test clip. You may want to pre-tin the metal end of the clip before soldering the wire to it. Be careful not to apply too much heat, the plastic parts of the test clip melt easily. The completed test clip ends (with the caps still removed) are shown in the following picture.

Mini test clips soldered to the test lead wires

Push the caps onto the test clips and then solder the banana plug end of the cable. This is fairly straightforward, push the pre-tinned wire through the big hole and apply heat with the soldering iron until solder inserted in the hole (with the wire in it) melts. You should feed enough solder into the hole to fill it quite completely. It will take a while (about 30-60 seconds) to heat up the metal parts of the banana plugs and it will also take a fair amount of time for the parts to cool down again. Don't move the parts while the solder is cooling down, otherwise you will get a "cold" solder joint (looks dull and greyish as opposed to bright and silverish). The picture below shows the banana plug ends after soldering but before putting on the colored plastic sleeves.

Banana plugs soldered to the test lead wires

To finish your test cables, put the colored plastic sleeves onto the banana plugs and snap the ends in place.

E2. Capacitor Charge/Discharge. Build the circuit below (the same as for prelab P2) on your breadboard. The 100 nF capacitor should have a "104" marking on it (it's the 6'th capacitor from the left on the second picture).

Multisim setup for charging/discharging capacitor C

Connect the waveform generator and the oscilloscope (use the probe in the 10:1 setting and check for the correct setting on the oscilloscope) to your circuit. Use the same settings for the waveform generator that you found in prelab problem P2. Check that the charge/discharge waveform is correct. What happens if you increase the frequency of the waveform to 1 kHz. Why does it happen?

Next, build the following "unknown capacitor" circuit (shown below, same as in problem P2) on your breadboard. To make this work with the capacitors from your kit you may have to use some series or parallel combinations of capacitors to get the correct capacitance values.

Schematic of a circuit with 5 capacitors and unknown equivalent
      capacitance

Use the strategy that you developed in prelab problem P2 to determine the equivalent capacitance of this circuit. How does the capacitance change if you remove C5? Use this as a check for you measurement procedure since it is easy to compute the equivalent capacitance if C5 is removed. Show the measurements and the computations that you made for this check in your lab report.

E3. RC Lowpass and Highpass Filters. In this experiment you are going to implement the LPF and the HPF from prelab problem P3 and measure the (magnitude) of the gain G (amplitude of sinusoidal output voltage over amplitude of sinusoidal input voltage) of the filters. Use the same frequencies as given in P3. For the 22 uF capacitor of the LPF you will have to use two 47 uF electrolytic capacitors from your kit, connected back to back (either + marks or - marks connected together) as shown in the following schematic.

Electrolytic capacitors connected for ac operation

The reason for this is that electrolytic capacitors, which are used when large capacitance values are needed, require a voltage with correct polarity for their operation. These capacitors are made from aluminum foil that is oxidized on one side by an electrolytic process. The foil is submerged in some liquid or paste (the electrolyte) and current is passed through the liquid to the metal, forming the oxide layer that provides the insulation between the two "plates" (the aluminum foil and the electrolyte) of the capacitor. Applying a voltage with reversed polarity will damage (short circuit) the oxide layer and the capacitor will eventually become non-functional or even explode. Since we are going to use the capacitor with an ac voltage, we have to use the little trick, shown in the schematic above, of connecting two electrolytic capacitors with the same capacitance C in series, either with the two + terminals or with the two - terminals connected together as shown above.

For the 5 uF capacitor in the HPF, similarly use two 10 uF electrolytic capacitors connected back to back.

For both the LPF and the HPF, make a plot of (the magnitude of) the frequency response of the filters from your measurements, i.e., plot the gain G versus f in Hz. Filters are generally characterized by their "cutoff frequency" which is usually taken to be the frequency at which G is equal to 0.707 (1/sqrt(2)) times its maximum value. What are the cutoff frequencies of the LPF and the HPF that you measured in this experiment?