6.Experiments
.pdf
4.14. INDUCTOR-CAPACITOR "TANK" CIRCUIT |
183 |
4.14Inductor-capacitor "tank" circuit
PARTS AND MATERIALS
²Oscilloscope
²Assortment of non-polarized capacitors (0.1 ¹F to 10 ¹F)
²Step-down power transformer (120V / 6 V)
²10 k- resistors
²Six-volt battery
The power transformer is used simply as an inductor, with only one winding connected. The unused winding should be left open. A simple iron core, single-winding inductor (sometimes known as a choke) may also be used, but such inductors are more di±cult to obtain than power transformers.
CROSS-REFERENCES
Lessons In Electric Circuits, Volume 2, chapter 6: "Resonance"
LEARNING OBJECTIVES
²How to build a resonant circuit
²E®ects of capacitor size on resonant frequency
²How to produce antiresonance
SCHEMATIC DIAGRAM
L
C
ILLUSTRATION
184 |
CHAPTER 4. AC CIRCUITS |
touch
- clips + together
(transformer used as an inductor)
INSTRUCTIONS
If an inductor and a capacitor are connected in parallel with each other, and then brie°y energized by connection to a DC voltage source, oscillations will ensue as energy is exchanged from the capacitor to inductor and visa-versa. These oscillations may be viewed with an oscilloscope connected in parallel with the inductor/capacitor circuit. Parallel inductor/capacitor circuits are commonly known as tank circuits.
Important note: I recommend against using a PC/sound card as an oscilloscope for this experiment, because very high voltages can be generated by the inductor when the battery is disconnected (inductive "kickback"). These high voltages will surely damage the sound card's input, and perhaps other portions of the computer as well.
A tank circuit's natural frequency, called the resonant frequency, is determined by the size of the inductor and the size of the capacitor, according to the following equation:
fresonant = |
1 |
|
2π LC |
||
|
Many small power transformers have primary (120 volt) winding inductances of approximately 1 H. Use this ¯gure as a rough estimate of inductance for your circuit to calculate expected oscillation frequency.
Ideally, the oscillations produced by a tank circuit continue inde¯nitely. Realistically, oscillations will decay in amplitude over the course of several cycles due to the resistive and magnetic losses of the inductor. Inductors with a high "Q" rating will, of course, produce longer-lasting oscillations than low-Q inductors.
Try changing capacitor values and noting the e®ect on oscillation frequency. You might notice changes in the duration of oscillations as well, due to capacitor size. Since you know how to calculate resonant frequency from inductance and capacitance, can you ¯gure out a way to calculate inductor inductance from known values of circuit capacitance (as measured by a capacitance meter) and resonant frequency (as measured by an oscilloscope)?
Resistance may be intentionally added to the circuit { either in series or parallel { for the express purpose of dampening oscillations. This e®ect of resistance dampening tank circuit oscillation is
4.14. INDUCTOR-CAPACITOR "TANK" CIRCUIT |
185 |
known as antiresonance. It is analogous to the action of a shock absorber in dampening the bouncing of a car after striking a bump in the road.
COMPUTER SIMULATION
Schematic with SPICE node numbers:
Rstray
2
C1
0
is placed in the circuit to dampen oscillations and produce a more realistic simulation. A lower Rstray value causes longer-lived oscillations because less energy is dissipated. Eliminating this resistor from the circuit results in endless oscillation.
Netlist (make a text ¯le containing the following text, verbatim): tank circuit with loss
l1 1 0 1 ic=0 rstray 1 2 1000 c1 2 0 0.1u ic=6
.tran 0.1m 20m uic
.plot tran v(1,0)
.end
186 |
CHAPTER 4. AC CIRCUITS |
4.15Signal coupling
PARTS AND MATERIALS
²6 volt battery
²One capacitor, 0.22 ¹F (Radio Shack catalog # 272-1070 or equivalent)
²One capacitor, 0.047 ¹F (Radio Shack catalog # 272-134 or equivalent)
²Small "hobby" motor, permanent-magnet type (Radio Shack catalog # 273-223 or equivalent)
²Audio detector with headphones
²Length of telephone cable, several feet long (Radio Shack catalog # 278-872)
Telephone cable is also available from hardware stores. Any unshielded multiconductor cable will su±ce for this experiment. Cables with thin conductors (telephone cable is typically 24-gauge) produce a more pronounced e®ect.
CROSS-REFERENCES
Lessons In Electric Circuits, Volume 2, chapter 7: "Mixed-Frequency AC Signals" Lessons In Electric Circuits, Volume 2, chapter 8: "Filters"
LEARNING OBJECTIVES
²How to "couple" AC signals and block DC signals to a measuring instrument
²How stray coupling happens in cables
²Techniques to minimize inter-cable coupling
SCHEMATIC DIAGRAM
Telephone cable
Mtr
ILLUSTRATION
4.15. SIGNAL COUPLING |
187 |
Motor
|
- |
Telephone |
|
+ |
cable |
||
|
headphones
plug
Sensitivity
INSTRUCTIONS
Connect the motor to the battery using two of the telephone cable's four conductors. The motor should run, as expected. Now, connect the audio signal detector across the motor terminals, with the 0.047 ¹F capacitor in series, like this:
188 |
CHAPTER 4. AC CIRCUITS |
-
+
headphones
plug
Sensitivity
You should be able to hear a "buzz" or "whine" in the headphones, representing the AC "noise" voltage produced by the motor as the brushes make and break contact with the rotating commutator bars. The purpose of the series capacitor is to act as a high-pass ¯lter, so that the detector only receives the AC voltage across the motor's terminals, not any DC voltage. This is precisely how oscilloscopes provide an "AC coupling" feature for measuring the AC content of a signal without any DC bias voltage: a capacitor is connected in series with one test probe.
Ideally, one would expect nothing but pure DC voltage at the motor's terminals, because the motor is connected directly in parallel with the battery. Since the motor's terminals are electrically common with the respective terminals of the battery, and the battery's nature is to maintain a constant DC voltage, nothing but DC voltage should appear at the motor terminals, right? Well, because of resistance internal to the battery and along the conductor lengths, current pulses drawn by the motor produce oscillating voltage "dips" at the motor terminals, causing the AC "noise" heard by the detector:
4.15. SIGNAL COUPLING |
189 |
Rwire
Battery
Motor
Rwire
Use the audio detector to measure "noise" voltage directly across the battery. Since the AC noise is produced in this circuit by pulsating voltage drops along stray resistances, the less resistance we measure across, the less noise voltage we should detect:
-
+
headphones
Sensitivity
plug
You may also measure noise voltage dropped along either of the telephone cable conductors supplying power to the motor, by connecting the audio detector between both ends of a single cable conductor. The noise detected here originates from current pulses through the resistance of the wire:
190 |
CHAPTER 4. AC CIRCUITS |
-
+
headphones
Sensitivity
plug
Now that we have established how AC noise is created and distributed in this circuit, let's explore how it is coupled to adjacent wires in the cable. Use the audio detector to measure voltage between one of the motor terminals and one of the unused wires in the telephone cable. The 0.047 ¹F capacitor is not needed in this exercise, because there is no DC voltage between these points for the detector to detect anyway:
-
+
headphones
Sensitivity
plug
4.15. SIGNAL COUPLING |
191 |
The noise voltage detected here is due to stray capacitance between adjacent cable conductors creating an AC current "path" between the wires. Remember that no current actually goes through a capacitance, but the alternate charging and discharging action of a capacitance, whether it be intentional or unintentional, provides alternating current a pathway of sorts.
If we were to try and conduct a voltage signal between one of the unused wires and a point common with the motor, that signal would become tainted with noise voltage from the motor. This could be quite detrimental, depending on how much noise was coupled between the two circuits and how sensitive one circuit was to the other's noise. Since the primary coupling phenomenon in this circuit is capacitive in nature, higher-frequency noise voltages are more strongly coupled than lower-frequency noise voltages.
If the additional signal was a DC signal, with no AC expected in it, we could mitigate the problem of coupled noise by "decoupling" the AC noise with a relatively large capacitor connected across the DC signal's conductors. Use the 0.22 ¹F capacitor for this purpose, as shown:
-
+
"decoupling" capacitor
headphones
Sensitivity
plug
The decoupling capacitor acts as a practical short-circuit to any AC noise voltage, while not a®ecting DC voltage signals between those two points at all. So long as the decoupling capacitor value is signi¯cantly larger than the stray "coupling" capacitance between the cable's conductors, the AC noise voltage will be held to a minimum.
Another way of minimizing coupled noise in a cable is to avoid having two circuits share a common conductor. To illustrate, connect the audio detector between the two unused wires and listen for a noise signal:
192 |
CHAPTER 4. AC CIRCUITS |
-
+
headphones
Sensitivity
plug
There should be far less noise detected between any two of the unused conductors than between one unused conductor and one used in the motor circuit. The reason for this drastic reduction in noise is that stray capacitance between cable conductors tends to couple the same noise voltage to both of the unused conductors in approximately equal proportions. Thus, when measuring voltage between those two conductors, the detector only "sees" the di®erence between two approximately identical noise signals.