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**Experiment 1 * Part A: Circuit Basics, Equipment, Sound Waves**

* Part B: Resistors, Circuit Analysis, Voltage Dividers * Part C: Capture/PSpice

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**Motivation Modern Systems You will be able to communicate with EE’s**

mechanical component electrical component (computer component) You will be able to communicate with EE’s You will be able to take the electronics sections of the FE exam You will be using Engineering problem solving skills. sometimes these days they skip the electrical engineer entirely and the ME and computer programmer end up doing the electrical work. Last year one student told her boyfriend (a EE) that his feedback must be wrong because it was in the + side of the op-amp. She was correct. Civils have to take the PE exam. It is a good thing to have, especially if you want to sign your own house plans, etc. What is engineering?

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**Automobile Electronics**

Previously all mechanical systems have become increasingly electronic Over the past few years, for example, the automobile has begun to use more computers (microcontrollers) How many microcontrollers are typically found in a modern automobile?

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**Automobile Electronics**

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Part A Circuit Basics Equipment Sound Waves

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**Physical Model for a DC circuit**

pump = voltage source water = flow of current ocean = ground pipe = wire Physical Model for a DC circuit * pump = voltage source (pumps water up) = “V” * water flow = current flow from top of mountain into the ocean = “I” * ocean = “ground” = a resevoir of electrons = 0 * pipe = wire

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**Physical Model for Resistance**

pebbles in pipe = resistance to flow of current Physical Model for Resistance * pipe = wire (theoretically no resistance) * rocks in pipe = resistance to flow = “R”

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**Symbols Physical Model for Resistance**

* pipe = wire (theoretically no resistance) * rocks in pipe = resistance to flow = “R”

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**Physics vs. Electronics**

* atoms have positive nuclei and negative “free” electrons * electrons flow from negative to positive * in electronics, by definition, current is the flow of “positive charge” * In this course current flows always from + to – * Note symbols for the DC source and the resistance

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**Ohm’s Law : V = IR Ohm’s Law * V (voltage) measured in volts**

* I (current) measured in amps (generally milliamps) * R (resistance) measured in ohms * Ohm’s Law V=IR * Ohm’s Law for total circuit (VT = IT RT) * Ohm’s Law for a single component (VR1 = IR1 R1)

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**Alternating Current Generators**

* generate a voltage which varies with time * therefore the current varies with time * the electrons are pushed back and forth in the circuit * three phase generators (house current) have 3 pairs of magnets (60 Hertz) * we use a sine wave model (1 phase – 1 pair of magnets)

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**AC Circuits Note symbol for AC voltage source AC Circuits**

* similar to DC circuits at any one point in time * Ohm’s Law: v(t) = i(t) R * We use a sinusoid to model AC voltage in this class. * v(t) = Asin(t+) * maximum current imax = A/R Note symbol for AC voltage source

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**Review of Sinusoids Review of Sinusoids * v(t) = Asin(t+)**

* A = amplitude of sinusoid * period = T = length of one cycle (measured in seconds) * frequency = f = 1/T (measured in Hertz or cycles/second) * angular frequency = = 2f (measured in radians/second) * a whole cycle has 2 radians * phase shift = = -t0 = -2 (t0/T) (measured in radians) * phase shift is the fraction of the whole cycle that the cycle start point is from 0sec * phase is negated --> lead in phase, lag in time ... lag in phase, lead in time * peak-to-peak voltage = Vp-p = 2A * average voltage = Vave = 0V (no information) * root mean square voltage = (a DC value which gives information)

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**More on Phase Shift Negative phase shift: “Lag in phase, lead in time”**

Positive phase shift: “Lead in phase, lag in time” Review of Sinusoids * v(t) = Asin(t+) * A = amplitude of sinusoid * period = T = length of one cycle (measured in seconds) * frequency = f = 1/T (measured in Hertz or cycles/second) * angular frequency = = 2f (measured in radians/second) * a whole cycle has 2 radians * phase shift = = -t0 = -2 (t0/T) (measured in radians) * phase shift is the fraction of the whole cycle that the cycle start point is from 0sec * phase is negated --> lead in phase, lag in time ... lag in phase, lead in time * peak-to-peak voltage = Vp-p = 2A * average voltage = Vave = 0V (no information) * root mean square voltage = (a DC value which gives information)

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**Special Cases of Phase Shift**

Review of Sinusoids * v(t) = Asin(t+) * A = amplitude of sinusoid * period = T = length of one cycle (measured in seconds) * frequency = f = 1/T (measured in Hertz or cycles/second) * angular frequency = = 2f (measured in radians/second) * a whole cycle has 2 radians * phase shift = = -t0 = -2 (t0/T) (measured in radians) * phase shift is the fraction of the whole cycle that the cycle start point is from 0sec * phase is negated --> lead in phase, lag in time ... lag in phase, lead in time * peak-to-peak voltage = Vp-p = 2A * average voltage = Vave = 0V (no information) * root mean square voltage = (a DC value which gives information)

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**General form of the Sinusoid**

* add a DC offset * V(t) = Asin(t+) + VDCx * T, f, , , A, Vp-p all are found the same way * BUT Vave = VDC (sinusoid averages out) * you may see Vrms=sqrt(VDC2+A2/2), but the equipment (DMM) removes the DC offset information. So it is best to use only A/sqrt(2).

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Sinusoid Units

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**DC Source E3631A –Only for section 2**

TOGGLE OUTPUT ON/OFF ADJUST VOLTAGE LEVEL 0 to 6 VOLTS GROUND 0 to 25 VOLTS -25 to 0 VOLTS Do Not Use DC Source E3631A “Do not use” is the building ground. It does not complete the circuit. Note: The connection that looks like the ground symbol is the ground for the building, not the return path for the circuit.

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**DC Source for JEC-4201 DC Source E3631A**

“Do not use” is the building ground. It does not complete the circuit.

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**Function Generator 33120A – Only available in JEC 4107**

Note: The SYNC connection will give you a signal, but it will not be the one you have set the function generator to display. Do not accidentally plug into it.

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Function Generator

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Digital Multimeter 34401A – We will have some hand held meters in section 1 for resistance measurements Called DMM Note: Always use the voltage plugs on the right as indicated.

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Digital Multimeter Called DMM The IOBoard can read voltages but it isn’t an Ohmmeter, We will use hand held meters for resistance measurements

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**Oscilloscope 54600B – you guessed it – JEC 4107**

Note: Black lead of scope channel is ALWAYS ground

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Protoboards Protoboards * the banana plugs connections are not connected internally to the holes * the horizontal lines are all connected inside and are hooked to power and ground * the vertical lines are for hooking signals together * this is a voltage divider Note: Banana connectors are not connected internally to the holes in the board. Check continuity of power rails at top and bottom.

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**Reading Resistors Bands: XYZT Resistance =**

* Resistors are identified by a series of bands. * Most of our resistors have four bands.(XYZT) * The last band is tolerance T (generally gold +/- 5%) * The first two bands are tens and ones digit XY * The third band is order of magnitude 10Z * The order of the numbers 0-9 goes dark to light with ROYGBV in the middle. * True resistance may vary from the stated values Bands: XYZT Resistance =

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How Ears Work How Ears Work * If we hook an AC signal to a speaker, we can hear it. * The human ear can distinguish loudness and pitch. * What attributes of sine waves are related to loudness and pitch? * Note that the human ear is designed to hear certain pitches better than others. * What pitches can the human ear detect best? Pitch = frequency Amplitude = loudness Some pitches sound louder to your ears.

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Part A – Do the lab now Use your kit if you purchased one, purchase one if you haven’t Some of Part A can be done without the kit, just with the IOBoard If you don’t have a kit Make sure that you have the software loaded and that the IOBoard is working We have some spare protoboards and speakers There will be time during the next 2 classes to catch up Next class we start Part B of Experiment 1 Any questions?

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**Part B Resistors Voltage Dividers Impedance Capacitors and Inductors**

Equipment Impedances Circuit Analysis Agilent Intuilink Software

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**Combining Resistors in Series**

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**Combining Resistors in Parallel**

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**Measuring Voltage Total Voltage: Voltage across resistors:**

* generally voltages are measured at a point relative to ground (0) VA , VB , VC * voltage drop from a component is the difference of the voltages at either side VR1 = VA - VB VR2 = VB – VC * voltages attached by a wire to ground are 0 VC = 0 * voltages attached by a wire to the positive side of the source has the source voltage VA = V1 * voltage drops between a point and ground add up to the voltage at the point VA = V1 = VR1 + VR2 VB = VR2 * Note the two different models for the same circuit Total Voltage: Voltage across resistors: Voltage at points wrt GND:

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Voltage Dividers Voltage Dividers * voltages are divided up proportionally depending upon the resistors * series circuit only * you can find the voltage drop over any resistor in a voltage divider The voltage is divided up in a manner that is proportional to the resistances of the resistors in a series circuit.

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**More on Voltage Dividers**

Always add up resistors relative to ground to get the voltage at a point. More on Voltage Dividers * voltage dividers can apply to series circuits with more than one resistor * voltage drops add up to the voltage at any point * you can apply the voltage divider rule to a series piece of a circuit * you cannot apply the voltage divider rule to a resistor in parallel with other resistors You can use a voltage divider on a series portion of a circuit. You cannot use a voltage divider on a non-series circuit.

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**Impedance vs. Resistance**

Resistance is a property of a material that causes a reduction in the rate of flow of electrons. Impedance is the reduction in the rate of flow of electrons caused by the material (resistance) AND other the properties of the component involved (reactance). Resistors have no reactance. So the impedance of a resistor is equal to its resistance only. Reactance varies with the frequency of the input. Resistance remains the same at all frequencies. Both impedance and resistance are measured in ohms. Impedance * Impedance is a general measure of the way in which a circuit effects the flow of current through it. * In a circuit with all resistors, the impedance is the total resistance. * In a circuit with other components, the impedance has a resistance component and another component called, reactance.

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Impedance Definition: A general measure of how a component or group of components pushes against the current flowing through it. Impedance = resistance + reactance Impedance is used to refer to the behavior of circuits with resistors, capacitors and other components. When we consider components in a theoretical circuit diagram, the impedance of inductors and capacitors is their reactance only. Any resistance is modeled separately as a resistor. So theoretical capacitors and inductors have impedance, but no resistance. Impedance * Impedance is a general measure of the way in which a circuit effects the flow of current through it. * In a circuit with all resistors, the impedance is the total resistance. * In a circuit with other components, the impedance has a resistance component and another component called, reactance.

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**Comparison of Components**

Impedance * Impedance is a general measure of the way in which a circuit effects the flow of current through it. * In a circuit with all resistors, the impedance is the total resistance. * In a circuit with other components, the impedance has a resistance component and another component called, reactance.

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Capacitors Capacitors consist of two plates with a dielectric material in-between. When a potential difference is placed across the plates, a charge builds up until it is large enough to cause a discharge across the plates through the material. Capacitors - a capacitor is a device that stores and releases charge across a gap - capacitors have a “capacitance”, measured in farads - “C” in ANALOG library in PSpice - Reading Capacitors -- larger ones have the number of microfarads written on the BUT ignore letters like K following the number .068K = .068 microfarad larger capacitors have a direction the + lead is long or marked -- smaller ones are defined in terms of picofarads XYZ X = tens digit Y = one’s digit Z = order of magnitude THEN multiply by to get farads OR multiply by 10-6 to get microfarads 103 = 10x1000x10-6 = .01 microfarads 684 = 68X10000x10-6 = .68 microfarads

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**Reading Capacitors - towards ground**

- a capacitor is a device that stores and releases charge across a gap - capacitors have a “capacitance”, measured in farads - “C” in ANALOG library in PSpice - Reading Capacitors -- larger ones have the number of microfarads written on the BUT ignore letters like K following the number .068K = .068 microfarad larger capacitors have a direction the + lead is long or marked -- smaller ones are defined in terms of picofarads XYZ X = tens digit Y = one’s digit Z = order of magnitude THEN multiply by to get farads OR multiply by 10-6 to get microfarads 103 = 10x1000x10-6 = .01 microfarads 684 = 68X10000x10-6 = .68 microfarads Larger capacitors have the number of microfarads written on them directly. Smaller capacitors use a code based on the number of picofarads. We generally use microfarads, so… XYZ = XY * 10Z * mF

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Capacitors in Series

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**Capacitors in Parallel**

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**Understanding Capacitor Behavior**

- the current through a capacitor is determined by a CHANGE in voltage - for a graph, derivative is the slope of the V vs.t curve - no voltage change --> no current through the capacitor (open) - high voltage change --> high current through the capacitor (short) - high constant current --> high voltage drop (open) - no current --> no voltage drop (short)

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Capacitor Impedance Capacitor Impedance -- capacitors have an impedance (holds back flow of electrons) which depends upon frequency -- low frequency = low rate of voltage drop change -- high frequency = high rate of voltage drop change - ZC is the capacitor impedance, VC=ICZC is like VR=IRR, except impedance changes both the amplitude and phase and resistance changes only amplitude -- “equivalent impedance” at any one point in time is like finding a resistance. - we will learn how Z is related to the change in voltage in experiment 5 Note: Real capacitors have effectively no resistance, so impedance is reactance for all capacitors.

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**Comparison of Components**

Impedance * Impedance is a general measure of the way in which a circuit effects the flow of current through it. * In a circuit with all resistors, the impedance is the total resistance. * In a circuit with other components, the impedance has a resistance component and another component called, reactance.

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Inductors An inductor is a coil of wire through which a current is passed. The current can be either AC or DC.

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Inductors This generates a magnetic field, which induces a voltage proportional to the rate of change of the current.

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Combining Inductors Inductances add like resistances Series Parallel

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Inductor Impedance Note: Real inductors always have a small resistance (that is not shown in these circuits). The impedance of the theoretical inductor shown is only its reactance.

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**Comparison of Components**

Impedance * Impedance is a general measure of the way in which a circuit effects the flow of current through it. * In a circuit with all resistors, the impedance is the total resistance. * In a circuit with other components, the impedance has a resistance component and another component called, reactance.

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Equipment Impedances Each measuring device changes the circuit when you use it. The impedance of the device helps you understand how much. Device Impedances Function Generator: 50 ohms ‘Scope: 1Meg ohms DMM (DC voltage): 10Meg ohms DMM (AC voltage): 1Meg ohms DMM (DC current): 5 ohms (negligible) Equipment Impedances * Each piece of equipment has an impedance associated with it. * Whenever you measure anything in a circuit, you change the circuit. * You must know the impedance of the device to understand how it changes the circuit. * Device impedances are designed to have minimal effect on the circuit.

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**Effect of Impedance on Circuit**

* You cannot read the voltage inside the function generator: * You can read the load, the voltage outside the function generator: square * When the load is 50 ohms, the voltage across the load is 1Vp-p * When the load is 1MEG ohms, the voltage across the load is 2Vp-p. * The function generator says 1 Vp-p in both cases? Function generator thinks it is putting out the same thing. Output is clearly different.

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**Effect of Impedance on Circuit**

* You cannot read the voltage inside the function generator: * You can read the load, the voltage outside the function generator: square * When the load is 50 ohms, the voltage across the load is 1Vp-p * When the load is 1MEG ohms, the voltage across the load is 2Vp-p. * The function generator says 1 Vp-p in both cases? The IOBoard function generator has an output impedance of much less than 50Ω, so we can ignore it. Our battery however is a different story, as you will see in the experiment.

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Kirchoff’s Laws Kirchoff’s Laws * Kirchoff’s Voltage Law (KVL): the sum of the voltages in a loop is zero * Kirchoff’s Current Law (KCL): the sum of a currents entering a junction is equal to the sum of the currents exiting the junction * Also, if there is no junction, the currents must be the same sum of currents entering a junction is the same as the sum of the currents leaving a junction sum of voltages in any loop is zero

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**Circuit Analysis (Combination Method)**

* Use circuit combination rules and voltage dividers to find unknowns

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**Useful Aside: SI Suffixes**

pico p 10-12 nano n 10-9 micro (u) 10-6 milli m 10-3 Kilo k 103 Mega M (Meg) 106 Giga G 109 Tera T 1012 Circuit Analysis (Combination Method) * Use circuit combination rules and voltage dividers to find unknowns

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**Part C Capture PSpice Create circuits visually**

Set up simulation parameters PSpice Analyzes circuit Displays results

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Capture Capture * Capture is a program you can use to input a circuit schematic * It is far more sophisticated than we need for this course. * Some things we do use are indicated. * To rotate a part, hit the R key or right click on the part. * This is a brief overview of the program, the experiments have more details.

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**Simulations Simulations**

* In order to see the behavior of the circuit, you need to set up a simulation. * The run time depends on your frequency (which is 1K Hz). * To see two cycles (1/1K)*2 = 2ms * The step size related to how many samples per cycle to take. * If you are not given the step size, divide the run time by (easy and plenty)

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PSpice Note: To get copy of trace into word use Window menu ”copy to clipboard” PSpice * PSpice is like a simulated ‘scope with a lot more features * when you run the simulation, you see the scope output from the probes * the traces are identified by the pins of the components * to get a black on white picture into the clipboard (for use in Word) use Window->Copy to Clipboard menu

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Cursors Note: You can drag the left mouse button to move one cursor and the right mouse button to move the other. Cursors * The cursors indicate where you are on a trace * you can find minimum, maximum, etc * you can move along a trace with the mouse or arrows * you switch between cursors with the binoculars or right/left click * you can switch between traces by clicking the name of the trace

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**Adding Traces Note: To add a trace use Trace menu ”Add Trace”**

* You can add calculated traces * Use Trace-->Add Trace menu * Type in or click on signals and functions to create an expression and click OK

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Part D Oscilloscopes Lissajous Figures

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**Cathode Ray Tubes y input x input**

-- a cathode ray is a stream of electrons -- this stream can be bent using a magnetic field -- if you vary the magnetic field, you can control the position of the stream -- cathode ray movie: -- if you use two magnetic fields, you can create a raster display which covers a two dimensional plane (tv set, computer monitor,etc.) -- the periodic updating of the beam position (x and y) is called “sweep” Variation in potential difference (voltage) placed on plates causes electron beam to bend different amounts. “Sweep” refers to refreshing repeatedly at a fixed rate.

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**Cathode Ray Tube Animation**

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Oscilloscopes Oscilloscopes -- oscilloscopes are similar, except only one dimension (x) sweeps -- the other dimension (y) is linked to the input voltage signal -- the digital scope “triggers” periodically on a portion of the y signal (usually 0) -- it will redraw the signal starting at this trigger point for each sweep) Horizontal sweeps at a constant rate. Vertical plates are attached to an external voltage, the signal you attach to the scope.

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Lissajous Figures Lissajous Figures * Lissajous figures let you compare two signals * Lissajous figures let you create neat patterns

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Lissajous Figures Lissajous Figures -- instead of letting x sweep periodically, a Lissajous figure is created by putting a voltage signal on both x and y. -- this is accomplished using the MAIN/DELAYED button and the XY soft key Normally the scope will plot a voltage signal with respect to time. In a Lissajous figure, two voltage signals are plotted against each other.

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Lissajous Example 1 * Vy(t) and Vx(t) have the same frequency and phase shift (0)

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Lissajous Example 2

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Lissajous Example 3

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**More Figures More figures * shape depends upon phase shift**

* number of loops depends upon frequency ratio * if you have trouble, make sure the amplitudes are similar or equal * use the digital function generator to make final adjustments * you can use the run and stop keys on the ‘scope to freeze the image

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